Age and density dependent reproduction and survival
For the age- and density-dependent models, we utilized annual data on reproduction and survival for all individuals present within the studied time periods, regardless of whether they had produced a recruit or not (Table S1). In total, there were 5247 records of 2729 individuals (1325 females and 1361 males). We studied how annual recruit production and survival resulted in the observed means and (co)variance of individual life-histories by building age- and density-dependent reproduction and survival models.
We modelled annual survival and annual number of recruits of individuals using generalized linear mixed-effect models. Survival was modelled assuming a binomial error distribution and the annual number of recruits was modelled assuming an over dispersed Poisson error distribution. Both models had the same fixed and random effect structure, however the residual variance of the survival model was fixed to 1. We included as fixed effects, sex and age as a two-level categorical variable (0 = first year breeders and 1 = older individuals). We also fitted an interaction between sex and age, as we were expecting sex-specific patterns of age-dependent reproduction and survival (Stubberud et al. 2017). These models also had the mean population size and the annual deviations from the mean population size as fixed effects. This within-subject centering approach allowed us to model density regulation accounting for differences in the mean population size between populations, and allowed us to test for any spatial versus temporal effects of population size in recruitment and survival (van de Pol & Wright 2009). We fitted year, population and individual as random effects. We then proceeded to extend these models and fitted a multivariate mixed-effects model, where we estimated the covariance between yearly survival and recruit production at the individual and residual level (see Appendix S1C for model equations).