Supplementary material:
Commitment time depends on both current and target nest value in Temnothorax albipennis ant colonies.
Behavioral Ecology and Sociobiology
Carolina Doran1, 2*, Zac F. Newham1, Ben B. Phillips1 and Nigel R. Franks1.
1 – School of Biological Sciences, University of Bristol, Woodland Road, Bristol BS81UG, UK
2 – Champalimaud Neuroscience Programme, Champalimaud Centre for the Unknown, Av. Brasília, Lisbon 1400-038, Portugal
* Corresponding author:
a)Analysis of the different behaviours performed by colonies in each treatment.
treatment * behavCrosstabulationbehav / Total
emigrated / Failed to emigrate / Overnight emigration / Split
treatment / 1l-1d / Count / 1 / 3 / 2 / 0 / 6
Expected Count / 4.1 / .8 / .7 / .4 / 6.0
% of Total / 1.7% / 5.0% / 3.3% / 0.0% / 10.0%
1l-2d / Count / 5 / 0 / 1 / 0 / 6
Expected Count / 4.1 / .8 / .7 / .4 / 6.0
% of Total / 8.3% / 0.0% / 1.7% / 0.0% / 10.0%
1l-3d / Count / 5 / 0 / 0 / 1 / 6
Expected Count / 4.1 / .8 / .7 / .4 / 6.0
% of Total / 8.3% / 0.0% / 0.0% / 1.7% / 10.0%
1l-4d / Count / 6 / 0 / 0 / 0 / 6
Expected Count / 4.1 / .8 / .7 / .4 / 6.0
% of Total / 10.0% / 0.0% / 0.0% / 0.0% / 10.0%
2l-2d / Count / 4 / 2 / 0 / 0 / 6
Expected Count / 4.1 / .8 / .7 / .4 / 6.0
% of Total / 6.7% / 3.3% / 0.0% / 0.0% / 10.0%
2l-3d / Count / 4 / 1 / 0 / 1 / 6
Expected Count / 4.1 / .8 / .7 / .4 / 6.0
% of Total / 6.7% / 1.7% / 0.0% / 1.7% / 10.0%
2l-4d / Count / 5 / 0 / 1 / 0 / 6
Expected Count / 4.1 / .8 / .7 / .4 / 6.0
% of Total / 8.3% / 0.0% / 1.7% / 0.0% / 10.0%
3l-3d / Count / 0 / 2 / 2 / 2 / 6
Expected Count / 4.1 / .8 / .7 / .4 / 6.0
% of Total / 0.0% / 3.3% / 3.3% / 3.3% / 10.0%
3l-4d / Count / 5 / 0 / 1 / 0 / 6
Expected Count / 4.1 / .8 / .7 / .4 / 6.0
% of Total / 8.3% / 0.0% / 1.7% / 0.0% / 10.0%
4l-4d / Count / 6 / 0 / 0 / 0 / 6
Expected Count / 4.1 / .8 / .7 / .4 / 6.0
% of Total / 10.0% / 0.0% / 0.0% / 0.0% / 10.0%
Total / Count / 41 / 8 / 7 / 4 / 60
Expected Count / 41.0 / 8.0 / 7.0 / 4.0 / 60.0
% of Total / 68.3% / 13.3% / 11.7% / 6.7% / 100.0%
Chi-Square Tests
Value / df / Asymp. Sig. (2-sided) / Exact Sig. (2-sided)
Pearson Chi-Square / 43.214a / 27 / .025 / .018
Likelihood Ratio / 50.208 / 27 / .004 / .001
Fisher's Exact Test / 35.008 / .001
N of Valid Cases / 60
a. 40 cells (100.0%) have expected count less than 5. The minimum expected count is .40.
b)Analysis of effect of current nest value on the number of ants outside:
The residuals of the generalized linear mixed model are normally distributed, as shown by Shapiro-Wilk normality test (p = 0.6162).
R code and output:
#Number of ants
###########################################################
###########################################################
nants<-read.table("numberants.txt", header =TRUE)
colnames(nants)<-c("treatment", "colony", "numberants")
nants$treatment<-factor(nants$treatment, levels=c("1","2","3","4"), ordered=TRUE)
nants$colony<-factor(nants$colony, levels=c("1","2","3","4","5","6","7","8","9","10", "11", "12"), ordered=FALSE)
nants$numberants<-as.numeric(nants$numberants)
##models
nantsmod0 <-glmer(numberants~(1|colony), data=nants, family='poisson')
nantsmod1 <-glmer(numberants ~ treatment +(1|colony), data=nants, family='poisson')
summary(nantsmod1)
------
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation)['glmerMod']
Family:poisson (log)
Formula:numberants~ treatment +(1| colony)
Data:nants
AIC BIC logLikdeviancedf.resid
523.1 533.6 -256.6 513.1 55
Scaled residuals:
Min 1Q Median 3Q Max
-3.4777-1.3666-0.3402 1.5230 5.1086
Random effects:
Groups Name Variance Std.Dev.
