Allee effects and resilience in stochastic populations

Dennis, B. R.; Assas, Laila M; Elaydi, Saber; Kwessi, Eddy; Livadiotis, G.

doi:10.1007/s12080-015-0288-2

Cited by 83 publications

(61 citation statements)

References 56 publications

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“…Indeed, buffer mechanisms have been suggested to reduce the variation in population growth rates associated with the environmental noise [19], which in turn decreases the time populations spend at low abundances levels [48] and, consequently, may reduce the extinction risk of small populations subjected to negative effects of stochasticity. This theoretical scenario is likely to occur in our study system, where floaters buffer the extinction risk of small local populations subjected to both demographic and environmental stochasticity [5].…”

Section: Discussionmentioning

confidence: 99%

“…The buffer effect of floaters is expected to be particularly relevant in scenarios of severe habitat loss and fragmentation, where species often survive as small local breeding populations subjected to detrimental and synergic impacts of stochasticity and the Allee effect [48]. As widespread phenomena and major drivers of eco-evolutionary dynamics [9], habitat loss and fragmentation may provide researchers with a suitable general framework to investigate whether and how a suitable surplus of non-breeding individuals, such as floaters, may ameliorate the resilience and stability of small populations.…”

Section: Discussionmentioning

confidence: 99%

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Floaters may buffer the extinction risk of small populations: an empirical assessment

Robles

Ciudad

2017

Proc. R. Soc. B.

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The high extinction risk of small populations is commonly explained by reductions in fecundity and breeder survival associated with demographic and environmental stochasticity. However, ecological theory suggests that population extinctions may also arise from reductions in the number of floaters able to replace the lost breeders. This can be particularly plausible under harsh fragmentation scenarios, where species must survive as small populations subjected to severe effects of stochasticity. Using a woodpecker study in fragmented habitats (2004 -2016), we provide here empirical support for the largely neglected hypothesis that floaters buffer population extirpation risks. After controlling for population size, patch size and the intrinsic quality of habitat, populations in patches with floaters had a lower extinction probability than populations in patches without floaters (0.013 versus 0.131). Floaters, which often replace the lost breeders, were less likely to occur in small and low-quality patches, showing that population extirpations may arise from unnoticed reductions in floater numbers in poor-quality habitats. We argue that adequate pools of the typically overlooked floaters may buffer extirpation risks by reducing the detrimental impacts of demographic and environmental stochasticity. However, unravelling the influence of floaters in buffering stochastic effects and promoting population stability require additional studies in an ample array of species and stochastic scenarios.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Floaters may buffer the extinction risk of small populations: an empirical assessment

Robles

Ciudad

2017

Proc. R. Soc. B.

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“…Developing tools to capture this more nuanced resilience to repeated state-space perturbations represents a possible area for contribution from dynamical systems research. For an approach using stochastic differential equations, see Dennis et al [2015].…”

Section: Resilience To a One-time State Variable Perturbationmentioning

confidence: 99%

A Mathematical Review of Resilience in Ecology

Meyer

2016

Natural Resource Modeling

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Rising interest in the resilience of ecological systems has spawned diverse interpretations of the term's precise meaning, particularly in the context of resilience quantification. The purpose of this paper is twofold. The first aim is to use the language of dynamical systems to organize and scrutinize existing resilience definitions within a unified framework. The second aim is to provide an introduction for mathematicians to the ecological concept of resilience, a potential area for expanded quantitative research. To frame the discussion of resilience in dynamical systems terms, a model consisting of ordinary differential equations is assumed to represent the ecological system. The question “resilience of what to what?” posed by Carpenter et al. [2001] informs two broad categories of definitions, based on resilience to state variable perturbations and to parameter changes, respectively. Definitions of resilience to state variable perturbations include measures of basin size (relevant to one‐time perturbations) and basin steepness (relevant to repeated perturbations). Resilience to parameter changes has been quantified by viewing parameters as state variables but has also considered the reversibility of parameter shifts. Quantifying this reversibility and fully describing how recovery rates determine resilience to repeated state‐space perturbations emerge as two opportunities for mathematics research.

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“…Take for instance the concept of "potential functions". For continuous time, deterministic population dynamics models of the form dn/dt = m(n), the potential function is defined as the function u(n) satisfying du(n) dn = m(n)[51]. This function is deeply connected with deterministic waiting times.…”

mentioning

confidence: 99%

“…This function is deeply connected with deterministic waiting times. As Dennis et al[51] point out, the waiting time t(n) needed to reach abundance n from an initial abundance x can be written as a function of the potential function as follows…”

mentioning

confidence: 99%

Ecological change points: The strength of density dependence and the loss of history

Ponciano

Taper

Dennis

2017

Preprint

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Change points in the dynamics of animal abundances have extensively been recorded in historical time series records.Little attention has been paid to the theoretical dynamic consequences of such change-points. Here we propose a change-point model of stochastic population dynamics. This investigation embodies a shift of attention from the problem of detecting when a change will occur, to another non-trivial puzzle: using ecological theory to understand and predict the post-breakpoint behavior of the population dynamics. The proposed model and the explicit expressions derived here predict and quantify how density dependence modulates the influence of the pre-breakpoint parameters into the post-breakpoint dynamics. Time series transitioning from one stationary distribution to another contain information about where the process was before the change-point, where is it heading and how long it will take to transition, and here this information is explicitly stated. Importantly, our results provide a direct connection of the strength of density dependence with theoretical properties of dynamic systems, such as the concept of resilience. Finally, we illustrate how to harness such information through maximum likelihood estimation for state-space models, and test the model robustness to widely different forms of compensatory dynamics. The model can be used to estimate important quantities in the theory and practice of population recovery.

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Allee effects and resilience in stochastic populations

Cited by 83 publications

References 56 publications

Floaters may buffer the extinction risk of small populations: an empirical assessment

Floaters may buffer the extinction risk of small populations: an empirical assessment

A Mathematical Review of Resilience in Ecology

Ecological change points: The strength of density dependence and the loss of history

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