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.