colony(Intercept)0.2761 0.5254
Number of obs:60, groups: colony, 12
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 2.35103 0.16048 14.650 2e-16***
treatment.L-0.66738 0.11464 -5.8215.84e-09***
treatment.Q-0.06370 0.10061 -0.633 0.527
treatment.C-0.07198 0.08600 -0.837 0.403
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
Correlation of Fixed Effects:
(Intr)trtm.Ltrtm.Q
treatment.L0.216
treatment.Q0.120 0.641
treatment.C0.051 0.259 0.476
anova(nantsmod0, nantsmod1)
------
Data:nants
Models:
nantsmod0:numberants~(1| colony)
nantsmod1:numberants~ treatment +(1| colony)
Df AIC BIC logLikdeviance Chisq Chi DfPr(>Chisq)
nantsmod0 2572.77576.96-284.38 568.77
nantsmod1 5523.13533.60-256.56 513.1355.643 3 5.007e-12***
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
##Residuals
shapiro.test(resid(nantsmod1))
------
Shapiro-Wilk normality test
data: resid(nantsmod1)
W =0.984, p-value =0.6162
c)Current nest devaluation (repulsion):
The residuals of all the models are normally distributed, as shown by Shapiro-Wilk normality test (p = 0.2626, 0.2226, 0.9917, 0.4049, 0.8313, 0.9199 and 0.7893 respectively for total emigration time, time of first encounter, time of first tandem run, time between first tandem run and first carry and time between first and last carry, number of tandem runs and quorumrespectively; R output below), indicating a good model fit.
R code and output:
#REPULSION -> the current nest quality decreases 10 - Good; 9 - Medium; 7 - Satisfactory; 4 - Poor and target nest is always Good(dark)
###########################################################
###########################################################
repulsion<-read.delim("repulsion.txt", header = T)
colnames(repulsion)<-c("emigration", "treat", "colony", "size", "etime", "behaviour", "fe", "ftr", "fc", "lc", "ntr", "quorum")
repulsion$treat<-factor(repulsion$treat, levels=c("4", "7","9","10"), ordered=TRUE)
repulsion$colony<-factor(repulsion$colony, levels=c("1","2","3","4","5","6","7","8","9","10", "11", "12"), ordered=FALSE)
repulsion$size<-as.numeric(repulsion$size)
repulsion$etime<-as.numeric(repulsion$etime)#emigration time
repulsion$behaviour<-factor(repulsion$behaviour, levels=c("e", "on", "split", "ne"))
repulsion$fe<-as.numeric(repulsion$fe)# time first ant encounters the nest
repulsion$ftr<-as.numeric(repulsion$ftr)#time until first tandem run
repulsion$fc<-as.numeric(repulsion$fc)#time of first carry
repulsion$lc<-as.numeric(repulsion$lc)# Time of last carry
repulsion$ntr<-as.numeric(repulsion$ntr)# number of tandem runs
repulsion$quorum<-as.numeric(repulsion$quorum)# quorum
##Models
repmod0 <-lmer(log10(etime)~(1|colony), data= repulsion, REML =FALSE)
repmod1 <-lmer(log10(etime)~ treat +(1|colony), data= repulsion, REML =FALSE)
summary(repmod1)
------
Linear mixed model fit by maximum likelihood t-tests use Satterthwaite approximations to degrees of freedom [
merModLmerTest]
Formula:log10(etime)~ treat +(1| colony)
Data: repulsion
AIC BIC logLikdeviancedf.resid
-19.1 -12.6 15.6 -31.1 16
Scaled residuals:
Min 1Q Median 3Q Max
-1.27229-0.61896-0.05991 0.69669 1.22461
Random effects:
Groups Name Variance Std.Dev.
