The simplest model of spatially distributed population with reasonable migration of organisms

TL;DR

This paper introduces a simple, discrete-time model of spatially distributed populations where organisms migrate intelligently to maximize net reproduction, considering migration costs and global information.

Contribution

It presents a novel, minimalistic model of smart migration in a two-station population, highlighting how organisms optimize movement based on reproductive gains and costs.

Findings

Migration maximizes net reproduction under cost constraints

Model demonstrates properties of strategic spatial redistribution

Discrete-time approach captures key migration behaviors

Abstract

The simplest model of a smart spatial redistribution of individuals is proposed. A single-species population is considered, to be composed of two discrete subpopulations inhabiting two stations; migration is a transfer between them. The migration is not random and yields the maximization of net reproduction, with respect to the transaction costs. The organisms are supposed to be globally informed. Discrete time model is studied, since it shows all the features of a smart migrations, while the continuous time case brings no new knowledge but the technical problems. Some properties of the model are studied and discussed.