Ecological Archives E094-050-A3
Marion Tafani, Aurelie Cohas, Christophe Bonenfant, Jean-Michel Gaillard, and Dominique Allainé. 2013. Decreasing litter size of marmots over time: a life history response to climate change? Ecology. 94:580–586. http://dx.doi.org/10.1890/12-0833.1
Appendix C. Complementary analyses of lagged effects.
We tested for the effect on litter size of each seasonal climatic variable of interest at year t-1 and t-2 before mating (see manuscript for detailed description of the environmental variables considered.
Methods
We fitted Generalized Estimating Equations (GEE) models including female identity as a grouping factor to account for repeated measurements of the same individuals and mother age as a three-level fixed factor (unknown, prime-age, and old) to account for age variation in litter size (Berger et al., in prep). We then modeled litter size variation in relation to time and environmental variables (estimates and SE). In all models including a de-trended variable, year was added to account for the trend (Grosbois et al. 2008). We then measured the relative effects of each variable in a model using a deviance analysis (ANODEV, Skalski et al. 1993). We used GLMM to estimate the log-likelihood of each model. ANODEV corresponds to a comparison between the covariate model, and both the constant (i.e., baseline model) and the time-dependent (i.e., including year as a discrete factor) models. The corresponding Fcst/co/t statistic tests the null hypothesis that the climatic covariate has no effect on litter size; while the r² of the ANODEV quantifies how much of the temporal variation in litter size is accounted for by each climatic model (Grosbois et al. 2008) (see r²dev in Table C1).
Results
Only one of ten relationships provided a p-value just below 0.05, which likely occurred simply by chance and has no obvious biological meaning (Table C1).
Table C1. Effect of climatic variables at t-1 and t-2 before mating (and litter emergence) on the annual litter size variation in the Alpine marmots of La Grande Sassière, France. “De-trended” variables are entered in the model with their trend, stated as “(year)”. Climatic effects were tested with an analysis of deviance (ANODEV, see text for details). F statistic of ANODEV (noted F) and its associated value (p(F)) test the climatic covariate effect on litter size.
Climatic variable |
Time lag |
Estimate |
SE |
F |
p(F) |
Time period |
Snow |
t-1 |
-0.018 |
0.022 |
0.56 |
0.46 |
90–11 |
Winter Temperature |
t-1 |
-0.005 |
0.024 |
0.03 |
0.86 |
90–11 |
Winter severity (PCA first axis) |
t-1 |
-0.007 |
0.022 |
0.07 |
0.78 |
90–11 |
April NDVI |
t-1 |
0.005 |
0.018 |
0.02 |
0.88 |
90–08 |
April Temperature |
t-1 |
0.025 |
0.034 |
0.77 |
0.39 |
90–11 |
Snow |
t-2 |
-0.007 |
0.030 |
0.08 |
0.78 |
91–11 |
Winter Temperature |
t-2 |
0.003 |
0.023 |
0.11 |
0.75 |
91–11 |
Winter severity (PCA first axis) |
t-2 |
0.014 |
0.027 |
1.00 |
0.33 |
91–11 |
April NDVI |
t-2 |
-0.051 |
0.022 |
5.05 |
0.04 |
91–08 |
April Temperature |
t-2 |
0.019 |
0.027 |
1.05 |
0.32 |
91–11 |
Literature Cited
Grosbois, V., O. Gimenez, J. M. Gaillard, R. Pradel, C. Barbraud, J. Clobert, A. P. Møller, and H. Weimerskirch. 2008. Assessing the impact of climate variation on survival in vertebrate populations. Biological Reviews 83:357–399.
Skalski, J. R., A. Hoffman, and S. G. Smith. 1993. Testing the significance of individual- and cohort-level covariates in animal survival studies. Pages 9–28 in J. D. Lebreton and P. M. North, editors. Marked individuals in the study of bird population. Birkaüser Verlag, Basel, Switzerland.