colony (Intercept)0.0165360.12859
Residual 0.0057190.07563
Number of obs:22, groups: colony, 11
Fixed effects:
Estimate Std. Error dft value Pr(>|t|)
(Intercept) 2.12822 0.04322 9.02000 49.2442.81e-12***
treat.L 0.19618 0.0418414.77300 4.6890.000303***
treat.Q 0.02270 0.0375910.86300 0.6040.558379
treat.C -0.02834 0.03526 9.58100 -0.8040.441038
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
Correlation of Fixed Effects:
(Intr)tret.Ltret.Q
treat.L-0.061
treat.Q-0.141 0.122
treat.C-0.015 0.064 0.065
------
anova(repmod0, repmod1)
------
Data: repulsion
Models:
object: log10(etime)~(1| colony)
..1:log10(etime)~ treat +(1| colony)
Df AIC BIC logLikdeviance Chisq Chi DfPr(>Chisq)
object 3-10.465 -7.1916 8.2324 -16.465
..1 6-19.117-12.571115.5587 -31.11714.653 3 0.002139**
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
------
##Residuals
shapiro.test(resid(repmod1))
Shapiro-Wilk normality test
data: resid(repmod1)
W =0.946, p-value =0.2626
##Contrats
(contrasts(repulsion$treat)<-contr.treatment(levels(repulsion$treat),base=4))
repmod1.4 <-lmer(log10(etime)~ treat +(1|colony), data= repulsion, REML =FALSE)
summary(repmod1.4)
------
Linear mixed model fit by maximum likelihood
t-tests use Satterthwaite approximations to degrees of freedom ['merModLmerTest']
Formula:log10(etime)~ treat +(1| colony)
Data: repulsion
AIC BIC logLikdeviancedf.resid
-19.1 -12.6 15.6 -31.1 16
Scaled residuals:
Min 1Q Median 3Q Max
-1.27229-0.61896-0.05991 0.69669 1.22461
Random effects:
Groups Name Variance Std.Dev.
colony (Intercept)0.0165360.12859
Residual 0.0057190.07563
Number of obs:22, groups: colony, 11
Fixed effects:
Estimate Std. Error dft value Pr(>|t|)
(Intercept) 2.26483 0.0534817.65400 42.350 2e-16***
treat4 -0.25053 0.0592615.11500 -4.227 0.00072***
treat7 -0.21084 0.0570412.81200 -3.697 0.00275**
treat9 -0.08509 0.0562112.41500 -1.514 0.15511
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
Correlation of Fixed Effects:
(Intr) treat4 treat7
treat4 -0.551
treat7 -0.499 0.630
treat9 -0.491 0.593 0.614
(contrasts(repulsion$treat)<-contr.treatment(levels(repulsion$treat),base=3))
repmod1.3 <-lmer(log10(etime)~ treat +(1|colony), data= repulsion, REML =FALSE)
summary(repmod1.3)
------
Linear mixed model fit by maximum likelihood
t-tests use Satterthwaite approximations to degrees of freedom ['merModLmerTest']
Formula:log10(etime)~ treat +(1| colony)
Data: repulsion
AIC BIC logLikdeviancedf.resid
-19.1 -12.6 15.6 -31.1 16
Scaled residuals:
Min 1Q Median 3Q Max
-1.27229-0.61896-0.05991 0.69669 1.22461
Random effects:
Groups Name Variance Std.Dev.
colony (Intercept)0.0165360.12859
Residual 0.0057190.07563
Number of obs:22, groups: colony, 11
Fixed effects:
Estimate Std. Error dft value Pr(>|t|)
(Intercept) 2.17975 0.0553719.80200 39.364 2e-16***
treat4 -0.16544 0.0521610.73400 -3.172 0.00915**
treat7 -0.12576 0.04975 9.23800 -2.528 0.03173*
treat10 0.08509 0.0562112.41500 1.514 0.15511
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
Correlation of Fixed Effects:
(Intr) treat4 treat7
treat4 -0.503
treat7 -0.448 0.518
treat10 -0.541 0.404 0.426
(contrasts(repulsion$treat)<-contr.treatment(levels(repulsion$treat),base=2))
repmod1.2 <-lmer(log10(etime)~ treat +(1|colony), data= repulsion, REML =FALSE)
summary(repmod1.2)
------
Linear mixed model fit by maximum likelihood
t-tests use Satterthwaite approximations to degrees of freedom ['merModLmerTest']
Formula:log10(etime)~ treat +(1| colony)
Data: repulsion
AIC BIC logLikdeviancedf.resid
-19.1 -12.6 15.6 -31.1 16
Scaled residuals:
Min 1Q Median 3Q Max
-1.27229-0.61896-0.05991 0.69669 1.22461
Random effects:
Groups Name Variance Std.Dev.
