A spatially explicit Markovian individual-based model for terrestrial plant dynamics

TL;DR

This paper introduces a spatially explicit individual-based model for terrestrial plant populations, combining stochastic processes with deterministic limits to analyze plant dynamics and competition effects.

Contribution

It presents a novel measure-valued stochastic model that links individual plant characteristics and spatial positions to population-level behavior.

Findings

The model accurately describes plant spatial distribution and size evolution.

Monte Carlo simulations match theoretical predictions.

The deterministic limit provides insights into large population dynamics.

Abstract

An individual-based model (IBM) of a spatiotemporal terrestrial ecological population is proposed. This model is spatially explicit and features the position of each individual together with another characteristic, such as the size of the individual, which evolves according to a given stochastic model. The population is locally regulated through an explicit competition kernel. The IBM is represented as a measure-valued branching/diffusing stochastic process. The approach allows (i) to describe the associated Monte Carlo simulation and (ii) to analyze the limit process under large initial population size asymptotic. The limit macroscopic model is a deterministic integro-differential equation.