The Importance of Being Discrete (and Spatial)

R Durrett, S Levin

Theoretical population biology, Volume 46, Issue 3, December 1994, Pages 363–394

DOI http://dx.doi.org/10.1006/tpbi.1994.1032

Used by the Quanticol project

The Importance of Being Discrete(and Spatial): This paper compares four approaches to the modelling of spatially distributed systems. Mean-field approach(no spatial representation, individuals treated homogeneously), Reaction-diffusion approach(extend mean-field approach by adding reaction-diffusion factor), Patch models(group individuals to patches, patches have no difference, and can interact with all the rest patches stochastically), Interacting particle system(subdivide space into a grid of cells, individuals in a cell can only interact with their neighbours).

Case studies: Case 1: one species enhances the presence of the other -> all four approaches agree. Case 2: two species compete with a single resource-> the models with spatial representations disagree with the ones without spatial representation. Case 3: one species always do better than the other, but if the other dies out, it will also go extinction-> the first two approaches show that both the species die out, however the latter two approaches show that they can coexist.