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Abstract During their lifetimes, individuals in populations pass through different states, and the notion of an occupancy time describes the amount of time an individual spends in a given set of states. Questions related to this idea were studied in a recent paper by Roth and Caswell for cases where the environmental conditions are constant. However, it is truly important to consider the case where environments are changing randomly or in directional way through time, so the transition probabilities between different states change over time, motivating the use of time-dependent stage-structured models. Using absorbing inhomogenous Markov chains and the discrete-time McKendrick–von Foerster equation, we derive explicit formulas for the occupancy time, its expectation, and its higher-order moments for stage-structured models with time-dependent transition rates. The results provide insights into the dynamics of long lived plant or animal populations where individuals transition in both directions between reproductive and non reproductive stages. We apply our approach to study a specific time-dependent model of the Southern Fulmar, and obtain insights into how the number of breeding attempts depends on external conditions that vary through time. 

Abstract Forecasting tipping points in spatially extended systems is a key area of interest to ecologists. A slowly declining spatially distributed population is an important example of an ecological system that could exhibit a cascade of tipping points. Here, we develop a spatial two-patch model with environmental stochasticity that is slowly forced through population collapse, in the presence of changing environmental conditions. We begin with a basic spatial model, then introduce a fast–slow version of the model using geometric singular perturbation theory, followed by the inclusion of stochasticity. Using the spectral density of the fluctuating subpopulation in each patch, we derive analytic expressions for candidate indicators of population extinction and evaluate their performance through a simulation study. We find that coupling and spatial heterogeneity decrease the magnitude of the proposed indicators in coupled populations relative to isolated populations. Moreover, the degree of coupling dictates the trends in summary statistics. We conclude that this theory may be applied to other contexts, including the control of invasive species. 

Abstract Understanding mechanisms of coexistence is a central topic in ecology. Mathematical analysis of models of competition between two identical species moving at different rates of symmetric diffusion in heterogeneous environments show that the slower mover excludes the faster one. The models have not been tested empirically and lack inclusions of a component of directed movement toward favourable areas. To address these gaps, we extended previous theory by explicitly including exploitable resource dynamics and directed movement. We tested the mathematical results experimentally using laboratory populations of the nematode worm,Caenorhabditis elegans. Our results not only support the previous theory that the species diffusing at a slower rate prevails in heterogeneous environments but also reveal that moderate levels of a directed movement component on top of the diffusive movement allow species to coexist. Our results broaden the theory of species coexistence in heterogeneous space and provide empirical confirmation of the mathematical predictions. 

Abstract Mutualistic networks are vital ecological and social systems shaped by adaptation and evolution. They involve bipartite cooperation via the exchange of goods or services between actors of different types. Empirical observations of mutualistic networks across genres and geographic conditions reveal correlated nested and modular patterns. Yet, the underlying mechanism for the network assembly remains unclear. We propose a niche-based adaptive mechanism where both nestedness and modularity emerge simultaneously as complementary facets of an optimal niche structure. Key dynamical properties are revealed at different timescales. Foremost, mutualism can either enhance or reduce the network stability, depending on competition intensity. Moreover, structural adaptations are asymmetric, exhibiting strong hysteresis in response to environmental change. Finally, at the evolutionary timescale we show that the adaptive mechanism plays a crucial role in preserving the distinctive patterns of mutualism under species invasions and extinctions. 

Abstract One of the main factors that determines habitat suitability for sessile and territorial organisms is the presence or absence of another competing individual in that habitat. This type of competition arises in populations occupying patches in a metacommunity. Previous studies have looked at this process using a continuous-time modeling framework, where colonizations and extinctions occur simultaneously. However, different colonization processes may be performed by different species, which may affect the metacommunity dynamics. We address this issue by developing a discrete-time framework that describes these kinds of metacommunity interactions, and we consider different colonization dynamics. To understand potential dynamics, we consider specific functional forms that characterize the colonization and extinction processes of metapopulations competing for space as their limiting factor. We then provide a mathematical analysis of the models generated by this framework, and we compare these results to what is seen in nature and in previous models. 

Abstract Understanding how the biological invasion is driven by environmental factors will improve model prediction and advance early detection, especially in the context of accelerating anthropogenic ecological changes. Although a large body of studies has examined how favorable environments promote biological invasions, a more comprehensive and mechanistic understanding of invasive species response to unfavorable/stressful conditions is still developing. Grass invasion has been problematic across the globe; in particular, C 4 grass invaders, with high drought tolerance, adaptations to high temperatures, and high water use efficiency, could become more severe. Here, we conducted a rigorous microcosm experiment, with one of the most damaging invasive C 4 grass, cogongrass ( Imperata cylindrica ), to explore how cogongrass responds to soil water and nutrient stress. We further integrated the results of the microcosm study with a species distribution model to (1) corroborate greenhouse results with field observations and (2) validate the robustness of our findings at subcontinental scales. Both the microcosm experiments and species distribution model agreed that soil water stress had a stronger impact on cogongrass than the nutrient one. New vegetative growth of cogongrass continued to be inhibited by the prior water stress. The significant water effect on cogongrass total biomass was supported by the finding that both allometric and biochemical traits of cogongrass did not show significant responses to the changes in water treatment. Different to the conventional wisdom that nutrient enrichment plays a bigger role in facilitating biological invasions, this study highlighted the possibility that water conditions may have a more substantial effect on some aggressive invaders. Therefore, an important implication of this study on biological conservation is that field managers might take advantage of the negative effect of global drought on some invasive species to increase the efficiency of their controlling efforts because invasive species may become more vulnerable under drought effect. 

Abstract Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the complex dynamics induced by the network structure. We analyze one recently introduced model and derive important epidemiological quantities for the system. We derive the epidemic threshold and analyze the bifurcation that occurs, and we use asymptotic techniques to derive an approximation for the endemic equilibrium when it exists. We consider the sensitivity of this approximation to network parameters, and the implications for disease control measures are found to be in line with the results of existing studies.