R code for Demographic consequences of changing environmental periodicity

We used the demographic data of each species to model periodic differences in vital rates for each life-cycle stage using generalized linear models and mixed models (GLMs for the deterministic vital rates in dewy pines and GLMMs for all other vital rates). More specifically, we tested for the effect of season on marmot and meerkat vital rates and of post-fire habitat states (time since fire, TSF) on dewy pine vital rates. For all three species, we estimated stage-specific survival and probability of transition to another stage using a binomial distribution, and reproductive output using a Poisson distribution. In addition, we estimated meerkat helper emigration probability and dewy-pine flowering probability using a binomial distribution. In addition to fixed effects, we incorporated year random effects in all appropriate models to model year-specific differences among season-specific average vital-rates (for marmots and meerkats) or among vital-rate averages (for dewy pines). For the meerkats and dewy pines, we also incorporated the fixed effect of density on vital rates. For each modeled vital rate, we first selected the best random-effect structure where appropriate (i.e., testing whether a random effect on the average vital rate and the slope between seasons outperformed a random effect on the average vital rate only). We then selected the best fixed-effect variables using the Akaike Information Criterion corrected for small sample size (AICc). When the difference in AICc values was not significant (dAICc<2), we picked the model with fewer parameters or the most biologically relevant. For models using a Poisson distribution, we tested for over- and under-dispersion in the best model and fitted over- and under-dispersed models with a quasi-Poisson distribution when necessary.