On mathematical theory of selection: continuous time population dynamics |
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Authors: | Georgiy P Karev |
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Institution: | (1) Department of Rural Economy, University of Alberta, Edmonton, Alberta, Canada, T6G 2H1 |
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Abstract: | 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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Keywords: | |
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