ChisholmFilotas2009

Reference

Chisholm, R.A. and Filotas, E. (2009) Critical slowing down as an indicator of transitions in two-species models. Journal of Theoretical Biology, 257(1):142-149. (Scopus )

Abstract

Transitions in ecological systems often occur without apparent warning, and may represent shifts between alternative persistent states. Decreasing ecological resilience (the size of the basin of attraction around a stable state) can signal an impending transition, but this effect is difficult to measure in practice. Recent research has suggested that a decreasing rate of recovery from small perturbations (critical slowing down) is a good indicator of ecological resilience. Here we use analytical techniques to draw general conclusions about the conditions under which critical slowing down provides an early indicator of transitions in two-species predator-prey and competition models. The models exhibit three types of transition: the predator-prey model has a Hopf bifurcation and a transcritical bifurcation, and the competition model has two saddle-node bifurcations (in which case the system exhibits hysteresis) or two transcritical bifurcations, depending on the parameterisation. We find that critical slowing down is an earlier indicator of the Hopf bifurcation in predator-prey models in which prey are regulated by predation rather than by intrinsic density-dependent effects and an earlier indicator of transitions in competition models in which the dynamics of the rare species operate on slower timescales than the dynamics of the common species. These results lead directly to predictions for more complex multi-species systems, which can be tested using simulation models or real ecosystems. © 2008 Elsevier Ltd. All rights reserved.

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@ARTICLE { ChisholmFilotas2009,
    AUTHOR = { Chisholm, R.A. and Filotas, E. },
    TITLE = { Critical slowing down as an indicator of transitions in two-species models },
    JOURNAL = { Journal of Theoretical Biology },
    YEAR = { 2009 },
    VOLUME = { 257 },
    PAGES = { 142-149 },
    NUMBER = { 1 },
    ABSTRACT = { Transitions in ecological systems often occur without apparent warning, and may represent shifts between alternative persistent states. Decreasing ecological resilience (the size of the basin of attraction around a stable state) can signal an impending transition, but this effect is difficult to measure in practice. Recent research has suggested that a decreasing rate of recovery from small perturbations (critical slowing down) is a good indicator of ecological resilience. Here we use analytical techniques to draw general conclusions about the conditions under which critical slowing down provides an early indicator of transitions in two-species predator-prey and competition models. The models exhibit three types of transition: the predator-prey model has a Hopf bifurcation and a transcritical bifurcation, and the competition model has two saddle-node bifurcations (in which case the system exhibits hysteresis) or two transcritical bifurcations, depending on the parameterisation. We find that critical slowing down is an earlier indicator of the Hopf bifurcation in predator-prey models in which prey are regulated by predation rather than by intrinsic density-dependent effects and an earlier indicator of transitions in competition models in which the dynamics of the rare species operate on slower timescales than the dynamics of the common species. These results lead directly to predictions for more complex multi-species systems, which can be tested using simulation models or real ecosystems. © 2008 Elsevier Ltd. All rights reserved. },
    ADDRESS = { Complex Systems Laboratory, Département de Géographie, Université de Montréal, C.P. 6128, Succ. Centre-ville, Montréal, Que. H3C 3J7, Canada },
    COMMENT = { Cited By (since 1996):17 Export Date: 13 February 2014 Source: Scopus },
    KEYWORDS = { Alternative stable states, Critical slowing down, Leading indicators, Lotka-Volterra competition, Paradox of enrichment, Resilience },
    OWNER = { Luc },
    TIMESTAMP = { 2014.02.13 },
    URL = { http://www.scopus.com/inward/record.url?eid=2-s2.0-59649106299&partnerID=40&md5=807b68fff0d3158c5c618d18311d1203 },
}

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