On mathematical theory of selection: Continuous time population dynamics

Details On mathematical theory of selection: Continuous time population dynamics On mathematical theory of selection: Continuous time population dynamics

2008-12-22

arxiv.org/abs/0812.4280v2

Volume 60, Number 1 / January, 2010

Biology

Quantitative Biology

Populations and Evolution

29 pages; published in J. of Mathematical Biology

Scientific paper

Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct explicit solutions of the models are developed. All statistical characteristics of interest, such as the mean values of the fitness or any trait can be computed effectively, and the results depend in a crucial way on the initial distribution. The developed theory provides an effective method for solving selection systems; it reduces the initial complex model to a special system of ordinary differential equations (the escort system). Applications of the method to the Price equations are given; the solutions of some particular inhomogeneous Malthusian, Ricker and logistic-like models used but not solved in the literature are derived in explicit form.

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