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1. Asymmetric relationships and their effects on coexistence

   https://doi.org/10.1111/ele.14334  

   Albert, Pimsupa Jasmin ; Reuman, Daniel C. ( November 2023 , Ecology Letters)

   Species coexistence attracts wide interest in ecology. Modern coexistence theory (MCT) identifies coexistence mechanisms, one of which, storage effects, hinges on relationships between fluctuations in environmental and competitive pressures. However, such relationships are typically measured using covariance, which does not account for the possibility that environment and competition may be more related to each other when they are strong than when weak, or vice versa. Recent work showed that such ‘asymmetric tail associations’ (ATAs) are common between ecological variables, and are important for extinction risk, ecosystem stability, and other phenomena. We extend MCT, decomposing storage effects to show the influence of ATAs. Analysis of a simple model and an empirical example using diatoms illustrate that ATA influences can be comparable in magnitude to other mechanisms of coexistence and that ATAs can make the difference between species coexistence and competitive exclusion. ATA influences may be an important new mechanism of coexistence.

    

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2. Copulas and their potential for ecology

   https://doi.org/10.1016/bs.aecr.2020.01.003  

   Ghosh, S. ; Sheppard, L.W. ; Holder, M.T. ; Loecke, T.E. ; Reid, P.C. ; Bever, J.D. ; Reuman, D.C. ( April 2020 , Advances in ecological research)

   All branches of ecology study relationships among and between environmental and biological variables. However, standard approaches to studying such relationships, based on correlation and regression, provide only some of the complex information contained in the relationships. Other statistical approaches exist that provide a complete description of relationships between variables, based on the concept of the *copula*; they are applied in finance, neuroscience and elsewhere, but rarely in ecology. We explore the concepts that underpin copulas and the potential for those concepts to improve our understanding of ecology. We find that informative copula structure in dependencies between variables is common across all the environmental, species-trait, phenological, population, community, and ecosystem functioning datasets we considered. Many datasets exhibited asymmetric tail associations, whereby two variables were more strongly related in their left compared to right tails, or *vice versa*. We describe mechanisms by which observed copula structure and tail associations can arise in ecological data, including a Moran-like effect whereby dependence structures are inherited from environmental variables; and asymmetric or nonlinear influences of environments on ecological variables, such as under Liebig's law of the minimum. We also describe consequences of copula structure for ecological phenomena, including impacts on extinction risk, Taylor's law, and the temporal stability of ecosystem services. By documenting the importance of a complete description of dependence between variables, advancing conceptual frameworks, and demonstrating a powerful approach, we encourage widespread use of copulas in ecology, which we believe can benefit the discipline. 

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3. Tail‐dependent spatial synchrony arises from nonlinear driver–response relationships

   https://doi.org/10.1111/ele.13991  

   Walter, Jonathan A. ; Castorani, Max C. N. ; Bell, Tom W. ; Sheppard, Lawrence W. ; Cavanaugh, Kyle C. ; Reuman, Daniel C. ; Adler, ed., Frederick ( March 2022 , Ecology Letters)

   Spatial synchrony may be tail‐dependent, that is, stronger when populations are abundant than scarce, or vice‐versa. Here, ‘tail‐dependent’ follows from distributions having a lower tail consisting of relatively low values and an upper tail of relatively high values. We present a general theory of how the distribution and correlation structure of an environmental driver translates into tail‐dependent spatial synchrony through a non‐linear response, and examine empirical evidence for theoretical predictions in giant kelp along the California coastline. In sheltered areas, kelp declines synchronously (lower‐tail dependence) when waves are relatively intense, because waves below a certain height do little damage to kelp. Conversely, in exposed areas, kelp is synchronised primarily by periods of calmness that cause shared recovery (upper‐tail dependence). We find evidence for geographies of tail dependence in synchrony, which helps structure regional population resilience: areas where population declines are asynchronous may be more resilient to disturbance because remnant populations facilitate reestablishment.

    

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4. The spatial synchrony of species richness and its relationship to ecosystem stability

   https://doi.org/10.1002/ecy.3486  

   Walter, Jonathan A. ; Shoemaker, Lauren G. ; Lany, Nina K. ; Castorani, Max C. N. ; Fey, Samuel B. ; Dudney, Joan C. ; Gherardi, Laureano ; Portales‐Reyes, Cristina ; Rypel, Andrew L. ; Cottingham, Kathryn L. ; et al ( August 2021 , Ecology)

   Synchrony is broadly important to population and community dynamics due to its ubiquity and implications for extinction dynamics, system stability, and species diversity. Investigations of synchrony in community ecology have tended to focus on covariance in the abundances of multiple species in a single location. Yet, the importance of regional environmental variation and spatial processes in community dynamics suggests that community properties, such as species richness, could fluctuate synchronously across patches in a metacommunity, in an analog of population spatial synchrony. Here, we test the prevalence of this phenomenon and the conditions under which it may occur using theoretical simulations and empirical data from 20 marine and terrestrial metacommunities. Additionally, given the importance of biodiversity for stability of ecosystem function, we posit that spatial synchrony in species richness is strongly related to stability. Our findings show that metacommunities often exhibit spatial synchrony in species richness. We also found that richness synchrony can be driven by environmental stochasticity and dispersal, two mechanisms of population spatial synchrony. Richness synchrony also depended on community structure, including species evenness and beta diversity. Strikingly, ecosystem stability was more strongly related to richness synchrony than to species richness itself, likely because richness synchrony integrates information about community processes and environmental forcing. Our study highlights a new approach for studying spatiotemporal community dynamics and emphasizes the spatial dimensions of community dynamics and stability.

    

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5. Tail associations in ecological variables and their impact on extinction risk

   https://doi.org/10.1002/ecs2.3132  

   Ghosh, Shyamolina ; Sheppard, Lawrence W. ; Reuman, Daniel C. ( May 2020 , Ecosphere)

   Extreme climatic events (ECEs) are becoming more frequent and more intense due to climate change. Furthermore, there is reason to believe ECEs may modify tail associations between distinct population vital rates, or between values of an environmental variable measured in different locations. Tail associations between two variables are associations that occur between values in the left or right tails of the distributions of the variables. Two positively associated variables can be principally left‐tail associated (i.e., more correlated when they take low values than when they take high values) or right‐tail associated (more correlated when they take high than low values), even with the same overall correlation coefficient in both cases. We tested, in the context of non‐spatial stage‐structured matrix models, whether tail associations between stage‐specific vital rates may influence extinction risk. We also tested whether the nature of spatial tail associations of environmental variables can influence metapopulation extinction risk. For instance, if low values of an environmental variable reduce the growth rates of local populations, one may expect that left‐tail associations increase metapopulation extinction risks because then environmental catastrophes are spatially synchronized, presumably reducing the potential for rescue effects. For the non‐spatial, stage‐structured models we considered, left‐tail associations between vital rates did accentuate extinction risk compared to right‐tail associations, but the effect was small. In contrast, we showed that density dependence interacts with tail associations to influence metapopulation extinction risk substantially: For population models showing undercompensatory density dependence, left‐tail associations in environmental variables often strongly accentuated and right‐tail associations mitigated extinction risk, whereas the reverse was usually true for models showing overcompensatory density dependence. Tail associations and their asymmetries are taken into account in assessing risks in finance and other fields, but to our knowledge, our study is one of the first to consider how tail associations influence population extinction risk. Our modeling results provide an initial demonstration of a new mechanism influencing extinction risks and, in our view, should help motivate more comprehensive study of the mechanism and its importance for real populations in future work.

    

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