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2007, Volume 7, Issue 4: 683-698. Doi: 10.3934/dcdsb.2007.7.683
This issue Previous Article Next Article Renormalization group analysis of nonlinear diffusion equations with time dependent coefficients: Analytical results

Competitive exclusion and coexistence in a nonlinear refuge-mediated selection model

  • 1.

    Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010

  • 2.

    Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504

Received:  August 31, 2006
Revised:  January 31, 2007
Published:  October 2007
Abstract Related Papers Cited by
    Abstract
  • A selection model with $n$ traits is considered. It is assumed that the mortality function is density dependent and that individuals with "weak" traits are able to disperse to a safe refuge patch and avoid competition with individuals carrying the strongest trait. It is shown that if any subpopulation with a "weak" trait does not have a safe refuge then it will become extinct. Therefore, for survival of $n$ traits $n-1$ safe refuge patches are needed. When $n-1$ refuge patches are available global stability of the interior equilibrium is proved provided that the fittest trait is sufficiently better than the other traits. Finally, two special cases with linear and Beverton-Holt density dependent mortality functions are studied in detail.
    Mathematics Subject Classification: Primary: 92D25.

    Citation:
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