Modelling environmental stochasticity in a stage-structured population applying stochastic differential equations

Abstract

This work presents a new approach to incorporating environmental stochasticity into stage-structured models by combining population dynamics with stochastic differential equations theory. Random fluctuations were treated as Brownian motion, where the stochastic diffusion process here was the population size. The resulting SDEs model was discussed in terms of existence, uniqueness and stability of the solution. Numerical analyses were investigated in this work to analyze and visualize our model. Our approach allowed us to project the population behavior and to calculate the stochastic growth rate. The quasi-extinction risk was also studied by setting a threshold population size under different conditions. The proposed method was applied to a real dataset of a plant species populations, and the obtained results were in excellent agreement with previous studies. Therefore, our method can be an alternative way to incorporate stochasticity in such structured population models.