# American Institute of Mathematical Sciences

June  2007, 7(4): 683-698. doi: 10.3934/dcdsb.2007.7.683

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

 1 Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010, United States, United States 2 Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504

Received  September 2006 Revised  February 2007 Published  March 2007

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.
Citation: Azmy S. Ackleh, Youssef M. Dib, S. R.-J. Jang. Competitive exclusion and coexistence in a nonlinear refuge-mediated selection model. Discrete & Continuous Dynamical Systems - B, 2007, 7 (4) : 683-698. doi: 10.3934/dcdsb.2007.7.683
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