colony (Intercept)0.0165360.12859
Residual 0.0057190.07563
Number of obs:22, groups: colony, 11
Fixed effects:
Estimate Std. Error dft value Pr(>|t|)
(Intercept) 2.05399 0.0554219.78600 37.060 2e-16***
treat4 -0.03969 0.0500810.24700 -0.793 0.44599
treat9 0.12576 0.04975 9.23800 2.528 0.03173*
treat10 0.21084 0.0570412.81200 3.697 0.00275**
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
Correlation of Fixed Effects:
(Intr) treat4 treat9
treat4 -0.486
treat9 -0.450 0.454
treat10 -0.548 0.394 0.453
##dynamics 1
##Models
#first encounter
repfe0 <-lmer(log10(fe)~(1|colony), data=repulsion, REML =FALSE)
repfe1 <-lmer(log10(fe)~ treat +(1|colony), data=repulsion, REML =FALSE)
anova(repfe0, repfe1)
------
Data: repulsion
Models:
object: log10(fe)~(1| colony)
..1:log10(fe)~ treat +(1| colony)
Df AIC BIC logLikdeviance Chisq Chi DfPr(>Chisq)
object 323.37326.907-8.6865 17.373
..1 628.05535.124-8.0276 16.0551.3177 3 0.7249
shapiro.test(resid(repfe1))
------
Shapiro-Wilk normality test
data: resid(repfe1)
W =0.9461, p-value =0.2226
#first tandem run
repftr0 <-lmer(log10(ftr)~(1|colony), data=repulsion, REML =FALSE)
repftr1 <-lmer(log10(ftr)~ treat +(1|colony), data=repulsion, REML =FALSE)
anova(repftr0, repftr1)
------
Data: repulsion
Models:
object: log10(ftr)~(1| colony)
..1:log10(ftr)~ treat +(1| colony)
Df AIC BIC logLikdeviance Chisq Chi DfPr(>Chisq)
object 3 6.856110.262-0.42803 0.85606
..1 611.125917.939 0.43707-0.874141.7302 3 0.6302
shapiro.test(resid(repftr1))
------
Shapiro-Wilk normality test
data: resid(reptr1)
W =0.9882, p-value =0.9917
#time between ftr and fc
repftrfc0 <-lmer(log10(fc-ftr)~(1|colony), data=repulsion, REML =FALSE)
repftrfc1 <-lmer(log10(fc-ftr)~ treat +(1|colony), data=repulsion, REML =FALSE)
summary(repftrfc1)
------
Linear mixed model fit by maximum likelihood
t-tests use Satterthwaite approximations to degrees of freedom ['merModLmerTest']
Formula:log10(fc -ftr)~ treat +(1| colony)
Data: repulsion
AIC BIC logLikdeviancedf.resid
-4.3 2.2 8.2 -16.3 16
Scaled residuals:
Min 1Q Median 3Q Max
-1.2037-0.5178 0.1577 0.4128 1.2755
Random effects:
Groups Name Variance Std.Dev.
colony (Intercept)0.0613800.24775
Residual 0.0067260.08202
Number of obs:22, groups: colony, 11
Fixed effects:
Estimate Std. Error dft value Pr(>|t|)
(Intercept) 1.51027 0.0776910.35800 19.4391.73e-09***
treat.L 0.37857 0.0489812.58500 7.7303.98e-06***
treat.Q -0.01271 0.0419110.94300 -0.303 0.767
treat.C -0.05580 0.0386510.49400 -1.444 0.178
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
Correlation of Fixed Effects:
(Intr)tret.Ltret.Q
treat.L-0.047
treat.Q-0.098 0.153
treat.C-0.014 0.102 0.081
anova(repftrfc0, repftrfc1)
------
Data: repulsion
Models:
object: log10(fc -ftr)~(1| colony)
..1:log10(fc -ftr)~ treat +(1| colony)
Df AIC BIC logLikdeviance Chisq Chi DfPr(>Chisq)
object 314.31817.5909-4.1589 8.3178
..1 6-4.344 2.2022 8.1720-16.344024.662 3 1.817e-05***
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
shapiro.test(resid(repftrfc1))
------
Shapiro-Wilk normality test
data: resid(repftrfc1)
W =0.9556, p-value =0.4049
##Contrats
(contrasts(repulsion$treat)<-contr.treatment(levels(repulsion$treat),base=4))
repftrfc1.4 <-lmer(log10(fc-ftr)~ treat +(1|colony), data=repulsion, REML =FALSE)
summary(repftrfc1.4)
------
Linear mixed model fit by maximum likelihood t-tests use Satterthwaite
approximations to degrees of freedom [merModLmerTest]
Formula:log10(fc -ftr)~ treat +(1| colony)
Data: repulsion
AIC BIC logLikdeviancedf.resid
-4.3 2.2 8.2 -16.3 16
Scaled residuals:
Min 1Q Median 3Q Max
-1.2037-0.5178 0.1577 0.4128 1.2755
Random effects:
Groups Name Variance Std.Dev.
