Self-Regulation in Infinite Populations with Fission-Death Dynamics

TL;DR

This paper models the evolution of an infinite population with fission and death dynamics, demonstrating self-regulation through competition and constructing the evolution of population states in a specific measure class.

Contribution

It introduces a mathematical framework for population evolution with fission and death, focusing on self-regulation via competition in an infinite population setting.

Findings

Constructed evolution of states in sub-Poissonian measures

Demonstrated self-regulation through competition

Provided a rigorous mathematical model for population dynamics

Abstract

The evolution of an infinite population of interacting point entities placed in $\mathbb{R}^d$ is studied. The elementary evolutionary acts are death of an entity with rate that includes a competition term and independent fission into two entities. The population states are probability measures on the corresponding configuration space and the result is the construction of the evolution of states in the class of sub-Poissonian measures, that corresponds to the lack of clusters in such states. This is considered as a self-regulation in the population due to competition.