Individual Size Variation and Population Stability in a Seasonal Environment: A Discrete-Time Model and Its Calibration Using Grasshoppers

Abstract

Much recent literature is concerned with how variation among individuals (e.g., variability in their traits and fates) translates into higher-level (i.e., population and community) dynamics. Although several theoretical frameworks have been devised to deal with the effects of individual variation on population dynamics, there are very few reports of empirically based estimates of the sign and magnitude of these effects. Here we describe an analytical model for sizedependent, seasonal life cycles and evaluate the effect of individual size variation on population dynamics and stability. We demonstrate that the effect of size variation on the population net reproductive rate varies in both magnitude and sign, depending on season length. We calibrate our model with field data on size-and density-dependent growth and survival of the generalist grasshopper Melanoplus femurrubrum. Under deterministic dynamics (fixed season length), size variation impairs population stability, given naturally occurring densities. However, in the stochastic case, where season length exhibits yearly fluctuations, size variation reduces the variance in population growth rates, thus enhancing stability. This occurs because the effect of size variation on net reproductive rate is dependent on season length. We discuss several limitations of the current model and outline possible routes for future model development.Keywords: body size, individual variation, population stability, seasonal environment, univoltine lifecycle. Ecological entities are organized hierarchically into different levels of organization, such as the individual, the population, and the community (MacMahon et al. 1987;Allen and Hoekstra 1992;Pickett et al. 1994). The way in which these different organizational levels combine to influence the dynamics of natural systems remains a fundamental research topic in ecology (Lomnicki 1988;Nisbet et al. 1989; Abrams 1995;Levin et al. 1997;. Such research is motivated by the need to understand the level of mechanistic biological detail that must be included in ecological theory as well as how much can be safely abstracted while still achieving biologically faithful and quantitatively accurate descriptions of population and community dynamics.In the past 30 years, ecologists have become increasingly interested in linking individual phenotypic variation (in behavior, morphology, physiology, and life history) to population and community dynamics (e.g., Lomnicki 1978;Metz and Diekmann 1986;Begon and Wall 1987;Ebenman and Persson 1988;Nisbet et al. 1989;Bjørnstad and Hansen 1994;Uchmanski 1999;Schmitz 2000;de Roos et al. 2003). Specifically, many theoretical studies have demonstrated how age, stage, and size structure; cohort effects; and other forms of individual variation (e.g., in developmental and growth rates or in competitive ability) have important consequences for population dynamics, stability, and persistence (e.g., Bellows 1986aBellows , 1986bLomnicki 1988;Bjørnstad and Hansen 1994;de Roos 1997;Uchmanski 2000;Kendall ...

Variability in life‐history and ecological traits is a buffer against extinction in mammals

“…; González‐Suárez et al . ), although whether greater trait variability increases or reduces risk of extinction appears to be model and context dependent (Filin & Ovadia ).…”

A diffusion‐based approach to stochastic individual growth and energy budget, with consequences to life‐history optimization and population dynamics

“…This stabilizing effect is different from the one attributed to individual variation in demographic traits [e.g. (size‐related) variation in survival and fecundity; Bjørnstad & Hansen, 1994; Grimm & Uchmanski, 2002; Filin & Ovadia, 2007], as it occurs even in the absence of such variation. However, a similarity still exists in the sense that both an initial structure in the population (which can become exaggerated with time) and randomly generated variability in an initially homogeneous population, increase the within‐generation variability in individual fate, but decrease the between‐generation variability in the average fate (see also Uchmanski, 2000).…”

Consequences of individual size variation for survival of an insect herbivore: an analytical model and experimental field testing using the red-legged grasshopper

“…They showed that initial body-size variation can enhance population stability and persistence, i.e., cause longer extinction times in comparison to homogenous populations. A recent analytical model by Filin & Ovadia (2007) explored the effect of individual size variation on population dynamics and stability in a seasonal environment. The model shows that the effect of size variation on the population net reproductive rate varies in both magnitude and sign, depending on season length.…”

“…In the following, we incorporate variation in both mortality and individual size, in a similar manner to Bjørnstad & Hansen (1994), i.e., by using a Taylor expansion. However, we focus here on the effect of variation on within-season survival, rather than on among-season population dynamics and stability (see also Filin & Ovadia 2007). , for the effect of a) initial body size and b) body size variation on herbivore survival.…”