colony (Intercept)0.0613800.24775
Residual 0.0067260.08202
Number of obs:22, groups: colony, 11
Fixed effects:
Estimate Std. Error dft value Pr(>|t|)
(Intercept) 1.74539 0.0857414.64500 20.3583.78e-12***
treat4 -0.48296 0.0696312.70600 -6.9361.16e-05***
treat7 -0.35085 0.0652911.82900 -5.3730.000176***
treat9 -0.10669 0.0640411.67100 -1.6660.122295
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
Correlation of Fixed Effects:
(Intr) treat4 treat7
treat4 -0.403
treat7 -0.364 0.664
treat9 -0.358 0.625 0.649
(contrasts(repulsion$treat)<-contr.treatment(levels(repulsion$treat),base=3))
repftrfc1.3 <-lmer(log10(fc-ftr)~ treat +(1|colony), data=repulsion, REML =FALSE)
summary(repftrfc1.3)
------
Linear mixed model fit by maximum likelihood t-tests use Satterthwaite
approximations to degrees of freedom [merModLmerTest]
Formula:log10(fc -ftr)~ treat +(1| colony)
Data: repulsion
AIC BIC logLikdeviancedf.resid
-4.3 2.2 8.2 -16.3 16
Scaled residuals:
Min 1Q Median 3Q Max
-1.2037-0.5178 0.1577 0.4128 1.2755
Random effects:
Groups Name Variance Std.Dev.
colony (Intercept)0.0613800.24775
Residual 0.0067260.08202
Number of obs:22, groups: colony, 11
Fixed effects:
Estimate Std. Error dft value Pr(>|t|)
(Intercept) 1.63870 0.0867315.44700 18.8934.30e-12***
treat4 -0.37627 0.0581010.95100 -6.4764.67e-05***
treat7 -0.24416 0.0541910.29600 -4.506 0.00105**
treat10 0.10669 0.0640411.67100 1.666 0.12230
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
Correlation of Fixed Effects:
(Intr) treat4 treat7
treat4 -0.349
treat7 -0.311 0.515
treat10 -0.385 0.353 0.400
(contrasts(repulsion$treat)<-contr.treatment(levels(repulsion$treat),base=2))
repftrfc1.2 <-lmer(log10(fc-ftr)~ treat +(1|colony), data=repulsion, REML =FALSE)
summary(repftrfc1.2)
------
Linear mixed model fit by maximum likelihood t-tests use Satterthwaite
approximations to degrees of freedom [merModLmerTest]
Formula:log10(fc -ftr)~ treat +(1| colony)
Data: repulsion
AIC BIC logLikdeviancedf.resid
-4.3 2.2 8.2 -16.3 16
Scaled residuals:
Min 1Q Median 3Q Max
-1.2037-0.5178 0.1577 0.4128 1.2755
Random effects:
Groups Name Variance Std.Dev.
colony (Intercept)0.0613800.24775
Residual 0.0067260.08202
Number of obs:22, groups: colony, 11
Fixed effects:
Estimate Std. Error dft value Pr(>|t|)
(Intercept) 1.39454 0.0868115.46700 16.065 4.6e-11***
treat4 -0.13211 0.0554210.76300 -2.3840.036717*
treat9 0.24416 0.0541910.29600 4.5060.001053**
treat10 0.35085 0.0652911.82900 5.3730.000176***
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
Correlation of Fixed Effects:
(Intr) treat4 treat9
treat4 -0.335
treat9 -0.313 0.438
treat10 -0.392 0.344 0.438
#time between fc and lc
repfclc0 <-lmer(log(lc-fc)~(1|colony), data=repulsion, REML =FALSE)
repfclc1 <-lmer(log(lc-fc)~ treat +(1|colony), data=repulsion, REML =FALSE)
anova(repfclc0, repfclc1)
------
Data: repulsion
Models:
object:log(lc- fc)~(1| colony)
..1:log(lc- fc)~ treat +(1| colony)
Df AIC BIC logLikdevianceChisq Chi DfPr(>Chisq)
object 324.18427.457-9.0922 18.184
..1 622.45329.000-5.2267 10.4537.731 3 0.05191 .
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
shapiro.test(resid(repfclc1))
------
Shapiro-Wilk normality test
data: resid(repfclc1)
W =0.9754, p-value =0.8313
##Contrasts
(contrasts(repulsion$treat)<-contr.treatment(levels(repulsion$treat),base=4))
repfclc1.4 <-lmer(log(lc-fc)~ treat +(1|colony), data=repulsion, REML =FALSE)
summary(repfclc1.4)
------
Linear mixed model fit by maximum likelihood t-tests use Satterthwaite
approximations to degrees of freedom [merModLmerTest]
Formula:log(lc- fc)~ treat +(1| colony)
Data: repulsion
AIC BIC logLikdeviancedf.resid
22.5 29.0 -5.2 10.5 16
Scaled residuals:
Min 1Q Median 3Q Max
-1.68213-0.65444-0.02465 0.55968 1.88050
Random effects:
Groups Name Variance Std.Dev.
