glinski_metabolites
tested hypotheses
- observed vivo versus in vitro degradation rates are the same, or observed vivo rates are lower than in vitro rates (due to other degradation processes, uptake kinetics?)
- first order kinetics are michaelis-menton, second order
- are in vitro indicative of in vivo
things to do
- michaelis menton first order comparison for both experiments
- non-linear goodness of fit
install and load supporting libraries
## nodename
## "DZ2626UTPURUCKE"## [1] "R version 3.4.3 (2017-11-30)"##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## select##
## 'drc' has been loaded.## Please cite R and 'drc' if used for a publication,## for references type 'citation()' and 'citation('drc')'.## Loading required package: lme4## Loading required package: Matrix## [1] "list of loaded packages: "
## [1] "pbkrtest" "lme4" "Matrix" "scatterplot3d"
## [5] "ggplot2" "drc" "MASS" "xtable"
## [9] "zoo" "knitr" "dplyr" "rmarkdown"
## [13] "stats" "graphics" "grDevices" "utils"
## [17] "datasets" "methods" "base"import experimental exposure and microsomal data
Load csv files with experimental data and microsome data sets. The beolw may return false but still be OK if rstudio does not have privileges to data directory (e.g., attached drive).
## [1] "Root directory location: d:/git/glinski_metabolites/"## [1] "check to see if R can access files OK: FALSE"## time parent analyte matrix conc replicate
## 4 15 atrazine atrazine microsomes 0.5514354 1
## 47 0 atrazine atrazine microsomes NA 1
## 61 90 atrazine atrazine microsomes NA 3
## 92 0 atrazine atrazine microsomes 697.4815010 1
## 95 15 atrazine atrazine microsomes 161.9606512 1
## 98 30 atrazine atrazine microsomes 237.9761898 1
## 101 60 atrazine atrazine microsomes 255.9782700 1
## 104 90 atrazine atrazine microsomes 121.3271776 1
## 127 0 atrazine atrazine microsomes NA 1
## 134 31 atrazine atrazine microsomes NA 2
## 169 60 atrazine dea microsomes 0.3080022 4
## 206 15 atrazine dea microsomes NA 1
## 209 30 atrazine dea microsomes NA 1
## 212 60 atrazine dea microsomes NA 1
## 215 90 atrazine dea microsomes NA 1
## 231 90 atrazine dea microsomes NA 2
## 235 0 atrazine dea microsomes NA 3
## 255 30 atrazine dea microsomes NA 2
## 259 60 atrazine dea microsomes NA 3
## 344 0 atrazine dia microsomes 0.0000000 1
## 347 15 atrazine dia microsomes 0.3204253 1
## 350 30 atrazine dia microsomes 0.9284476 1
## 353 60 atrazine dia microsomes 1.5356847 1
## 356 90 atrazine dia microsomes 1.0590508 1
## 359 0 atrazine dia microsomes NA 1
## 365 30 atrazine dia microsomes NA 1
## 366 30 atrazine dia microsomes NA 2
## 370 60 atrazine dia microsomes NA 3
## 372 90 atrazine dia microsomes NA 2
## 379 15 atrazine dia microsomes NA 3
## 386 90 atrazine dia microsomes NA 1
## 478 60 fipronil fipsulf microsomes 0.0414000 2
## 547 15 fipronil fipronil microsomes 0.0000000 2
## 591 15 fipronil fipronil microsomes 55.7278739 1
## 635 0 triadimefon tdla microsomes 2.3211093 3
## 657 60 triadimefon tdla microsomes 0.7265999 1
## 668 15 triadimefon tdla microsomes 3.7310331 3
## 710 0 triadimefon tdla microsomes 5.2664595 3
## 713 15 triadimefon tdla microsomes 5.2998384 3
## 803 15 triadimefon tdlb microsomes 3.3031594 3
## 927 60 triadimefon triadimefon microsomes NA 1
## 936 15 triadimefon triadimefon microsomes NA 1
## 1023 0 triadimefon triadimefon microsomes 229.2656431 1
## microMexp X
## 4 0.7120 NA
## 47 50.0000 NA
## 61 50.0000 NA
## 92 125.0000 NA
## 95 125.0000 NA
## 98 125.0000 NA
## 101 125.0000 NA
## 104 125.0000 NA
## 127 250.0000 NA
## 134 250.0000 NA
## 169 10.0000 NA
## 206 125.0000 NA
## 209 125.0000 NA
## 212 125.0000 NA
## 215 125.0000 NA
## 231 0.7120 NA
## 235 3.1684 NA
## 255 250.0000 NA
## 259 250.0000 NA
## 344 125.0000 NA
## 347 125.0000 NA
## 350 125.0000 NA
## 353 125.0000 NA
## 356 125.0000 NA
## 359 0.7120 NA
## 365 0.7120 NA
## 366 0.7120 NA
## 370 0.7120 NA
## 372 0.7120 NA
## 379 3.1684 NA
## 386 3.1684 NA
## 478 75.0000 NA
## 547 10.0000 NA
## 591 150.0000 NA
## 635 0.6800 NA
## 657 10.0000 NA
## 668 2.8900 NA
## 710 100.0000 NA
## 713 100.0000 NA
## 803 2.8900 NA
## 927 10.0000 NA
## 936 2.8900 NA
## 1023 250.0000 NAexperimental exposure data structure
Check out structure of imported data sets.
## 'data.frame': 352 obs. of 6 variables:
## $ time : int 2 2 2 2 4 4 4 4 12 12 ...
## $ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ analyte : Factor w/ 8 levels "ATZ","DEA","DIA",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ matrix : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 1 1 1 1 1 ...
## $ conc : num 3.07 3.69 4.7 1.89 7.62 ...
## $ replicate: int 1 2 3 4 1 2 3 4 1 2 ...Set time and replicate fields as factors for later statistical inference.
microsome experiment data structure
Check out structure of imported data set for the microsome analysis.
## 'data.frame': 994 obs. of 8 variables:
## $ time : int 0 0 0 15 15 30 30 30 60 60 ...
## $ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ analyte : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ matrix : Factor w/ 1 level "microsomes": 1 1 1 1 1 1 1 1 1 1 ...
## $ conc : num 1.21 1.6 1.36 1.35 1.21 ...
## $ replicate: int 1 2 3 2 3 1 2 3 1 2 ...
## $ microMexp: num 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 ...
## $ X : logi NA NA NA NA NA NA ...Set time and replicate fields as factors for later statistical inference.
## 'data.frame': 994 obs. of 8 variables:
## $ time : int 0 0 0 15 15 30 30 30 60 60 ...
## $ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ analyte : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ matrix : Factor w/ 1 level "microsomes": 1 1 1 1 1 1 1 1 1 1 ...
## $ conc : num 1.21 1.6 1.36 1.35 1.21 ...
## $ replicate: Factor w/ 4 levels "1","2","3","4": 1 2 3 2 3 1 2 3 1 2 ...
## $ microMexp: num 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 ...
## $ X : logi NA NA NA NA NA NA ...analyze microsomal data
The microsomal experiment has 3-4 replicates for each pesticide. The experiment progressively increases the concentration of the substrate (microMexp) and measures the enzyme velocity. At each substrate concentration the reaction is quenched after a specific period of time (0, 15, 30, 60, 90 mins). This time series data is used to estimate a slope associated with each substrate concentration. Substrate concentration and linear velocity slopes are then fit using Michaelis-Menten kinetics to estimate reaction rates for each pesticide.
non-linear fitting
We use the dose-response model (drm) package from R for the fitting of the rate constant. We provide it the 2-parameter Michaelis-Menton function (mm2) as an argument. It uses the MM.2 function that is in the drc package and therefore is a drc object that contains a list of class drcMean, containing the mean function, the self starter function, the parameter names and other components such as derivatives and a function for calculating ED values. It is not shifted (??) so uses the fit f(x,(c,d,e)) = c + (d-c)/(1+e/x). Where x is the dose, it is a strictly increasing function so we reverse the sign of the slopes for the parents. e is the dose halfway between c and d, for the 2-parameter model c = 0.
## Michaelis-Menten
## (2 parameters)
## In 'drc': MM.2atrazine
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 0.712"
## ind
## [1,] 1 0 1.2080499
## [2,] 2 0 1.5958074
## [3,] 3 0 1.3622627
## [4,] 4 15 1.3469113
## [5,] 5 15 1.2124448
## [6,] 6 30 1.1349183
## [7,] 7 30 1.0824669
## [8,] 8 30 1.1138895
## [9,] 9 60 0.9180152
## [10,] 10 60 0.8199161
## [11,] 11 60 0.8304017
## [12,] 12 90 0.6019329
## [13,] 13 90 0.5146155
## [14,] 14 90 0.5430465
## [1] "least squares linear regression for substrate = 0.712"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 1.398706 -0.009293
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.19066 -0.03719 -0.01498 0.03347 0.19710
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.3987059 0.0386612 36.18 1.27e-13 ***
## Time[ind] -0.0092933 0.0007396 -12.56 2.89e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09072 on 12 degrees of freedom
## Multiple R-squared: 0.9294, Adjusted R-squared: 0.9235
## F-statistic: 157.9 on 1 and 12 DF, p-value: 2.893e-08
##
## (Intercept) Time[ind]
## 1.39870589 -0.00929334
## 2.5 % 97.5 %
## (Intercept) 1.31447036 1.482941425
## Time[ind] -0.01090489 -0.007681791
## [1] "weighted linear regression for substrate = 0.712"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 9 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 1.391987016 -0.009212117
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 0.0535
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.1839 -0.0323 -0.0141 0.0341 0.2038
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 1.3920 0.0314 44.3291
## Time[ind] -0.0092 0.0006 -15.3343
##
## Residual standard error: 0.05352 on 12 degrees of freedom
## (Intercept) Time[ind]
## 1.391987016 -0.009212117
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## ind
## [1,] 15 0 7.925056
## [2,] 16 0 8.535005
## [3,] 17 0 7.899000
## [4,] 18 15 8.712917
## [5,] 19 15 8.046755
## [6,] 20 15 8.073616
## [7,] 21 30 7.256438
## [8,] 22 30 7.355159
## [9,] 23 30 7.326464
## [10,] 24 60 5.106467
## [11,] 25 60 6.116857
## [12,] 26 60 6.612799
## [13,] 27 60 6.416351
## [14,] 28 90 7.579707
## [15,] 29 90 5.426896
## [16,] 30 90 5.468859
## [1] "least squares linear regression for substrate = 10"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 8.22302 -0.02746
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.4691 -0.3045 -0.1079 0.2423 1.8278
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.223019 0.289635 28.391 8.92e-14 ***
## Time[ind] -0.027457 0.005648 -4.861 0.000252 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7161 on 14 degrees of freedom
## Multiple R-squared: 0.628, Adjusted R-squared: 0.6014
## F-statistic: 23.63 on 1 and 14 DF, p-value: 0.0002518
##
## (Intercept) Time[ind]
## 8.22301942 -0.02745731
## 2.5 % 97.5 %
## (Intercept) 7.60181496 8.84422388
## Time[ind] -0.03957117 -0.01534345
## [1] "weighted linear regression for substrate = 10"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 8.28012829 -0.03063472
##
## Degrees of freedom: 16 total; 14 residual
## Scale estimate: 0.355
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -1.33558 -0.15978 -0.03016 0.23286 2.05670
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 8.2801 0.1561 53.0337
## Time[ind] -0.0306 0.0030 -10.0619
##
## Residual standard error: 0.3552 on 14 degrees of freedom
## (Intercept) Time[ind]
## 8.28012829 -0.03063472
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 3.1684"
## ind
## [1,] 31 0 3.856505
## [2,] 32 0 3.856469
## [3,] 33 0 4.000676
## [4,] 34 15 3.592665
## [5,] 35 15 3.566235
## [6,] 36 15 3.407026
## [7,] 37 30 3.230388
## [8,] 38 30 3.182488
## [9,] 39 30 3.039758
## [10,] 40 60 2.523246
## [11,] 41 60 2.351721
## [12,] 42 60 2.405224
## [13,] 43 90 1.868645
## [14,] 44 90 2.090715
## [15,] 45 90 1.793542
## [1] "least squares linear regression for substrate = 3.1684"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 3.8540 -0.0223
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.16435 -0.08220 0.00248 0.04602 0.24362
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.8540242 0.0458583 84.04 < 2e-16 ***
## Time[ind] -0.0222992 0.0009055 -24.63 2.71e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1133 on 13 degrees of freedom
## Multiple R-squared: 0.979, Adjusted R-squared: 0.9774
## F-statistic: 606.5 on 1 and 13 DF, p-value: 2.71e-12
##
## (Intercept) Time[ind]
## 3.85402419 -0.02229925
## 2.5 % 97.5 %
## (Intercept) 3.7549534 3.9530949
## Time[ind] -0.0242554 -0.0203431
## [1] "weighted linear regression for substrate = 3.1684"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 8 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 3.86465594 -0.02275624
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0772
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.1475603 -0.0585546 0.0005195 0.0502352 0.2741208
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 3.8647 0.0496 77.8848
## Time[ind] -0.0228 0.0010 -23.2266
##
## Residual standard error: 0.07717 on 13 degrees of freedom
## (Intercept) Time[ind]
## 3.86465594 -0.02275624
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## ind
## [1,] 46 0 49.36255
## [2,] 47 0 45.63559
## [3,] 48 15 47.33018
## [4,] 49 15 49.35531
## [5,] 50 15 47.17151
## [6,] 51 30 50.59649
## [7,] 52 30 48.66029
## [8,] 53 30 45.11503
## [9,] 54 60 46.32181
## [10,] 55 60 45.69771
## [11,] 56 60 46.83574
## [12,] 57 90 44.33320
## [13,] 58 90 43.14627
## [1] "least squares linear regression for substrate = 50"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 48.59636 -0.04483
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.9608 -0.7524 -0.2088 0.9292 3.3450
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 48.59636 0.78210 62.136 2.32e-15 ***
## Time[ind] -0.04483 0.01618 -2.771 0.0182 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.737 on 11 degrees of freedom
## Multiple R-squared: 0.411, Adjusted R-squared: 0.3575
## F-statistic: 7.677 on 1 and 11 DF, p-value: 0.0182
##
## (Intercept) Time[ind]
## 48.59636117 -0.04483029
## 2.5 % 97.5 %
## (Intercept) 46.87496515 50.317757197
## Time[ind] -0.08044212 -0.009218455
## [1] "weighted linear regression for substrate = 50"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 48.68982363 -0.04752188
##
## Degrees of freedom: 13 total; 11 residual
## Scale estimate: 1.48
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -3.05424 -0.80549 -0.07965 0.99723 3.33233
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 48.6898 0.8305 58.6254
## Time[ind] -0.0475 0.0172 -2.7658
##
## Residual standard error: 1.478 on 11 degrees of freedom
## (Intercept) Time[ind]
## 48.68982363 -0.04752188
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## ind
## [1,] 59 0 57.52955
## [2,] 60 0 54.79227
## [3,] 61 0 71.19048
## [4,] 62 15 54.59374
## [5,] 63 15 51.29412
## [6,] 64 15 56.87161
## [7,] 65 30 50.13677
## [8,] 66 30 46.09059
## [9,] 67 30 54.93692
## [10,] 68 60 55.87491
## [11,] 69 60 67.85864
## [12,] 70 60 55.49677
## [13,] 71 90 48.47103
## [14,] 72 90 61.24224
## [15,] 73 90 28.95872
## [1] "least squares linear regression for substrate = 75"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 58.3096 -0.1014
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -20.2269 -4.3244 -0.7146 3.4589 15.6317
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 58.30963 3.80308 15.33 1.05e-09 ***
## Time[ind] -0.10138 0.07509 -1.35 0.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.397 on 13 degrees of freedom
## Multiple R-squared: 0.123, Adjusted R-squared: 0.0555
## F-statistic: 1.823 on 1 and 13 DF, p-value: 0.2
##
## (Intercept) Time[ind]
## 58.3096265 -0.1013778
## 2.5 % 97.5 %
## (Intercept) 50.0935756 66.52567748
## Time[ind] -0.2636035 0.06084778
## [1] "weighted linear regression for substrate = 75"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 11 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 56.19939386 -0.04860932
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 4.97
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -22.8658 -3.7648 0.1958 2.4030 14.9911
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 56.1994 3.0801 18.2459
## Time[ind] -0.0486 0.0608 -0.7993
##
## Residual standard error: 4.971 on 13 degrees of freedom
## (Intercept) Time[ind]
## 56.19939386 -0.04860932
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## ind
## [1,] 74 0 91.15168
## [2,] 75 0 87.78347
## [3,] 76 0 88.10440
## [4,] 77 15 88.83436
## [5,] 78 15 85.08037
## [6,] 79 15 83.34356
## [7,] 80 30 87.40290
## [8,] 81 30 77.14189
## [9,] 82 30 81.17033
## [10,] 83 60 82.38969
## [11,] 84 60 78.82099
## [12,] 85 60 74.48075
## [13,] 86 90 81.10749
## [14,] 87 90 72.11741
## [15,] 88 90 74.72567
## [1] "least squares linear regression for substrate = 100"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 87.7853 -0.1421
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.3806 -2.3313 -0.2712 3.1552 6.1106
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 87.78529 1.45078 60.51 < 2e-16 ***
## Time[ind] -0.14209 0.02865 -4.96 0.000261 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.585 on 13 degrees of freedom
## Multiple R-squared: 0.6543, Adjusted R-squared: 0.6277
## F-statistic: 24.61 on 1 and 13 DF, p-value: 0.0002606
##
## (Intercept) Time[ind]
## 87.7852945 -0.1420931
## 2.5 % 97.5 %
## (Intercept) 84.6510853 90.91950363
## Time[ind] -0.2039779 -0.08020826
## [1] "weighted linear regression for substrate = 100"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 11 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 87.9249593 -0.1454162
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 4.03
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -6.4206 -2.3961 -0.1415 3.1402 6.2700
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 87.9250 1.5969 55.0609
## Time[ind] -0.1454 0.0315 -4.6120
##
## Residual standard error: 4.033 on 13 degrees of freedom
## (Intercept) Time[ind]
## 87.9249593 -0.1454162
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## ind
