Mathematical Modeling of Population Dynamics under Environmental Uncertainty

Abstract

Natural populations fluctuate because births, deaths and movements are shaped by chance events and by variable environmental conditions. This article reviews mathematical approaches for modeling population dynamics under environmental uncertainty, from deterministic growth equations to stochastic differential equations, random-environment matrix models and simulation-based methods. The distinction between demographic and environmental stochasticity is emphasised, together with the stochastic growth rate as a measure of long-term performance and persistence. A simulation of logistic growth with multiplicative noise illustrates how variability can cause populations to diverge widely from deterministic expectations. Parameter estimation with state-space and Bayesian frameworks is discussed, as are numerical methods and applications in conservation, fisheries, pest management and epidemiology. Limitations related to data scarcity, structural uncertainty and non-stationary climates are highlighted, and directions for future research are proposed.