Demographic fluctuations in a population of anomalously diffusing individuals

TL;DR

This paper analytically investigates how death, reproduction, and social behaviors influence spatial clustering and fluctuations in populations of individuals exhibiting anomalous diffusion, modeled via CTRW, revealing limits where dynamics resemble Brownian motion or non-migration.

Contribution

It provides a comprehensive analytical framework for understanding demographic fluctuations in anomalously diffusing populations, incorporating social behaviors and trap-induced transport effects.

Findings

Growth rate of fluctuations is independent of Hurst exponent in both limits.

Social behaviors can suppress or enhance spatial clustering.

Dynamics can resemble Brownian motion or non-migration depending on social interactions.

Abstract

The phenomenon of spatial clustering induced by death and reproduction in a population of anomalously diffusing individuals is studied analytically. The possibility of social behaviors affecting the migration strategies has been taken into exam, in the case anomalous diffusion is produced by means of a continuous time random walk (CTRW). In the case of independently diffusing individuals, the dynamics appears to coincide with that of (dying and reproducing) Brownian walkers. In the strongly social case, the dynamics coincides with that of non-migrating individuals. In both limits, the growth rate of the fluctuations becomes independent of the Hurst exponent of the CTRW. The social behaviors that arise when transport in a population is induced by a spatial distribution of random traps, have been analyzed.