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By John Burdon Sanderson Haldane

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Extra resources for A Mathematical Theory of Natural and Artificial Selection

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KOENIGS. Darb. Bull. (2) 7, p. 340, 1883. HALDANE. Trans. Camb. Phil. Soc. 23, p. 19, 1924. HALDANE. Biol. Proc. Camb. Phil. Soc. 1, p. 158, 1924. 7. MBTZ. Proc. Nat. Ac. Sci. 12, p. 690, 1926. 220 Mr Haldane, A mathematical theory A mathematical theory of natural and artificial selection. ) By Mr J. B. S. HALDANE, Trinity College. ] It is generally believed that isolation has played an important part in evolution. g. a cave or a desert, it must not be swamped in each generation by migrants from the original habitat.

Hence there are two types of heterozygous male, which may be symbolized by A(a) and (A)a according as the A is received from the mother or father. They yield A and a spermatozoa respectively, the other genotypes behaving normally. In the absence of selection let eggs and spermatozoa be produced by the mth generation in the proportions umA : la and vmA : la, respectively. The next generation is therefore : ? umvmAA : (um + vm)Aa : laa. J umvmAA : umA(a): vm(A)a : laa. Hence which is the same as equation (6'0) of Part I (5).

AB : rnrn'aB. aB : (qnsn' + qn'sn)Abab : (rnsn' + rn'sn) aBab : snsn'abab. , are given by the same expressions with I' substituted for I. , same constant value u, while pn + rn _ pn' + rn' _ VOL. XX11I. PART IV. 25 370 Mr Haldane, A mathematical theory of We may therefore write: uv P + X n. Pn - rn'- v Xn'; Sn' = + *»')• . •. 2xn+1 = (1 - 21) (xn + xn'); 2xn+1' = (1 - 2V) {xn + xn'). Hence if x0 + x0' = c, (6-0). Hence the proportions of the various types of gamete approach asymptotically those which would be reached in one generation without linkage, the ratio of successive differences from the final values being l — l—l'.

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