colony (Intercept)0.03295 0.1815
Residual 0.06808 0.2609
Number of obs:22, groups: colony, 11
Fixed effects:
Estimate Std. Error dft value Pr(>|t|)
(Intercept) 4.6140 0.126821.0310 36.401 2e-16***
treat4 -0.4432 0.171319.3600 -2.588 0.0179*
treat7 -0.4735 0.173915.2540 -2.722 0.0156*
treat9 -0.2584 0.173214.4670 -1.492 0.1571
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
Correlation of Fixed Effects:
(Intr) treat4 treat7
treat4 -0.674
treat7 -0.622 0.546
treat9 -0.619 0.523 0.527
(contrasts(repulsion$treat)<-contr.treatment(levels(repulsion$treat),base=3))
repfclc1.3 <-lmer(log(lc-fc)~ treat +(1|colony), data=repulsion, REML =FALSE)
summary(repfclc1.3)
------
Linear mixed model fit by maximum likelihood t-tests use Satterthwaite
approximations to degrees of freedom [merModLmerTest]
Formula:log(lc- fc)~ treat +(1| colony)
Data: repulsion
AIC BIC logLikdeviancedf.resid
22.5 29.0 -5.2 10.5 16
Scaled residuals:
Min 1Q Median 3Q Max
-1.68213-0.65444-0.02465 0.55968 1.88050
Random effects:
Groups Name Variance Std.Dev.
colony (Intercept)0.03295 0.1815
Residual 0.06808 0.2609
Number of obs:22, groups: colony, 11
Fixed effects:
Estimate Std. Error dft value Pr(>|t|)
(Intercept) 4.3556 0.137421.9800 31.707 2e-16***
treat4 -0.1848 0.168211.2270 -1.099 0.295
treat7 -0.2151 0.1689 8.1490 -1.274 0.238
treat10 0.2584 0.173214.4670 1.492 0.157
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
Correlation of Fixed Effects:
(Intr) treat4 treat7
(contrasts(repulsion$treat)<-contr.treatment(levels(repulsion$treat),base=2))
repfclc1.2 <-lmer(log(lc-fc)~ treat +(1|colony), data=repulsion, REML =FALSE)
summary(repfclc1.2)
------
Linear mixed model fit by maximum likelihood t-tests use Satterthwaite
approximations to degrees of freedom [merModLmerTest]
Formula:log(lc- fc)~ treat +(1| colony)
Data: repulsion
AIC BIC logLikdeviancedf.resid
22.5 29.0 -5.2 10.5 16
Scaled residuals:
Min 1Q Median 3Q Max
-1.68213-0.65444-0.02465 0.55968 1.88050
Random effects:
Groups Name Variance Std.Dev.
colony (Intercept)0.03295 0.1815
Residual 0.06808 0.2609
Number of obs:22, groups: colony, 11
Fixed effects:
Estimate Std. Error dft value Pr(>|t|)
(Intercept) 4.14051 0.1374321.97600 30.129 2e-16***
treat4 0.03031 0.16451 9.72500 0.184 0.8576
treat9 0.21513 0.16889 8.14900 1.274 0.2379
treat10 0.47353 0.1739515.25400 2.722 0.0156*
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
Correlation of Fixed Effects:
(Intr) treat4 treat9
treat4 -0.660
treat9 -0.615 0.491
treat10 -0.692 0.489 0.490
#Number of tandem runs
repntr0 <-lmer(log10(ntr)~(1|colony), data=repulsion, REML =FALSE)
repntr1 <-lmer(log10(ntr)~ treat +(1|colony), data=repulsion, REML =FALSE)
anova(repntr0, repntr1)
------
Data: repulsion
Models:
object: log10(ntr)~(1| colony)
..1:log10(ntr)~ treat +(1| colony)
Df AIC BIC logLikdeviance Chisq Chi DfPr(>Chisq)
object 3 9.124612.531-1.56229 3.12458
..1 611.538718.352 0.23065-0.461293.5859 3 0.3098
shapiro.test(resid(repntr1))
------
Shapiro-Wilk normality test
data: resid(repntr1)
W =0.9808, p-value =0.9199
#Quorum
repquorum0 <-lmer(log10(quorum)~(1|colony), data=repulsion, REML =FALSE)
repquorum1 <-lmer(log10(quorum)~ treat +(1|colony), data=repulsion, REML =FALSE)
anova(repquorum0, repquorum1)
------
Data: repulsion
Models:
object: log10(quorum)~(1| colony)
..1:log10(quorum)~ treat +(1| colony)
Df AIC BIC logLikdeviance Chisq Chi DfPr(>Chisq)
object 34.5327 7.80580.73365 -1.4673
..1 67.053413.59962.47331 -4.94663.4793 3 0.3235
shapiro.test(resid(repquorum1))
------
Shapiro-Wilk normality test
data: resid(repquorum1)
W =0.9734, p-value =0.7893
d)For Target nest Attraction:
The residuals of all the models are normally distributed as tested with Shapiro-Wilk normality test (p = 0.129, 0.1368, 0.8968, 0.7564, 0.4784, 0.1077, 0.6016 respectively for total emigration time, time of first encounter, time of first tandem run, time between first tandem run and first carry and time between first and last carry, number of tandem runs and quorumrespectively; R output below), indicating a good model fit.
