Fast migration and emergent population dynamics

TL;DR

This paper investigates how rapid migration between patches affects overall population dynamics, revealing that the well-mixed assumption often does not replicate local patch behavior and depends on specific conditions.

Contribution

It provides a general condition under which a well-mixed population system mirrors the dynamics of individual patches, highlighting cases where emergent behaviors occur.

Findings

Well-mixed systems do not always replicate local patch dynamics.

A general condition determines when well-mixed dynamics match local patches.

Emergent population behaviors can arise from coupling, requiring case-by-case analysis.

Abstract

We consider population dynamics on a network of patches, each of which has a the same local dynamics, with different population scales (carrying capacities). It is reasonable to assume that if the patches are coupled by very fast migration the whole system will look like an individual patch with a large effective carrying capacity. This is called a "well-mixed" system. We show that, in general, it is not true that the well-mixed system has the same dynamics as each local patch. Different global dynamics can emerge from coupling, and usually must be figured out for each individual case. We give a general condition which must be satisfied for well-mixed systems to have the same dynamics as the constituent patches.