Averaging principle for a type of Caputo fractional stochastic differential equations.

The averaging principle for Caputo fractional stochastic differential equations has recently attracted much attention. In this paper, we investigate the averaging principle for a type of Caputo fractional stochastic differential equation. Comparing with the existing literature, we shall use different estimate methods to investigate the averaging principle, which will enrich the development of theory for Caputo fractional stochastic differential equations.

Environmental degradation amplifies species' responses to temperature variation in a trophic interaction.

Land-use and climate change are two of the primary drivers of the current biodiversity crisis. However, we lack understanding of how single-species and multispecies associations are affected by interactions between multiple environmental stressors. We address this gap by examining how environmental degradation interacts with daily stochastic temperature variation to affect individual life history and population dynamics in a host-parasitoid trophic interaction, using the Indian meal moth, Plodia interpunctella, and its parasitoid wasp Venturia canescens. We carried out a single-generation individual life-history experiment and a multigeneration microcosm experiment during which individuals and microcosms were maintained at a mean temperature of 26°C that was either kept constant or varied stochastically, at four levels of host resource degradation, in the presence or absence of parasitoids. At the individual level, resource degradation increased juvenile development time and decreased adult body size in both species. Parasitoids were more sensitive to temperature variation than their hosts, with a shorter juvenile stage duration than in constant temperatures and a longer adult life span in moderately degraded environments. Resource degradation also altered the host's response to temperature variation, leading to a longer juvenile development time at high resource degradation. At the population level, moderate resource degradation amplified the effects of temperature variation on host and parasitoid populations compared with no or high resource degradation and parasitoid overall abundance was lower in fluctuating temperatures. Top-down regulation by the parasitoid and bottom-up regulation driven by resource degradation contributed to more than 50% of host and parasitoid population responses to temperature variation. Our results demonstrate that environmental degradation can strongly affect how species in a trophic interaction respond to short-term temperature fluctuations through direct and indirect trait-mediated effects. These effects are driven by species differences in sensitivity to environmental conditions and modulate top-down (parasitism) and bottom-up (resource) regulation. This study highlights the need to account for differences in the sensitivity of species' traits to environmental stressors to understand how interacting species will respond to simultaneous anthropogenic changes.

Strong convergence rate of truncated Euler-Maruyama method for stochastic differential delay equations with Poisson jumps.

We study a class of super-linear stochastic differential delay equations with Poisson jumps (SDDEwPJs). The convergence and rate of the convergence of the truncated Euler-Maruyama numerical solutions to SDDEwPJs are investigated under the generalized Khasminskii-type condition.

Stochastic hybrid delay population dynamics: well-posed models and extinction.

Nonlinear differential equations have been used for decades for studying fluctuations in the populations of species, interactions of species with the environment, and competition and symbiosis between species. Over the years, the original non-linear models have been embellished with delay terms, stochastic terms and more recently discrete dynamics. In this paper, we investigate stochastic hybrid delay population dynamics (SHDPD), a very general class of population dynamics that comprises all of these phenomena. For this class of systems, we provide sufficient conditions to ensure that SHDPD have global positive, ultimately bounded solutions, a minimum requirement for a realistic, well-posed model. We then study the question of extinction and establish conditions under which an ecosystem modelled by SHDPD is doomed.