Abstract
The current extinction and climate change crises pressure us to predict population dynamics with ever‐greater accuracy. Although predictions rest on the well‐advanced theory of age‐structured populations, two key issues remain poorly explored. Specifically, how the age‐dependency in demographic rates and the year‐to‐year interactions between survival and fecundity affect stochastic population growth rates. We use inference, simulations and mathematical derivations to explore how environmental perturbations determine population growth rates for populations with different age‐specific demographic rates and when ages are reduced to stages. We find that stage‐ vs. age‐based models can produce markedly divergent stochastic population growth rates. The differences are most pronounced when there are survival‐fecundity‐trade‐offs, which reduce the variance in the population growth rate. Finally, the expected value and variance of the stochastic growth rates of populations with different age‐specific demographic rates can diverge to the extent that, while some populations may thrive, others will inevitably go extinct.
Highlights
During the last century, the species extinction rate has increased to more than 1000 times the background rate, and the number of threatened species continues to rise (Barnosky et al 2011; Ceballos et al 2015)
In order to explore our derivation on the full-age-dependent and the one-adultstage models, we ran a single simulation of 10 000 time steps for each of the 25 combinations of age-specific fecundity and survival, with which we confirmed that our decompositions were exact
We show that for any stochastic population model with transitions given by a Leslie matrix (Leslie 1945), the expected value of the yearly population growth rate is given by ke 1⁄4 E1⁄2kt 1⁄4 k~ þ Cwb þ Cwp for t ! 0; ð3Þ
Summary
The species extinction rate has increased to more than 1000 times the background rate, and the number of threatened species continues to rise (Barnosky et al 2011; Ceballos et al 2015). Climate change can influence extinction risk by increasing temporal variation in demographic rates such as survival and fecundity, which in turn reduces long-run population growth rates (Pearson et al 2014). Using some of these mortality profiles in combination with a range of age-specific fecundity trajectories, we employed stochastic simulations, theoretical decompositions of the expected value, ke, and variance, Vk, and approximations to the long-run stochastic population growth rate, re We used these simulations and decompositions to compare the dynamics of populations with different age-specific demographic rates, and to determine the performance of models with a reduced number of age classes, as commonly used in management and conservation studies. We determined the relationship between the age-specific trajectories, the magnitude of the environmental variation and the average time to extinction
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