Impact of stochasticity in immigration and reintroduction on colonizing and extirpating populations

Noise-induced dynamics in a single species model with Allee effect driven by correlated colored noises

In this paper, a single species model with Allee effect driven by correlated colored noises is proposed and investigated. The stationary probability density of the model is obtained using the approximative Fokker-Planck equation, and its shape is discussed in detail. P-bifurcation and noise-induced bistability are explored, followed by the observation of noise-enhanced stability through mean first passage time analysis. Our findings demonstrate that: (i) noise can induce P-bifurcation, causing the structure of a stationary probability distribution to shift from unimodal to monotonic under positive correlation and switch from unimodal to bimodal under negative correlation; (ii) correlation time promotes population growth, leading to a higher probability of large population size and delaying the extinction process; (iii) noise-enhanced stability induced by multiplicative noise depends on both additive noise and correlation time, while it always exists for additive noise.

Influence of the components of propagule pressure, Allee effects, and stochasticity on the time to establish introduced populations

Forecasting whether individuals of an introduced population will succeed to establish is a challenge in invasion and conservation biology. The present work aims to decouple the impact of the components of propagule pressure on the time for population establishment in the presence of Allee effects and stochasticity in propagule sizes. The mean first passage time (MFPT) for a population to reach a viable size is used as a measure of the establishment success for the introduction processes involving periodic introductions. By fixing the introduction rate (mean number of introduced individuals per unit time) and varying the period of introduction from small ranges (small and frequent introductions) to large ones (infrequent and large releases), we study the influence of introduction distribution over time. These patterns of introduction are compared in a semi-stochastic model by observing which factors minimize the MFPT from an initially absent population, and hence, ensure the fastest population establishment. We investigate the influence on these minima of the introduction rate, variability in the introduction sizes, and occurrence of catastrophes that temporarily wipe out the population. Whereas most investigated cases show that infrequent and large introductions favor population establishment as expected, small and frequent introductions are preferred when the introduction rate is large and/or the variability in the introduction size is strong. Moreover, we observed counterintuitively that catastrophes strongly increase MFPT at small periods of introduction. In addition, we showed that stochasticity in introduction tends to increase the MFPT except when the introduction rate is small and introductions are evenly spread out in time.