Integral projection models for stage-structured populations with individual heterogeneity
Stage-structured population models are applied in many contexts. A common approximation is that stage transitions are a Markov process, where there is a simple probability of changing stage given the current stage. This assumption leads to the common stage-structured matrix models. In this talk I will discuss models that generalize from this simple assumption by allowing individual heterogeneity using an integral projection model framework.
I will make three main points. First, I will show how stage-structured models with individual heterogeneity in development can be formulated in the integral projection model framework. A general class of models will be given in which there is a distribution of the time spent in each stage, and these distributions may be correlated. The models also include stage-specific mortality and fecundity. Placing them in the IPM framework is useful because a large amount of theoretical underpinnings automatically apply and the models can be readily combined with size-and-stage models. Second, I will show how the basic goals of linear demographic theory, namely long-term population growth rate, sensitivities and elasticities, can be calculated using Monte Carlo integration of the Euler-Lotka equation. In practical terms, this allows use of simulations of individual life trajectories rather than setting up a large matrix. For problems with many dimensions of individual heterogeneity (many stages), this can be advantageous in simplicity and efficiency. Finally, I will show how individual heterogeneity and correlations among stage durations within individuals can strongly impact life history evolution using two-stage models with standard types of tradeoffs among growth, reproduction and survival. This contrasts with the common use of stage-structured matrix models for developing life history theory, which do not allow realistic treatment of stage durations or correlations.