MODELLING ECO-EVOLUTIONARY DYNAMICS OF AN INVASIVE PLANT UNDER DUAL PRESSURE OF NATIVE HERBIVORES AND SOIL MICROBIAL COMPETITION
By
Arvindra Singh1, Poonam Sinha2 and Arun Kumar Tripathi3
1,2,3Department of Mathematics, S.M.S. Government Model Science College, Gwalior, Madhya Pradesh, India - 474009
Email: asrathaurr@gmail.com, sinhapoonam1966@gmail.com, tripathiarun3108@gmail.com
(Received: May 22, 2025; In format: August 29, 2025; Revised: October 14, 2025; Accepted: October 30, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55215
Abstract
Invasive plant species pose a significant threat to biodiversity, ecosystem stability and agricultural productivity. This study present a novel mathematical model to explore the Eco-evolutionary dynamics of an invasive plant under simultaneous pressures from native herbivores and soil microbial competitors. The model incorporates an adaptation trait that evolves in herbivores based on invasive biomass, along with competition from native soil microbes that suppress the invader’s root system. The system is analyzed using tools from dynamical system theory, including equilibrium analysis, boundedness, stability through jacobian eigenvalue analysis, and bifurcation due to trait thresholds. Result reveal the existence of two biological meaningful equilibrium states and highlight the presence of a transcritical bifurcation triggered by the invasive biomass crossing a critical threshold. Numerical simulations show how Ecoevolutionary feedback loop can suppress invasions and stabilize community dynamics over time. This study underscores the importance of integrating adaptive behavior and below-ground interactions in ecological modeling to devise more effective invasive species management strategies.
2020 Mathematical Sciences Classification: 92D40, 92C80, 34C11, 19A13
Keywords and Phrases: Invasive plant, Plant-Herbivore, Boundedness, Stability.