Dynamics of heterogeneous populations and communities and evolution of distributions

Pages: 487 - 496, Issue Special, August 2005

 Abstract        Full Text (215.0K)              

Georgy P. Karev - Oak Ridge Institute for Science and Education (ORISE) 8600 Rockville Pike, Bldg. 38A, Rm. 5N511N, Bethesda, MD 20894, United States (email)

Abstract: Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Inhomogeneous models of populations and communities allow for birth and death rates to vary among individuals; recently, theorems of existence and asymptotic of solutions of such models were investigated. Here we develop another approach to modeling heterogeneous populations by reducing the model to the Cauchy problem for a special system of ODEs. As a result, the total population size and current distribution of the vector-parameter can be found in explicit analytical form or computed effectively. The developed approach is extended to the models of inhomogeneous communities.

Keywords:  Heterogeneous populations, evolution of the distribution of traits.
Mathematics Subject Classification:  Primary: 92B05.

Received: September 2004;      Revised: April 2005;      Published: September 2005.