Partitioning variance in population growth for models with environmental and demographic stochasticity

Abstract

How demographic factors lead to variation or change in growth rates can be investigated using life table response experiments (LTRE) based on structured population models. Traditionally, LTREs focused on decomposing the asymptotic growth rate, but more recently decompositions of annual ‘realized’ growth rates using ‘transient’ LTREs have gained in popularity. Transient LTREs have been used particularly to understand how variation in vital rates translate into variation in growth for populations under long‐term study. For these, complete population models may be constructed to investigate how temporal variation in environmental drivers affect vital rates. Such investigations have usually come down to estimating covariate coefficients for the effects of environmental variables on vital rates, but formal ways of assessing how they lead to variation in growth rates have been lacking. We extend transient LTREs to further partition the contributions from vital rates into contributions from temporally varying factors that affect them. The decomposition allows one to compare the resultant effect on the growth rate of different environmental factors, as well as density dependence, which may each act via multiple vital rates. We also show how realized growth rates can be decomposed into separate components from environmental and demographic stochasticity. The latter is typically omitted in LTRE analyses. We illustrate these extensions with an integrated population model (IPM) for data from a 26 years study on northern wheatears (Oenanthe oenanthe), a migratory passerine bird breeding in an agricultural landscape. For this population, consisting of around 50–120 breeding pairs per year, we partition variation in realized growth rates into environmental contributions from temperature, rainfall, population density and unexplained random variation via multiple vital rates, and from demographic stochasticity. The case study suggests that variation in first year survival via the unexplained random component, and adult survival via temperature are two main factors behind environmental variation in growth rates. More than half of the variation in growth rates is suggested to come from demographic stochasticity, demonstrating the importance of this factor for populations of moderate size.

Nonlinear life table response experiment analysis: Decomposing nonlinear and nonadditive population growth responses to changes in environmental drivers

“…For example, in the case of stochastic fluctuations in drivers, nonlinear growth responses can alter both the mean and the variance of annual population growth rates (Maldonado‐Chaparro et al., 2018), which in turn can alter the long‐term stochastic population growth rate (Tuljapurkar, 1990). While we have focused on the response of the asymptotic, deterministic population growth rate to driver changes, an interesting question is whether the underlying components of nonlinearity we have assessed here make similar contributions to nonlinearity of the long‐term or transient population growth rate in a stochastic environment, the latter of which has been explored in a few recent LTRE studies (Knape et al., 2023; Koons et al., 2016; Maldonado‐Chaparro et al., 2018). Nonlinear vital rate responses are particularly relevant in stochastic environments because driver variation can alter both the variance and arithmetic mean of the vital rates, and the latter effect could in some situations increase long‐term stochastic growth (Boyce et al., 2006; Koons et al., 2009; Le Coeur et al., 2022).…”

Dynamics of a goshawk population across half a century is driven by the variation of first‐year survival

“…Some of the temporal variation in demographic rates, and hence their effect on population growth, is due to environmental variation (changes in demographic rates that are caused by environmental factors and are the same for all individuals), and some is due to demographic stochasticity. We calculated the difference between the actual estimated population size and the expected population size obtained in the absence of demographic stochasticity, from which the population growth rates resulting from environmental stochasticity alone and from demographic stochasticity alone were calculated (Knape et al., 2023 ). The contribution of environmental stochasticity was calculated from the latter.…”