Building integral projection models with nonindependent vital rates

Abstract

Population dynamics are functions of several demographic processes including survival, reproduction, somatic growth, and maturation. The rates or probabilities for these processes can vary by time, by location, and by individual. These processes can co‐vary and interact to varying degrees, e.g., an animal can only reproduce when it is in a particular maturation state. Population dynamics models that treat the processes as independent may yield somewhat biased or imprecise parameter estimates, as well as predictions of population abundances or densities. However, commonly used integral projection models (IPMs) typically assume independence across these demographic processes. We examine several approaches for modelling between process dependence in IPMs and include cases where the processes co‐vary as a function of time (temporal variation), co‐vary within each individual (individual heterogeneity), and combinations of these (temporal variation and individual heterogeneity). We compare our methods to conventional IPMs, which treat vital rates independent, using simulations and a case study of Soay sheep (Ovis aries). In particular, our results indicate that correlation between vital rates can moderately affect variability of some population‐level statistics. Therefore, including such dependent structures is generally advisable when fitting IPMs to ascertain whether or not such between vital rate dependencies exist, which in turn can have subsequent impact on population management or life‐history evolution.

Evaluating the importance of individual heterogeneity in reproduction to Weddell seal population dynamics using integral projection models

“…Results of the few empirical studies on the topic corroborate predictions for the asymptotic population growth rate (Coulson, 2012;Fung et al, 2022;Lindberg et al, 2013;. Including unobserved individual heterogeneity in recruitment and survival rates in population models for black brant Branta bernicla nigricans resulted in large changes to reproductive values and smaller changes to population growth rate when compared with results from modelling that ignored individual heterogeneity (Lindberg et al, 2013).…”

“…Theoretical investigations suggest that unobserved individual heterogeneity in vital rates can influence the net reproductive rate, generation time, demographic, and environmental variance but that the asymptotic growth rate typically is less sensitive to such heterogeneity unless heritability is strong (Vindenes & Langangen, 2015). Results of the few empirical studies on the topic corroborate predictions for the asymptotic population growth rate (Coulson, 2012; Fung et al, 2022; Lindberg et al, 2013; Plard, Gaillard, Coulson, Delorme, et al, 2015). Including unobserved individual heterogeneity in recruitment and survival rates in population models for black brant Branta bernicla nigricans resulted in large changes to reproductive values and smaller changes to population growth rate when compared with results from modelling that ignored individual heterogeneity (Lindberg et al, 2013).…”

“…The covariation between the individual random effect of survival and reproduction was modelled given existing evidence for a correlation between the two parameters in our study population (Paterson et al, 2018). Additionally, there is some evidence to suggest ignoring the correlation of random effects has little effect on estimates of population growth but may bias elasticities (Fung et al, 2022). Point estimates were used to parameterize pre-breeder survival probability.…”

Integrated integral population models

“…However, its structure can be easily modified to take into account intrinsic and extrinsic factors that may affect a population’s dynamics as well as methodological issues that may have an impact on the estimation of individual-or population-level parameters. Intrinsic factors include all potential variables, inherent to the individual (e.g., size, sex, and age), that may produce fitness variation among individuals (Riecke et al, 2019; Ellner et al, 2016; Fung et al, 2022); we can even include the individual as a random effect to address dependencies among databases sharing the same individuals (Ellner et al, 2016; Fung et al, 2022). Extrinsic factors include both abiotic and biotic environmental variables (e.g., climate, intraspecific interactions) that may also affect an individual’s fitness (Ellner et al, 2016; Plard et al, 2019a; 2019b).…”

“…The history of the study of population dynamics has been the history of the development of increasingly complex models (Benton et al, 2006; Metcalf & Pavard 2006; Evans, 2012; Riecke et al, 2019). These models aim to make a more detailed description of the structure of a population and the drivers that determine its dynamics (Ellner & Rees 2006; Schaub & Abadi, 2011; Ellner et al 2016; Plard et al, 2019a; 2019b) This complexity goes hand in hand with a need for higher maths literacy among demographers, and computational power (Besbeas & Morgan, 2019; Plard et al, 2019b; Fung et al, 2022; Frost et al, 2023). In recent years, data integration has allowed us to obtain better descriptions and forecasting of a population’s behaviour by incorporating data at both the individual and population levels (Evans et al, 2016; Zipkin & Saunders, 2018; Zipkin et al, 2019; Frost et al, 2023).…”