GLORIA Temperature
Robbie Hart
4/4/2017
Temperature
In each of the following, I’ve run linear regressions of our dependent variables just for North and South plots, against three temperature measurements from the loggers in those plots (considering only months where the loggers recorded data for all days): annual mean of daily mean temperatures, annual mean of daily maximum temperatures, and annual mean of daily minimum temperatures. I first do this for baseline dependent variables, and then for our deltas (change across the two surveys).
Baseline
Initital richness (N)
Mean, minimum and mamxum temperatures significant (I’ve plotted mean).
##
## Call:
## lm(formula = survey1Richness ~ mean, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.0844 -3.1602 0.4436 2.9989 8.4914
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.2760 0.6290 13.158 < 2e-16 ***
## mean 1.0538 0.2344 4.496 2.15e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.005 on 86 degrees of freedom
## Multiple R-squared: 0.1903, Adjusted R-squared: 0.1809
## F-statistic: 20.21 on 1 and 86 DF, p-value: 2.15e-05##
## Call:
## lm(formula = survey1Richness ~ max, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.5669 -3.3636 0.1218 3.0406 7.5871
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.9985 0.8472 8.261 1.57e-12 ***
## max 0.8879 0.1940 4.578 1.57e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.992 on 86 degrees of freedom
## Multiple R-squared: 0.1959, Adjusted R-squared: 0.1866
## F-statistic: 20.96 on 1 and 86 DF, p-value: 1.571e-05##
## Call:
## lm(formula = survey1Richness ~ min, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.924 -3.299 0.611 2.961 9.453
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.8469 0.4658 21.139 < 2e-16 ***
## min 0.8011 0.2265 3.537 0.000656 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.159 on 86 degrees of freedom
## Multiple R-squared: 0.127, Adjusted R-squared: 0.1168
## F-statistic: 12.51 on 1 and 86 DF, p-value: 0.0006559
Initital frequency
Mean and minimum temperatures significant (I’ve plotted min).
##
## Call:
## lm(formula = survey1Frequency ~ mean, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -264.77 -88.55 -24.45 76.06 364.01
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 238.187 20.976 11.355 < 2e-16 ***
## mean 20.818 7.817 2.663 0.00924 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 133.6 on 86 degrees of freedom
## Multiple R-squared: 0.07619, Adjusted R-squared: 0.06545
## F-statistic: 7.093 on 1 and 86 DF, p-value: 0.009238##
## Call:
## lm(formula = survey1Frequency ~ max, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -227.55 -97.69 -2.64 67.83 365.65
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 276.4668 29.4971 9.373 8.57e-15 ***
## max 0.7248 6.7530 0.107 0.915
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 139 on 86 degrees of freedom
## Multiple R-squared: 0.0001339, Adjusted R-squared: -0.01149
## F-statistic: 0.01152 on 1 and 86 DF, p-value: 0.9148##
## Call:
## lm(formula = survey1Frequency ~ min, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -229.90 -85.68 -31.41 87.60 338.46
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 260.480 14.106 18.466 < 2e-16 ***
## min 29.685 6.859 4.328 4.05e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 125.9 on 86 degrees of freedom
## Multiple R-squared: 0.1788, Adjusted R-squared: 0.1693
## F-statistic: 18.73 on 1 and 86 DF, p-value: 4.05e-05
Initital diversity (D1)
Mean, minimum and maximum temperatures significant (I’ve plotted mean).
##
## Call:
## lm(formula = survey1D1 ~ mean, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.7403 -2.1702 0.1883 1.7979 4.8879
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.7174 0.3854 12.240 < 2e-16 ***
## mean 0.7143 0.1436 4.973 3.33e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.454 on 86 degrees of freedom
## Multiple R-squared: 0.2233, Adjusted R-squared: 0.2143
## F-statistic: 24.73 on 1 and 86 DF, p-value: 3.334e-06##
## Call:
## lm(formula = survey1D1 ~ max, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.4999 -2.1416 0.1611 2.0412 5.1220
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.8945 0.5216 7.466 6.28e-11 ***
## max 0.5904 0.1194 4.944 3.74e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.458 on 86 degrees of freedom
## Multiple R-squared: 0.2213, Adjusted R-squared: 0.2123
## F-statistic: 24.44 on 1 and 86 DF, p-value: 3.745e-06##
## Call:
## lm(formula = survey1D1 ~ min, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.5470 -2.4737 0.2634 2.0248 5.3909
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.7767 0.2869 20.132 < 2e-16 ***
## min 0.5517 0.1395 3.954 0.000157 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.562 on 86 degrees of freedom
## Multiple R-squared: 0.1538, Adjusted R-squared: 0.144
## F-statistic: 15.63 on 1 and 86 DF, p-value: 0.0001575
Initital thermophily (S_f)
Mean, minimum and maximum temperatures significant (I’ve plotted max).
