Inhomogeneous maps and mathematical theory of selection

Journal of Difference Equations and Applications

Volumn 14, Issue 1, 2008, Pages 31-58

  Karev, Georgy P ^a  

^a NATIONAL INSTITUTES OF HEALTH   (United States)

Author keywords

Dynamics of distribution; Equations of Price; Fundamental theorem of natural selection; Inhomogeneous difference equation; Population model

Indexed keywords

EID: 36549053997     PISSN: 10236198     EISSN: 15635120     Source Type: Journal    
DOI: 10.1080/10236190701470233     Document Type: Article

References (33)

1. Barton, M.N. and Turelli, M., 1987, Adaptive landscapes, genetic distance and the evolution of quantitative characters. Genetical Research, 49, 157-173.
2. Berezovskaya, F., Karev, G. and Snell, T., 2005, Modeling the dynamics of natural rotifer populations: phase-parametric analysis. Ecological Complexity, 2, 395.
3. Burger, R., 2000, The Mathematical Theory of Recombination, Selection, and Mutation (New York: Wiley).
4. Crow, J.F. and Kimura, M., 1979, Efficiency of truncation selection. Proceedings of the National Academy of Sciences USA, 76, 396.
5. Crow, J.F. and Nagilaki, T., 1976, The rate of a character correlated with fitness. The American Naturalist, 110, 207.
6. Edwards, A.W.F., 1994, The fundamental theorem of natural selection. Biological Review, 69, 443.
7. Ewens, W.J., 2004, Mathematical Population Genetics, 2nd ed. (New York: Springer-Verlag).
8. Fisher, R. A., 1999, The Genetical Theory of Natural Selection: A Complete Variorum Edition (Oxford: Oxford University Press).
9. Frank, S.A., 1997, The Price equation, Fishers fundamental theorem, kin selection and causal analysis. Evolution, 1712, 51.
10. Frank, S.A., 1998, Foundation of Social Evolution (Princeton: Princeton University Press).
11. Frank, S.A. and Slatkin, M., 1992, Fishers fundamental theorem of natural selection. Trends in Evolution and Ecology, 7, 92.
12. Gorban, A.N., 1984, Equilibrium encircling. Equations of Chemical Kinetics and their Thermodynamic Analysis (Novosibirsk [in Russian]: Nauka).
13. Gorban, A.N., 2005, Systems with inheritance: dynamics of distributions with conservation of support, natural selection and finite-dimensional asymptotics, http://arxiv.org/PS_cache/ cond-mat/pdf/0405/ 0405451.pdf
14. Haldane, J.B.S., 1990, The Causes of Evolution (Princeton: Princeton Science Library, University Press).
15. Hamilton, W.D., 1970, Selfish and spiteful behavior in an evolutionary models. Nature, London 228, 1218.
16. Karev, G.P., 2006, Inhomogeneous maps: the basic theorems and some applications. In: R.P. Agarval and P. Kanishka (Eds.) Proceeding of the Conference on Differential and Difference Equations and Applications, p. 509.
17. Karev, G., Novozhilov, A. and Berezovskaya, F., 2006, Modeling the dynamics of inhomogeneous natural rotifer populations under toxicant exposure. Journal of Ecological Modeling (submitted; preprint http://arxiv. org/ftp/q-bio/papers/0509/0509009.pdf).
18. Knudsen, T., 2004, General selection theory and economic evolution: the Price equation and the genotype/phenotype distinction. Journal of Economic Methodology, 11.
19. Kotz, S., Balakrishnan, N. and Jonson, N., 2000, Continuous Multivariate Distributions (New York: Wiley), vol. 1.
20. Lewontin, R.C., 1974, The Genetic Basis of Evolutionary Change (New York: Columbia University Press).
21. Li, C.C., 1967, Fundamental theorem of natural selection. Nature, London 214, 505.
22. Page, K.M. and Nowak, M.A., 2002, Unifying evolutionary dynamics. Journal of Theoretical Biology, 219, 93.
23. Price, G.R., 1970, Selection and covariance. Nature, 227, 520.
24. Price, G.R., 1972a, Extension of covariance selection mathematics. Annals of Human Genetics, 35, 485.
25. Price, G.R., 1972b, Fishers fundamental theorem made clear. Annals of Human Genetics, 36, 129.
26. Price, G.R., 1995, The nature of selection. Journal of Theoretical Biology, 175, 389.
27. Rice, S.H., 2006, Evolutionary Theory (Sunderland, MA: Sinauer Associates, Inc.).
28. Ricker, W., 1954, Stock and recruitment. Journal of the Fisheries Research Board of Canada, 11, 559-663.
29. Robertson, A., 1968, The spectrum of generic variation. In: R.C. Lewontin (Ed.) Population Biology and Evolution (Syracuse: University Press), p. 5.
30. Roughgarden, J., 1979, Theory of Population Genetics and Evolutionary Ecology: An Introduction (New York: MacMillan Publishing Co. Inc.).
31. Semevsky, F.N. and Semenov, S.M., 1982, Mathematical Modeling of Ecological Processes (Leningrad: [in Russian] Gidrometeoizdat).
32. Snell, T.W. and Serra, M., 1998, Dynamics of natural rotifer populations. Hydrobiologia, 368, 29.
33. Shnol, E.E. and Kondrashov, A.S., 1994, Some relations between different characteristics of selection. Journal of Mathematical Biology, 32, 835.