American Institute of Mathematical Sciences

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2005, 2005(Special): 487-496. doi: 10.3934/proc.2005.2005.487

Dynamics of heterogeneous populations and communities and evolution of distributions

Georgy P. Karev 1,

1. 

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

Received  September 2004 Revised  April 2005 Published  September 2005

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: evolution of the distribution of traits., Heterogeneous populations.
Mathematics Subject Classification: Primary: 92B0.
Citation: Georgy P. Karev. Dynamics of heterogeneous populations and communities and evolution of distributions. Conference Publications, 2005, 2005 (Special) : 487-496. doi: 10.3934/proc.2005.2005.487
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