Spinal study of a population model for colonial species with interactions and environmental noise

TL;DR

This paper develops a stochastic model for colonial species dynamics incorporating interactions and environmental noise, providing new analytical tools and simulation methods to understand resource distribution and population behavior.

Contribution

It introduces a novel structured branching process with a diffusion-based trait evolution, extending existing models with a $ ext{psi}$-spine construction and a new simulation approach.

Findings

The model captures the impact of environmental noise correlation on resource distribution.

The $ ext{psi}$-spine construction enables analytical and simulation advancements.

The simulation method shows improved efficiency for ecological population modeling.

Abstract

We introduce and study a stochastic model for the dynamics of colonial species, which reproduce through fission or fragmentation. The fission rate depends on the relative sizes of colonies in the population, and the growth rate of colonies is influenced by intrinsic and environmental stochasticities. Our setting thus captures the effect of an external noise, correlating the trait dynamics of all colonies. In particular, we study the effect of the strength of this correlation on the distribution of resources between colonies. We then extend this model to a large class of structured branching processes with interactions in which the particle type evolves according to a diffusion. The branching and death rates are general functions of the whole population. In this framework, we derive a $\psi$-spine construction and a Many-to-One formula, extending previous works on interacting branching processes. Using this spinal construction, we also propose an alternative simulation method and illustrate its efficiency on the colonial population model. The extended framework we propose can model various ecological systems with interactions, and individual and environmental noises.