MATHEMATICAL MODELS IN POPULATION ECOLOGY AND EVOLUTIONARY DYNAMICS: FRAMEWORKS, APPLICATIONS, AND INSIGHTS

Abstract

Mathematical modeling plays a pivotal role in understanding the complex interactions between organisms and their environment. In population ecology and evolutionary dynamics, mathematical models help to quantify population growth, species interactions, genetic variability, and the evolutionary pressures acting upon populations. This article explores various classes of mathematical models used in these fields, including deterministic, stochastic, and spatial models. We discuss foundational models such as the Lotka–Volterra equations, logistic growth, and replicator dynamics, as well as their modern extensions incorporating age-structure, spatial heterogeneity, and evolutionary game theory. Through graphical representations and case studies, especially from South Asian ecosystems, we highlight the models' utility in predicting species persistence, evolutionary stable strategies, and biodiversity maintenance. Our synthesis underscores the importance of interdisciplinary integration between mathematics, ecology, and evolutionary biology for solving real-world biodiversity and conservation challenges.