##
## Call:
## lm(formula = S_f ~ mean, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1195 -0.1502 0.1231 0.6608 1.7555
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.82954 0.16479 23.239 < 2e-16 ***
## mean 0.16897 0.06141 2.751 0.00723 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.049 on 86 degrees of freedom
## Multiple R-squared: 0.08091, Adjusted R-squared: 0.07022
## F-statistic: 7.57 on 1 and 86 DF, p-value: 0.007234##
## Call:
## lm(formula = S_f ~ max, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1994 -0.3553 0.1640 0.6021 1.6756
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.58561 0.22093 16.230 < 2e-16 ***
## max 0.15272 0.05058 3.019 0.00333 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.041 on 86 degrees of freedom
## Multiple R-squared: 0.09585, Adjusted R-squared: 0.08534
## F-statistic: 9.117 on 1 and 86 DF, p-value: 0.003333##
## Call:
## lm(formula = S_f ~ min, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.0800 -0.1895 0.0731 0.6698 1.7950
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.08590 0.11961 34.160 <2e-16 ***
## min 0.12136 0.05817 2.087 0.0399 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.068 on 86 degrees of freedom
## Multiple R-squared: 0.04818, Adjusted R-squared: 0.03712
## F-statistic: 4.354 on 1 and 86 DF, p-value: 0.03989
Deltas
Change in richness (∆N)
Mean, minimum and mamxum temperatures significant (I’ve plotted mean).
##
## Call:
## lm(formula = rawChangeRichness ~ mean, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.602 -1.696 -0.490 1.604 7.071
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.9340 0.3951 2.364 0.02034 *
## mean 0.4257 0.1472 2.891 0.00486 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.516 on 86 degrees of freedom
## Multiple R-squared: 0.08858, Adjusted R-squared: 0.07799
## F-statistic: 8.359 on 1 and 86 DF, p-value: 0.004859##
## Call:
## lm(formula = rawChangeRichness ~ max, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.4102 -1.5884 -0.2949 1.5852 7.0856
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.4314 0.5338 0.808 0.42123
## max 0.3551 0.1222 2.906 0.00466 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.515 on 86 degrees of freedom
## Multiple R-squared: 0.08939, Adjusted R-squared: 0.0788
## F-statistic: 8.442 on 1 and 86 DF, p-value: 0.00466##
## Call:
## lm(formula = rawChangeRichness ~ min, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9968 -1.7730 -0.4726 1.5033 7.4938
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.5761 0.2870 5.492 3.98e-07 ***
## min 0.3118 0.1396 2.234 0.0281 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.562 on 86 degrees of freedom
## Multiple R-squared: 0.05485, Adjusted R-squared: 0.04386
## F-statistic: 4.991 on 1 and 86 DF, p-value: 0.02808
Turnover
Mamxum temperature only signficant.
##
## Call:
## lm(formula = turnover ~ mean, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.3851 -0.1033 0.0174 0.1207 0.4062
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.32639 0.02924 11.163 <2e-16 ***
## mean 0.02065 0.01090 1.895 0.0615 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1862 on 86 degrees of freedom
## Multiple R-squared: 0.04008, Adjusted R-squared: 0.02892
## F-statistic: 3.591 on 1 and 86 DF, p-value: 0.06146##
## Call:
## lm(formula = turnover ~ max, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.37479 -0.09746 0.01981 0.10084 0.46234
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.24654 0.03743 6.586 3.43e-09 ***
## max 0.03191 0.00857 3.724 0.00035 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1764 on 86 degrees of freedom
## Multiple R-squared: 0.1388, Adjusted R-squared: 0.1288
## F-statistic: 13.87 on 1 and 86 DF, p-value: 0.00035##
## Call:
## lm(formula = turnover ~ min, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.37344 -0.10510 0.01419 0.12435 0.36107
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.365029 0.021274 17.159 <2e-16 ***
## min 0.003246 0.010345 0.314 0.754
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1899 on 86 degrees of freedom
## Multiple R-squared: 0.001143, Adjusted R-squared: -0.01047
## F-statistic: 0.09843 on 1 and 86 DF, p-value: 0.7545
Change in frequency
Mean and mamxum temperatures significant (I’ve plotted mean).