## [1,] 89 0 132.1385
## [2,] 90 0 128.5571
## [3,] 91 15 127.8622
## [4,] 92 15 128.3235
## [5,] 93 30 125.4579
## [6,] 94 30 124.6120
## [7,] 95 60 117.3174
## [8,] 96 60 126.8128
## [9,] 97 90 118.5064
## [10,] 98 90 117.3016
## [1] "least squares linear regression for substrate = 125"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 129.9684 -0.1354
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.5287 -1.0923 -0.2625 0.6374 4.9666
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 129.96843 1.29571 100.307 1.09e-13 ***
## Time[ind] -0.13537 0.02558 -5.291 0.000736 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.614 on 8 degrees of freedom
## Multiple R-squared: 0.7778, Adjusted R-squared: 0.75
## F-statistic: 28 on 1 and 8 DF, p-value: 0.0007361
##
## (Intercept) Time[ind]
## 129.9684341 -0.1353713
## 2.5 % 97.5 %
## (Intercept) 126.9805276 132.95634051
## Time[ind] -0.1943674 -0.07637517
## [1] "weighted linear regression for substrate = 125"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 129.9094905 -0.1359321
##
## Degrees of freedom: 10 total; 8 residual
## Scale estimate: 1.52
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -4.4361 -1.0081 -0.1910 0.7363 5.0592
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 129.9095 1.1313 114.8324
## Time[ind] -0.1359 0.0223 -6.0854
##
## Residual standard error: 1.52 on 8 degrees of freedom
## (Intercept) Time[ind]
## 129.9094905 -0.1359321
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## ind
## [1,] 99 0 167.6688
## [2,] 100 0 163.4321
## [3,] 101 0 170.5737
## [4,] 102 0 161.3269
## [5,] 103 15 166.2076
## [6,] 104 15 172.0808
## [7,] 105 15 160.6937
## [8,] 106 15 165.3167
## [9,] 107 30 159.6171
## [10,] 108 30 163.8883
## [11,] 109 30 163.2166
## [12,] 110 30 147.6768
## [13,] 111 60 158.6096
## [14,] 112 60 155.3368
## [15,] 113 60 164.3544
## [16,] 114 60 154.8116
## [17,] 115 90 144.3980
## [18,] 116 90 157.4613
## [19,] 117 90 158.6914
## [20,] 118 90 142.9719
## [1] "least squares linear regression for substrate = 150"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 166.3323 -0.1645
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.720 -2.968 1.394 2.929 8.216
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 166.33228 2.05831 80.810 < 2e-16 ***
## Time[ind] -0.16450 0.04064 -4.048 0.000755 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.873 on 18 degrees of freedom
## Multiple R-squared: 0.4765, Adjusted R-squared: 0.4474
## F-statistic: 16.38 on 1 and 18 DF, p-value: 0.0007553
##
## (Intercept) Time[ind]
## 166.3322788 -0.1645019
## 2.5 % 97.5 %
## (Intercept) 162.0079348 170.65662281
## Time[ind] -0.2498859 -0.07911792
## [1] "weighted linear regression for substrate = 150"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 9 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 166.4937036 -0.1556801
##
## Degrees of freedom: 20 total; 18 residual
## Scale estimate: 4.84
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -14.146 -3.162 1.167 2.569 7.922
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 166.4937 2.1892 76.0531
## Time[ind] -0.1557 0.0432 -3.6016
##
## Residual standard error: 4.838 on 18 degrees of freedom
## (Intercept) Time[ind]
## 166.4937036 -0.1556801
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## ind
## [1,] 119 0 307.3284
## [2,] 120 0 265.9378
## [3,] 121 15 291.3287
## [4,] 122 15 348.5203
## [5,] 123 15 380.5695
## [6,] 124 30 264.3975
## [7,] 125 30 240.4972
## [8,] 126 60 340.8683
## [9,] 127 60 244.0251
## [10,] 128 60 274.4346
## [11,] 129 90 289.9871
## [12,] 130 90 240.9444
## [13,] 131 90 327.4026
## [1] "least squares linear regression for substrate = 250"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 304.8179 -0.2638
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -56.408 -38.880 -9.533 46.324 79.708
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 304.8179 20.9715 14.535 1.59e-08 ***
## Time[ind] -0.2638 0.3901 -0.676 0.513
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 45.96 on 11 degrees of freedom
## Multiple R-squared: 0.03991, Adjusted R-squared: -0.04737
## F-statistic: 0.4572 on 1 and 11 DF, p-value: 0.5129
##
## (Intercept) Time[ind]
## 304.8178653 -0.2637669
## 2.5 % 97.5 %
## (Intercept) 258.659892 350.9758386
## Time[ind] -1.122323 0.5947897
## [1] "weighted linear regression for substrate = 250"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 304.8178653 -0.2637669
##
## Degrees of freedom: 13 total; 11 residual
## Scale estimate: 59.5
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -56.408 -38.880 -9.533 46.324 79.708
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 304.8179 20.9715 14.5349
## Time[ind] -0.2638 0.3901 -0.6762
##
## Residual standard error: 59.5 on 11 degrees of freedom
## (Intercept) Time[ind]
## 304.8178653 -0.2637669
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"## 'data.frame': 9 obs. of 2 variables:
## $ sub: num 0.712 10 3.168 50 75 ...
## $ vel: num 46.1 153.2 113.8 237.6 243 ...
## sub vel
## 1 0.7120 46.06058
## 2 10.0000 153.17362
## 3 3.1684 113.78122
## 4 50.0000 237.60942
## 5 75.0000 243.04658
## 6 100.0000 727.08109
## 7 125.0000 679.66027
## 8 150.0000 778.40045
## 9 250.0000 1318.83430## [1] "here are the rates"##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 20316.8 56747.7 0.3580 0.7309
## e:(Intercept) 3608.1 10593.6 0.3406 0.7434
##
## Residual standard error:
##
## 109.7349 (7 degrees of freedom)## No test available
##
## ModelDf Log lik Df Chisq value p value
##
## DRC model
We are interested in the reaction rate, v, which is a function of available substrate (pesticide) and the presence of an enzyme. We get Vmax from the asymptote and K = 0.5*Vmax. Biochemical reactions with a single substrate are typically assumed to follow Michaelis-Menten kinetics even if they deviate from the basic model assumptions.
We are fitting the 2-parameter model.
Used to estimate slopes.
dea
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.036297037" "Concs = 0.020155338" "Concs = 0"
## [4] "Concs = 0.556132535" "Concs = 0.426402494" "Concs = 0.367645414"
## [7] "Concs = 0.875251483" "Concs = 0.773924251" "Concs = 0.782702264"
## [10] "Concs = 1.213136274" "Concs = 1.251229589" "Concs = 1.396543005"
## [13] "Concs = 1.905345081" "Concs = 1.728273154" "Concs = 1.633832066"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.13401337 0.01873467
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.136
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.186302 -0.094788 -0.006864 0.085930 0.179198
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.1340 0.0514 2.6076
## Time[ind] 0.0187 0.0010 18.4625
##
## Residual standard error: 0.1362 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.13401337 0.01873467
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29" "Indices = 30"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0.008626567" "Concs = 0"
## [4] "Concs = 0.103194408" "Concs = 0.112578897" "Concs = 0.159184181"
## [7] "Concs = 0.221372739" "Concs = 0.168939786" "Concs = 0.193731234"
## [10] "Concs = NA" "Concs = 0.341243934" "Concs = 0.378947201"
## [13] "Concs = 0.359831218" "Concs = 0.432928865" "Concs = 0.459337307"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.037411413 0.004672527
##
## Degrees of freedom: 14 total; 12 residual
## (1 observation deleted due to missingness)
## Scale estimate: 0.0399
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.098108 -0.027841 -0.001453 0.021647 0.061184
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0374 0.0174 2.1461
## Time[ind] 0.0047 0.0003 13.3781
##
## Residual standard error: 0.03987 on 12 degrees of freedom
## (1 observation deleted due to missingness)
## (Intercept) Time[ind]
## 0.037411413 0.004672527
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 31" "Indices = 32" "Indices = 33" "Indices = 34"
## [5] "Indices = 35" "Indices = 36" "Indices = 37" "Indices = 38"
## [9] "Indices = 39" "Indices = 40" "Indices = 41" "Indices = 42"
## [13] "Indices = 43" "Indices = 44" "Indices = 45"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.010932763" "Concs = 0.00906186" "Concs = 0.011427564"
## [4] "Concs = 0.317229914" "Concs = 0.297863205" "Concs = 0.30576652"
## [7] "Concs = 0.490665066" "Concs = 0.510387221" "Concs = 0.480437347"
## [10] "Concs = 0.85701012" "Concs = 0.914180319" "Concs = 0.767670679"
## [13] "Concs = 1.119176244" "Concs = 0.905643096" "Concs = 1.044016346"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.10072516 0.01127992
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.106
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.21028 -0.08060 0.02794 0.04942 0.13666
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.1007 0.0362 2.7845
## Time[ind] 0.0113 0.0007 15.7929
##
## Residual standard error: 0.1057 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.10072516 0.01127992
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 46" "Indices = 47" "Indices = 48" "Indices = 49"
## [5] "Indices = 50" "Indices = 51" "Indices = 52" "Indices = 53"
## [9] "Indices = 54" "Indices = 55" "Indices = 56" "Indices = 57"
## [13] "Indices = 58" "Indices = 59" "Indices = 60"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.06413735" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.265350105" "Concs = 0.252666719" "Concs = 0.310628256"
## [7] "Concs = 0.489641626" "Concs = 0.484022887" "Concs = 0.487698201"
## [10] "Concs = 0.844772967" "Concs = 0.903936454" "Concs = 0.905600859"
## [13] "Concs = 1.124440012" "Concs = 1.429855138" "Concs = 0.946655192"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 12 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.06356831 0.01316417
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0735
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.301688 -0.036107 0.004319 0.040373 0.181512
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0636 0.0318 2.0008
## Time[ind] 0.0132 0.0006 20.9847
##
## Residual standard error: 0.07353 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.06356831 0.01316417
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 61" "Indices = 62" "Indices = 63" "Indices = 64"
## [5] "Indices = 65" "Indices = 66" "Indices = 67" "Indices = 68"
## [9] "Indices = 69" "Indices = 70" "Indices = 71"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 90"
## [11] "Times = 90"
## [1] "Concs = NA" "Concs = 0.007921774" "Concs = 0.031483454"
## [4] "Concs = 0.494202961" "Concs = 0.462344121" "Concs = 0.807147968"
## [7] "Concs = 0.848352727" "Concs = 1.611138851" "Concs = 1.76792633"
## [10] "Concs = 2.133194979" "Concs = 1.795991956"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.10230072 0.02323912
##
## Degrees of freedom: 10 total; 8 residual
## (1 observation deleted due to missingness)
## Scale estimate: 0.0974
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.397829 -0.068269 0.009565 0.047488 0.271279
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.1023 0.0610 1.6780
## Time[ind] 0.0232 0.0012 19.3057
##
## Residual standard error: 0.09744 on 8 degrees of freedom
## (1 observation deleted due to missingness)
## (Intercept) Time[ind]
## 0.10230072 0.02323912
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 0.712"
## [1] "Indices = 72" "Indices = 73" "Indices = 74" "Indices = 75"
## [5] "Indices = 76" "Indices = 77" "Indices = 78" "Indices = 79"
## [9] "Indices = 80" "Indices = 81" "Indices = 82" "Indices = 83"
## [13] "Indices = 84" "Indices = 85"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0" "Concs = 0.052966765" "Concs = 0.022152242"
## [7] "Concs = 0.042043283" "Concs = 0.017249246" "Concs = 0.040066167"
## [10] "Concs = 0.151616937" "Concs = 0.090030163" "Concs = 0.131931926"
## [13] "Concs = 0.09273422" "Concs = 0.109945027"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 10 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.001771916 0.001289181
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 0.0139
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.025064 -0.006333 -0.001077 0.008580 0.072494
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0018 0.0111 0.1600
## Time[ind] 0.0013 0.0002 5.4207
##
## Residual standard error: 0.01391 on 12 degrees of freedom
## (Intercept) Time[ind]
## 0.001771916 0.001289181
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 3.1684"
## [1] "Indices = 86" "Indices = 87" "Indices = 88" "Indices = 89"
## [5] "Indices = 90" "Indices = 91" "Indices = 92" "Indices = 93"
## [9] "Indices = 94" "Indices = 95" "Indices = 96" "Indices = 97"
## [13] "Indices = 98" "Indices = 99"
## [1] "Times = 0" "Times = 0" "Times = 15" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0.081663688"
## [4] "Concs = 0.098250742" "Concs = 0.064161633" "Concs = 0.107585902"
## [7] "Concs = 0.09756452" "Concs = 0.142322491" "Concs = 0.191711135"
## [10] "Concs = 0.185437222" "Concs = 0.21711368" "Concs = 0.265270616"
## [13] "Concs = 0.260794682" "Concs = 0.246155621"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 10 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.02743315 0.00266125
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 0.0178
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.027433 -0.008817 -0.001673 0.011885 0.035052
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0274 0.0131 2.0982
## Time[ind] 0.0027 0.0002 10.6704
##
## Residual standard error: 0.0178 on 12 degrees of freedom
## (Intercept) Time[ind]
## 0.02743315 0.00266125
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 100" "Indices = 101" "Indices = 102" "Indices = 103"
## [5] "Indices = 104" "Indices = 105" "Indices = 106" "Indices = 107"
## [9] "Indices = 108" "Indices = 109" "Indices = 110" "Indices = 111"
## [13] "Indices = 112"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.304504501" "Concs = 0.327456277" "Concs = 0.357391952"
## [7] "Concs = 0.649535281" "Concs = 0.541989813" "Concs = 1.114144819"
## [10] "Concs = 1.032829952" "Concs = 1.857454502" "Concs = 1.848929556"
## [13] "Concs = 1.381369076"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 11 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.009238479 0.019350499
##
## Degrees of freedom: 13 total; 11 residual
## Scale estimate: 0.0832
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.369414 -0.047764 -0.009238 0.057896 0.106671
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0092 0.0372 0.2482
## Time[ind] 0.0194 0.0007 26.5778
##
## Residual standard error: 0.08323 on 11 degrees of freedom
## (Intercept) Time[ind]
## 0.009238479 0.019350499
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 113" "Indices = 114" "Indices = 115" "Indices = 116"
## [5] "Indices = 117" "Indices = 118" "Indices = 119" "Indices = 120"
## [9] "Indices = 121" "Indices = 122" "Indices = 123" "Indices = 124"
## [13] "Indices = 125" "Indices = 126" "Indices = 127" "Indices = 128"
## [17] "Indices = 129" "Indices = 130" "Indices = 131" "Indices = 132"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 0" "Times = 15"
## [6] "Times = 15" "Times = 15" "Times = 15" "Times = 30" "Times = 30"
## [11] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 60"
## [16] "Times = 60" "Times = 90" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.019939329" "Concs = 0.048466882" "Concs = 0.026079286"
## [4] "Concs = 0" "Concs = 0.634852481" "Concs = 0.425731557"
## [7] "Concs = 0.685758141" "Concs = 0.655886478" "Concs = 1.175719405"
## [10] "Concs = 0.819943874" "Concs = 1.100162014" "Concs = 0.985930582"
## [13] "Concs = 1.968440394" "Concs = 1.271576575" "Concs = 1.873663272"
## [16] "Concs = 1.701164984" "Concs = 2.39611731" "Concs = 1.275943895"
## [19] "Concs = 2.093301823" "Concs = 2.344177507"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.18458313 0.02376598
##
## Degrees of freedom: 20 total; 18 residual
## Scale estimate: 0.225
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -1.04758 -0.16004 0.04663 0.12228 0.35790
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.1846 0.0830 2.2229
## Time[ind] 0.0238 0.0016 14.4951
##
## Residual standard error: 0.2248 on 18 degrees of freedom
## (Intercept) Time[ind]
## 0.18458313 0.02376598
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"## 'data.frame': 9 obs. of 2 variables:
## $ sub: num 50 10 100 75 125 ...
## $ vel: num 93.7 23.4 56.4 65.8 116.2 ...
## sub vel
## 1 50.0000 93.673356
## 2 10.0000 23.362635
## 3 100.0000 56.399623
## 4 75.0000 65.820831
## 5 125.0000 116.195578
## 6 0.7120 6.445907
## 7 3.1684 13.306248
## 8 250.0000 96.752493
## 9 150.0000 118.829886## [1] "here are the rates"##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 119.069 24.416 4.8767 0.0018 **
## e:(Intercept) 31.905 25.855 1.2340 0.2570
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error:
##
## 20.38128 (7 degrees of freedom)## No test available
##
## ModelDf Log lik Df Chisq value p value
##
## DRC model
We are interested in the reaction rate, v, which is a function of available substrate (pesticide) and the presence of an enzyme. We get Vmax from the asymptote and K = 0.5*Vmax. Biochemical reactions with a single substrate are typically assumed to follow Michaelis-Menten kinetics even if they deviate from the basic model assumptions.
We are fitting the 2-parameter model.
Used to estimate slopes.
dia
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.585463603" "Concs = 0.261545192" "Concs = 0.250839807"
## [7] "Concs = 0.51028234" "Concs = 0.542636363" "Concs = 0.456010453"
## [10] "Concs = 0.771175727" "Concs = 0.831308115" "Concs = 0.840152987"
## [13] "Concs = 1.307705125" "Concs = 1.163648794" "Concs = 1.092201395"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.06775371 0.01264067
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0938
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.113213 -0.061386 0.004181 0.038634 0.328100
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0678 0.0324 2.0888
## Time[ind] 0.0126 0.0006 19.7373
##
## Residual standard error: 0.09385 on 13 degrees of freedom## (Intercept) Time[ind]
## 0.06775371 0.01264067
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29" "Indices = 30" "Indices = 31"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 60" "Times = 90" "Times = 90"
## [16] "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.063028732" "Concs = 0.056638774" "Concs = NA"
## [7] "Concs = 0.102314087" "Concs = 0.102958703" "Concs = 0.055763938"
## [10] "Concs = NA" "Concs = 0.214565616" "Concs = 0.202136134"
## [13] "Concs = 0.190219138" "Concs = 0.190000776" "Concs = 0.325779675"
## [16] "Concs = 0.26769978"## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Ran 20 iterations without convergence
##
## Coefficients:
## (Intercept) Time[ind]
## 0.005144853 0.003125718
##
## Degrees of freedom: 14 total; 12 residual
## (2 observations deleted due to missingness)
## Scale estimate: 0.0108
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.0964587 -0.0051449 0.0004644 0.0082382 0.0393202
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0051 0.0078 0.6607
## Time[ind] 0.0031 0.0001 20.9819
##
## Residual standard error: 0.01083 on 12 degrees of freedom
## (2 observations deleted due to missingness)
## (Intercept) Time[ind]
## 0.005144853 0.003125718
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 32" "Indices = 33" "Indices = 34" "Indices = 35"
## [5] "Indices = 36" "Indices = 37" "Indices = 38" "Indices = 39"
## [9] "Indices = 40" "Indices = 41" "Indices = 42" "Indices = 43"
## [13] "Indices = 44" "Indices = 45" "Indices = 46"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.199686369" "Concs = 0.226193885" "Concs = 0.183498938"
## [7] "Concs = 0.277277734" "Concs = 0.320753808" "Concs = 0.342265185"
## [10] "Concs = 0.577987791" "Concs = 0.621738846" "Concs = 0.622069014"
## [13] "Concs = 0.690327949" "Concs = 0.607358803" "Concs = 0.673085734"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.067751080 0.007403565
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0904
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.126713 -0.064369 0.004694 0.049898 0.110104
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0678 0.0320 2.1186
## Time[ind] 0.0074 0.0006 11.7251
##
## Residual standard error: 0.09041 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.067751080 0.007403565
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 47" "Indices = 48" "Indices = 49" "Indices = 50"
## [5] "Indices = 51" "Indices = 52" "Indices = 53" "Indices = 54"
## [9] "Indices = 55" "Indices = 56" "Indices = 57" "Indices = 58"
## [13] "Indices = 59" "Indices = 60" "Indices = 61"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.181875613" "Concs = 0.220572965" "Concs = 0.134445009"
## [7] "Concs = 0.271493213" "Concs = 0.240135574" "Concs = 0.294733329"
## [10] "Concs = 0.549334509" "Concs = 0.593493808" "Concs = 0.579429136"
## [13] "Concs = 0.626545938" "Concs = 0.989677724" "Concs = 0.589031821"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 9 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.021326852 0.008701103
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0445
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.21539 -0.02133 -0.01087 0.03303 0.18525
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0213 0.0243 0.8769
## Time[ind] 0.0087 0.0005 18.1203
##
## Residual standard error: 0.04452 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.021326852 0.008701103
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 62" "Indices = 63" "Indices = 64" "Indices = 65"
## [5] "Indices = 66" "Indices = 67" "Indices = 68" "Indices = 69"
## [9] "Indices = 70" "Indices = 71"
## [1] "Times = 0" "Times = 0" "Times = 15" "Times = 15" "Times = 30"
## [6] "Times = 30" "Times = 60" "Times = 60" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0.25671841"
## [4] "Concs = 0.250484194" "Concs = 0.468843857" "Concs = 0.464918482"
## [7] "Concs = 1.103609505" "Concs = 1.162619293" "Concs = 1.351454855"
## [10] "Concs = 1.149727466"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 9 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.01891677 0.01495899
##
## Degrees of freedom: 10 total; 8 residual
## Scale estimate: 0.0242
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.2154981 -0.0176303 -0.0008052 0.0118583 0.2461633
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0189 0.0181 1.0477
## Time[ind] 0.0150 0.0004 41.9602
##
## Residual standard error: 0.02425 on 8 degrees of freedom
## (Intercept) Time[ind]
## 0.01891677 0.01495899
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 0.712"
## [1] "Indices = 72" "Indices = 73" "Indices = 74" "Indices = 75"
## [5] "Indices = 76" "Indices = 77" "Indices = 78" "Indices = 79"
## [9] "Indices = 80" "Indices = 81"
## [1] "Times = 0" "Times = 0" "Times = 15" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 60" "Times = 60" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0" "Concs = 0" "Concs = 0.026940754"
## [7] "Concs = 0.080149289" "Concs = 0.027380501" "Concs = 0.061935383"
## [10] "Concs = 0.071298111"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## -0.0053994871 0.0007975344
##
## Degrees of freedom: 10 total; 8 residual
## Scale estimate: 0.00973
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.0150721 -0.0065635 0.0002381 0.0053995 0.0376967
##
## Coefficients:
## Value Std. Error t value
## (Intercept) -0.0054 0.0057 -0.9527
## Time[ind] 0.0008 0.0001 7.0325
##
## Residual standard error: 0.009731 on 8 degrees of freedom
## (Intercept) Time[ind]
## -0.0053994871 0.0007975344
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 3.1684"
## [1] "Indices = 82" "Indices = 83" "Indices = 84" "Indices = 85"
## [5] "Indices = 86" "Indices = 87" "Indices = 88" "Indices = 89"
## [9] "Indices = 90" "Indices = 91" "Indices = 92" "Indices = 93"
## [13] "Indices = 94"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.049477598" "Concs = 0.049432813" "Concs = 0.050456874"
## [7] "Concs = 0.063998501" "Concs = 0.037395121" "Concs = 0.068845504"
## [10] "Concs = 0.083597324" "Concs = 0.096720338" "Concs = 0.108999109"
## [13] "Concs = 0.135728061"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.011168802 0.001248868
##
## Degrees of freedom: 13 total; 11 residual
## Scale estimate: 0.0167
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.017255 -0.011169 -0.002504 0.012161 0.019576
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0112 0.0062 1.7952
## Time[ind] 0.0012 0.0001 9.6669
##
## Residual standard error: 0.01666 on 11 degrees of freedom
## (Intercept) Time[ind]
## 0.011168802 0.001248868
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 95" "Indices = 96" "Indices = 97" "Indices = 98"
## [5] "Indices = 99" "Indices = 100" "Indices = 101" "Indices = 102"
## [9] "Indices = 103" "Indices = 104" "Indices = 105" "Indices = 106"
## [13] "Indices = 107" "Indices = 108" "Indices = 109"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.595748019" "Concs = 0.609228827" "Concs = 0.810403963"
## [7] "Concs = 1.130313908" "Concs = NA" "Concs = 1.094019425"
## [10] "Concs = 2.040786946" "Concs = 2.060489665" "Concs = 1.546144988"
## [13] "Concs = 3.125991996" "Concs = 2.961111344" "Concs = 2.766158119"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 9 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.08547631 0.03207666
##
## Degrees of freedom: 14 total; 12 residual
## (1 observation deleted due to missingness)
## Scale estimate: 0.125
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.46393 -0.08548 0.02992 0.04937 0.24378
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0855 0.0605 1.4127
## Time[ind] 0.0321 0.0012 27.4658
##
## Residual standard error: 0.1246 on 12 degrees of freedom
## (1 observation deleted due to missingness)
## (Intercept) Time[ind]
## 0.08547631 0.03207666
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 110" "Indices = 111" "Indices = 112" "Indices = 113"
## [5] "Indices = 114" "Indices = 115" "Indices = 116" "Indices = 117"
## [9] "Indices = 118" "Indices = 119" "Indices = 120" "Indices = 121"
## [13] "Indices = 122" "Indices = 123" "Indices = 124" "Indices = 125"
## [17] "Indices = 126" "Indices = 127" "Indices = 128" "Indices = 129"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 0" "Times = 15"
## [6] "Times = 15" "Times = 15" "Times = 15" "Times = 30" "Times = 30"
## [11] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 60"
## [16] "Times = 60" "Times = 90" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0" "Concs = 0.397134148" "Concs = 0.200692165"
## [7] "Concs = 0.438951389" "Concs = 0.389074132" "Concs = 0.735668645"
## [10] "Concs = 0.641012348" "Concs = 0.895177769" "Concs = 0.833089226"
## [13] "Concs = 1.091832924" "Concs = 0.77221084" "Concs = 1.267592057"
## [16] "Concs = 1.113093549" "Concs = 1.656276416" "Concs = 0.817747445"
## [19] "Concs = 1.357629712" "Concs = 1.915166937"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 16 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.09310748 0.01699426
##
## Degrees of freedom: 20 total; 18 residual
## Scale estimate: 0.138
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.80484 -0.09311 0.01701 0.10138 0.29258
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0931 0.0698 1.3340
## Time[ind] 0.0170 0.0014 12.3313
##
## Residual standard error: 0.1381 on 18 degrees of freedom
## (Intercept) Time[ind]
## 0.09310748 0.01699426
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"## 'data.frame': 9 obs. of 2 variables:
## $ sub: num 50 10 100 75 125 ...
## $ vel: num 63.2 15.6 37 43.5 74.8 ...
## sub vel
## 1 50.0000 63.203351
## 2 10.0000 15.628591
## 3 100.0000 37.017826
## 4 75.0000 43.505515
## 5 125.0000 74.794933
## 6 0.7120 3.987672
## 7 3.1684 6.244342
## 8 250.0000 160.383308
## 9 150.0000 84.971320## [1] "here are the rates"##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 5340.7 16494.0 0.3238 0.7556
## e:(Intercept) 8568.7 27021.7 0.3171 0.7604
##
## Residual standard error:
##
## 16.48602 (7 degrees of freedom)## No test available
##
## ModelDf Log lik Df Chisq value p value
##
## DRC model
triadimefon
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 0.68082"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 1.055195513" "Concs = 1.716416889" "Concs = 1.052273474"
## [4] "Concs = 0.938633567" "Concs = 0.950248963" "Concs = 0.930818982"
## [7] "Concs = 0.858111542" "Concs = 0.870265496" "Concs = 0.874485426"
## [10] "Concs = 0.823645984" "Concs = 0.832430656" "Concs = 0.826119617"
## [13] "Concs = 0.817168177" "Concs = 0.817187563" "Concs = 0.816771202"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.997266592 -0.002429795
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0572
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.06626 -0.02892 -0.01905 0.03859 0.71915
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.9973 0.0210 47.5261
## Time[ind] -0.0024 0.0004 -5.8645
##
## Residual standard error: 0.05721 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.997266592 -0.002429795
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 7.075345016" "Concs = 6.990021457" "Concs = 6.934400108"
## [4] "Concs = 7.582634214" "Concs = 6.195218961" "Concs = 6.437182055"
## [7] "Concs = 5.377257944" "Concs = 5.321074247" "Concs = 5.115101438"
## [10] "Concs = 2.737595497" "Concs = 2.383571745" "Concs = 4.432786364"
## [13] "Concs = 4.492543529" "Concs = 4.706424998"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 7 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 6.71631533 -0.03004519
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 0.681
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -2.5300 -0.4798 0.1948 0.4052 1.3170
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 6.7163 0.3330 20.1663
## Time[ind] -0.0300 0.0067 -4.5026
##
## Residual standard error: 0.6806 on 12 degrees of freedom
## (Intercept) Time[ind]
## 6.71631533 -0.03004519
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 2.89"
## [1] "Indices = 30" "Indices = 31" "Indices = 32" "Indices = 33"
## [5] "Indices = 34" "Indices = 35" "Indices = 36" "Indices = 37"
## [9] "Indices = 38" "Indices = 39" "Indices = 40" "Indices = 41"
## [13] "Indices = 42" "Indices = 43"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 1.777329525" "Concs = 1.804715957" "Concs = 1.934785731"
## [4] "Concs = 1.434605415" "Concs = 1.672519857" "Concs = 1.373576496"
## [7] "Concs = 1.378953779" "Concs = 1.252246261" "Concs = 1.103395037"
## [10] "Concs = 1.073980287" "Concs = 1.03524126" "Concs = 0.952606695"
## [13] "Concs = 0.896534444" "Concs = 0.898012906"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 7 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 1.725759061 -0.009823543
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 0.105
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.17881 -0.06114 0.00931 0.07331 0.20903
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 1.7258 0.0558 30.9211
## Time[ind] -0.0098 0.0011 -9.2001
##
## Residual standard error: 0.1048 on 12 degrees of freedom
## (Intercept) Time[ind]
## 1.725759061 -0.009823543
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 44" "Indices = 45" "Indices = 46" "Indices = 47"
## [5] "Indices = 48" "Indices = 49" "Indices = 50" "Indices = 51"
## [9] "Indices = 52" "Indices = 53" "Indices = 54" "Indices = 55"
## [13] "Indices = 56" "Indices = 57" "Indices = 58"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 16" "Times = 17" "Times = 18" "Times = 19"
## [11] "Times = 20" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 39.44332312" "Concs = 40.07390834" "Concs = 35.6664438"
## [4] "Concs = 33.26858913" "Concs = 28.71837314" "Concs = 40.88681967"
## [7] "Concs = 25.24439217" "Concs = 36.71636819" "Concs = 41.57720177"
## [10] "Concs = 36.61330013" "Concs = 35.13544755" "Concs = 31.75029212"
## [13] "Concs = 29.38972896" "Concs = 30.68177634" "Concs = 31.70843431"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 37.52823692 -0.08070698
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 2.76
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -10.9925 -1.3987 0.4172 1.6795 5.5017
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 37.5282 1.2962 28.9531
## Time[ind] -0.0807 0.0289 -2.7941
##
## Residual standard error: 2.76 on 13 degrees of freedom
## (Intercept) Time[ind]
## 37.52823692 -0.08070698
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 59" "Indices = 60" "Indices = 61" "Indices = 62"
## [5] "Indices = 63" "Indices = 64" "Indices = 65" "Indices = 66"
## [9] "Indices = 67" "Indices = 68" "Indices = 69" "Indices = 70"
## [13] "Indices = 71" "Indices = 72" "Indices = 73"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 73.82935275" "Concs = 69.81459059" "Concs = 72.37204855"
## [4] "Concs = 67.82074535" "Concs = 68.2563384" "Concs = 68.54841895"
## [7] "Concs = 68.13810367" "Concs = 67.01772769" "Concs = 63.94802795"
## [10] "Concs = 64.13247413" "Concs = 63.88083801" "Concs = 60.44713839"
## [13] "Concs = 61.56996061" "Concs = 64.02141502" "Concs = 59.47011182"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 70.5414464 -0.1109491
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 1.5
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -3.4374 -0.8917 -0.1952 0.9695 3.4654
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 70.5414 0.8050 87.6250
## Time[ind] -0.1109 0.0159 -6.9799
##
## Residual standard error: 1.503 on 13 degrees of freedom
## (Intercept) Time[ind]
## 70.5414464 -0.1109491
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 74" "Indices = 75" "Indices = 76" "Indices = 77"
## [5] "Indices = 78" "Indices = 79" "Indices = 80" "Indices = 81"
## [9] "Indices = 82" "Indices = 83" "Indices = 84" "Indices = 85"
## [13] "Indices = 86" "Indices = 87" "Indices = 88"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 109.3199937" "Concs = 104.4849272" "Concs = 109.1666963"
## [4] "Concs = 109.8399004" "Concs = 113.5827498" "Concs = 114.1444056"
## [7] "Concs = 110.3922061" "Concs = 107.3962739" "Concs = 108.8977191"
## [10] "Concs = 108.1725461" "Concs = 104.4949296" "Concs = 109.1134227"
## [13] "Concs = 104.4988435" "Concs = 100.9234253" "Concs = 101.7288349"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 111.19791229 -0.08429047
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 2.79
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -6.71299 -1.88043 -0.09365 1.87753 4.21085
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 111.1979 1.1916 93.3145
## Time[ind] -0.0843 0.0235 -3.5824
##
## Residual standard error: 2.792 on 13 degrees of freedom
## (Intercept) Time[ind]
## 111.19791229 -0.08429047
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 89" "Indices = 90" "Indices = 91" "Indices = 92"
## [5] "Indices = 93" "Indices = 94" "Indices = 95" "Indices = 96"
## [9] "Indices = 97" "Indices = 98" "Indices = 99" "Indices = 100"
## [13] "Indices = 101" "Indices = 102" "Indices = 103"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 107.5365248" "Concs = 127.5663033" "Concs = 126.8308018"
## [4] "Concs = 106.5228047" "Concs = 135.7677165" "Concs = 106.6195125"
## [7] "Concs = 103.9682822" "Concs = 133.2578786" "Concs = 134.0194733"
## [10] "Concs = 105.1755811" "Concs = 121.0935634" "Concs = 120.6467177"
## [13] "Concs = 103.405648" "Concs = 103.7554597" "Concs = 119.5785281"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 121.7354023 -0.1201474
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 13.9
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -14.199 -11.332 5.095 7.612 15.888
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 121.7354 4.8954 24.8673
## Time[ind] -0.1201 0.0967 -1.2430
##
## Residual standard error: 13.86 on 13 degrees of freedom
## (Intercept) Time[ind]
## 121.7354023 -0.1201474
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 104" "Indices = 105" "Indices = 106" "Indices = 107"
## [5] "Indices = 108" "Indices = 109" "Indices = 110" "Indices = 111"
## [9] "Indices = 112" "Indices = 113" "Indices = 114" "Indices = 115"
## [13] "Indices = 116" "Indices = 117" "Indices = 118"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 136.4221117" "Concs = 136.379058" "Concs = 129.4961115"
## [4] "Concs = 137.8091818" "Concs = 131.9793127" "Concs = 157.7963414"
## [7] "Concs = 124.5114441" "Concs = 127.6369723" "Concs = 154.8965192"
## [10] "Concs = 132.7699361" "Concs = 97.16035365" "Concs = 114.5318893"
## [13] "Concs = 131.7957906" "Concs = 143.1419758" "Concs = 131.1273703"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 8 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 134.44160061 -0.04431801
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 7.33
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -34.6222 -5.2103 0.9874 3.0064 24.0195
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 134.4416 4.5823 29.3391
## Time[ind] -0.0443 0.0905 -0.4898
##
## Residual standard error: 7.333 on 13 degrees of freedom
## (Intercept) Time[ind]
## 134.44160061 -0.04431801
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 119" "Indices = 120" "Indices = 121" "Indices = 122"
## [5] "Indices = 123" "Indices = 124" "Indices = 125" "Indices = 126"
## [9] "Indices = 127" "Indices = 128" "Indices = 129" "Indices = 130"
## [13] "Indices = 131" "Indices = 132"
## [1] "Times = 0" "Times = 0" "Times = 15" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 261.549615" "Concs = 326.9796946" "Concs = 266.8345989"
## [4] "Concs = 264.2922486" "Concs = 275.5322522" "Concs = 261.2512151"
## [7] "Concs = 285.8702782" "Concs = 313.1209636" "Concs = 328.5136848"
## [10] "Concs = 332.5575402" "Concs = 294.3280544" "Concs = 278.96352"
## [13] "Concs = 237.618938" "Concs = 260.2516169"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 289.2108635 -0.1081183
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 35.6
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -41.861 -22.661 -6.287 23.266 49.834
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 289.2109 14.8017 19.5390
## Time[ind] -0.1081 0.2823 -0.3829
##
## Residual standard error: 35.59 on 12 degrees of freedom
## (Intercept) Time[ind]
## 289.2108635 -0.1081183
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"## 'data.frame': 9 obs. of 2 variables:
## $ sub: num 0.681 10 2.89 50 75 ...
## $ vel: num 12.1 150.2 49.1 403.5 554.7 ...
## sub vel
## 1 0.68082 12.14897
## 2 10.00000 150.22595
## 3 2.89000 49.11772
## 4 50.00000 403.53491
## 5 75.00000 554.74564
## 6 100.00000 421.45233
## 7 125.00000 600.73708
## 8 150.00000 221.59003
## 9 250.00000 540.59158## [1] "here are the rates"##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 534.106 92.306 5.7863 0.0006729 ***
## e:(Intercept) 18.379 15.312 1.2003 0.2690493
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error:
##
## 121.6792 (7 degrees of freedom)## No test available
##
## ModelDf Log lik Df Chisq value p value
##
## DRC model
tdla
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 0.68"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14"
## [1] "Times = 0" "Times = 0" "Times = 15" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.911333779" "Concs = 0.538623139" "Concs = 0.274067068"
## [4] "Concs = 0.295482796" "Concs = 0.240279185" "Concs = 0.257746875"
## [7] "Concs = 0.308331891" "Concs = 0.308676715" "Concs = 0.25011887"
## [10] "Concs = 0.37258778" "Concs = 0.288696798" "Concs = 0.223412134"
## [13] "Concs = 0.250234863" "Concs = 0.212692933"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 13 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.33336175 -0.00112991
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 0.0327
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.0761339 -0.0204420 0.0003049 0.0219885 0.5779720
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.3334 0.0220 15.1640
## Time[ind] -0.0011 0.0004 -2.6944
##
## Residual standard error: 0.03267 on 12 degrees of freedom
## (Intercept) Time[ind]
## 0.33336175 -0.00112991
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 15" "Indices = 16" "Indices = 17" "Indices = 18"
## [5] "Indices = 19" "Indices = 20" "Indices = 21" "Indices = 22"
## [9] "Indices = 23" "Indices = 24" "Indices = 25" "Indices = 26"
## [13] "Indices = 27" "Indices = 28"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 1.018010717" "Concs = 1.006352529" "Concs = 1.006022683"
## [4] "Concs = 0.656082156" "Concs = 0.613384138" "Concs = 0.648345515"
## [7] "Concs = 0.97315514" "Concs = 0.957123696" "Concs = 0.919138229"
## [10] "Concs = 1.467786187" "Concs = 1.525372593" "Concs = 1.652830116"
## [13] "Concs = 1.583931982" "Concs = 1.587496374"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.763609368 0.009380002
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 0.252
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.2909 -0.1164 -0.0221 0.1846 0.2544
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.7636 0.0815 9.3739
## Time[ind] 0.0094 0.0016 5.7470
##
## Residual standard error: 0.2523 on 12 degrees of freedom
## (Intercept) Time[ind]
## 0.763609368 0.009380002
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 2.89"
## [1] "Indices = 29" "Indices = 30" "Indices = 31" "Indices = 32"
## [5] "Indices = 33" "Indices = 34" "Indices = 35" "Indices = 36"
## [9] "Indices = 37" "Indices = 38" "Indices = 39" "Indices = 40"
## [13] "Indices = 41" "Indices = 42"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.967608564" "Concs = 1.104071328" "Concs = 1.232020771"
## [4] "Concs = 1.089981806" "Concs = 0.962740371" "Concs = 1.30210336"
## [7] "Concs = 1.429231051" "Concs = 1.521298076" "Concs = 2.093039311"
## [10] "Concs = 2.181520068" "Concs = 1.944692162" "Concs = 2.111347812"
## [13] "Concs = 2.37727648" "Concs = 2.200482444"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 1.02311637 0.01433486
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 0.193
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.27540 -0.13931 0.01878 0.07775 0.29831
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 1.0231 0.0863 11.8493
## Time[ind] 0.0143 0.0017 8.6778
##
## Residual standard error: 0.1934 on 12 degrees of freedom
## (Intercept) Time[ind]
## 1.02311637 0.01433486
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 43" "Indices = 44" "Indices = 45" "Indices = 46"
## [5] "Indices = 47" "Indices = 48" "Indices = 49" "Indices = 50"
## [9] "Indices = 51" "Indices = 52" "Indices = 53" "Indices = 54"
## [13] "Indices = 55" "Indices = 56" "Indices = 57"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 5.183692755" "Concs = 5.288137946" "Concs = 4.784272534"
## [4] "Concs = 3.082573879" "Concs = 3.042434157" "Concs = 3.580371528"
## [7] "Concs = 3.391053517" "Concs = 3.946105993" "Concs = 3.834987724"
## [10] "Concs = 4.261556467" "Concs = 4.914986114" "Concs = 4.584590488"
## [13] "Concs = 4.976952649" "Concs = 4.746707742" "Concs = 4.95610163"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 9 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 3.924377589 0.008666301
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.698
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -1.01194 -0.41169 0.04236 0.37162 1.36376
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 3.9244 0.3847 10.2005
## Time[ind] 0.0087 0.0076 1.1409
##
## Residual standard error: 0.6977 on 13 degrees of freedom
## (Intercept) Time[ind]
## 3.924377589 0.008666301
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 58" "Indices = 59" "Indices = 60" "Indices = 61"
## [5] "Indices = 62" "Indices = 63" "Indices = 64" "Indices = 65"
## [9] "Indices = 66" "Indices = 67" "Indices = 68" "Indices = 69"
## [13] "Indices = 70" "Indices = 71" "Indices = 72"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 2.156819763" "Concs = 1.976073713" "Concs = 2.164685233"
## [4] "Concs = 1.915486338" "Concs = 1.871421816" "Concs = 1.904115966"
## [7] "Concs = 2.323880269" "Concs = 1.922349719" "Concs = 1.984507804"
## [10] "Concs = 2.756656604" "Concs = 2.61971313" "Concs = 2.531743911"
## [13] "Concs = 3.126097153" "Concs = 3.090615235" "Concs = 3.137674604"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 11 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 1.83645163 0.01343346
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.182
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.31711 -0.12815 0.04515 0.10320 0.32823
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 1.8365 0.0978 18.7822
## Time[ind] 0.0134 0.0019 6.9582
##
## Residual standard error: 0.1816 on 13 degrees of freedom
## (Intercept) Time[ind]
## 1.83645163 0.01343346
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 73" "Indices = 74" "Indices = 75" "Indices = 76"
## [5] "Indices = 77" "Indices = 78" "Indices = 79" "Indices = 80"
## [9] "Indices = 81" "Indices = 82" "Indices = 83" "Indices = 84"
## [13] "Indices = 85"
## [1] "Times = 0" "Times = 0" "Times = 15" "Times = 15" "Times = 30"
## [6] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 3.665038064" "Concs = 4.929996704" "Concs = 3.247700116"
## [4] "Concs = 4.448925817" "Concs = 3.964352006" "Concs = 4.642993841"
## [7] "Concs = 4.543916406" "Concs = 4.365953811" "Concs = 4.91659626"
## [10] "Concs = 4.946841298" "Concs = 5.323415111" "Concs = 5.610391673"
## [13] "Concs = 5.447082915"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 8 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 3.88781862 0.01646824
##
## Degrees of freedom: 13 total; 11 residual
## Scale estimate: 0.357
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.88714 -0.22278 0.07093 0.24043 1.04218
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 3.8878 0.2106 18.4628
## Time[ind] 0.0165 0.0039 4.2421
##
## Residual standard error: 0.3565 on 11 degrees of freedom
## (Intercept) Time[ind]
## 3.88781862 0.01646824
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 86" "Indices = 87" "Indices = 88" "Indices = 89"
## [5] "Indices = 90" "Indices = 91" "Indices = 92" "Indices = 93"
## [9] "Indices = 94" "Indices = 95" "Indices = 96" "Indices = 97"
## [13] "Indices = 98" "Indices = 99" "Indices = 100"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 3.435420024" "Concs = 4.97730785" "Concs = 4.825739914"
## [4] "Concs = 3.975016459" "Concs = 4.864396394" "Concs = 3.779106429"
## [7] "Concs = 4.123881939" "Concs = 3.650943656" "Concs = 5.50644677"
## [10] "Concs = 4.807257346" "Concs = 6.000486305" "Concs = 5.098368211"
## [13] "Concs = 5.156782065" "Concs = 5.738264141" "Concs = 5.42544885"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 4.19059517 0.01454007
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.746
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.97585 -0.46830 -0.07375 0.54542 0.93749
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 4.1906 0.2630 15.9349
## Time[ind] 0.0145 0.0052 2.8002
##
## Residual standard error: 0.7456 on 13 degrees of freedom
## (Intercept) Time[ind]
## 4.19059517 0.01454007
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 101" "Indices = 102" "Indices = 103" "Indices = 104"
## [5] "Indices = 105" "Indices = 106" "Indices = 107" "Indices = 108"
## [9] "Indices = 109" "Indices = 110" "Indices = 111" "Indices = 112"
## [13] "Indices = 113" "Indices = 114" "Indices = 115"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 5.906076855" "Concs = 5.310456154" "Concs = 5.316828489"
## [4] "Concs = 5.663191766" "Concs = 5.426740549" "Concs = 6.978063453"
## [7] "Concs = 4.92771323" "Concs = 5.515269474" "Concs = 7.451213493"
## [10] "Concs = 7.851784896" "Concs = 4.606893218" "Concs = 5.46616595"
## [13] "Concs = 8.552435256" "Concs = 9.168552858" "Concs = 8.094227355"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 9 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 5.30861592 0.03104684
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 1.01
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -2.56453 -0.53616 0.00184 0.63891 1.21119
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 5.3086 0.4417 12.0183
## Time[ind] 0.0310 0.0087 3.5598
##
## Residual standard error: 1.009 on 13 degrees of freedom
## (Intercept) Time[ind]
## 5.30861592 0.03104684
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 116" "Indices = 117" "Indices = 118" "Indices = 119"
## [5] "Indices = 120" "Indices = 121" "Indices = 122" "Indices = 123"
## [9] "Indices = 124" "Indices = 125" "Indices = 126" "Indices = 127"
## [13] "Indices = 128" "Indices = 129" "Indices = 130"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 1.161490438" "Concs = 1.330165483" "Concs = 1.276159877"
## [4] "Concs = 1.61720898" "Concs = 1.740756052" "Concs = 1.791062644"
## [7] "Concs = 2.034457774" "Concs = 2.298567384" "Concs = 2.005605464"
## [10] "Concs = 2.531605274" "Concs = 2.413976625" "Concs = 2.927399787"
## [13] "Concs = 3.522201259" "Concs = 3.463756836" "Concs = 3.15599886"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 1.33031671 0.02275505
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.177
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.2816433 -0.1092241 -0.0001512 0.1024527 0.2855991
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 1.3303 0.0755 17.6184
## Time[ind] 0.0228 0.0015 15.2628
##
## Residual standard error: 0.1771 on 13 degrees of freedom
## (Intercept) Time[ind]
## 1.33031671 0.02275505
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"## 'data.frame': 9 obs. of 2 variables:
## $ sub: num 0.68 10 2.89 50 75 100 125 150 250
## $ vel: num -5.65 46.9 71.67 43.33 67.17 ...
## sub vel
## 1 0.68 -5.64955
## 2 10.00 46.90001
## 3 2.89 71.67428
## 4 50.00 43.33150
## 5 75.00 67.16731
## 6 100.00 82.34119
## 7 125.00 72.70033
## 8 150.00 155.23421
## 9 250.00 113.77527## [1] "here are the rates"##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 94.7700 22.1926 4.2703 0.003699 **
## e:(Intercept) 5.2049 10.7357 0.4848 0.642605
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error:
##
## 36.04578 (7 degrees of freedom)## No test available
##
## ModelDf Log lik Df Chisq value p value
##
## DRC model
tdlb
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 0.68"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.402082422" "Concs = 0.229623234" "Concs = 1.029164926"
## [4] "Concs = 0.246173803" "Concs = 0.260813596" "Concs = 0.21820036"
## [7] "Concs = 0.216021451" "Concs = 0.254508505" "Concs = 0.247048129"
## [10] "Concs = 0.153683269" "Concs = 0.218675147" "Concs = 0.173579791"
## [13] "Concs = 0.099158476" "Concs = 0.117730117" "Concs = 0.098721871"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 10 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.298524176 -0.002117459
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0282
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.068901 -0.018386 -0.005949 0.015778 0.730641
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.2985 0.0172 17.3528
## Time[ind] -0.0021 0.0003 -6.2337
##
## Residual standard error: 0.02815 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.298524176 -0.002117459
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29" "Indices = 30"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.591058602" "Concs = 0.59099425" "Concs = 0.596447836"
## [4] "Concs = 0.605361148" "Concs = 0.600460446" "Concs = 0.614107575"
## [7] "Concs = 1.000522185" "Concs = 0.977505725" "Concs = 0.925246462"
## [10] "Concs = 0.532628472" "Concs = 1.430213953" "Concs = 1.469717558"
## [13] "Concs = 1.4730288" "Concs = 1.430790279" "Concs = 1.474137926"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.57011461 0.01043547
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.14
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.66361 -0.09553 0.02088 0.06820 0.27347
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.5701 0.0624 9.1413
## Time[ind] 0.0104 0.0012 8.4742
##
## Residual standard error: 0.1399 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.57011461 0.01043547
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 2.89"
## [1] "Indices = 31" "Indices = 32" "Indices = 33" "Indices = 34"
## [5] "Indices = 35" "Indices = 36" "Indices = 37" "Indices = 38"
## [9] "Indices = 39" "Indices = 40" "Indices = 41" "Indices = 42"
## [13] "Indices = 43" "Indices = 44"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.444051523" "Concs = 0.522131537" "Concs = 0.647377217"
## [4] "Concs = 1.006052863" "Concs = 0.896578201" "Concs = 1.244393935"
## [7] "Concs = 1.329682897" "Concs = 1.395238486" "Concs = 1.720792883"
## [10] "Concs = 1.785675601" "Concs = 1.510536853" "Concs = 1.434768667"
## [13] "Concs = 1.627688816" "Concs = 1.4854364"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.77467568 0.01088587
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 0.357
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.33062 -0.22123 0.01335 0.20711 0.35785
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.7747 0.1077 7.1945
## Time[ind] 0.0109 0.0021 5.2844
##
## Residual standard error: 0.3565 on 12 degrees of freedom
## (Intercept) Time[ind]
## 0.77467568 0.01088587
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 45" "Indices = 46" "Indices = 47" "Indices = 48"
## [5] "Indices = 49" "Indices = 50" "Indices = 51" "Indices = 52"
## [9] "Indices = 53" "Indices = 54" "Indices = 55" "Indices = 56"
## [13] "Indices = 57" "Indices = 58" "Indices = 59"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 4.420008817" "Concs = 4.455853897" "Concs = 3.88486422"
## [4] "Concs = 3.354917958" "Concs = 3.163346168" "Concs = 3.782311427"
## [7] "Concs = 4.201759321" "Concs = 4.686352643" "Concs = 4.678803809"
## [10] "Concs = 6.224916378" "Concs = 6.611086305" "Concs = 6.317376061"
## [13] "Concs = 6.974457131" "Concs = 6.689927878" "Concs = 6.783763921"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 3.66610476 0.03662654
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.642
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -1.05216 -0.35288 -0.07855 0.40745 0.78975
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 3.6661 0.2504 14.6437
## Time[ind] 0.0366 0.0049 7.4094
##
## Residual standard error: 0.6422 on 13 degrees of freedom
## (Intercept) Time[ind]
## 3.66610476 0.03662654
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 60" "Indices = 61" "Indices = 62" "Indices = 63"
## [5] "Indices = 64" "Indices = 65" "Indices = 66" "Indices = 67"
## [9] "Indices = 68" "Indices = 69" "Indices = 70" "Indices = 71"
## [13] "Indices = 72" "Indices = 73" "Indices = 74"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 2.139127395" "Concs = 1.925635709" "Concs = 1.972983193"
## [4] "Concs = 2.619651895" "Concs = 2.444620075" "Concs = 2.590170122"
## [7] "Concs = 3.656825463" "Concs = 3.151748549" "Concs = 3.165542915"
## [10] "Concs = 5.005868893" "Concs = 4.625552648" "Concs = 4.703858162"
## [13] "Concs = 6.05746387" "Concs = 5.962852161" "Concs = 5.870416575"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 7 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 1.94399274 0.04489882
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.108
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.17285 -0.07089 -0.01237 0.06926 0.36795
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 1.9440 0.0611 31.7958
## Time[ind] 0.0449 0.0012 37.1923
##
## Residual standard error: 0.1076 on 13 degrees of freedom
## (Intercept) Time[ind]
## 1.94399274 0.04489882
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 75" "Indices = 76" "Indices = 77" "Indices = 78"
## [5] "Indices = 79" "Indices = 80" "Indices = 81" "Indices = 82"
## [9] "Indices = 83" "Indices = 84" "Indices = 85" "Indices = 86"
## [13] "Indices = 87" "Indices = 88" "Indices = 89"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 4.340154496" "Concs = 5.746715294" "Concs = 6.239756024"
## [4] "Concs = 5.07924542" "Concs = 6.622466721" "Concs = 7.675132104"
## [7] "Concs = 6.988408726" "Concs = 8.790287998" "Concs = 8.213244554"
## [10] "Concs = 9.919792078" "Concs = 10.56863759" "Concs = 10.70603998"
## [13] "Concs = 12.46725643" "Concs = 13.07253625" "Concs = 12.65724209"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 10 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 5.65402796 0.07885133
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.477
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -1.75755 -0.37435 0.09269 0.32141 0.83833
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 5.6540 0.3146 17.9732
## Time[ind] 0.0789 0.0062 12.6946
##
## Residual standard error: 0.4772 on 13 degrees of freedom
## (Intercept) Time[ind]
## 5.65402796 0.07885133
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 90" "Indices = 91" "Indices = 92" "Indices = 93"
## [5] "Indices = 94" "Indices = 95" "Indices = 96" "Indices = 97"
## [9] "Indices = 98" "Indices = 99" "Indices = 100" "Indices = 101"
## [13] "Indices = 102" "Indices = 103" "Indices = 104"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 3.521226196" "Concs = 4.943307935" "Concs = 4.765753969"
## [4] "Concs = 5.063397684" "Concs = 5.998752957" "Concs = 5.064421433"
## [7] "Concs = 6.628504248" "Concs = 5.845275026" "Concs = 8.057762608"
## [10] "Concs = 8.979581881" "Concs = 10.11723473" "Concs = 9.1649147"
## [13] "Concs = 10.65628882" "Concs = 11.49107644" "Concs = 10.73563287"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 7 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 4.41750674 0.07548815
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.72
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.89628 -0.48592 0.03279 0.39859 1.37561
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 4.4175 0.2993 14.7587
## Time[ind] 0.0755 0.0059 12.7730
##
## Residual standard error: 0.7197 on 13 degrees of freedom
## (Intercept) Time[ind]
## 4.41750674 0.07548815
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 105" "Indices = 106" "Indices = 107" "Indices = 108"
## [5] "Indices = 109" "Indices = 110" "Indices = 111" "Indices = 112"
## [9] "Indices = 113" "Indices = 114" "Indices = 115" "Indices = 116"
## [13] "Indices = 117" "Indices = 118" "Indices = 119"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 7.640849396" "Concs = 7.10603124" "Concs = 6.640858802"
## [4] "Concs = 9.089124895" "Concs = 8.803908189" "Concs = 11.98416488"
## [7] "Concs = 9.939688614" "Concs = 10.20547106" "Concs = 13.94661101"
## [10] "Concs = 16.79956857" "Concs = 10.45604655" "Concs = 12.66707679"
## [13] "Concs = 19.81332574" "Concs = 21.96311112" "Concs = 19.53811526"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 7 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 7.1604842 0.1399395
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 1.71
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -5.1008 -0.8364 -0.1705 0.8615 2.7246
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 7.1605 0.9066 7.8981
## Time[ind] 0.1399 0.0179 7.8174
##
## Residual standard error: 1.71 on 13 degrees of freedom
## (Intercept) Time[ind]
## 7.1604842 0.1399395
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 120" "Indices = 121" "Indices = 122" "Indices = 123"
## [5] "Indices = 124" "Indices = 125" "Indices = 126" "Indices = 127"
## [9] "Indices = 128" "Indices = 129" "Indices = 130" "Indices = 131"
## [13] "Indices = 132" "Indices = 133" "Indices = 134"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 16"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 1.882425922" "Concs = 2.195061335" "Concs = 2.256987196"
## [4] "Concs = 2.75479897" "Concs = 3.000097525" "Concs = 3.101102812"
## [7] "Concs = 3.558031493" "Concs = 4.11837035" "Concs = 3.670459998"
## [10] "Concs = 5.129625668" "Concs = 4.946854195" "Concs = 5.887165323"
## [13] "Concs = 7.340919995" "Concs = 7.2807978" "Concs = 6.475160389"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 2.1112848 0.0545614
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.339
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.54665 -0.20948 0.01583 0.21519 0.50220
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 2.1113 0.1430 14.7644
## Time[ind] 0.0546 0.0028 19.3319
##
## Residual standard error: 0.3393 on 13 degrees of freedom
## (Intercept) Time[ind]
## 2.1112848 0.0545614
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"## 'data.frame': 9 obs. of 2 variables:
## $ sub: num 0.68 10 2.89 50 75 100 125 150 250
## $ vel: num -10.6 52.2 54.4 183.1 224.5 ...
## sub vel
## 1 0.68 -10.58730
## 2 10.00 52.17737
## 3 2.89 54.42935
## 4 50.00 183.13272
## 5 75.00 224.49410
## 6 100.00 394.25665
## 7 125.00 377.44074
## 8 150.00 699.69766
## 9 250.00 272.80699## [1] "here are the rates"##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 580.844 233.349 2.4892 0.04165 *
## e:(Intercept) 65.065 70.236 0.9264 0.38508
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error:
##
## 140.4322 (7 degrees of freedom)## No test available
##
## ModelDf Log lik Df Chisq value p value
##
## DRC model
fipronil
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 10.57355056" "Concs = 7.131297707" "Concs = 7.981665852"
## [4] "Concs = 0.760199385" "Concs = 1.187171779" "Concs = 0.834748222"
## [7] "Concs = 1.254233702" "Concs = 0.921331337" "Concs = 1.038856477"
## [10] "Concs = 1.236949156" "Concs = 0.821536565" "Concs = 1.117931895"
## [13] "Concs = 1.271923746" "Concs = 0.999477721"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 7 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 4.77392000 -0.05518259
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 3.01
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -3.1860 -2.1139 -0.3251 1.4259 5.7996
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 4.7739 1.1172 4.2731
## Time[ind] -0.0552 0.0214 -2.5818
##
## Residual standard error: 3.011 on 12 degrees of freedom
## (Intercept) Time[ind]
## 4.77392000 -0.05518259
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 2.89"
## [1] "Indices = 15" "Indices = 16" "Indices = 17" "Indices = 18"
## [5] "Indices = 19" "Indices = 20" "Indices = 21" "Indices = 22"
## [9] "Indices = 23" "Indices = 24" "Indices = 25" "Indices = 26"
## [13] "Indices = 27" "Indices = 28" "Indices = 29"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 3.553166435" "Concs = 2.185797914" "Concs = 4.160901096"
## [4] "Concs = 0.961731316" "Concs = 0.608701865" "Concs = 2.021395291"
## [7] "Concs = 0.34095865" "Concs = 1.416552854" "Concs = 4.678731136"
## [10] "Concs = 1.597568113" "Concs = 2.059112975" "Concs = 4.336224939"
## [13] "Concs = 0.73593197" "Concs = 1.01143428" "Concs = 2.098949857"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 8 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 2.40740669 -0.01119571
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 1.04
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -1.7306 -0.6594 -0.2181 0.9225 2.6072
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 2.4074 0.6844 3.5175
## Time[ind] -0.0112 0.0135 -0.8285
##
## Residual standard error: 1.037 on 13 degrees of freedom
## (Intercept) Time[ind]
## 2.40740669 -0.01119571
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 30" "Indices = 31" "Indices = 32" "Indices = 33"
## [5] "Indices = 34" "Indices = 35" "Indices = 36" "Indices = 37"
## [9] "Indices = 38" "Indices = 39" "Indices = 40" "Indices = 41"
## [13] "Indices = 42" "Indices = 43" "Indices = 44"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 57.00766972" "Concs = 59.13744418" "Concs = 52.24750551"
## [4] "Concs = 44.67698383" "Concs = 3.819060247" "Concs = 12.37000976"
## [7] "Concs = 15.34578007" "Concs = 13.08895186" "Concs = 11.97726763"
## [10] "Concs = 14.81813289" "Concs = 13.10848562" "Concs = 7.910416718"
## [13] "Concs = 13.23099713" "Concs = 4.710351591" "Concs = 11.65193188"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 37.9917238 -0.3961134
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 18.7
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -28.2310 -11.8910 0.5932 11.7582 21.1457
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 37.9917 6.5765 5.7769
## Time[ind] -0.3961 0.1299 -3.0505
##
## Residual standard error: 18.72 on 13 degrees of freedom
## (Intercept) Time[ind]
## 37.9917238 -0.3961134
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 45" "Indices = 46" "Indices = 47" "Indices = 48"
## [5] "Indices = 49" "Indices = 50" "Indices = 51" "Indices = 52"
## [9] "Indices = 53" "Indices = 54" "Indices = 55" "Indices = 56"
## [13] "Indices = 57" "Indices = 58"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 120.1840369" "Concs = 145.3520797" "Concs = 142.3332536"
## [4] "Concs = 115.428861" "Concs = 124.2452738" "Concs = 133.9244833"
## [7] "Concs = 155.8614698" "Concs = 133.3381427" "Concs = 112.8005214"
## [10] "Concs = 148.8202467" "Concs = 129.1596217" "Concs = 128.0330109"
## [13] "Concs = 130.3403839" "Concs = 29.18643658"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 134.7988101 -0.1242694
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 14.3
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -94.428 -13.079 2.561 7.332 24.791
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 134.7988 7.5838 17.7747
## Time[ind] -0.1243 0.1451 -0.8565
##
## Residual standard error: 14.26 on 12 degrees of freedom
## (Intercept) Time[ind]
## 134.7988101 -0.1242694
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 200"
## [1] "Indices = 59" "Indices = 60" "Indices = 61" "Indices = 62"
## [5] "Indices = 63" "Indices = 64" "Indices = 65" "Indices = 66"
## [9] "Indices = 67" "Indices = 68" "Indices = 69" "Indices = 70"
## [13] "Indices = 71" "Indices = 72" "Indices = 73"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 161.3373216" "Concs = 140.3753919" "Concs = 143.641415"
## [4] "Concs = 143.5820327" "Concs = 117.0381728" "Concs = 105.3992543"
## [7] "Concs = 120.601107" "Concs = 115.1379412" "Concs = 126.1830373"
## [10] "Concs = 91.91948648" "Concs = 106.6462813" "Concs = 72.50149496"
## [13] "Concs = 112.4063583" "Concs = 105.3992543" "Concs = 111.7531537"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 135.3425626 -0.4178514
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 17.8
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -37.770 -9.853 3.376 11.158 25.995
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 135.3426 7.3189 18.4923
## Time[ind] -0.4179 0.1445 -2.8915
##
## Residual standard error: 17.84 on 13 degrees of freedom
## (Intercept) Time[ind]
## 135.3425626 -0.4178514
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 74" "Indices = 75" "Indices = 76" "Indices = 77"
## [5] "Indices = 78" "Indices = 79" "Indices = 80" "Indices = 81"
## [9] "Indices = 82" "Indices = 83" "Indices = 84" "Indices = 85"
## [13] "Indices = 86" "Indices = 87" "Indices = 88"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 235.9498416" "Concs = 283.6965927" "Concs = 228.2284198"
## [4] "Concs = 263.2111879" "Concs = 209.7915555" "Concs = 143.1352"
## [7] "Concs = 178.2755482" "Concs = 234.8467813" "Concs = 92.39442817"
## [10] "Concs = 193.7183918" "Concs = 253.2836456" "Concs = 228.8587399"
## [13] "Concs = 145.9716406" "Concs = 185.3666498" "Concs = 152.9051623"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 235.9725402 -0.7131667
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 38.3
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -122.1831 -22.3491 -0.0227 27.9727 60.1011
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 235.9725 18.4816 12.7680
## Time[ind] -0.7132 0.3649 -1.9543
##
## Residual standard error: 38.27 on 13 degrees of freedom
## (Intercept) Time[ind]
## 235.9725402 -0.7131667
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"## 'data.frame': 6 obs. of 2 variables:
## $ sub: num 10 2.89 50 150 200 250
## $ vel: num 276 56 1981 621 2089 ...
## sub vel
## 1 10.00 275.91293
## 2 2.89 55.97857
## 3 50.00 1980.56687
## 4 150.00 621.34678
## 5 200.00 2089.25688
## 6 250.00 3565.83353## [1] "here are the rates"##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 27430.7 113663.3 0.2413 0.8212
## e:(Intercept) 2121.6 9640.7 0.2201 0.8366
##
## Residual standard error:
##
## 973.0673 (4 degrees of freedom)## No test available
##
## ModelDf Log lik Df Chisq value p value
##
## DRC model
fipsulf
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.218453069" "Concs = 0.16722553" "Concs = 0.177409431"
## [4] "Concs = 0.51830331" "Concs = 0.552214025" "Concs = 0.537364947"
## [7] "Concs = 0.913205394" "Concs = 1.016825543" "Concs = 0.901827084"
## [10] "Concs = 1.42587892" "Concs = 1.446211798" "Concs = 1.577890064"
## [13] "Concs = 1.999928264" "Concs = 2.086184093" "Concs = 2.088468137"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 7 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.23088822 0.02060305
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0611
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.085234 -0.031411 -0.002569 0.032564 0.167846
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.2309 0.0280 8.2602
## Time[ind] 0.0206 0.0006 37.3306
##
## Residual standard error: 0.06107 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.23088822 0.02060305
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 2.89"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29" "Indices = 30"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.024236972" "Concs = 0.022488202" "Concs = 0.025605583"
## [4] "Concs = 0.153953365" "Concs = 0.14676346" "Concs = 0.150213178"
## [7] "Concs = 0.255979534" "Concs = 0.273005759" "Concs = 0.277157181"
## [10] "Concs = 0.600301918" "Concs = 0.578169686" "Concs = 0.619389899"
## [13] "Concs = 0.72919882" "Concs = 0.855702746" "Concs = 1.005390251"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 7 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.011529754 0.009462775
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0209
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.133981 -0.012866 -0.001127 0.013392 0.142211
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0115 0.0114 1.0106
## Time[ind] 0.0095 0.0002 42.0051
##
## Residual standard error: 0.02087 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.011529754 0.009462775
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 31" "Indices = 32" "Indices = 33" "Indices = 34"
## [5] "Indices = 35" "Indices = 36" "Indices = 37" "Indices = 38"
## [9] "Indices = 39" "Indices = 40" "Indices = 41" "Indices = 42"
## [13] "Indices = 43" "Indices = 44" "Indices = 45"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.785110353" "Concs = 0.651662128" "Concs = 0.623272931"
## [4] "Concs = 1.389739341" "Concs = 1.129679656" "Concs = 1.171944943"
## [7] "Concs = 0.985037522" "Concs = 1.525224345" "Concs = 1.371585733"
## [10] "Concs = 2.350595335" "Concs = 2.151757802" "Concs = 2.044295988"
## [13] "Concs = 2.879243198" "Concs = 2.483251478" "Concs = 2.593598032"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.77463889 0.02158359
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.182
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.43711 -0.12327 0.01047 0.09259 0.29135
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.7746 0.0849 9.1189
## Time[ind] 0.0216 0.0017 12.8679
##
## Residual standard error: 0.1823 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.77463889 0.02158359
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 46" "Indices = 47" "Indices = 48" "Indices = 49"
## [5] "Indices = 50" "Indices = 51" "Indices = 52" "Indices = 53"
## [9] "Indices = 54" "Indices = 55" "Indices = 56" "Indices = 57"
## [13] "Indices = 58"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.076232122" "Concs = 0.11093207" "Concs = 0.100698461"
## [4] "Concs = 0.563272498" "Concs = 0.126440587" "Concs = 0.39526057"
## [7] "Concs = 0.846041523" "Concs = 0.893588458" "Concs = 0.911664361"
## [10] "Concs = 0.669794737" "Concs = 1.21631006" "Concs = 1.162617749"
## [13] "Concs = 1.251568939"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.23494866 0.01127804
##
## Degrees of freedom: 13 total; 11 residual
## Scale estimate: 0.235
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.27768 -0.13425 -0.03366 0.15915 0.33837
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.2349 0.1055 2.2260
## Time[ind] 0.0113 0.0022 5.2411
##
## Residual standard error: 0.2353 on 11 degrees of freedom
## (Intercept) Time[ind]
## 0.23494866 0.01127804
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 59" "Indices = 60" "Indices = 61" "Indices = 62"
## [5] "Indices = 63" "Indices = 64" "Indices = 65" "Indices = 66"
## [9] "Indices = 67" "Indices = 68" "Indices = 69" "Indices = 70"
## [13] "Indices = 71" "Indices = 72" "Indices = 73"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 1.13821052" "Concs = 0.334004631" "Concs = 0.316680231"
## [4] "Concs = 0.918283437" "Concs = 0.90859124" "Concs = 1.020530824"
## [7] "Concs = 1.343619416" "Concs = 1.498547233" "Concs = 1.547942907"
## [10] "Concs = 1.768354064" "Concs = 1.991371294" "Concs = 1.8610216"
## [13] "Concs = 2.114823643" "Concs = 2.540092398" "Concs = 2.212077131"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 7 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.71345477 0.01851378
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.248
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.39677 -0.12509 0.02937 0.16374 0.42476
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.7135 0.1161 6.1434
## Time[ind] 0.0185 0.0023 8.0739
##
## Residual standard error: 0.2477 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.71345477 0.01851378
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 74" "Indices = 75" "Indices = 76" "Indices = 77"
## [5] "Indices = 78" "Indices = 79" "Indices = 80" "Indices = 81"
## [9] "Indices = 82" "Indices = 83" "Indices = 84" "Indices = 85"
## [13] "Indices = 86" "Indices = 87" "Indices = 88"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.238292686" "Concs = 0.169686663" "Concs = 0.214656616"
## [4] "Concs = 0.896250609" "Concs = 1.003144725" "Concs = 0.878415124"
## [7] "Concs = 1.296498301" "Concs = 1.188470589" "Concs = 1.332743895"
## [10] "Concs = 1.838994297" "Concs = 1.735055265" "Concs = 1.867403256"
## [13] "Concs = 2.350429219" "Concs = 2.217648418" "Concs = 2.313686352"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 12 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.4930084 0.0211471
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.157
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.32332 -0.13058 0.06105 0.09580 0.20532
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.4930 0.0816 6.0416
## Time[ind] 0.0211 0.0016 13.1247
##
## Residual standard error: 0.1565 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.4930084 0.0211471
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 89" "Indices = 90" "Indices = 91" "Indices = 92"
## [5] "Indices = 93" "Indices = 94" "Indices = 95" "Indices = 96"
## [9] "Indices = 97" "Indices = 98" "Indices = 99" "Indices = 100"
## [13] "Indices = 101" "Indices = 102" "Indices = 103"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.490201412" "Concs = 0.500310765" "Concs = 0.501022601"
## [4] "Concs = 1.255933807" "Concs = 1.075230731" "Concs = 1.154821858"
## [7] "Concs = 1.506153651" "Concs = 1.58449239" "Concs = 1.763878617"
## [10] "Concs = 2.22530088" "Concs = 2.148002728" "Concs = 2.084269049"
## [13] "Concs = 2.471763558" "Concs = 2.574367323" "Concs = 2.385468469"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 3 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.76080280 0.02102169
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.268
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.27060 -0.22039 0.06216 0.15285 0.37243
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.7608 0.0940 8.0903
## Time[ind] 0.0210 0.0019 11.3215
##
## Residual standard error: 0.2683 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.76080280 0.02102169
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 104" "Indices = 105" "Indices = 106" "Indices = 107"
## [5] "Indices = 108" "Indices = 109" "Indices = 110" "Indices = 111"
## [9] "Indices = 112" "Indices = 113" "Indices = 114" "Indices = 115"
## [13] "Indices = 116" "Indices = 117" "Indices = 118"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.688691412" "Concs = 0.680203691" "Concs = 0.671715969"
## [7] "Concs = 1.128032043" "Concs = 1.057705208" "Concs = 1.0791266"
## [10] "Concs = 1.670842039" "Concs = 1.655483305" "Concs = 1.672054571"
## [13] "Concs = 2.11584115" "Concs = 2.394723427" "Concs = 2.276703681"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.21108314 0.02380321
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.179
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.23753 -0.14388 0.03278 0.11632 0.20285
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.2111 0.0635 3.3230
## Time[ind] 0.0238 0.0013 18.9784
##
## Residual standard error: 0.1787 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.21108314 0.02380321
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"## 'data.frame': 8 obs. of 2 variables:
## $ sub: num 10 2.89 50 75 100 125 150 250
## $ vel: num 103 47.3 107.9 56.4 92.6 ...
## sub vel
## 1 10.00 103.01524
## 2 2.89 47.31387
## 3 50.00 107.91797
## 4 75.00 56.39019
## 5 100.00 92.56888
## 6 125.00 105.73549
## 7 150.00 105.10846
## 8 250.00 119.01603## [1] "here are the rates"##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 102.0337 9.5991 10.630 4.085e-05 ***
## e:(Intercept) 2.2813 1.7809 1.281 0.2475
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error:
##
## 21.75614 (6 degrees of freedom)## No test available
##
## ModelDf Log lik Df Chisq value p value
##
## DRC model
exposure experiment analysis
Results presentation and discussion for parent analytes (atrazine, triadimenon, and fipronil) and their xenobiotic metabolites.
Toxicity of parents and metabolites discussion.
Microsomal analysis of soil and amphibian data for 0 (soil only), 2, 4, 12, 24, and 48 hours after exposure.
Database has factors for time, parent (mapped to analyte), analyte (can be either parent or metabolite), matrix (amphibian or soil), and tank (potentially a nuisance variable).
## Classes 'grouped_df', 'tbl_df', 'tbl' and 'data.frame': 352 obs. of 6 variables:
## $ time : int 2 2 2 2 4 4 4 4 12 12 ...
## $ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ analyte : Factor w/ 8 levels "ATZ","DEA","DIA",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ matrix : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 1 1 1 1 1 ...
## $ conc : num 3.07 3.69 4.7 1.89 7.62 ...
## $ replicate: Factor w/ 4 levels "1","2","3","4": 1 2 3 4 1 2 3 4 1 2 ...
## - attr(*, "vars")= chr "parent" "analyte" "matrix" "time"
## - attr(*, "drop")= logi TRUE
## - attr(*, "indices")=List of 86
## ..$ : int 0 1 2 3
## ..$ : int 4 5 6 7
## ..$ : int 8 9 10 11
## ..$ : int 12 13 14 15
## ..$ : int 16 17 18 19
## ..$ : int 20 21 22 23
## ..$ : int 24 25 26 27
## ..$ : int 28 29 30 31
## ..$ : int 32 33 34 35
## ..$ : int 36 37 38 39
## ..$ : int 40 41 42 43
## ..$ : int 88 89 90 91
## ..$ : int 92 93 94 95
## ..$ : int 96 97 98 99
## ..$ : int 100 101 102 103
## ..$ : int 104 105 106 107
## ..$ : int 108 109 110 111
## ..$ : int 112 113 114 115
## ..$ : int 116 117 118 119
## ..$ : int 120 121 122 123
## ..$ : int 124 125 126 127
## ..$ : int 128 129 130 131
## ..$ : int 44 45 46 47
## ..$ : int 48 49 50 51
## ..$ : int 52 53 54 55
## ..$ : int 56 57 58 59
## ..$ : int 60 61 62 63
## ..$ : int 64 65 66 67
## ..$ : int 68 69 70 71
## ..$ : int 72 73 74 75
## ..$ : int 76 77 78 79
## ..$ : int 80 81 82 83
## ..$ : int 84 85 86 87
## ..$ : int 308 309 310 311
## ..$ : int 312 313 314 315
## ..$ : int 316 317 318 319
## ..$ : int 320 321 322 323
## ..$ : int 324 325 326 327
## ..$ : int 328 329 330 331 332 333 334 335
## ..$ : int 336 337 338 339
## ..$ : int 340 341 342 343
## ..$ : int 344 345 346 347
## ..$ : int 348 349 350 351
## ..$ : int 264 265 266 267
## ..$ : int 268 269 270 271
## ..$ : int 272 273 274 275
## ..$ : int 276 277 278 279
## ..$ : int 280 281 282 283
## ..$ : int 284 285 286 287 288 289 290 291
## ..$ : int 292 293 294 295
## ..$ : int 296 297 298 299
## ..$ : int 300 301 302 303
## ..$ : int 304 305 306 307
## ..$ : int 176 177 178 179
## ..$ : int 180 181 182 183
## ..$ : int 184 185 186 187
## ..$ : int 188 189 190 191
## ..$ : int 192 193 194 195
## ..$ : int 196 197 198 199
## ..$ : int 200 201 202 203
## ..$ : int 204 205 206 207
## ..$ : int 208 209 210 211
## ..$ : int 212 213 214 215
## ..$ : int 216 217 218 219
## ..$ : int 220 221 222 223
## ..$ : int 224 225 226 227
## ..$ : int 228 229 230 231
## ..$ : int 232 233 234 235
## ..$ : int 236 237 238 239
## ..$ : int 240 241 242 243
## ..$ : int 244 245 246 247
## ..$ : int 248 249 250 251
## ..$ : int 252 253 254 255
## ..$ : int 256 257 258 259
## ..$ : int 260 261 262 263
## ..$ : int 132 133 134 135
## ..$ : int 136 137 138 139
## ..$ : int 140 141 142 143
## ..$ : int 144 145 146 147
## ..$ : int 148 149 150 151
## ..$ : int 152 153 154 155
## ..$ : int 156 157 158 159
## ..$ : int 160 161 162 163
## ..$ : int 164 165 166 167
## ..$ : int 168 169 170 171
## ..$ : int 172 173 174 175
## - attr(*, "group_sizes")= int 4 4 4 4 4 4 4 4 4 4 ...
## - attr(*, "biggest_group_size")= int 8
## - attr(*, "labels")='data.frame': 86 obs. of 4 variables:
## ..$ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## ..$ analyte: Factor w/ 8 levels "ATZ","DEA","DIA",..: 1 1 1 1 1 1 1 1 1 1 ...
