Allee Effects Plus Noise Induce Population Dynamics Resembling Binary Markov Highs and Lows

• Main Authors: Gordillo, L.F (Author), Greenwood, P.E (Author)
• Format: Article
• Language: English
• Published: Springer 2022
• Subjects: Allee effects; article; Binary Markov process; Demographic noise; demography; Environmental noise; Markov chain; Mathematical Concepts; Models, Biological; noise; occupation; population density; Population Density; population dynamics; Population Dynamics; retention time; simulation; stochastic model; Stochastic Processes
• Online Access: View Fulltext in Publisher

 We show that the combination of Allee effects and noise can produce a stochastic process with alternating sudden decline to a low population phase, followed, after a random time, by abrupt increase in population density. We introduce a new, flexible, deterministic model of attenuated Allee effects, which interpolates between the logistic and a usual Allee model. Into this model, we incorporate environmental and demographic noise. The solution of the resulting Kolmogorov forward equation shows a dichotomous distribution of residence times with heavy occupation of high, near saturation, and low population states. Investigation of simulated sample paths reveals that indeed attenuated Allee effects and noise, acting together, produce alternating, sustained, low and high population levels. We find that the transition times between the two types of states are approximately exponentially distributed, with different parameters, rendering the embedded hi-low process approximately Markov. © 2022, The Author(s), under exclusive licence to Society for Mathematical Biology.