##
## Call:
## lm(formula = rawChangeFrequency ~ mean, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -391.37 -45.30 4.02 36.53 282.20
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.038 15.341 0.589 0.5573
## mean 12.635 5.717 2.210 0.0298 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 97.7 on 86 degrees of freedom
## Multiple R-squared: 0.05374, Adjusted R-squared: 0.04274
## F-statistic: 4.884 on 1 and 86 DF, p-value: 0.02976##
## Call:
## lm(formula = rawChangeFrequency ~ max, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -378.47 -56.57 0.51 40.34 268.90
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.325 20.777 -0.208 0.8356
## max 10.128 4.757 2.129 0.0361 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 97.89 on 86 degrees of freedom
## Multiple R-squared: 0.05008, Adjusted R-squared: 0.03904
## F-statistic: 4.534 on 1 and 86 DF, p-value: 0.03609##
## Call:
## lm(formula = rawChangeFrequency ~ min, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -401.13 -49.43 -0.75 39.06 293.63
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 27.612 11.027 2.504 0.0142 *
## min 10.019 5.362 1.868 0.0651 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 98.46 on 86 degrees of freedom
## Multiple R-squared: 0.03901, Adjusted R-squared: 0.02783
## F-statistic: 3.491 on 1 and 86 DF, p-value: 0.06512
Change in diversity
Maximum temperatures only signficant.
##
## Call:
## lm(formula = delta.D1.f ~ mean, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.6797 -1.0341 -0.1492 0.8051 4.9555
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.11509 0.25980 4.292 4.62e-05 ***
## mean 0.15816 0.09682 1.634 0.106
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.655 on 86 degrees of freedom
## Multiple R-squared: 0.0301, Adjusted R-squared: 0.01882
## F-statistic: 2.669 on 1 and 86 DF, p-value: 0.106##
## Call:
## lm(formula = delta.D1.f ~ max, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.8034 -0.9428 0.0329 0.8262 5.2772
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.59844 0.34129 1.753 0.08309 .
## max 0.21929 0.07813 2.807 0.00619 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.608 on 86 degrees of freedom
## Multiple R-squared: 0.08391, Adjusted R-squared: 0.07325
## F-statistic: 7.877 on 1 and 86 DF, p-value: 0.006193##
## Call:
## lm(formula = delta.D1.f ~ min, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7481 -1.0242 -0.2445 0.8557 4.5224
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.39478 0.18782 7.426 7.55e-11 ***
## min 0.05064 0.09134 0.554 0.581
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.677 on 86 degrees of freedom
## Multiple R-squared: 0.003562, Adjusted R-squared: -0.008024
## F-statistic: 0.3074 on 1 and 86 DF, p-value: 0.5807
Change in thermophily (thermophilization)
Not correlated with any temperature metric.
##
## Call:
## lm(formula = D_f ~ mean, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.5555 -0.1584 -0.0261 0.1128 2.8416
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.12449 0.06908 1.802 0.075 .
## mean -0.04018 0.02574 -1.561 0.122
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.44 on 86 degrees of freedom
## Multiple R-squared: 0.02755, Adjusted R-squared: 0.01624
## F-statistic: 2.436 on 1 and 86 DF, p-value: 0.1222##
## Call:
## lm(formula = D_f ~ max, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.53526 -0.15573 -0.03858 0.09101 2.81465
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.20245 0.09265 2.185 0.0316 *
## max -0.04160 0.02121 -1.961 0.0531 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4365 on 86 degrees of freedom
## Multiple R-squared: 0.04282, Adjusted R-squared: 0.03169
## F-statistic: 3.847 on 1 and 86 DF, p-value: 0.05306##
## Call:
## lm(formula = D_f ~ min, data = ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.56213 -0.10835 -0.02448 0.10771 2.89171
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.06093 0.04967 1.227 0.223
## min -0.02475 0.02415 -1.025 0.308
##
## Residual standard error: 0.4435 on 86 degrees of freedom
## Multiple R-squared: 0.01206, Adjusted R-squared: 0.0005767
## F-statistic: 1.05 on 1 and 86 DF, p-value: 0.3083| ***************************** |
| ***************************** |
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Season and aspect?
So, as above, the temperatures that our loggers recorded in the North (N) and South (S) plot clusters correlate with the thermophily of that plot cluster.
However, it looks like the S quadrat clusters show a much tighter correlation than N. If we break this down by months, it becomes clear that for most months (all but July-October), temperatures on the N do not actually correlate well with the thermophily of plants at the plot.
In the European analysis, GLORIA central used July Minimum temperature as their metric for temperature. This was because it had the highest correlation with the thermophily of plants. Here’s the figure they present (blue is minimum, green mean, and red maximum). 
They interpret this to mean “It is the temperature in the first part of the growing period which is most decisive for plant growth”.
Our correlations look different. As we saw above, it’s clear that for several months out of the year (presumably when they are under snow), temperatures do not correlate well with plant thermophily at the North sites. (Because of the gaps in our data, I’ve also indicated how many observations – summitsXyears – go into each of these correlations)
Is it possible that this is an instersting result? Could we connect it somehow to the fact that southern rather than northern sites are seeing increased richness, diversity, etc? Perhaps temperature is just more limiting on the plants at southern sites and so those plots are more quickly affected by the increasing temperature. If northern sites are controlled more by snow duration, then maybe there are more complex interactions with precipitation.