## ..$ matrix : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 2 2 2 2 2 ...
## ..$ time : int 2 4 12 24 48 0 2 4 12 24 ...
## ..- attr(*, "vars")= chr "parent" "analyte" "matrix" "time"
## ..- attr(*, "drop")= logi TRUE## # A tibble: 352 x 6
## # Groups: parent, analyte, matrix, time [86]
## time parent analyte matrix conc replicate
## <int> <fctr> <fctr> <fctr> <dbl> <fctr>
## 1 2 atrazine ATZ amphib 3.07 1
## 2 2 atrazine ATZ amphib 3.69 2
## 3 2 atrazine ATZ amphib 4.70 3
## 4 2 atrazine ATZ amphib 1.89 4
## 5 4 atrazine ATZ amphib 7.62 1
## 6 4 atrazine ATZ amphib 4.13 2
## 7 4 atrazine ATZ amphib 2.05 3
## 8 4 atrazine ATZ amphib 7.63 4
## 9 12 atrazine ATZ amphib 2.45 1
## 10 12 atrazine ATZ amphib 3.79 2
## # ... with 342 more rows## # A tibble: 86 x 7
## # Groups: parent, analyte, matrix [?]
## parent analyte matrix time count ConcMean ConcSD
## <fctr> <fctr> <fctr> <int> <int> <dbl> <dbl>
## 1 atrazine ATZ amphib 2 4 3.34 1.18
## 2 atrazine ATZ amphib 4 4 5.36 2.75
## 3 atrazine ATZ amphib 12 4 3.12 1.26
## 4 atrazine ATZ amphib 24 4 1.55 0.610
## 5 atrazine ATZ amphib 48 4 1.00 0.355
## 6 atrazine ATZ soil 0 4 15.9 2.59
## 7 atrazine ATZ soil 2 4 19.0 4.35
## 8 atrazine ATZ soil 4 4 18.8 2.70
## 9 atrazine ATZ soil 12 4 20.6 3.89
## 10 atrazine ATZ soil 24 4 25.0 4.45
## # ... with 76 more rows## <!-- html table generated in R 3.4.3 by xtable 1.8-2 package -->
## <!-- Mon Jan 22 14:34:30 2018 -->
## <table border=1>
## <tr> <th> </th> <th> parent </th> <th> analyte </th> <th> matrix </th> <th> time </th> <th> count </th> <th> ConcMean </th> <th> ConcSD </th> </tr>
## <tr> <td align="right"> 1 </td> <td> atrazine </td> <td> ATZ </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 3.34 </td> <td align="right"> 1.18 </td> </tr>
## <tr> <td align="right"> 2 </td> <td> atrazine </td> <td> ATZ </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 5.36 </td> <td align="right"> 2.75 </td> </tr>
## <tr> <td align="right"> 3 </td> <td> atrazine </td> <td> ATZ </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 3.12 </td> <td align="right"> 1.26 </td> </tr>
## <tr> <td align="right"> 4 </td> <td> atrazine </td> <td> ATZ </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 1.55 </td> <td align="right"> 0.61 </td> </tr>
## <tr> <td align="right"> 5 </td> <td> atrazine </td> <td> ATZ </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 1.00 </td> <td align="right"> 0.35 </td> </tr>
## <tr> <td align="right"> 6 </td> <td> atrazine </td> <td> ATZ </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 15.93 </td> <td align="right"> 2.59 </td> </tr>
## <tr> <td align="right"> 7 </td> <td> atrazine </td> <td> ATZ </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 19.03 </td> <td align="right"> 4.35 </td> </tr>
## <tr> <td align="right"> 8 </td> <td> atrazine </td> <td> ATZ </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 18.77 </td> <td align="right"> 2.70 </td> </tr>
## <tr> <td align="right"> 9 </td> <td> atrazine </td> <td> ATZ </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 20.61 </td> <td align="right"> 3.89 </td> </tr>
## <tr> <td align="right"> 10 </td> <td> atrazine </td> <td> ATZ </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 25.00 </td> <td align="right"> 4.45 </td> </tr>
## <tr> <td align="right"> 11 </td> <td> atrazine </td> <td> ATZ </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 26.43 </td> <td align="right"> 4.38 </td> </tr>
## <tr> <td align="right"> 12 </td> <td> atrazine </td> <td> DEA </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 13 </td> <td> atrazine </td> <td> DEA </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.03 </td> </tr>
## <tr> <td align="right"> 14 </td> <td> atrazine </td> <td> DEA </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.05 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 15 </td> <td> atrazine </td> <td> DEA </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 16 </td> <td> atrazine </td> <td> DEA </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.02 </td> </tr>
## <tr> <td align="right"> 17 </td> <td> atrazine </td> <td> DEA </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 18 </td> <td> atrazine </td> <td> DEA </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 19 </td> <td> atrazine </td> <td> DEA </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 20 </td> <td> atrazine </td> <td> DEA </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 21 </td> <td> atrazine </td> <td> DEA </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 22 </td> <td> atrazine </td> <td> DEA </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 23 </td> <td> atrazine </td> <td> DIA </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.33 </td> <td align="right"> 0.12 </td> </tr>
## <tr> <td align="right"> 24 </td> <td> atrazine </td> <td> DIA </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.94 </td> <td align="right"> 0.76 </td> </tr>
## <tr> <td align="right"> 25 </td> <td> atrazine </td> <td> DIA </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 1.08 </td> <td align="right"> 0.51 </td> </tr>
## <tr> <td align="right"> 26 </td> <td> atrazine </td> <td> DIA </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 1.99 </td> <td align="right"> 1.35 </td> </tr>
## <tr> <td align="right"> 27 </td> <td> atrazine </td> <td> DIA </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.66 </td> <td align="right"> 0.53 </td> </tr>
## <tr> <td align="right"> 28 </td> <td> atrazine </td> <td> DIA </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 29 </td> <td> atrazine </td> <td> DIA </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> -0.01 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 30 </td> <td> atrazine </td> <td> DIA </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.02 </td> </tr>
## <tr> <td align="right"> 31 </td> <td> atrazine </td> <td> DIA </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.07 </td> </tr>
## <tr> <td align="right"> 32 </td> <td> atrazine </td> <td> DIA </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.03 </td> </tr>
## <tr> <td align="right"> 33 </td> <td> atrazine </td> <td> DIA </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.06 </td> <td align="right"> 0.06 </td> </tr>
## <tr> <td align="right"> 34 </td> <td> fipronil </td> <td> F. sulfone </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.35 </td> <td align="right"> 0.29 </td> </tr>
## <tr> <td align="right"> 35 </td> <td> fipronil </td> <td> F. sulfone </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.40 </td> <td align="right"> 0.48 </td> </tr>
## <tr> <td align="right"> 36 </td> <td> fipronil </td> <td> F. sulfone </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.61 </td> <td align="right"> 0.57 </td> </tr>
## <tr> <td align="right"> 37 </td> <td> fipronil </td> <td> F. sulfone </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 1.25 </td> <td align="right"> 0.53 </td> </tr>
## <tr> <td align="right"> 38 </td> <td> fipronil </td> <td> F. sulfone </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.91 </td> <td align="right"> 0.57 </td> </tr>
## <tr> <td align="right"> 39 </td> <td> fipronil </td> <td> F. sulfone </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 8 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 40 </td> <td> fipronil </td> <td> F. sulfone </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 41 </td> <td> fipronil </td> <td> F. sulfone </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 42 </td> <td> fipronil </td> <td> F. sulfone </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 43 </td> <td> fipronil </td> <td> F. sulfone </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 44 </td> <td> fipronil </td> <td> FIP </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 1.87 </td> <td align="right"> 1.35 </td> </tr>
## <tr> <td align="right"> 45 </td> <td> fipronil </td> <td> FIP </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 1.30 </td> <td align="right"> 0.52 </td> </tr>
## <tr> <td align="right"> 46 </td> <td> fipronil </td> <td> FIP </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.57 </td> <td align="right"> 0.24 </td> </tr>
## <tr> <td align="right"> 47 </td> <td> fipronil </td> <td> FIP </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.27 </td> <td align="right"> 0.05 </td> </tr>
## <tr> <td align="right"> 48 </td> <td> fipronil </td> <td> FIP </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.21 </td> <td align="right"> 0.13 </td> </tr>
## <tr> <td align="right"> 49 </td> <td> fipronil </td> <td> FIP </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 8 </td> <td align="right"> 0.41 </td> <td align="right"> 0.45 </td> </tr>
## <tr> <td align="right"> 50 </td> <td> fipronil </td> <td> FIP </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.87 </td> <td align="right"> 0.24 </td> </tr>
## <tr> <td align="right"> 51 </td> <td> fipronil </td> <td> FIP </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.82 </td> <td align="right"> 0.17 </td> </tr>
## <tr> <td align="right"> 52 </td> <td> fipronil </td> <td> FIP </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.70 </td> <td align="right"> 0.11 </td> </tr>
## <tr> <td align="right"> 53 </td> <td> fipronil </td> <td> FIP </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.36 </td> <td align="right"> 0.06 </td> </tr>
## <tr> <td align="right"> 54 </td> <td> triadimefon </td> <td> TDL A </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.06 </td> <td align="right"> 0.02 </td> </tr>
## <tr> <td align="right"> 55 </td> <td> triadimefon </td> <td> TDL A </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.05 </td> </tr>
## <tr> <td align="right"> 56 </td> <td> triadimefon </td> <td> TDL A </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.02 </td> </tr>
## <tr> <td align="right"> 57 </td> <td> triadimefon </td> <td> TDL A </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 58 </td> <td> triadimefon </td> <td> TDL A </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 59 </td> <td> triadimefon </td> <td> TDL A </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 60 </td> <td> triadimefon </td> <td> TDL A </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 61 </td> <td> triadimefon </td> <td> TDL A </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 62 </td> <td> triadimefon </td> <td> TDL A </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 63 </td> <td> triadimefon </td> <td> TDL A </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 64 </td> <td> triadimefon </td> <td> TDL A </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 65 </td> <td> triadimefon </td> <td> TDL B </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.02 </td> </tr>
## <tr> <td align="right"> 66 </td> <td> triadimefon </td> <td> TDL B </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.13 </td> <td align="right"> 0.05 </td> </tr>
## <tr> <td align="right"> 67 </td> <td> triadimefon </td> <td> TDL B </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.05 </td> </tr>
## <tr> <td align="right"> 68 </td> <td> triadimefon </td> <td> TDL B </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 69 </td> <td> triadimefon </td> <td> TDL B </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.03 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 70 </td> <td> triadimefon </td> <td> TDL B </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 71 </td> <td> triadimefon </td> <td> TDL B </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 72 </td> <td> triadimefon </td> <td> TDL B </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 73 </td> <td> triadimefon </td> <td> TDL B </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 74 </td> <td> triadimefon </td> <td> TDL B </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 75 </td> <td> triadimefon </td> <td> TDL B </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 76 </td> <td> triadimefon </td> <td> TDN </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.39 </td> <td align="right"> 0.08 </td> </tr>
## <tr> <td align="right"> 77 </td> <td> triadimefon </td> <td> TDN </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.55 </td> <td align="right"> 0.30 </td> </tr>
## <tr> <td align="right"> 78 </td> <td> triadimefon </td> <td> TDN </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.75 </td> <td align="right"> 0.32 </td> </tr>
## <tr> <td align="right"> 79 </td> <td> triadimefon </td> <td> TDN </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.87 </td> <td align="right"> 0.86 </td> </tr>
## <tr> <td align="right"> 80 </td> <td> triadimefon </td> <td> TDN </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.25 </td> <td align="right"> 0.08 </td> </tr>
## <tr> <td align="right"> 81 </td> <td> triadimefon </td> <td> TDN </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 3.11 </td> <td align="right"> 0.85 </td> </tr>
## <tr> <td align="right"> 82 </td> <td> triadimefon </td> <td> TDN </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 3.66 </td> <td align="right"> 1.34 </td> </tr>
## <tr> <td align="right"> 83 </td> <td> triadimefon </td> <td> TDN </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 5.28 </td> <td align="right"> 0.37 </td> </tr>
## <tr> <td align="right"> 84 </td> <td> triadimefon </td> <td> TDN </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 5.93 </td> <td align="right"> 1.00 </td> </tr>
## <tr> <td align="right"> 85 </td> <td> triadimefon </td> <td> TDN </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 4.82 </td> <td align="right"> 0.32 </td> </tr>
## <tr> <td align="right"> 86 </td> <td> triadimefon </td> <td> TDN </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 4.18 </td> <td align="right"> 0.44 </td> </tr>
## </table>The amphibian data set summary statistics. Atrazine peaks at 4 hours and then declines monotonically. DEA peaks at 12 hours and DIA at 24. Fipronil steadily declines from its first observation at 2 hours with fipronil sulfone not peaking until 24 hours. Triadimenon peaks at 24 hours with its metabolites tdla and tdlb peaking at 4 hours.
## Classes 'grouped_df', 'tbl_df', 'tbl' and 'data.frame': 86 obs. of 7 variables:
## $ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ analyte : Factor w/ 8 levels "ATZ","DEA","DIA",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ matrix : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 2 2 2 2 2 ...
## $ time : int 2 4 12 24 48 0 2 4 12 24 ...
## $ count : int 4 4 4 4 4 4 4 4 4 4 ...
## $ ConcMean: num 3.34 5.36 3.12 1.55 1 ...
## $ ConcSD : num 1.175 2.752 1.257 0.61 0.355 ...
## - attr(*, "vars")= chr "parent" "analyte" "matrix"
## - attr(*, "drop")= logi TRUE## # A tibble: 6 x 7
## # Groups: parent, analyte, matrix [2]
## parent analyte matrix time count ConcMean ConcSD
## <fctr> <fctr> <fctr> <int> <int> <dbl> <dbl>
## 1 atrazine ATZ amphib 2 4 3.34 1.18
## 2 atrazine ATZ amphib 4 4 5.36 2.75
## 3 atrazine ATZ amphib 12 4 3.12 1.26
## 4 atrazine ATZ amphib 24 4 1.55 0.610
## 5 atrazine ATZ amphib 48 4 1.00 0.355
## 6 atrazine DEA amphib 2 4 0.0139 0.00522## # A tibble: 15 x 7
## # Groups: parent, analyte, matrix [3]
## parent analyte matrix time count ConcMean ConcSD
## <fctr> <fctr> <fctr> <int> <int> <dbl> <dbl>
## 1 atrazine ATZ amphib 2 4 3.34 1.18
## 2 atrazine ATZ amphib 4 4 5.36 2.75
## 3 atrazine ATZ amphib 12 4 3.12 1.26
## 4 atrazine ATZ amphib 24 4 1.55 0.610
## 5 atrazine ATZ amphib 48 4 1.00 0.355
## 6 atrazine DEA amphib 2 4 0.0139 0.00522
## 7 atrazine DEA amphib 4 4 0.0444 0.0284
## 8 atrazine DEA amphib 12 4 0.0540 0.0128
## 9 atrazine DEA amphib 24 4 0.0365 0.0131
## 10 atrazine DEA amphib 48 4 0.0195 0.0196
## 11 atrazine DIA amphib 2 4 0.329 0.125
## 12 atrazine DIA amphib 4 4 0.942 0.761
## 13 atrazine DIA amphib 12 4 1.08 0.506
## 14 atrazine DIA amphib 24 4 1.99 1.35
## 15 atrazine DIA amphib 48 4 0.662 0.531## [1] "ATZ"
## [1] "DEA"
## [1] "DIA"## # A tibble: 10 x 7
## # Groups: parent, analyte, matrix [2]
## parent analyte matrix time count ConcMean ConcSD
## <fctr> <fctr> <fctr> <int> <int> <dbl> <dbl>
## 1 fipronil F. sulfone amphib 2 4 0.347 0.287
## 2 fipronil F. sulfone amphib 4 4 0.397 0.477
## 3 fipronil F. sulfone amphib 12 4 0.613 0.573
## 4 fipronil F. sulfone amphib 24 4 1.25 0.526
## 5 fipronil F. sulfone amphib 48 4 0.907 0.566
## 6 fipronil FIP amphib 2 4 1.87 1.35
## 7 fipronil FIP amphib 4 4 1.30 0.522
## 8 fipronil FIP amphib 12 4 0.566 0.240
## 9 fipronil FIP amphib 24 4 0.268 0.0511
## 10 fipronil FIP amphib 48 4 0.212 0.131## # A tibble: 0 x 7
## # Groups: parent, analyte, matrix [0]
## # ... with 7 variables: parent <fctr>, analyte <fctr>, matrix <fctr>, time
## # <int>, count <int>, ConcMean <dbl>, ConcSD <dbl>The soil data set summary statistics. Atrazine in soil showing an upwards trend (need to test if significant) with dia and dea levels very low indicating little degradation in soil over the 48 hour period. Fipronil and triadimenon data also indicating little degradation in soil.
