Functional Ecology Author Guidelines s1

Intra individual variability in fecal cortisol metabolites varies with lifetime

exploration and reproductive life history in eastern chipmunks (Tamias striatus)

Behavioural Ecology and Sociobiology

P.-O. Montiglio* a, D. Garant b, F. Pelletier c, D. Réale a a Chaire de recherche du Canada en écologie comportementale, Département des Sciences

Biologiques, Université du Québec à Montréal, CP 8888 succursale centre- ville,

Montréal (Qc). H3C 3P8, Canada. b Département de biologie, Faculté des sciences, Université de Sherbrooke, 2500 boul. de

l'Université, Sherbrooke (Qc), J1K 2R1, Canada. c Chaire de recherche du Canada en démographie évolutive et conservation, Département

de biologie, Faculté des sciences, Université de Sherbrooke, 2500 boul. de l'Université,

Sherbrooke (Qc), J1K 2R1, Canada.

* Corresponding author: [email protected]

1 Supplementary material C

Example of code used to fit the model analysing female cortisol level. The code used the R package nlme (Pinheiro and Bates 2000) and R 2.14.1 (R Development Core Team, 2013). Code is presented in black, followed by an explanation of its meaning (# signs and text in red). library(nlme) #package developped by Pinheiro and Bates (2000). Additional information on the general approach to estimate variance covariates can be found in Pinheiro and Bates (2000), Mixed effects models in S and S-plus , Springer-Verlag, New York.

Full.Model = lme(log(cort+1) ~ (age + reproductive.status + exploration + litter.size)^2 # This specifies the fixed effects, all main effects and their two ways interactions. Fixed effects are estimated before random effects by the model.

, random=list(~1|id, ~1|date) # random effects estimating between individual and day variation. It allows the model to compute the day by day cortisol level for each individual differently.

, weights = varComb(varExp(1,~ exploration), varExp(1,~litter.size), varExp(1,~litter.size*exploration)) # variance covariate estimating the relationship between an individual's residual variance and exploration, litter size and their interaction. This acheives the same thing as extracting the residuals from a model and conducting a regression on them, yet this model provides more robust results against un-balanced data and assumptions about data distribution.

, data=data) # the data are structured as a data frame with one row for each cortisol sample, and one column for each variable.

# The final model is obtained after simplifying the fixed effect structure by AIC.

Final.Model = lme(log(cort+1) ~ -1 + reproductive.status + exploration + age

, random=list(~1|id, ~1|date)

2 , weights = varComb(varExp(1,~exploration), varExp(1,~litter.size), varExp(1, ~ litter.size*exploration))

, data=data)

# Model with a similar fixed effect structure, but without an interaction between litter size and exploration as variance covariate.

Final.Model.without.interaction = lme(log(cort+1) ~ -1 + reproductive.status + exploration + age

, random=list(~1|id, ~1|date)

, weights = varComb(varExp(1,~exploration), varExp(1,~litter.size))

, data=data)

anova(Final.Model, Final.Model.without.interaction) # testing whether the interaction between litter size and exploration as a variance covariate is significant.