Can bounded environmental fluctuations shield species from extinction? Insights from a non-diffusive stochastic allee growth model

Populations experiencing Allee effects are characterized by a critical density below which extinction occurs and above which persistence is possible. Classical models incorporating environmental stochasticity often predict inevitable extinction, mainly because they assume normally distributed environmental variation with unbounded effect sizes. In contrast, natural environmental fluctuations are typically bounded and non-normal. To account for this, population dynamics are analyzed using piecewise-deterministic Markov processes (PDMPs), where environmental states evolve through a finite-state Markov chain. The analysis reveals two threshold densities: populations below the lower threshold collapse deterministically, while those above the upper threshold persist. At intermediate densities, stochastic bistability emerges, with extinction and persistence occurring at complementary probabilities. Persistence fails when carrying capacities in one state fall below Allee thresholds in another, particularly when environmental change alters per-capita growth rates in non-monotonic ways, such as through increased predation or mate limitation. These findings demonstrate that incorporating realistic bounded fluctuations alters persistence predictions, with significant implications for conservation and management.