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Understanding how populations respond to increasingly variable conditions is a major objective for natural resource managers forecasting extinction risk. The lesson from current modelling is clear: increasing environmental variability increases population abundance variability. We show that this paradigm fails to describe a broad class of empirically observed dynamics, namely endogenously driven population cycles. In contrast to the dominant paradigm, these populations can exhibit reduced long-run population variance under increasing environmental variability. We provide evidence for a mechanistic explanation of this phenomenon that relies on how stochasticity interacts with long transient dynamics present in the deterministic cycling model. This interaction stands in contrast to the often assumed additivity of stochastic and deterministic drivers of population fluctuations. We show evidence for the phenomenon in two cyclical populations: flour beetles and Canadian lynx. We quantify the impact of the phenomenon with new theory that partitions the effects of nonlinear dynamics and stochastic variation on dynamical systems. In both empirical examples, the partitioning shows that the interaction between deterministic and stochastic dynamics reduces the variance in population size. Our results highlight that previous predictions about extinction under environmental variability may prove inadequate to understand the effects of climate change in some populations. 

Abstract Genetic connectivity lies at the heart of evolutionary theory, and landscape genetics has rapidly advanced to understand how gene flow can be impacted by the environment. Isolation by landscape resistance, often inferred through the use of circuit theory, is increasingly identified as being critical for predicting genetic connectivity across complex landscapes. Yet landscape impediments to migration can arise from fundamentally different processes, such as landscape gradients causing directional migration and mortality during migration, which can be challenging to address. Spatial absorbing Markov chains (SAMC) have been introduced to understand and predict these (and other) processes affecting connectivity in ecological settings, but the relationship of this framework to landscape genetics remains unclear. Here, we relate the SAMC to population genetics theory, provide simulations to interpret the extent to which the SAMC can predict genetic metrics and demonstrate how the SAMC can be applied to genomic data using an example with an endangered species, the Panama City crayfish Procambarus econfinae , where directional migration is hypothesized to occur. The use of the SAMC for landscape genetics can be justified based on similar grounds to using circuit theory, as we show how circuit theory is a special case of this framework. The SAMC can extend circuit‐theoretic connectivity modelling by quantifying both directional resistance to migration and acknowledging the difference between migration mortality and resistance to migration. Our empirical example highlights that the SAMC better predicts population structure than circuit theory and least‐cost analysis by acknowledging asymmetric environmental gradients (i.e. slope) and migration mortality in this species. These results provide a foundation for applying the SAMC to landscape genetics. This framework extends isolation‐by‐resistance modelling to account for some common processes that can impact gene flow, which can improve predicting genetic connectivity across complex landscapes. 

Successful public health regimes for COVID-19 push below unity long-term regionalR_t—the average number of secondary cases caused by an infectious individual. We use a susceptible-infectious-recovered (SIR) model for two coupled populations to make the conceptual point that asynchronous, variable local control, together with movement between populations, elevates long-term regionalR_t, and cumulative cases, and may even prevent disease eradication that is otherwise possible. For effective pandemic mitigation strategies, it is critical that models encompass both spatiotemporal heterogeneity in transmission and movement. 

Abstract Habitat loss is often considered the greatest near‐term threat to biodiversity, while the impact of habitat fragmentation remains intensely debated. A key issue of this debate centers on the problem of scale–landscape or patch–at which to assess the consequences of fragmentation. Yet patterns are often confounded across scales, and experimental designs that could solve this scaling problem remain scarce. We conducted two field experiments in 30 experimental landscapes in which we manipulated habitat loss, fragmentation, and patch size for a community of four insect herbivores that specialize on the cactusOpuntia. In the first experiment, we destroyed 2088Opuntiapatches in either aggregated or random patterns and compared the relative effects of landscape‐scale loss and fragmentation to those of local patch size on species occurrence. This experiment focused on manipulating the relative separation of remaining patches, where we hypothesized that aggregated loss would disrupt dispersal more than random loss, leading to lower occurrence. In the second experiment, we destroyed 759Opuntiapatches to generate landscapes that varied in patch number and size for a given amount of habitat loss and assessed species occurrence. This experiment focused on manipulating the subdivision of remaining habitat, where we hypothesized that an increase in the number of patches for a given amount of loss would lead to negative effects on occurrence. For both, we expected that occurrence would increase with patch size. We find strong evidence for landscape‐scale effects of habitat fragmentation, with aggregated loss and a larger number of patches for a given amount of habitat loss leading to a lower frequency of patches occupied in landscapes. In both experiments, occurrence increased with patch size, yet interactions of patch size and landscape‐scale loss and fragmentation drove species occurrence in patches. Importantly, the direction of effects were consistent across scales and effects of patch size were sufficient to predict the effects of habitat loss and fragmentation across entire landscapes. Our experimental results suggest that changes at both the patch and landscape scales can impact populations, but that a long‐standing pattern—the patch‐size effect—captures much of the key variation shaping patterns of species occurrence.