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We give a comprehensive review of Chesson's coexistence theory, summarizing, for the first time, all its fundamental details in one single document. Our goal is for both theoretical and empirical ecologists to be able to use the theory to interpret their findings, and to get a precise sense of the limits of its applicability. To this end, we introduce an explicit handling of limiting factors, and a new way of defining the scaling factors that partition invasion growth rates into the different mechanisms contributing to coexistence. We explain terminology such as relative nonlinearity, storage effect, and growth-density covariance, both in a formal setting and through their biological interpretation. We review the theory's applications and contributions to our current understanding of species coexistence. While the theory is very general, it is not well suited to all problems, so we carefully point out its limitations. Finally, we critique the paradigm of decomposing invasion growth rates into stabilizing and equalizing components: we argue that these concepts are useful when used judiciously, but have often been employed in an overly simplified way to justify false claims., Funding Agencies|Swedish Research Council [VR 2017-05245]; NSF [DEB 1457515]

Species abundance distributions must reflect the dynamic processes involved in community assembly, but whether and when specific processes lead to distinguishable signals is not well understood. Biodiversity and species abundances may be shaped by a variety of influences, but particular attention has been paid to competition, which can involve neutral dynamics, where competitor abundances are governed only by demographic stochasticity and immigration, and dynamics driven by trait differences that enable stable coexistence through the formation of niches. Key recent studies of the species abundance patterns of communities with niches employ simple models with pre-imposed niche structure. These studies suggest that species abundance distributions are insensitive to the relative contributions of niche and neutral processes, especially when diversity is much higher than the number of niches. Here we analyze results from a stochastic population model with competition driven by trait differences. With this model, niche structure emerges as clumps of species that persist along the trait axis, and leads to more substantial differences from neutral species abundance distributions than have been previously shown. We show that heterogeneity in between-niche interaction strength (i.e., in the strength of competition between species in different niches) plays the dominant role in shaping the species abundances along the trait axis, acting as a biotic filter favoring species at the centers of niches. Furthermore, we show that heterogeneity in within-niche interactions (i.e., in the competition between species in the same niche) counteracts the influence of heterogeneity in between-niche interactions on the SAD to some degree. Our results suggest that competitive interactions that produce niches can also influence the shapes of SADs., Funding Agencies|National Science Foundation - Advancing Theory in Biology program [1038678]; National Science Foundation [OCI-1053575]; Tulane Center for Computational Science

Species abundance distributions must reflect the dynamic processes involved in community assembly, but whether and when specific processes lead to distinguishable signals is not well understood. Biodiversity and species abundances may be shaped by a variety of influences, but particular attention has been paid to competition, which can involve neutral dynamics, where competitor abundances are governed only by demographic stochasticity and immigration, and dynamics driven by trait differences that enable stable coexistence through the formation of niches. Key recent studies of the species abundance patterns of communities with niches employ simple models with pre-imposed niche structure. These studies suggest that species abundance distributions are insensitive to the relative contributions of niche and neutral processes, especially when diversity is much higher than the number of niches. Here we analyze results from a stochastic population model with competition driven by trait differences. With this model, niche structure emerges as clumps of species that persist along the trait axis, and leads to more substantial differences from neutral species abundance distributions than have been previously shown. We show that heterogeneity in between-niche interaction strength (i.e., in the strength of competition between species in different niches) plays the dominant role in shaping the species abundances along the trait axis, acting as a biotic filter favoring species at the centers of niches. Furthermore, we show that heterogeneity in within-niche interactions (i.e., in the competition between species in the same niche) counteracts the influence of heterogeneity in between-niche interactions on the SAD to some degree. Our results suggest that competitive interactions that produce niches can also influence the shapes of SADs., Funding Agencies|National Science Foundation - Advancing Theory in Biology program [1038678]; National Science Foundation [OCI-1053575]; Tulane Center for Computational Science

