%0 Journal Article %1 wilson1998resolving %A Wilson, William G. %D 1998 %J The American Naturalist %K demographic_models individual_based_model population_model simulations %N 2 %P 116-134 %R 10.1086/286106 %T Resolving Discrepancies between Deterministic Population Models and Individual‐Based Simulations %U https://doi.org/10.1086/286106 %V 151 %X ABSTRACT This work ties together two distinct modeling frameworks for population dynamics: an individual‐based simulation and a set of coupled integrodifferential equations involving population densities. The simulation model represents an idealized predator‐prey system formulated at the scale of discrete individuals, explicitly incorporating their mutual interactions, whereas the population‐level framework is a generalized version of reaction‐diffusion models that incorporate population densities coupled to one another by interaction rates. Here I use various combinations of long‐range dispersal for both the offspring and adult stages of both prey and predator species, providing a broad range of spatial and temporal dynamics, to compare and contrast the two model frameworks. Taking the individual‐based modeling results as given, two examinations of the reaction‐dispersal model are made: linear stability analysis of the deterministic equations and direct numerical solution of the model equations. I also modify the numerical solution in two ways to account for the stochastic nature of individual‐based processes, which include independent, local perturbations in population density and a minimum population density within integration cells, below which the population is set to zero. These modifications introduce new parameters into the population‐level model, which I adjust to reproduce the individual‐based model results. The individual‐based model is then modified to minimize the effects of stochasticity, producing a match of the predictions from the numerical integration of the population‐level model without stochasticity.

@article{wilson1998resolving, abstract = { ABSTRACT This work ties together two distinct modeling frameworks for population dynamics: an individual‐based simulation and a set of coupled integrodifferential equations involving population densities. The simulation model represents an idealized predator‐prey system formulated at the scale of discrete individuals, explicitly incorporating their mutual interactions, whereas the population‐level framework is a generalized version of reaction‐diffusion models that incorporate population densities coupled to one another by interaction rates. Here I use various combinations of long‐range dispersal for both the offspring and adult stages of both prey and predator species, providing a broad range of spatial and temporal dynamics, to compare and contrast the two model frameworks. Taking the individual‐based modeling results as given, two examinations of the reaction‐dispersal model are made: linear stability analysis of the deterministic equations and direct numerical solution of the model equations. I also modify the numerical solution in two ways to account for the stochastic nature of individual‐based processes, which include independent, local perturbations in population density and a minimum population density within integration cells, below which the population is set to zero. These modifications introduce new parameters into the population‐level model, which I adjust to reproduce the individual‐based model results. The individual‐based model is then modified to minimize the effects of stochasticity, producing a match of the predictions from the numerical integration of the population‐level model without stochasticity. }, added-at = {2023-05-27T01:53:38.000+0200}, author = {Wilson, William G.}, biburl = {https://www.bibsonomy.org/bibtex/233aee520a405f167892f5ef58f87c433/peter.ralph}, doi = {10.1086/286106}, eprint = {https://doi.org/10.1086/286106}, interhash = {b7fcde2da2e1566163dd471ffc19e8f9}, intrahash = {33aee520a405f167892f5ef58f87c433}, journal = {The American Naturalist}, keywords = {demographic_models individual_based_model population_model simulations}, note = {PMID: 18811412}, number = 2, pages = {116-134}, timestamp = {2023-05-27T01:53:38.000+0200}, title = {Resolving Discrepancies between Deterministic Population Models and Individual‐Based Simulations}, url = {https://doi.org/10.1086/286106 }, volume = 151, year = 1998 }