## # A tibble: 18 x 7
## # Groups: parent, analyte, matrix [3]
## parent analyte matrix time count ConcMean ConcSD
## <fctr> <fctr> <fctr> <int> <int> <dbl> <dbl>
## 1 atrazine ATZ soil 0 4 15.9 2.59
## 2 atrazine ATZ soil 2 4 19.0 4.35
## 3 atrazine ATZ soil 4 4 18.8 2.70
## 4 atrazine ATZ soil 12 4 20.6 3.89
## 5 atrazine ATZ soil 24 4 25.0 4.45
## 6 atrazine ATZ soil 48 4 26.4 4.38
## 7 atrazine DEA soil 0 4 0 0
## 8 atrazine DEA soil 2 4 0.00157 0.000633
## 9 atrazine DEA soil 4 4 0.00300 0.00154
## 10 atrazine DEA soil 12 4 0.00547 0.00423
## 11 atrazine DEA soil 24 4 0.00731 0.00174
## 12 atrazine DEA soil 48 4 0.00878 0.00377
## 13 atrazine DIA soil 0 4 0 0
## 14 atrazine DIA soil 2 4 - 0.00773 0.00737
## 15 atrazine DIA soil 4 4 0.0205 0.0202
## 16 atrazine DIA soil 12 4 0.0770 0.0678
## 17 atrazine DIA soil 24 4 0.0430 0.0300
## 18 atrazine DIA soil 48 4 0.0637 0.0582## # A tibble: 10 x 7
## # Groups: parent, analyte, matrix [2]
## parent analyte matrix time count ConcMean ConcSD
## <fctr> <fctr> <fctr> <int> <int> <dbl> <dbl>
## 1 fipronil F. sulfone soil 2 8 0.0102 0.0129
## 2 fipronil F. sulfone soil 4 4 0.0219 0.0108
## 3 fipronil F. sulfone soil 12 4 0.0183 0.00501
## 4 fipronil F. sulfone soil 24 4 0.0192 0.00914
## 5 fipronil F. sulfone soil 48 4 0.0126 0.00552
## 6 fipronil FIP soil 2 8 0.408 0.447
## 7 fipronil FIP soil 4 4 0.868 0.244
## 8 fipronil FIP soil 12 4 0.817 0.170
## 9 fipronil FIP soil 24 4 0.702 0.109
## 10 fipronil FIP soil 48 4 0.356 0.0585## # A tibble: 0 x 7
## # Groups: parent, analyte, matrix [0]
## # ... with 7 variables: parent <fctr>, analyte <fctr>, matrix <fctr>, time
## # <int>, count <int>, ConcMean <dbl>, ConcSD <dbl>pdf(paste(micro.graphics,"data_mean_barcharts",".pdf", sep=""))
par(mfrow=c(3,1))
print(parents)## [1] atrazine triadimefon fipronil
## Levels: atrazine fipronil triadimefon for(parent in parents){
i=0
print(parent)
temp.parent <- micro.group.stats.amphib[which(micro.group.stats.amphib$parent==parent),]
print(temp.parent)
parent.analytes <- unique(temp.parent$analyte)
for(analyte in parent.analytes){
print(parent)
print(analyte)
analytetemp <- micro.group.stats.amphib[which(micro.group.stats.amphib$analyte==analyte),]
xvalues <- as.numeric(as.character(analytetemp$time))
points.y <- micro.amphib[which(micro.amphib$analyte==analyte),]$conc
points.x <- as.numeric(as.character(micro.amphib[which(micro.amphib$analyte==analyte),]$time))
#create empty plot if needed
if(i==0){
parenttemp <- micro.group.stats.amphib[which(micro.group.stats.amphib$parent==parent),]
maxconc <- max(points.y)
#plot(xvalues,analytetemp$ConcMean,type="l", xlim=c(0,48),
# ylim = c(0,maxconc), main=parent,col="black", xlab="Hours", ylab="Concentration")
#axis(1,at=xvalues)
i=1
}
##add line for parent metabolite
#if(analyte %in% parents){
# lines(xvalues,analytetemp$ConcMean,type="l",col="red")
# points(points.x, points.y, col = "red")
#}else{
##add line for daughter metabolite
# lines(xvalues,analytetemp$ConcMean,type="l",col="blue")
# points(points.x, points.y, col = "blue")
#}
}
}## [1] "atrazine"
## # A tibble: 15 x 7
## # Groups: parent, analyte, matrix [3]
## parent analyte matrix time count ConcMean ConcSD
## <fctr> <fctr> <fctr> <int> <int> <dbl> <dbl>
## 1 atrazine ATZ amphib 2 4 3.34 1.18
## 2 atrazine ATZ amphib 4 4 5.36 2.75
## 3 atrazine ATZ amphib 12 4 3.12 1.26
## 4 atrazine ATZ amphib 24 4 1.55 0.610
## 5 atrazine ATZ amphib 48 4 1.00 0.355
## 6 atrazine DEA amphib 2 4 0.0139 0.00522
## 7 atrazine DEA amphib 4 4 0.0444 0.0284
## 8 atrazine DEA amphib 12 4 0.0540 0.0128
## 9 atrazine DEA amphib 24 4 0.0365 0.0131
## 10 atrazine DEA amphib 48 4 0.0195 0.0196
## 11 atrazine DIA amphib 2 4 0.329 0.125
## 12 atrazine DIA amphib 4 4 0.942 0.761
## 13 atrazine DIA amphib 12 4 1.08 0.506
## 14 atrazine DIA amphib 24 4 1.99 1.35
## 15 atrazine DIA amphib 48 4 0.662 0.531
## [1] "atrazine"
## [1] "ATZ"
## [1] "atrazine"
## [1] "DEA"
## [1] "atrazine"
## [1] "DIA"
## [1] "triadimefon"
## # A tibble: 15 x 7
## # Groups: parent, analyte, matrix [3]
## parent analyte matrix time count ConcMean ConcSD
## <fctr> <fctr> <fctr> <int> <int> <dbl> <dbl>
## 1 triadimefon TDL A amphib 2 4 0.0551 0.0211
## 2 triadimefon TDL A amphib 4 4 0.0815 0.0462
## 3 triadimefon TDL A amphib 12 4 0.0363 0.0152
## 4 triadimefon TDL A amphib 24 4 0.0240 0.00752
## 5 triadimefon TDL A amphib 48 4 0.0155 0.00485
## 6 triadimefon TDL B amphib 2 4 0.0836 0.0164
## 7 triadimefon TDL B amphib 4 4 0.130 0.0543
## 8 triadimefon TDL B amphib 12 4 0.0766 0.0486
## 9 triadimefon TDL B amphib 24 4 0.0418 0.0117
## 10 triadimefon TDL B amphib 48 4 0.0295 0.00344
## 11 triadimefon TDN amphib 2 4 0.387 0.0759
## 12 triadimefon TDN amphib 4 4 0.549 0.300
## 13 triadimefon TDN amphib 12 4 0.755 0.318
## 14 triadimefon TDN amphib 24 4 0.865 0.860
## 15 triadimefon TDN amphib 48 4 0.249 0.0798
## [1] "triadimefon"
## [1] "TDL A"
## [1] "triadimefon"
## [1] "TDL B"
## [1] "triadimefon"
## [1] "TDN"
## [1] "fipronil"
## # A tibble: 10 x 7
## # Groups: parent, analyte, matrix [2]
## parent analyte matrix time count ConcMean ConcSD
## <fctr> <fctr> <fctr> <int> <int> <dbl> <dbl>
## 1 fipronil F. sulfone amphib 2 4 0.347 0.287
## 2 fipronil F. sulfone amphib 4 4 0.397 0.477
## 3 fipronil F. sulfone amphib 12 4 0.613 0.573
## 4 fipronil F. sulfone amphib 24 4 1.25 0.526
## 5 fipronil F. sulfone amphib 48 4 0.907 0.566
## 6 fipronil FIP amphib 2 4 1.87 1.35
## 7 fipronil FIP amphib 4 4 1.30 0.522
## 8 fipronil FIP amphib 12 4 0.566 0.240
## 9 fipronil FIP amphib 24 4 0.268 0.0511
## 10 fipronil FIP amphib 48 4 0.212 0.131
## [1] "fipronil"
## [1] "F. sulfone"
## [1] "fipronil"
## [1] "FIP"dev.off()## png
## 2pdf(paste(micro.graphics,"data_mean_scatterplot",".pdf", sep=""))
par(mfrow=c(3,1))
print(parents)## [1] atrazine triadimefon fipronil
## Levels: atrazine fipronil triadimefon for(parent in parents){
i=0
print(parent)
temp.parent <- micro.group.stats.amphib[which(micro.group.stats.amphib$parent==parent),]
print(temp.parent)
parent.analytes <- unique(temp.parent$analyte)
for(analyte in parent.analytes){
print(parent)
print(analyte)
analytetemp <- micro.group.stats.amphib[which(micro.group.stats.amphib$analyte==analyte),]
xvalues <- as.numeric(as.character(analytetemp$time))
points.y <- micro.amphib[which(micro.amphib$analyte==analyte),]$conc
points.x <- as.numeric(as.character(micro.amphib[which(micro.amphib$analyte==analyte),]$time))
#create empty plot if needed
if(i==0){
parenttemp <- micro.group.stats.amphib[which(micro.group.stats.amphib$parent==parent),]
maxconc <- max(points.y)
plot(xvalues,analytetemp$ConcMean,type="l", xlim=c(0,48),
ylim = c(0,maxconc), main=parent,col="black", xlab="Hours", ylab="Concentration")
axis(1,at=xvalues)
i=1
}
#add line for parent metabolite
if(analyte %in% parents){
lines(xvalues,analytetemp$ConcMean,type="l",col="red")
points(points.x, points.y, col = "red")
}else{
#add line for daughter metabolite
lines(xvalues,analytetemp$ConcMean,type="l",col="blue")
points(points.x, points.y, col = "blue")
}
}
}## [1] "atrazine"
## # A tibble: 15 x 7
## # Groups: parent, analyte, matrix [3]
## parent analyte matrix time count ConcMean ConcSD
## <fctr> <fctr> <fctr> <int> <int> <dbl> <dbl>
## 1 atrazine ATZ amphib 2 4 3.34 1.18
## 2 atrazine ATZ amphib 4 4 5.36 2.75
## 3 atrazine ATZ amphib 12 4 3.12 1.26
## 4 atrazine ATZ amphib 24 4 1.55 0.610
## 5 atrazine ATZ amphib 48 4 1.00 0.355
## 6 atrazine DEA amphib 2 4 0.0139 0.00522
## 7 atrazine DEA amphib 4 4 0.0444 0.0284
## 8 atrazine DEA amphib 12 4 0.0540 0.0128
## 9 atrazine DEA amphib 24 4 0.0365 0.0131
## 10 atrazine DEA amphib 48 4 0.0195 0.0196
## 11 atrazine DIA amphib 2 4 0.329 0.125
## 12 atrazine DIA amphib 4 4 0.942 0.761
## 13 atrazine DIA amphib 12 4 1.08 0.506
## 14 atrazine DIA amphib 24 4 1.99 1.35
## 15 atrazine DIA amphib 48 4 0.662 0.531
## [1] "atrazine"
## [1] "ATZ"## [1] "atrazine"
## [1] "DEA"
## [1] "atrazine"
## [1] "DIA"
## [1] "triadimefon"
## # A tibble: 15 x 7
## # Groups: parent, analyte, matrix [3]
## parent analyte matrix time count ConcMean ConcSD
## <fctr> <fctr> <fctr> <int> <int> <dbl> <dbl>
## 1 triadimefon TDL A amphib 2 4 0.0551 0.0211
## 2 triadimefon TDL A amphib 4 4 0.0815 0.0462
## 3 triadimefon TDL A amphib 12 4 0.0363 0.0152
## 4 triadimefon TDL A amphib 24 4 0.0240 0.00752
## 5 triadimefon TDL A amphib 48 4 0.0155 0.00485
## 6 triadimefon TDL B amphib 2 4 0.0836 0.0164
## 7 triadimefon TDL B amphib 4 4 0.130 0.0543
## 8 triadimefon TDL B amphib 12 4 0.0766 0.0486
## 9 triadimefon TDL B amphib 24 4 0.0418 0.0117
## 10 triadimefon TDL B amphib 48 4 0.0295 0.00344
## 11 triadimefon TDN amphib 2 4 0.387 0.0759
## 12 triadimefon TDN amphib 4 4 0.549 0.300
## 13 triadimefon TDN amphib 12 4 0.755 0.318
## 14 triadimefon TDN amphib 24 4 0.865 0.860
## 15 triadimefon TDN amphib 48 4 0.249 0.0798
## [1] "triadimefon"
## [1] "TDL A"## [1] "triadimefon"
## [1] "TDL B"
## [1] "triadimefon"
## [1] "TDN"
## [1] "fipronil"
## # A tibble: 10 x 7
## # Groups: parent, analyte, matrix [2]
## parent analyte matrix time count ConcMean ConcSD
## <fctr> <fctr> <fctr> <int> <int> <dbl> <dbl>
## 1 fipronil F. sulfone amphib 2 4 0.347 0.287
## 2 fipronil F. sulfone amphib 4 4 0.397 0.477
## 3 fipronil F. sulfone amphib 12 4 0.613 0.573
## 4 fipronil F. sulfone amphib 24 4 1.25 0.526
## 5 fipronil F. sulfone amphib 48 4 0.907 0.566
## 6 fipronil FIP amphib 2 4 1.87 1.35
## 7 fipronil FIP amphib 4 4 1.30 0.522
## 8 fipronil FIP amphib 12 4 0.566 0.240
## 9 fipronil FIP amphib 24 4 0.268 0.0511
## 10 fipronil FIP amphib 48 4 0.212 0.131
## [1] "fipronil"
## [1] "F. sulfone"## [1] "fipronil"
## [1] "FIP"dev.off()## png
## 2la de da
turn times series to zoo objects
estimate lambdas using maximum likelihood for each time series
library(maxLik)
MLexp <- function(times, data){
expLik <- function(param) { y <- data t <- times alpha1 <- param[1] lambda1 <- param[2]-1(alpha1-lambda1t) - y/(exp(alpha1-lambda1*t)) }
max.fit <- maxLik(expLik, start = c(1,1)) crit <- qt(.975, length(data)-2) max.intercept.CI <- c(summary(max.fit)\(est[1,1]-crit*summary(max.fit)\)est[1,2],summary(max.fit)\(est[1,1]+crit*summary(max.fit)\)est[1,2]) max.decayrate.CI <- c(-1summary(max.fit)\(est[2,1]-crit*summary(max.fit)\)est[2,2],-1summary(max.fit)\(est[2,1]+crit*summary(max.fit)\)est[2,2]) max.halflife.CI <- c(log(2)/max.decayrate.CI[2],log(2)/max.decayrate.CI[1])
paste(“MLE for Initial Concentration =”,max.fit\(est[1], "MLE for decay rate =", max.fit\)est[2], “MLE for half life =”, -log(.5)/max.fit$est[2])
temp.list <- list(max.fit\(est[1], max.fit\)est[2], -log(.5)/max.fit$est[2], max.intercept.CI, max.decayrate.CI, max.halflife.CI, vcov(max.fit) ) return(temp.list) }
MLexp.intercept <- function(times, data) { temp.fit <- MLexp(times,data) temp.fit[[1]] }
MLexp.decayrate <- function(times, data) { temp.fit <- MLexp(times,data) temp.fit[[2]] }
MLexp.halflife <- function(times,data) { temp.fit <- MLexp(times,data) temp.fit[[3]] }
MLexp.intercept.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[4]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }
MLexp.decayrate.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[5]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }
MLexp.halflife.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[6]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }
microsome experiment analysis
data in csv format