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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This research was supported [in part] by the Intramural Research Program of the NIH, National Library of Medicine. The author thanks Dr. E. Koonin, Dr. F. Berezovsky, Dr. A. Novozhilov and anonymous reviewer for valuable comments.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Karev, G.P. On mathematical theory of selection: continuous time population dynamics. J. Math. Biol. 60, 107–129 (2010). https://doi.org/10.1007/s00285-009-0252-0
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DOI: https://doi.org/10.1007/s00285-009-0252-0
Keywords
- Selection system
- Dynamics of distribution
- The Price equation
- Inhomogeneous logistic model
- Replicator equation