Noise and determinism in Trinidadian guppy population dynamics

Natural populations are often nonlinear and exhibit substantial variability. A central question is how stochasticity interacts with density-dependent regulation to shape population stability. We address this using four long-term time series of Trinidadian guppies and find that their dynamics are well described by a stochastic logistic model with multiplicative environmental noise. The model predicts that stochasticity does not merely add fluctuations around deterministic carrying capacity, but alters the equilibrium structure. Using stochastic bifurcation theory, we show that increasing noise shifts the most-probable population size below the deterministic equilibrium and can push populations closer to a noise-induced bifurcation, even when mean growth rates remain positive. The effects of stochasticity across populations align with known ecological differences among streams, particularly the effects of light level and seasonality. The analysis also identifies populations most sensitive to perturbations, which are not detected by standard early warning indicators. Temporal and spectral analyses further show that intrinsic growth rate governs local recovery, while seasonal variation interacts with density-dependence to shape longer-term population fluctuations. Together, our results show that stochasticity can alter resilience and vulnerability by reshaping ecological stability landscapes.