Group Dispersal Modelling Revisited

TL;DR

This paper revisits grouped dispersal modeling by developing a continuous measure-valued process, introducing two propagule types, and analyzing its asymptotics and PDE system, providing a rigorous mathematical framework for dependent dispersal.

Contribution

It introduces a novel measure-valued process for grouped dispersal with two propagule types and analyzes its asymptotic behavior and associated PDE system.

Findings

Derived the infinitesimal generator of the process

Established large population asymptotics

Proved existence and uniqueness of solutions to the PDE system

Abstract

In this paper we revisit the notion of grouped dispersal that have been introduced by Soubeyrand and co-authors \cite{soubeyrand2011patchy} to model the simultaneous (and hence dependent) dispersal of several propagules from a single source in a homogeneous environment. We built a time continuous measure valued process that takes into account the main feature of a grouped dispersal and derive its infinitesimal generator. To cope with the mutligeneration aspect associated to the demography we introduce two types of propagules in the description of the population which is one of the main innovations here. We also provide a rigorous description of the process and its generator. We derive as well, some large population asymptotics of the process unveilling the degenerate ultra parabolic system of PDE satisfied by the density of population. Finally, we also show that such a PDE system has a non-trivial solution which is unique in a certain functional space.