R code and output:
#ATTRACTION -> the target nest quality increases 1 - Poor; 2 - Satisfactory; 3 - Medium; 4 - Good and the current nest is always Poor(light)
###########################################################
###########################################################
###########################################################
###########################################################
attraction<-read.delim("attraction.txt", header = T)
colnames(attraction)<-c("emigration", "treat", "colony", "size", "etime", "behaviour", "fe","ftr", "fc", "lc", "ntr", "quorum")
attraction$treat<-factor(attraction$treat, levels=c("1","2","3","4"), ordered=TRUE)
attraction$colony<-factor(attraction$colony, levels=c("1","2","3","4","5","6","7","8","9","10", "11", "12"), ordered=FALSE)
attraction$size<-as.numeric(attraction$size)
attraction$etime<-as.numeric(attraction$etime)
attraction$behaviour<-factor(attraction$behaviour, levels=c("e", "on", "split", "ne"), ordered=FALSE)
attraction$fe<-as.numeric(attraction$fe)# time first ant encounters the nest
attraction$ftr<-as.numeric(attraction$ftr)# first tandem run
attraction$fc<-as.numeric(attraction$fc)# first carry
attraction$lc<-as.numeric(attraction$lc)# last carry
attraction$ntr<-as.numeric(attraction$ntr)# number of tandem runs
attraction$quorum<-as.numeric(attraction$quorum)# quorum
windows(10,4)
par(mfrow=c(1,3))
hist(attraction$etime, col='red')
hist(log10(attraction$etime), col='red')#####
hist(sqrt(attraction$etime), col='red')
boxplot(log10(etime)~ treat, data= attraction, varwidth=TRUE, col='red', outcol='red', names=c('Poor','Satisfactory','Medium','Good' ), main ='Total emigration times from Poor current nest', ylab='Log (Time)', xlab='Target nest qualities')
atmod0 <-lmer(log10(etime)~(1|colony), data= attraction, REML =FALSE)
atmod1 <-lmer(log10(etime)~ treat +(1|colony), data= attraction, REML =FALSE)
summary(atmod1)
------
Linear mixed model fit by maximum likelihood t-tests use Satterthwaite approximations to degrees of freedom [
merModLmerTest]
Formula:log10(etime)~ treat +(1| colony)
Data: attraction
AIC BIC logLikdeviancedf.resid
-4.6 0.4 8.3 -16.6 11
Scaled residuals:
Min 1Q Median 3Q Max
-1.40957-0.58250-0.08642 0.27705 2.29962
Random effects:
Groups Name Variance Std.Dev.
colony (Intercept)0.00000 0.0000
Residual 0.02205 0.1485
Number of obs:17, groups: colony, 11
Fixed effects:
Estimate Std. Error dft value Pr(>|t|)
(Intercept) 2.24238 0.0464617.00000 48.263 2e-16***
treat.L -0.30759 0.1096117.00000 -2.806 0.0121*
treat.Q -0.04756 0.0929217.00000 -0.512 0.6153
treat.C -0.02875 0.0724917.00000 -0.397 0.6966
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
Correlation of Fixed Effects:
(Intr)tret.Ltret.Q
treat.L-0.605
treat.Q 0.489-0.605
treat.C-0.305 0.319-0.305
anova(atmod0, atmod1)
------
Data: attraction
Models:
object: log10(etime)~(1| colony)
..1:log10(etime)~ treat +(1| colony)
Df AIC BIC logLikdeviance Chisq Chi DfPr(>Chisq)
object 3 0.45802.957642.7710 -5.542
..1 6-4.60450.394758.3023 -16.60511.062 3 0.01139*
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
##residuals
shapiro.test(resid(atmod1))
------
Shapiro-Wilk normality test
data: resid(atmod1)
W =0.9165, p-value =0.129
##Contrasts
(contrasts(attraction$treat)<-contr.treatment(levels(attraction$treat),base=4))
atmod1.4 <-lmer(log10(etime)~ treat +(1|colony), data= attraction, REML =FALSE)
summary(atmod1.4)
------
Linear mixed model fit by maximum likelihood
t-tests use Satterthwaite approximations to degrees of freedom ['merModLmerTest']
Formula:log10(etime)~ treat +(1| colony)
Data: attraction
AIC BIC logLikdeviancedf.resid
-4.6 0.4 8.3 -16.6 11
Scaled residuals:
Min 1Q Median 3Q Max
-1.40957-0.58250-0.08642 0.27705 2.29962
Random effects:
Groups Name Variance Std.Dev.
