The competitive dynamics of populations subject to an Allee effect

Abstract The Allee effect is introduced into intraspecific and two-species competitive models. We use phase plane analysis and simulation to investigate the dynamics of these models. Combining simple modeling and simulations, we demonstrate that the Allee effect alone could lead to alternative stable states in two-species competitive systems. In such systems, if interspecific competition is intense, both species may go extinct even if their population densities are high. Compared to a Lotka–Volterra competitive system, systems including Allee effect show obvious destabilization.

[1]  W. C. Allee.  The social life of animals , 1938 .

[2]  Robert M. May,et al.  Theoretical Ecology: Principles and Applications , 1981 .

[3]  R. Lande.  Genetics and demography in biological conservation. , 1988, Science.

[4]  M. Gilpin,et al.  Multiple domains of attraction in competition communities , 1976, Nature.

[5]  Scott Ferson,et al.  Risk assessment in conservation biology , 1993 .

[6]  Density-Dependent Selection II. The Allee Effect , 1979, The American Naturalist.

[7]  V. Volterra.  Variations and Fluctuations of the Number of Individuals in Animal Species living together , 1928 .

[8]  P. Kareiva,et al.  Allee Dynamics and the Spread of Invading Organisms , 1993 .

[9]  M. Begon,et al.  Population Ecology: A Unified Study of Animals and Plants , 1982 .

[10]  Richard R. Veit,et al.  Dispersal, Population Growth, and the Allee Effect: Dynamics of the House Finch Invasion of Eastern North America , 1996, The American Naturalist.

[11]  R. Lande,et al.  Extinction Thresholds in Demographic Models of Territorial Populations , 1987, The American Naturalist.

[12]  Michael A. McCarthy,et al.  The Allee effect, finding mates and theoretical models , 1997 .

[13]  Ilkka Hanski,et al.  Single‐species metapopulation dynamics: concepts, models and observations , 1991 .

[14]  Alfred J. Lotka,et al.  The growth of mixed populations: Two species competing for a common food supply , 1978 .

[15]  W. Kunin.  Sex and the single mustard : population density and pollinator behavior effects on seed-set , 1993 .

[16]  M. Begon,et al.  Ecology: Individuals, Populations and Communities , 1986 .

[17]  B. Young,et al.  Do Tropical Bird‐Pollinated Plants Exhibit Density‐Dependent Interactions? Field Experiments , 1991 .

[18]  P. Amarasekare,et al.  Allee Effects in Metapopulation Dynamics , 1998, The American Naturalist.

[19]  Ilkka Hanski,et al.  Allee effect and population dynamics in the Glanville fritillary butterfly , 1998 .

[20]  R. Lande,et al.  Optimal harvesting, economic discounting and extinction risk in fluctuating populations , 1994, Nature.

[21]  J. Beddington.  Age distribution and the stability of simple discrete time population models. , 1974, Journal of theoretical biology.

[22]  Brian Dennis,et al.  ALLEE EFFECTS: POPULATION GROWTH, CRITICAL DENSITY, AND THE CHANCE OF EXTINCTION , 1989 .

[23]  Frederic A. Hopf,et al.  The role of the Allee effect in species packing , 1985 .

[24]  A. Dobson,et al.  The population dynamics and conservation of primate populations. , 1989, Conservation biology : the journal of the Society for Conservation Biology.

[25]  Thomas Stephan,et al.  Stochastic extinction models discrete in time , 1994 .

[26]  T. Allison.  Pollen Production and Plant Density Affect Pollination and Seed Production in Taxus Canadensis , 1990 .

[27]  R. May.  Thresholds and breakpoints in ecosystems with a multiplicity of stable states , 1977, Nature.

[28]  T. Birkhead.  The Effect of Habitat and Density on Breeding Success in the Common Guillemot (Uria aalge) , 1977 .

[29]  W. C. Allee.  Animal Aggregations: A Study in General Sociology , 1931 .