ALE_Experiment
Kenzie Cooke
2024-06-16
2/19 to 3/23 (t1-t3)
After fixing lights, took new data point. 33 total days of growth
Total calfification by ta
Wet weight converted to dry weight, corrected for density and standardized to initial surface area.
Linear mixed effect model
to check for random effects (tank, genotype)
BW from t1 to t3, growth ~ ta, 1|geno, 1|tank
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: gr_sa ~ ta_mmol + (1 | geno) + (1 | tank)
## Data: bw.2
##
## REML criterion at convergence: -18.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.52156 -0.76504 -0.08502 0.71612 2.29665
##
## Random effects:
## Groups Name Variance Std.Dev.
## tank (Intercept) 0.001164 0.03411
## geno (Intercept) 0.003134 0.05598
## Residual 0.028081 0.16757
## Number of obs: 40, groups: tank, 4; geno, 3
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.14740 0.13703 35.67225 -1.076 0.289
## ta_mmol 0.21962 0.03523 33.46123 6.234 4.58e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## ta_mmol -0.943## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## ta_mmol 1.0914 1.0914 1 33.461 38.866 4.577e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## gr_sa ~ ta_mmol + (1 | geno) + (1 | tank)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 5 9.1535 -8.3071
## (1 | geno) 4 8.7768 -9.5535 0.75354 1 0.3854
## (1 | tank) 4 9.0659 -10.1318 0.17533 1 0.6754## Backward reduced random-effect table:
##
## Eliminated npar logLik AIC LRT Df Pr(>Chisq)
## <none> 5 9.1535 -8.3071
## (1 | tank) 1 4 9.0659 -10.1318 0.17533 1 0.6754
## (1 | geno) 2 3 8.7235 -11.4471 0.68466 1 0.4080
##
## Backward reduced fixed-effect table:
## Eliminated Df Sum of Sq RSS AIC F value Pr(>F)
## ta_mmol 0 1 1.0983 2.2732 -112.71 35.526 6.452e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Model found:
## gr_sa ~ ta_mmol
Shows no significant tank or genotype effect. Suggests appropriate model is growth ~ ta. Create regular linear model and check residuals:
Linear model, bw growth ~ ta
##
## Call:
## lm(formula = gr_sa ~ ta_mmol, data = bw.2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.27762 -0.15434 -0.00852 0.14678 0.44663
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.13995 0.13735 -1.019 0.315
## ta_mmol 0.21908 0.03676 5.960 6.45e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1758 on 38 degrees of freedom
## Multiple R-squared: 0.4832, Adjusted R-squared: 0.4696
## F-statistic: 35.53 on 1 and 38 DF, p-value: 6.452e-07## Analysis of Variance Table
##
## Response: gr_sa
## Df Sum Sq Mean Sq F value Pr(>F)
## ta_mmol 1 1.0983 1.09835 35.526 6.452e-07 ***
## Residuals 38 1.1748 0.03092
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Linear extension by TA
linear mixed effect models
LE via ImageJ (t1-t3)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: gr_t1t3 ~ ta_mmol + (1 | geno) + (1 | tank)
## Data: le
##
## REML criterion at convergence: -148.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.0585 -0.5947 -0.0384 0.5662 2.2390
##
## Random effects:
## Groups Name Variance Std.Dev.
## tank (Intercept) 0.000e+00 0.000000
## geno (Intercept) 7.492e-05 0.008656
## Residual 9.529e-04 0.030869
## Number of obs: 40, groups: tank, 4; geno, 3
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.010169 0.024776 36.928248 -0.410 0.6839
## ta_mmol 0.015429 0.006476 36.666579 2.383 0.0225 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## ta_mmol -0.959
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## ta_mmol 0.005409 0.005409 1 36.667 5.6765 0.02249 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## gr_t1t3 ~ ta_mmol + (1 | geno) + (1 | tank)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 5 74.142 -138.28
## (1 | geno) 4 73.782 -139.56 0.7198 1 0.3962
## (1 | tank) 4 74.142 -140.28 0.0000 1 1.0000## Backward reduced random-effect table:
##
## Eliminated npar logLik AIC LRT Df Pr(>Chisq)
## <none> 5 74.142 -138.28
## (1 | tank) 1 4 74.142 -140.28 0.0000 1 1.0000
## (1 | geno) 2 3 73.782 -141.56 0.7198 1 0.3962
##
## Backward reduced fixed-effect table:
## Eliminated Df Sum of Sq RSS AIC F value Pr(>F)
## ta_mmol 0 1 0.0050135 0.043286 -271.15 4.9779 0.03165 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Model found:
## gr_t1t3 ~ ta_mmol## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: gr_t1t3 ~ ta_mmol * geno + (1 | tank)
## Data: le
##
## REML criterion at convergence: -125.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1262 -0.5356 0.1579 0.5349 1.7629