colony (Intercept)0.00000 0.0000
Residual 0.02205 0.1485
Number of obs:17, groups: colony, 11
Fixed effects:
Estimate Std. Error dft value Pr(>|t|)
(Intercept) 2.00583 0.0606217.00000 33.090 2e-16***
treat1 0.42554 0.1603817.00000 2.653 0.01672*
treat2 0.30983 0.0899117.00000 3.446 0.00308**
treat3 0.21084 0.0899117.00000 2.345 0.03142*
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
Correlation of Fixed Effects:
(Intr) treat1 treat2
treat1 -0.378
treat2 -0.674 0.255
treat3 -0.674 0.255 0.455
(contrasts(attraction$treat)<- contr.treatment(levels(attraction$treat),base=3))
atmod1.3 <-lmer(log10(etime)~ treat +(1|colony), data= attraction, REML =FALSE)
summary(atmod1.3)
------
Linear mixed model fit by maximum likelihood
t-tests use Satterthwaite approximations to degrees of freedom ['merModLmerTest']
Formula:log10(etime)~ treat +(1| colony)
Data: attraction
AIC BIC logLikdeviancedf.resid
-4.6 0.4 8.3 -16.6 11
Scaled residuals:
Min 1Q Median 3Q Max
-1.40957-0.58250-0.08642 0.27705 2.29962
Random effects:
Groups Name Variance Std.Dev.
colony (Intercept)0.00000 0.0000
Residual 0.02205 0.1485
Number of obs:17, groups: colony, 11
Fixed effects:
Estimate Std. Error dft value Pr(>|t|)
(Intercept) 2.21666 0.0664017.00000 33.382 2e-16***
treat1 0.21470 0.1626517.00000 1.320 0.2043
treat2 0.09899 0.0939117.00000 1.054 0.3066
treat4 -0.21084 0.0899117.00000 -2.345 0.0314*
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
Correlation of Fixed Effects:
(Intr) treat1 treat2
treat1 -0.408
treat2 -0.707 0.289
treat4 -0.739 0.302 0.522
(contrasts(attraction$treat)<-contr.treatment(levels(attraction$treat),base=2))
atmod1.2 <-lmer(log10(etime)~ treat +(1|colony), data= attraction, REML =FALSE)
summary(atmod1.2)
------
Linear mixed model fit by maximum likelihood
t-tests use Satterthwaite approximations to degrees of freedom ['merModLmerTest']
Formula:log10(etime)~ treat +(1| colony)
Data: attraction
AIC BIC logLikdeviancedf.resid
-4.6 0.4 8.3 -16.6 11
Scaled residuals:
Min 1Q Median 3Q Max
-1.40957-0.58250-0.08642 0.27705 2.29962
Random effects:
Groups Name Variance Std.Dev.
colony (Intercept)0.00000 0.0000
Residual 0.02205 0.1485
Number of obs:17, groups: colony, 11
Fixed effects:
Estimate Std. Error dft value Pr(>|t|)
(Intercept) 2.31565 0.0664017.00000 34.873 2e-16***
treat1 0.11571 0.1626517.00000 0.711 0.48649
treat3 -0.09899 0.0939117.00000 -1.054 0.30656
treat4 -0.30983 0.0899117.00000 -3.446 0.00308**
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’1
Correlation of Fixed Effects:
(Intr) treat1 treat3
treat1 -0.408
treat3 -0.707 0.289
treat4 -0.739 0.302 0.522
##dynamics 1
##Models
#first encounter
atfe0 <-lmer(log10(fe)~(1|colony), data= attraction, REML =FALSE)
atfe1 <-lmer(log10(fe)~ treat +(1|colony), data= attraction, REML =FALSE)
anova(atfe0, atfe1)
------
Data: attraction
Models:
object: log10(fe)~(1| colony)
..1:log10(fe)~ treat +(1| colony)
Df AIC BIC logLikdeviance Chisq Chi DfPr(>Chisq)
object 323.87627.41-8.9380 17.876
..1 625.09232.16-6.5459 13.0924.7842 3 0.1883
shapiro.test(resid(atfe1))
------
Shapiro-Wilk normality test
data: resid(atfe1)
W =0.9366, p-value =0.1368
#first tandem run
atftr0 <-lmer(log10(ftr)~(1|colony), data= attraction, REML =FALSE)
atftr1 <-lmer(log10(ftr)~ treat +(1|colony), data= attraction, REML =FALSE)