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A selection-migration model in population genetics. (English) Zbl 0325.92009

MSC:
92D10Genetics
92D25Population dynamics (general)
References:
[1]Aronson, D. G., Weinberger, H. F.: Nonlinear diffusion in population genetics, combustion. and nerve propogation. Proc. Tulane Progr. in Partial Differential Eqns. Springer Lecture Notes in Mathematics, 1975.
[2]Chafee, N.: Asymptotic behaviour for solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary conditions. J. Differential Equations.
[3]Chafee, N.: Behaviour of solutions leaving the neighborhood of a saddle point for a nonlinear evolution equation, preprint.
[4]Conley, C.: An application of Wazewski’s method to a nonlinear boundary value problem which arises in population genetics, Univ. of Wisconsin Math. Research Center Tech. Summary Report No. 1444, 1974.
[5]Fisher, R. A.: Gene frequencies in a cline determined by selection and diffusion. Biometrics 6, 353-361 (1950). · doi:10.2307/3001780
[6]Fleming, W. H.: A nonlinear parabolic equation arising from a selection-migration model in genetics. IRIA Seminars Review, 1974.
[7]Haldane, J. B. S.: The theory of a cline. J. Genet. 48, 277-284 (1948). · doi:10.1007/BF02986626
[8]Hestenes, M. R.: Calculus of Variations and Optimal Control Theory. Wiley 1966.
[9]Hoppensteadt, F. C.: Analysis of a Stable Polymorphism Arising in a Selection-Migration Model in Population Genetics dispersion and selection. J. Math. Biology 2, 235-240 (1975). · Zbl 0318.92020 · doi:10.1007/BF00277152
[10]Karlin, S.: Population division and migration-selection interaction. Population Genetics and Ecology. Academic Press 1976.
[11]Karlin, S., Richter-Dyn, N.: Some theoretical analysis of migration-selection interaction in a cline: a generalized 2 range environment. Population Genetics and Ecology. Academic Press 1976.
[12]Karlin, S., McGregor J., unpublished.
[13]Lions, J. L.: Équations Differentielles Operationelles. Berlin-Göttingen-Heidelberg: Springer, 1961.
[14]Lions, J. L.: Quelques Méthodes de Résolution des Problèmes aux Limites Nonlinéaires. Dunod, 1969.
[15]Lions, J. L., Magenes, E.: Problèmes aux Limites Non-Homogènes et Applications, vols. I, II. Dunod 1968.
[16]Nagylaki, T.: Conditions for the existence of clines. Univ. of Wisconsin Madison Genetics Lab paper No. 1787, 1974.
[17]Slatkin, M.: Gene flow and selection in a cline. Genetics 75, 733-756 (1973).