##
## Random effects:
## Groups Name Variance Std.Dev.
## tank (Intercept) 0.0000000 0.00000
## Residual 0.0009772 0.03126
## Number of obs: 40, groups: tank, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.004146 0.036039 34.000000 0.115 0.909
## ta_mmol 0.014087 0.009900 34.000000 1.423 0.164
## genoM -0.064009 0.064893 34.000000 -0.986 0.331
## genoS -0.005618 0.055905 34.000000 -0.100 0.921
## ta_mmol:genoM 0.015327 0.017248 34.000000 0.889 0.380
## ta_mmol:genoS -0.004373 0.014991 34.000000 -0.292 0.772
##
## Correlation of Fixed Effects:
## (Intr) ta_mml genoM genoS t_mm:M
## ta_mmol -0.978
## genoM -0.555 0.543
## genoS -0.645 0.630 0.358
## ta_mmol:gnM 0.561 -0.574 -0.980 -0.362
## ta_mmol:gnS 0.646 -0.660 -0.359 -0.979 0.379
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## ta_mmol 0.0065236 0.0065236 1 34 6.6759 0.01424 *
## geno 0.0010223 0.0005111 2 34 0.5231 0.59739
## ta_mmol:geno 0.0012226 0.0006113 2 34 0.6256 0.54100
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Backward reduced random-effect table:
##
## Eliminated npar logLik AIC LRT Df Pr(>Chisq)
## <none> 8 62.78 -109.56
## (1 | tank) 1 7 62.78 -111.56 0 1 1
##
## Backward reduced fixed-effect table:
## Eliminated Df Sum of Sq RSS AIC F value Pr(>F)
## ta_mmol:geno 1 2 0.0012226 0.034447 -274.29 0.6256 0.54100
## geno 2 2 0.0038253 0.038272 -274.08 1.9989 0.15025
## ta_mmol 0 1 0.0050135 0.043286 -271.15 4.9779 0.03165 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Model found:
## gr_t1t3 ~ ta_mmolSignificant effect of ta on linear extension, no sig effect of tank or geno.
Most simple model: gr_t1t3 ~ ta anova results: p=0.032
##
## Call:
## lm(formula = gr_t1t3 ~ ta_mmol, data = le)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.057874 -0.022652 -0.004399 0.020996 0.070595
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.007608 0.024790 -0.307 0.7606
## ta_mmol 0.014802 0.006634 2.231 0.0317 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03174 on 38 degrees of freedom
## Multiple R-squared: 0.1158, Adjusted R-squared: 0.09256
## F-statistic: 4.978 on 1 and 38 DF, p-value: 0.03165## Analysis of Variance Table
##
## Response: gr_t1t3
## Df Sum Sq Mean Sq F value Pr(>F)
## ta_mmol 1 0.005014 0.0050135 4.9779 0.03165 *
## Residuals 38 0.038272 0.0010072
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Individual regressions by genotype (S, C, M):
## # A tibble: 6 × 18
## # Groups: geno [3]
## geno term estimate std.error statistic p.value r.squared adj.r.squared
## <fct> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 C (Intercept) 0.00415 0.0431 0.0962 0.925 0.0862 0.0253
## 2 C ta_mmol 0.0141 0.0118 1.19 0.253 0.0862 0.0253
## 3 M (Intercept) -0.0599 0.0628 -0.954 0.372 0.314 0.216
## 4 M ta_mmol 0.0294 0.0164 1.79 0.116 0.314 0.216
## 5 S (Intercept) -0.00147 0.0216 -0.0680 0.947 0.195 0.128
## 6 S ta_mmol 0.00971 0.00570 1.70 0.114 0.195 0.128
## # ℹ 10 more variables: sigma <dbl>, statistic.1 <dbl>, p.value.1 <dbl>,
## # df <dbl>, logLik <dbl>, AIC <dbl>, BIC <dbl>, deviance <dbl>,
## # df.residual <int>, nobs <int>Ana: The individual regressions are not significant. I guess that does not matter since genotype was not significant, so in theory all data should be ran together?
Scatter plots with regression
Total calcification
Linear regression
BW from t1 to t3 w linear regression
Growth standardized to initial surface area:
Growth standardized to initial mass:
Non-linear regression
BW from t1 to t3 with non-linear regression
growth standardized to surface area
Check fit of log regression:
##
## Call:
## lm(formula = gr_sa ~ log(ta), data = bw.2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.27317 -0.15576 -0.01542 0.13821 0.44314
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.3549 0.9795 -5.467 3.06e-06 ***
## log(ta) 0.7355 0.1197 6.145 3.60e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1732 on 38 degrees of freedom
## Multiple R-squared: 0.4984, Adjusted R-squared: 0.4852
## F-statistic: 37.76 on 1 and 38 DF, p-value: 3.599e-07
check fit of non log regression
##
## Call:
## lm(formula = gr_sa ~ ta, data = bw.2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.27762 -0.15434 -0.00852 0.14678 0.44663
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.400e-01 1.373e-01 -1.019 0.315
## ta 2.191e-04 3.676e-05 5.960 6.45e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1758 on 38 degrees of freedom
## Multiple R-squared: 0.4832, Adjusted R-squared: 0.4696
## F-statistic: 35.53 on 1 and 38 DF, p-value: 6.452e-07
Compare the two models:
## Analysis of Variance Table
##
## Model 1: gr_sa ~ ta
## Model 2: gr_sa ~ log(ta)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 38 1.1748
## 2 38 1.1401 0 0.034701outcome???
Similar R-squared, seems linear regression a bit better.
Example of log regression plot:
Linear Extension
Linear regression
Linear extension (via ImageJ) with linear regression (t1-t3)
Adding error bars for TA:
Carb Chemistry
Was alkalinity statistically different between treatments?
## Df Sum Sq Mean Sq F value Pr(>F)
## treatment 3 22.428 7.476 591.3 <2e-16 ***
## Residuals 36 0.455 0.013
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = ta_mmol ~ treatment, data = bw.2)
##
## $treatment
## diff lwr upr p adj
## ELEV-AMB 1.1656999 1.0302712 1.3011286 0.0000000
## HI-AMB 1.7037780 1.5683493 1.8392067 0.0000000
## XHI-AMB 1.9401692 1.8047406 2.0755979 0.0000000
## HI-ELEV 0.5380781 0.4026495 0.6735068 0.0000000
## XHI-ELEV 0.7744694 0.6390407 0.9098980 0.0000000
## XHI-HI 0.2363912 0.1009625 0.3718199 0.0002108yes…
Stability of treatment over time:
Stability of treatments over time with mean and error bars:
