Robust Permanence for Ecological Maps

Roth, Grégory; Salceanu, Paul L.; Schreiber, Sebastian J.

doi:10.1137/16m1066440

Cited by 13 publications

(26 citation statements)

References 33 publications

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“…When the equilibrium is stable, invasion cannot occur and the invader population size should return to 0 when perturbed. When the zero equilibrium of the invader is unstable, the invading population can grow in numbers when perturbed above zero (Roth et al., in press ). Coexistence is predicted to occur when the zero equilibria of both species are unstable when evaluated at the single species equilibrium of the other species.…”

Section: Methodsmentioning

confidence: 99%

“…Coexistence is predicted to occur when the zero equilibria of both species are unstable when evaluated at the single species equilibrium of the other species. This general approach is valid for a wide range of complex population and community dynamics including those that are chaotic (Roth et al., in press ). For the scenarios modeled here, the single species equilibrium distributions were stable across the range of niche shift and size‐dependent competitive asymmetries (Appendix : Fig.…”

Section: Methodsmentioning

confidence: 99%

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Predicting coexistence in species with continuous ontogenetic niche shifts and competitive asymmetry

Bassar

Travis

Coulson

2017

Ecology

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A longstanding problem in ecology is whether structured life cycles impede or facilitate coexistence between species. Theory based on populations with only two discrete stages in the life-cycle indicates that for two species to coexist, at least one must shift its niche between stages and each species must be a better competitor in one of the niches. However, in many cases, niche shifts are associated with changes in an underlying continuous trait like body size and we have few predictions concerning conditions for coexistence for such a widespread form of ontogenetic development. We develop a framework for analyzing species coexistence based on Integral Projection Models (IPMs) that incorporates continuous ontogenetic changes in both the resource niche and competitive ability. We parameterize the model using experimental data from Trinidadian guppies and show how niche shifts and competitive symmetries impact species coexistence. Overall, our results show that the effects of competition on fitness depend upon trait-mediated niche-separation, trait-mediated competitive asymmetry in the part of the niche that is shared across body sizes, and the sensitivity of fitness to body size. Interactions among these processes generate multiple routes to coexistence. We discuss how our modeling framework expands results from two-stage models to mutli-stage or continuous stage models and allows for deriving predictions that can be tested in populations displaying continuous changes in niche use and competitive ability.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Predicting coexistence in species with continuous ontogenetic niche shifts and competitive asymmetry

Bassar

Travis

Coulson

2017

Ecology

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“…When the trivial equilibrium of the invader is unstable, then the population should move towards a positive attractor. The interpretation of an unstable equilibrium under these conditions is that each species could grow when rare (Roth et al 2016). When the trivial equilibrium of the invader is stable, then the population should return towards N i = 0.…”

Section: Model Analysismentioning

confidence: 99%

“…When the trivial equilibrium of the invader is stable, then the population should return towards N i = 0. Such an approach is valid for a wide range of population and community dynamics including those that are chaotic (Roth et al 2016).…”

Section: Model Analysismentioning

confidence: 99%

Predicting Coexistence in Species with Continuous Ontogenetic Niche Shifts and Competitive Asymmetry

Bassar

Travis²,

Coulson

2017

Preprint

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A longstanding problem in ecology is whether structured life cycles impede or facilitate coexistence between species. Theory based on populations with two discrete stages in the life-cycle indicates that coexistence requires at least one species to shift its niche between stages and that each species is a better competitor in one of the niches. However, in many cases, niche shifts are associated with changes in an underlying continuous trait like organism size and we have few predictions for how the conditions for coexistence are affected by this type of ontogenetic dynamics. Here we develop a framework for analyzing species coexistence based on Integral Projection Models (IPMs) that incorporates continuous ontogenetic changes in both the resource niche and competitive ability. We parameterize the model using experimental data from Trinidadian guppies and make predictions about how niche shifts and competitive symmetries allow or prevent species coexistence. Overall, our results show that the effects of competition on fitness depend upon trait-mediated niche-separation, trait-mediated competitive asymmetry in the part of the niche that is shared across body sizes, and the sensitivity of fitness to body size. When all three conditions are considered, we find multiple ecological and evolutionary routes to coexistence. When both species can shift their niche with increasing body size and competition for resources among the species and sizes is symmetric, then the species that shifts its niche to a greater degree with ontogeny will competitively exclude the other species. When competitive ability increases with increasing body size, then the two species can coexist when the better competitor shifts its niche with body size to a lesser degree than the weaker competitior. This region of coexistence shrinks as the better competitor increasingly shifts its niche with increasing size. When both species shift their niches with size, but each is a better competitor on resources used by smaller or larger individuals, then the model predicts an alternative stable state over some range of niche shifts. We discuss how our results provide new insights into species coexistence and the evolutionary consequences of size-structured interspecific competition.

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“… 2011a ; Roth et al. 2017 ). However, there is no general framework for dealing explicitly with both internal and external variables.…”

Section: Introductionmentioning

confidence: 99%

Robust permanence for ecological equations with internal and external feedbacks

Patel

Schreiber

2017

J. Math. Biol.

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Species experience both internal feedbacks with endogenous factors such as trait evolution and external feedbacks with exogenous factors such as weather. These feedbacks can play an important role in determining whether populations persist or communities of species coexist. To provide a general mathematical framework for studying these effects, we develop a theorem for coexistence for ecological models accounting for internal and external feedbacks. Specifically, we use average Lyapunov functions and Morse decompositions to develop sufficient and necessary conditions for robust permanence, a form of coexistence robust to large perturbations of the population densities and small structural perturbations of the models. We illustrate how our results can be applied to verify permanence in non-autonomous models, structured population models, including those with frequency-dependent feedbacks, and models of eco-evolutionary dynamics. In these applications, we discuss how our results relate to previous results for models with particular types of feedbacks.

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Robust Permanence for Ecological Maps

Cited by 13 publications

References 33 publications

Predicting coexistence in species with continuous ontogenetic niche shifts and competitive asymmetry

Predicting coexistence in species with continuous ontogenetic niche shifts and competitive asymmetry

Predicting Coexistence in Species with Continuous Ontogenetic Niche Shifts and Competitive Asymmetry

Robust permanence for ecological equations with internal and external feedbacks

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