Stochastic environments and migrating population dynamics

Environmental stochasticity is pivotal in shaping population dynamics by introducing random fluctuations in habitat conditions, resource availability, and survival probabilities. These fluctuations often drive critical ecological processes, influencing persistence, extinction, and adaptive strategies. Especially in the context of population migration, environmental stochasticity plays a critical role in shaping movement patterns, survival rates, and population structure. There are various forms of population migration, and among them, partial migration is a widespread phenomenon, where only a portion of the population undertakes seasonal or periodic movements while the rest remain resident in the same area year-round. In this study, we develop discrete time stochastic population models to investigate how environmental fluctuations and disturbances affects partially migrating populations. In one class of models, random fluctuations are incorporated through density-dependent fertility functions, while in another class of models, episodic disturbance events are addressed that reduce migratory populations. By deriving the stochastic growth rate through the dominant Lyapunov exponent, we establish thresholds for population persistence and extinction. Furthermore, we explore the conditions under which partial migration emerges as an evolutionarily stable strategy (ESS) in fluctuating environments and with disturbance events. As an application, we develop our framework to incorporate temperature-dependent fertility functions, analyzing the impact of climate-driven temperature fluctuations on population dynamics. Our findings reveal that environmental stochasticity can either enhance or undermine the persistence of partially migratory populations, depending on the nature of the disturbances and the distribution of environmental variability. Numerical simulations validate these theoretical insights, demonstrating how extreme events, such as climatic shocks, shape migration patterns and population structure. This study advances the understanding of partial migration dynamics, offering a robust framework for predicting population responses to environmental changes in the context of ongoing climate variability.