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, we utilized annual data on reproduction and survival for all adult individuals within the studied time periods (Table S1). From this data we estimated the weighted mean age of the parents reproducing in a year for each population. This was estimate as the mean age of the successfully reproducing parents weighted by the number of recruits they produced separately (see appendix S1 for formulas). We estimated the weighted mean age at reproduction in a population each year for males and females. We then fitted a mixed-effect model that had as response variable the weighted mean age of reproducing individuals in a given year in a given population 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 the weighted mean age at reproduction was related to the ecological factors determining population growth, we fitted another mixed-effect model where the mean age at reproduction was also 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 each individual in a given years as survival plus half the number of recruits contributed to the next year, because, in the absence of dispersal, this metric of fitness directly connects to local population dynamics of sexually reproducing species (Sæther & Engen 2015). Importantly, this measure of fitness will determine the changes in population size across years that are not caused by immigration and emigration. Importantly, the mean fitness in the population in a given year 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.