Statistical modelling of annual variation for inference on stochastic population dynamics using Integral Projection Models

Temporal fluctuations in vital rates such as survival, growth or reproduction alter long-term population dynamics and can change the dynamics from invasion and population persistence to extinction. Projections of population dynamics made in the absence of such fluctuations may consequently be misleading. However, data for estimation of yearly fluctuations in demographic parameters are often limited. Accordingly, the current diverse range of statistical and demographic modelling strategies used for stochastic population modelling may influence predictions. We used simulations to explore the effects of different methods of parameter estimation on projections of population dynamics obtained using stochastic integral projection models (IPMs). The simulations were built from data on a monocarpic thistle, Carlina vulgaris, and an ungulate, Soay sheep, Ovis aries; these populations are subject to yearly fluctuation in vital rates facilitating the exploration of the effects of different methods of model construction on the properties of stochastic IPMs. Specifically, we looked at effects on the stochastic growth rate, log λ_s, and the mean and variance in the one-step population growth rate (N_t+1/N_t). Our analyses showed that none of the tested approaches resulted in large biases in the estimation of log λ_s. However, when realistic study durations (e.g. 12 years) were used for statistical modelling, the confidence intervals around the λ_s estimates remained large. Estimation of the variance in one-step population growth rates, on the other hand, was strongly sensitive to the method employed, and the overestimation and underestimation of the variance were also influenced by the life history of the organism. Our findings highlight the need to consider the influences of statistical and demographic modelling approaches when population dynamics have significant temporal stochasticity, as in population viability analyses and evolutionary predictions of bet hedging.