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      Chaos and Bifurcations of a Leslie-Gower Food Chain with Strong Allee Effect

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      Journal: Discrete Dynamics in Nature and Society
      Publisher: Hindawi Limited

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          Abstract

          Allee effect, as an important biological phenomenon, has been considered in many ecosystems, whereas, its influence on interactions of three or more species is little investigated. In this paper we modify a three-species Leslie-Gower type food chain system by incorporating the strong Allee effect into the source. Our results show that the existence of Allee effect contributes to the occurrence of more complex dynamics of the system, including Hopf, saddle-node, transcritical, saddle-node-Hopf, period-doubling, and period-halving bifurcations and chaos.

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          Consequences of the Allee effect for behaviour, ecology and conservation.

          Philip A. Stephens, William J. Sutherland (1999)
          Warder C. Allee brought attention to the possibility of a positive relationship between aspects of fitness and population size 50 years ago. Until recently, however, this concept was generally regarded as an intriguing but relatively unimportant aspect of population ecology. Increasing appreciation that Allee effects must be incorporated into models of population dynamics and habitat use, together with recent interest in the implications of sociality for conservation, have shown that for ecology and conservation the consequences of the Allee effect are profound. The Allee effect can be regarded not only as a suite of problems associated with rarity, but also as the basis of animal sociality.
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            Animal aggregations, a study in general sociology. / by W. C. Allee.

            W. Allee (1931)
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              Size-dependent life-history traits promote catastrophic collapses of top predators.

              André de Roos, Lennart Persson (2002)
              Catastrophic population collapses such as observed in many exploited fish populations have been argued to result from depensatory growth mechanisms (i.e., reduced reproductive success at low population densities, also known as Allee effect). Empirical support for depensation from population-level data is, however, hard to obtain and inconclusive. Using a size-structured, individual-based model we show that catastrophic population collapses may nonetheless be an intrinsic property of many communities, because of two general aspects of individual life history: size- and food-dependent individual growth and individual mortality decreasing with body size. Positive density dependence, characteristic for depensatory growth mechanisms and catastrophic behavior, results as a direct and robust consequence of the interplay between these individual life-history traits, which are commonly found in many species.
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                Author and article information

                Journal
                Title: Discrete Dynamics in Nature and Society
                Abbreviated Title: Discrete Dynamics in Nature and Society
                Publisher: Hindawi Limited
                ISSN (Print): 1026-0226
                ISSN (Electronic): 1607-887X
                Publication date Created: 2015
                Publication date (Print): 2015
                Volume: 2015
                Issue:
                Pages: 1-10
                Article
                DOI: 10.1155/2015/430985
                SO-VID: 47c479f5-9106-4ea1-b92e-d45c672bdfc3
                Copyright © © 2015
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                http://creativecommons.org/licenses/by/3.0/

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