(D) Effects of population dynamics on the mean age of reproduction
To explore how population dynamics affected the mean age of parents of recruits each year in each population (Tjk ), we utilized annual data on reproduction and survival for all adult individuals i present within the studied time periods (Table S1). From this data we estimated the weighted mean age of the parents reproducing in year j and population k as:
\(T_{\text{jk}}=\frac{\sum_{i=1}^{n_{\text{jk}}}\text{hF}^{(ijk)}}{\sum_{i=1}^{n_{\text{jk}}}F^{(ijk)}}\), (eq. S4)
where h is the age and F is the number of recruiting offspring produced by individual i in population j in yeark . The sum is taken for all individuals breeding in year jin population k (\(n_{\text{jk}}\)). We estimated the mean age at reproduction in a population each year for males and females separately. We then fitted a mixed-effect model that had as response variable the mean age of reproducing individuals in a given year in a given population (Tjk ), and as fixed effects sex and the mean and annual deviations of population size to distinguish between effects of spatial versus temporal fluctuations in population size on the mean age at reproduction of a population.
To further examine how Tjk was related to the ecological factors determining population growth, we fitted another mixed-effect model where the mean age at reproduction (Tjk ) was fitted as a response variable and the mean fitness of the population in each year and sex as fixed effects. We estimated the fitness of individual i in year j as survival plus half the number of recruits to the next year, because, in the absence of dispersal, this metric of fitness accounts for sexual reproduction and directly connects to local population dynamics (Sæther & Engen 2015):
\(w_{\text{ij}}=S_{\text{ij}}+\ \frac{1}{2}F_{\text{ij}}\) . (eq. S5)
The average fitness of a population each year was thus estimated as the mean fitness of all individuals breeding in a year in a population:
\({\overset{\overline{}}{w}}_{\text{jk}}=\frac{1}{N_{\text{jk}}}\sum_{i=1}^{n_{\text{jk}}}w_{\text{hij}}\), (eq. S6)
where the sum is taken for all individuals breeding in year j in population k . Here, n is the number of adults breeding in year j in population k . Importantly,\({\overset{\overline{}}{w}}_{\text{jk}}\) will determine the changes in population size across years that are not caused by immigration and emigration, but it could be affected by recapture probabilities. The mean fitness in the population directly connects to the expected population growth and should reflect current levels of competition in the population (Sæther & Engen 2015), either because of variation in environmental conditions and/or due to variation in population density relative to the amount of resources. To control for the effects of age structure in determining the mean age at reproduction, we also fitted the two above mentioned models including the mean age of all the adults breeding in the population as an additional fixed effect.
We modelled the mean age of the successfully reproducing parents\(T_{\text{jk}}\ \)in year \(j\) in population \(k\) as
\(T_{\text{jk}}=c+\beta_{1}S_{i}+\ \beta_{2}{\overset{\overline{}}{n}}_{k}+\beta_{3}(n_{\text{jk}}-{\overset{\overline{}}{n}}_{k})\ +Y_{j}+P_{k}+e_{\text{jk}}\)(eq. S7)
where \(c\) is the average age of the successfully reproducing parents in the meta-population. \(\beta_{1}\) is the coefficient reflecting average sex differences in the mean age at reproduction (\(S_{i}\)=0 for females; \(S_{i}\)=1for males). This model had also as fixed effect\((\beta_{2}\)) for the mean population size (\({\overset{\overline{}}{n}}_{k}\)) of population (\(k\)) and the effect (\(\beta_{3}\)) of yearly deviations from the mean population size in number of individuals\((n_{\text{jk}}-{\overset{\overline{}}{n}}_{k})\). 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 the mean age of the successfully reproducing parents (van de Pol & Wright 2009). Here, year-specific values \((Y_{j})\), population-specific values (\(P_{k}\)), and within-population residual deviations \(e_{\text{jk}}\), were all assumed to come from separate normal distributions for each life-history trait with variances \(V_{Y}\), \(V_{P}\) and \(V_{e_{g}}\). We also fitted a model with the same random effect structure, but the fixed effect structure differed in that instead of the effect of the average population size (\(\beta_{2}\)) and the yearly deviations from the average population size (\(\beta_{3})\), we fitted the effect (\(\beta_{4}\)) of the mean fitness\({\overset{\overline{}}{w}}_{\text{jk}}\) of population \(k\) in year\(j\) as another fixed effect. To further corroborate the results we included the mean age of all in the individuals we inferred to be present in each population in each year to account for potential effects of age structure (\(\beta_{5})\) in the results in both of the models mentioned in this section (D).