We give a comprehensive review of Chesson's coexistence theory, summarizing, for the first time, all its fundamental details in one single document. Our goal is for both theoretical and empirical ecologists to be able to use the theory to interpret their findings, and to get a precise sense of the limits of its applicability. To this end, we introduce an explicit handling of limiting factors, and a new way of defining the scaling factors that partition invasion growth rates into the different mechanisms contributing to coexistence. We explain terminology such as relative nonlinearity, storage effect, and growth-density covariance, both in a formal setting and through their biological interpretation. We review the theory's applications and contributions to our current understanding of species coexistence. While the theory is very general, it is not well suited to all problems, so we carefully point out its limitations. Finally, we critique the paradigm of decomposing invasion growth rates into stabilizing and equalizing components: we argue that these concepts are useful when used judiciously, but have often been employed in an overly simplified way to justify false claims., Funding Agencies|Swedish Research Council [VR 2017-05245]; NSF [DEB 1457515]

Species abundance distributions must reflect the dynamic processes involved in community assembly, but whether and when specific processes lead to distinguishable signals is not well understood. Biodiversity and species abundances may be shaped by a variety of influences, but particular attention has been paid to competition, which can involve neutral dynamics, where competitor abundances are governed only by demographic stochasticity and immigration, and dynamics driven by trait differences that enable stable coexistence through the formation of niches. Key recent studies of the species abundance patterns of communities with niches employ simple models with pre-imposed niche structure. These studies suggest that species abundance distributions are insensitive to the relative contributions of niche and neutral processes, especially when diversity is much higher than the number of niches. Here we analyze results from a stochastic population model with competition driven by trait differences. With this model, niche structure emerges as clumps of species that persist along the trait axis, and leads to more substantial differences from neutral species abundance distributions than have been previously shown. We show that heterogeneity in between-niche interaction strength (i.e., in the strength of competition between species in different niches) plays the dominant role in shaping the species abundances along the trait axis, acting as a biotic filter favoring species at the centers of niches. Furthermore, we show that heterogeneity in within-niche interactions (i.e., in the competition between species in the same niche) counteracts the influence of heterogeneity in between-niche interactions on the SAD to some degree. Our results suggest that competitive interactions that produce niches can also influence the shapes of SADs., Funding Agencies|National Science Foundation - Advancing Theory in Biology program [1038678]; National Science Foundation [OCI-1053575]; Tulane Center for Computational Science

We give a comprehensive review of Chesson's coexistence theory, summarizing, for the first time, all its fundamental details in one single document. Our goal is for both theoretical and empirical ecologists to be able to use the theory to interpret their findings, and to get a precise sense of the limits of its applicability. To this end, we introduce an explicit handling of limiting factors, and a new way of defining the scaling factors that partition invasion growth rates into the different mechanisms contributing to coexistence. We explain terminology such as relative nonlinearity, storage effect, and growth-density covariance, both in a formal setting and through their biological interpretation. We review the theory's applications and contributions to our current understanding of species coexistence. While the theory is very general, it is not well suited to all problems, so we carefully point out its limitations. Finally, we critique the paradigm of decomposing invasion growth rates into stabilizing and equalizing components: we argue that these concepts are useful when used judiciously, but have often been employed in an overly simplified way to justify false claims., Funding Agencies|Swedish Research Council [VR 2017-05245]; NSF [DEB 1457515]

Species abundance distributions must reflect the dynamic processes involved in community assembly, but whether and when specific processes lead to distinguishable signals is not well understood. Biodiversity and species abundances may be shaped by a variety of influences, but particular attention has been paid to competition, which can involve neutral dynamics, where competitor abundances are governed only by demographic stochasticity and immigration, and dynamics driven by trait differences that enable stable coexistence through the formation of niches. Key recent studies of the species abundance patterns of communities with niches employ simple models with pre-imposed niche structure. These studies suggest that species abundance distributions are insensitive to the relative contributions of niche and neutral processes, especially when diversity is much higher than the number of niches. Here we analyze results from a stochastic population model with competition driven by trait differences. With this model, niche structure emerges as clumps of species that persist along the trait axis, and leads to more substantial differences from neutral species abundance distributions than have been previously shown. We show that heterogeneity in between-niche interaction strength (i.e., in the strength of competition between species in different niches) plays the dominant role in shaping the species abundances along the trait axis, acting as a biotic filter favoring species at the centers of niches. Furthermore, we show that heterogeneity in within-niche interactions (i.e., in the competition between species in the same niche) counteracts the influence of heterogeneity in between-niche interactions on the SAD to some degree. Our results suggest that competitive interactions that produce niches can also influence the shapes of SADs., Funding Agencies|National Science Foundation - Advancing Theory in Biology program [1038678]; National Science Foundation [OCI-1053575]; Tulane Center for Computational Science

