Extinction Analysis of Stochastic Predator–Prey System with Stage Structure and Crowley–Martin Functional Response

In this paper, we researched some dynamical behaviors of a stochastic predator–prey system, which is considered under the combination of Crowley–Martin functional response and stage structure. First, we obtained the existence and uniqueness of the global positive solution of the system. Then, we studied the stochastically ultimate boundedness of the solution. Furthermore, we established two sufficient conditions, which are separately given to ensure the stochastic extinction of the prey and predator populations. In the end, we carried out the numerical simulations to explain some cases.

Species abundance plays a dominant role in local and regional extinctions in freshwater communities and allows the identification of selective extinctions

ABSTRACTRecent declines in global biodiversity emphasize that understanding the factors that determine extinction risk should be a priority for ecologists and conservation biologists. A key question is whether extinctions are nonrandom and selective, in which case knowledge of selectivity may help predict and prevent future extinction. We suggest, however, that a premature focus on the identification of selective, trait-based determinants of extinctions risk is problematic if the potential importance of stochastic extinction processes are not first considered. Within this context we aimed to determine the roles that stochastic extinction and species abundance play in extinction risk by applying a rarefaction-based null model approach to analyzing biodiversity declines and extinctions in an experimental system. We focused on aquatic macroinvertebrate declines and extinction caused by predation by fish (Lepomis cyanellus) in semi-natural freshwater mesocosms. We found that null-predicted local extirpations based on the random loss of individuals were a significant predictor of observed local extirpations, and that the majority of observed extinctions were consistent with stochastic mechanisms of extinction, as predicted by a rarefaction model. We were able to identify a number of selective extinctions that were not predicted by the rarefaction model, and while these were relatively rare, they contributed to greater-than-expected loss of diversity at both local (mesocosm) and regional (whole experiment) spatial scales. Our results confirm that species abundance and occupancy are among the most important factors in identifying extinction risk in response to a disturbance. Moreover, owing to our use of a stochastic null model, we also conclude that measures of abundance are important indicators of extinction probability because they are operated on by the random loss of individuals, suggesting that stochastic extinction is an important process in this system and in biodiversity loss in general.

Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage

We extend the classical SIRS epidemic model incorporating media coverage from a deterministic framework to a stochastic differential equation (SDE) and focus on how environmental fluctuations of the contact coefficient affect the extinction of the disease. We give the conditions of existence of unique positive solution and the stochastic extinction of the SDE model and discuss the exponentialp-stability and global stability of the SDE model. One of the most interesting findings is that if the intensity of noise is large, then the disease is prone to extinction, which can provide us with some useful control strategies to regulate disease dynamics.