Habitat destruction and the extinction debt

Tilman, David; May, Robert M.; Lehman, Clarence; Nowak, Martin A.

doi:10.1038/371065a0

Cited by 2,395 publications

(1,911 citation statements)

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“…One general way to explain these cases might be to relate them to catastrophic changes in the ecosystem properties such as, in mathematical terms, the disappearance of a steady state as a result of saddle-node bifurcation (Scheffer et al, 2009, Boettiger andHastings, 2012). Another scenario of regime shifts can be the existence of long-living transients, which provides an alternative explanation of sudden species extinction (Tilman et al, 1994, Schreiber, 2003. However, specific biological mechanisms and factors resulting in long living transients in various models using different mathematical frameworks often remain obscure (Hastings, 2004).…”

Section: Introductionmentioning

confidence: 99%

Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect

Морозов

Banerjee

Petrovskii

2016

Journal of Theoretical Biology

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Traditionally, mathematical modelling in population ecology is mainly focused on asymptotical behaviour of the model, i.e. as given by the system attractors. Recently, however, transient regimes and especially long-term transients have been recognized as playing a crucial role in the dynamics of ecosystems. In particular, long-term transients are a potential explanation of ecological regime shifts, when an apparently healthy population suddenly collapses and goes extinct.In this paper, we show that the interplay between delay in maturation and a strong Allee effect can result in long-term transients in a single species system. We first derive a simple 'conceptual' model of the population dynamics that incorporates both a strong Allee effect and maturation delay. Unlike much of the previous work, our approach is not empirical since our model is derived from basic principles. We show that the model exhibits a high complexity in its asymptotic dynamics including multi-periodic and chaotic attractors. We then show the existence of long-term transient dynamics in the system, when the population size oscillates for a long time between locally stable stationary states before it eventually settles either at the persistence equilibrium or goes extinct. The parametric space of the model is found to have a complex structure with the basins of attraction corresponding to the persistence and extinction states being of a complicated shape. This impedes the prediction of the eventual fate of the population, as a small variation in the maturation delay or the initial population size can either bring the population to extinction or ensure its persistence.3

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Section: Introductionmentioning

confidence: 99%

Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect

Морозов

Banerjee

Petrovskii

2016

Journal of Theoretical Biology

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“…While competitive exclusion may be irrelevant locally, if a species is going to survive longer than the life-span of a single habitat, their regulation and competitive exclusion has to be considered globally, on a metapopulation level (Tilman et al, 1994;Parvinen & Meszéna, in prep.). Chesson (1994Chesson ( , 2000b) distinguish between two types of fluctuation-induced stabilizing mechanisms: "storage effect" and "effect of relative non-linearity".…”

Section: Fluctuating Environmentmentioning

confidence: 99%

Competitive exclusion and limiting similarity: A unified theory

Meszéna

Gyllenberg

Pásztor

et al. 2006

Theoretical Population Biology

225

279

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“…It is known that both can lead to species extinction under conditions that correspond to excessive change, including those that result in the destruction of the species' habitat [51].…”

Section: Introductionmentioning

confidence: 99%

Resource Consumption, Sustainability, and Cancer

2014

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Preserving a system's viability in the presence of diversity erosion is critical if the goal is to sustainably support biodiversity. Reduction in population heterogeneity, whether inter-or intraspecies, may increase population fragility, either decreasing its ability to adapt e ectively to environmental changes or facilitating the survival and success of ordinarily rare phenotypes. The latter may result in over-representation of individuals who may participate in resource utilization patterns that can lead to over-exploitation, exhaustion, and, ultimately, collapse of both the resource and the population that depends on it. Here, we aim to identify regimes that can signal whether a consumer-resource system is capable of supporting viable degrees of heterogeneity. The framework used here is an expansion of a previously introduced consumer-resource type system of a population of individuals classi ed by their resource consumption. Application of the Reduction Theorem to the system enables us to evaluate the health of the system through tracking both the mean value of the parameter of resource (over)consumption, and the population variance, as both change over time. The article concludes with a discussion that highlights applicability of the proposed system to investigation of systems that are a ected by particularly devastating overly-adapted populations, namely, cancerous cells. Potential intervention approaches for system management are discussed in the context of cancer therapies.

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Habitat destruction and the extinction debt

Cited by 2,395 publications

References 24 publications

Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect

Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect

Competitive exclusion and limiting similarity: A unified theory

Resource Consumption, Sustainability, and Cancer

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