Chenggui Yuan

Natural populations experience variable environments. Anthropogenically driven environmental change, in particular, is expected to impose trends on key demographic parameters such as reproduction and survival. Theoretical studies of how such environmental changes affect populations have highlighted dynamical phenomena including bifurcation-related tipping points – typically identified by comparing different, but constant, environmental states – and long transients – that can arise after sudden environmental perturbations. However, real-world environmental trends are neither instantaneous nor slow enough to justify treating the environment as constant, motivating recent interest in r-tipping points – regime shifts induced by \emph{r}, the rate of environmental change in demographic parameters. Most existing work examines this phenomenon in complex ecological models and for specific values of \emph{r}. Here, we develop tools to help ecologists investigate how populations and communities respond to environmental trends across a continuum of \emph{r} values. Using a simple density-dependent model, we identify four qualitatively distinct responses to a trend as a function of \emph{r} – patterns that traditional methods fail to reveal – and we visualize them using an \emph{r-bifurcation diagram} introduced here. We also describe and mathematically explain the emergence of abrupt regime shifts linked to delayed bifurcations, revealed by a novel \emph{superimposition diagram}. These findings are robust across modelling frameworks and ecological contexts, providing new insights into interactions between short- and long-term environmental change processes.

This paper investigates neutral-type McKean-Vlasov stochastic differential equations in which the drift and diffusion coefficients depend on both the segment process and its distribution. Under a one-sided Lipschitz condition on the drift coefficient, we establish a Freidlin-Wentzell-type large deviation principle for the solution process by using the extended contraction principle combined with an exponential approximation technique. Our results extend existing large deviation principles for McKean-Vlasov equations to the neutral case.

This paper investigates neutral-type McKean-Vlasov stochastic differential equations in which the drift and diffusion coefficients depend on both the segment process and its distribution. Under a one-sided Lipschitz condition on the drift coefficient, we establish a Freidlin-Wentzell-type large deviation principle for the solution process by using the extended contraction principle combined with an exponential approximation technique. Our results extend existing large deviation principles for McKean-Vlasov equations to the neutral case.

In this paper, we consider slow-fast McKean–Vlasov stochastic differential equations driven by fractional Brownian motions with Hurst parameter [ ] and Brownian motions. We give a definition of the large deviation principle (LDP) on the product space related to fractional Brownian motion and Brownian motion, which is different from the traditional definition for LDP. Under some proper assumptions on coefficients, LDP is investigated for this type of equations by using the weak convergence method.

Climate change is projected to increase the frequency and intensity of extreme heat events, and may increase humidity levels, leading to coupled thermal and hydric stress. However, how humidity modulates the impacts of heat stress on species and their interactions is currently unknown. Using an insect host‐parasitoid interaction: the Indian meal moth, Plodia interpunctella, and its endoparasitoid wasp, Venturia canescens, we investigated how humidity interacted with heat stress duration, applied at different host developmental stages, to affect life history traits. Hosts parasitized as 4th instar larvae and unparasitized hosts were maintained in high‐ (60.8% RH) or low‐humidity (32.5% RH) at constant 28°C. They were then exposed to a 38°C thermal stress with a duration of 0 (no heat stress), 6 or 72 h in either the 4th or 5th host instar. Neither humidity nor heat stress duration affected emergence of unparasitized hosts, but increasing heat stress duration during the 4th instar decreased parasitoid emergence irrespective of humidity. When applied during the 5th instar, increasing heat duration decreased parasitoid emergence under low humidity, but no effect of heat stress was found under high humidity. Moreover, experiencing longer heat stress in the 4th instar increased host larval development time and decreased body size under high humidity, but this effect differed under low humidity; increasing heat duration in the 5th instar decreased parasitoid body sizes only under low humidity. Larval stage and heat stress duration directly affected parasitized host survival time, with a concomitant indirect reduction of parasitoid sizes. We show that humidity modifies key life history responses of hosts and parasitoids to heat stress in species‐specific ways, highlighting the potential importance of humidity in regulating host‐parasitoid interactions and their population dynamics. Finally, we emphasize that interactions between environmental stressors need to be considered in climate change research.