We give a comprehensive review of Chesson's coexistence theory, summarizing, for the first time, all its fundamental details in one single document. Our goal is for both theoretical and empirical ecologists to be able to use the theory to interpret their findings, and to get a precise sense of the limits of its applicability. To this end, we introduce an explicit handling of limiting factors, and a new way of defining the scaling factors that partition invasion growth rates into the different mechanisms contributing to coexistence. We explain terminology such as relative nonlinearity, storage effect, and growth-density covariance, both in a formal setting and through their biological interpretation. We review the theory's applications and contributions to our current understanding of species coexistence. While the theory is very general, it is not well suited to all problems, so we carefully point out its limitations. Finally, we critique the paradigm of decomposing invasion growth rates into stabilizing and equalizing components: we argue that these concepts are useful when used judiciously, but have often been employed in an overly simplified way to justify false claims., Funding Agencies|Swedish Research Council [VR 2017-05245]; NSF [DEB 1457515]

We give a comprehensive review of Chesson's coexistence theory, summarizing, for the first time, all its fundamental details in one single document. Our goal is for both theoretical and empirical ecologists to be able to use the theory to interpret their findings, and to get a precise sense of the limits of its applicability. To this end, we introduce an explicit handling of limiting factors, and a new way of defining the scaling factors that partition invasion growth rates into the different mechanisms contributing to coexistence. We explain terminology such as relative nonlinearity, storage effect, and growth-density covariance, both in a formal setting and through their biological interpretation. We review the theory's applications and contributions to our current understanding of species coexistence. While the theory is very general, it is not well suited to all problems, so we carefully point out its limitations. Finally, we critique the paradigm of decomposing invasion growth rates into stabilizing and equalizing components: we argue that these concepts are useful when used judiciously, but have often been employed in an overly simplified way to justify false claims., Funding Agencies|Swedish Research Council [VR 2017-05245]; NSF [DEB 1457515]

Species abundance distributions must reflect the dynamic processes involved in community assembly, but whether and when specific processes lead to distinguishable signals is not well understood. Biodiversity and species abundances may be shaped by a variety of influences, but particular attention has been paid to competition, which can involve neutral dynamics, where competitor abundances are governed only by demographic stochasticity and immigration, and dynamics driven by trait differences that enable stable coexistence through the formation of niches. Key recent studies of the species abundance patterns of communities with niches employ simple models with pre-imposed niche structure. These studies suggest that species abundance distributions are insensitive to the relative contributions of niche and neutral processes, especially when diversity is much higher than the number of niches. Here we analyze results from a stochastic population model with competition driven by trait differences. With this model, niche structure emerges as clumps of species that persist along the trait axis, and leads to more substantial differences from neutral species abundance distributions than have been previously shown. We show that heterogeneity in between-niche interaction strength (i.e., in the strength of competition between species in different niches) plays the dominant role in shaping the species abundances along the trait axis, acting as a biotic filter favoring species at the centers of niches. Furthermore, we show that heterogeneity in within-niche interactions (i.e., in the competition between species in the same niche) counteracts the influence of heterogeneity in between-niche interactions on the SAD to some degree. Our results suggest that competitive interactions that produce niches can also influence the shapes of SADs., Funding Agencies|National Science Foundation - Advancing Theory in Biology program [1038678]; National Science Foundation [OCI-1053575]; Tulane Center for Computational Science