RESOLVING DISCREPANCIES BETWEEN DETERMINISTIC POPULATION-MODELS AND INDIVIDUAL-BASED SIMULATIONS

This work ties together two distinct modeling frameworks for populatio n dynamics: an individual-based simulation and a set of coupled integr odifferential equations involving population densities. The simulation model represents an idealized predator-prey system formulated at the scale of discrete individuals, explicitly incorporating their mutual i nteractions, whereas the population-level framework is a generalized v ersion of reaction-diffusion models that incorporate population densit ies coupled to one another by interaction rates. Here I use various co mbinations of long-range dispersal for both the offspring and adult st ages of both prey and predator species, providing a broad range oi spa tial and temporal dynamics, to compare and contrast the two model fram eworks. Taking the individual-based modeling results as given, two exa minations of the reaction-dispersal model are made: Linear stability a nalysis of the deterministic equations and direct numerical solution o f the model equations. I also modify the numerical solution in two way s to account for the stochastic nature of individual-based processes, which include independent, local perturbations in population density a nd a minimum population density within integration cells, below which the population is set to zero. These modifications introduce new param eters into the population-level model, which I adjust to reproduce the individual-based model results. The individual-based model is then mo dified to minimize the effects of stochasticity, producing a match of the predictions from the numerical integration of the population-level model without stochasticity.