A stochastic hormesis Ricker model and its application to multiple fields

Random noise pervades ecosystems and has the potential for having major impacts on the growth processes of pest populations. In this paper, we aim to investigate the impact of random perturbations on the hormesis Ricker model by considering control measures applied within each generation which can generate hormetic effects, where randomness is characterized by a uniform discrete distribution and white noise, respectively. The main results indicate that the addition of discrete randomness will make the model appear with blurred orbits when the intrinsic growth rate is large enough. The position of the random variable, at the end of each generation or within each generation, cause the blurred orbits to exhibit various forms. Moreover, the effects of variances and expectations of the discrete uniform random variable on the dynamics are evaluated. Further, the introduction of randomness increases the hormetic zone and the maximum response, but can increase or decrease the monotonically increasing interval under different parameter values. In contrast, the stochastic model characterized by white noise, exhibits only a small effect on the bifurcation diagrams with respect to the intrinsic growth rate and the hormesis, which may be attributed to the mean of its noise being zero. Finally, we fit the stochastic model to experimental hormetic data sets observed in multiple fields, and our results demonstrate that the stochastic hormesis Ricker model can capture the characteristics of these data accurately. These findings could provide valuable insights into the understanding of the complexities of pest population dynamics, with implications for better pest control, resource management and for other complex biological systems such as toxicology and drug development.