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).