INDIVIDUAL VARIATION AND ENVIRONMENTAL STOCHASTICITY: IMPLICATIONS FOR MATRIX MODEL PREDICTIONS

Abstract

Populations are characterized by variability among individuals, a result of both intrinsic differences among individuals and environmental effects on individual performance. Despite the ubiquity of individual variation, its implications for population model choice are not fully understood. Population models that use state variables representing individual features such as age or size assume that these state variables can predict the population trajectory. However, state variables are often chosen based on convenience or necessity; only rarely are they tested for importance and accuracy when individuals vary. We examined whether matrix projection models, a common choice in population modeling, provide accurate predictions when individuals vary in a population. With both density-dependent and density-independent formulations, we tested whether matrix projection models that used size as a state variable captured the dynamics of populations projected with an individual-based simulation (or i-state configuration model). We varied the initial size distribution of individuals, the degree to which individual growth was size dependent, the tendency for positive correlations in growth through time, and the amount of stochasticity in growth, and we asked what conditions affect the accuracy of matrix models. Stochasticity alone did not compromise the predictions of matrix models; rather, only populations with individual variation generated by strong size-dependent growth and growth correlations were poorly described by matrix models. Otherwise, matrix models captured the trajectories of populations with a fair degree of accuracy. Overall, our results provide guidance as to when and how individual variation must be included in population projections, and when a simple matrix model framework is inadequate. Corresponding Editor: A. R. Solow

Keywords

Affiliated Institutions

• University of Chicago US
• Education Northwest US

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