(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).