2007/01/31 by Georgy P. Karev, Karev, Georgy P.
Biochemistry, Genetics and Molecular Biology · Social Sciences · #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #Gene Regulatory Network Analysis #Populations and Evolution (q-bio.PE) #Quantitative Methods (q-bio.QM) #q-bio.PE #q-bio.QM
paper · pdf · doi:10.48550/arxiv.q-bio/0701054
35 pages, 5 figures; submitted to JDEA
arxiv created 2007/01/31 · openalex publication_date 2007/01/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we develop a theory of general selection systems with discrete time and explore the evolution of selection systems, in particular, inhomogeneous populations. We show that the knowledge of the initial distribution of the selection system allows us to determine explicitly the system distribution at the entire time interval. All statistical characteristics of interest, such as mean values of the fitness or any trait can be predicted effectively for indefinite time and these predictions dramatically depend on the initial distribution. The Fisher Fundamental theorem of natural selection (FTNS) and more general the Price equations are the famous results of the mathematical selection theory. We show that the problem of dynamic insufficiency for the Price equations and for the FTNS can be resolved within the framework of selection systems. Effective formulas for solutions of the Price equations and for the FTNS are derived. Applications of the developed theory to some other problems of mathematical biology (dynamics of inhomogeneous logistic and Ricker model, selection in rotifer populations) are also given. Complex behavior of the total population size, the mean fitness (in contrast to the plain FTNS) and other traits is possible for inhomogeneous populations with density-dependent fitness. The temporary dynamics of these quantities can be investigated with the help of suggested methods.