Regulation mechanisms in spatial stochastic development models

TL;DR

This paper analyzes regulation mechanisms in spatial stochastic development models, focusing on how local and global controls affect density growth, with a proof that superstable competition kernels can prevent unbounded density increase.

Contribution

It introduces a detailed analysis of regulation mechanisms, especially the role of superstable kernels in controlling density growth in spatial stochastic models.

Findings

Local self-regulation can suppress unbounded growth

Superstable kernels are effective in controlling density

Density behavior is characterized under different regulation mechanisms

Abstract

The aim of this paper is to analyze different regulation mechanisms in spatial continuous stochastic development models. We describe the density behavior for models with global mortality and local establishment rates. We prove that the local self-regulation via a competition mechanism (density dependent mortality) may suppress a unbounded growth of the averaged density if the competition kernel is superstable.