Savanna dynamics with grazing, browsing, and migration effects

TL;DR

This paper analyzes the complex dynamics of savanna ecosystems, focusing on how grazing, browsing, and migration influence species coexistence and ecological stability through mathematical modeling of traveling waves.

Contribution

It provides a rigorous mathematical analysis of traveling waves in savanna systems, highlighting conditions for coexistence and ecological stability considering multiple species interactions.

Findings

Existence of traveling waves from extinction to coexistence.

Identification of waves from grass-only to co-existence states.

Estimation of minimum plant biomass for ecosystem stability.

Abstract

This article explores the dynamics of savanna ecosystems with grazing, browsing, and migration effects. Covering over one-eighth of the Earth's land area and supporting about one-fifth of the global population, the savanna is an ecological system whose importance has only recently garnered significant attention from biologists. The interactions between organisms in this ecosystem are highly complex, and fundamental mathematical issues remain unresolved. We rigorously analyze traveling waves in savanna systems and focus on whether trees, grass, grazers, and browsers coexist. We demonstrate the existence of various traveling waves, including waves transitioning from extinction to co-existence and waves from a grass-vegetation state (where only grass and grazers exist) to co-existence. Due to the biodiversity of species in grassland ecosystems, it is not appropriate to consider overly simplified models of competition between grasses and trees. From both a biological and mathematical perspective, factors such as animal grazing, browsing, and migration (which facilitates seed dispersal) play a crucial role in promoting ecological stability and coexistence. Additionally, we estimate the nonzero minimum value of the total plant biomass within the savanna dynamic system to better understand the persistence and stability of sustainable development within the ecosystem.