A Mathematical Theory of Natural and Artificial Selection by John Burdon Sanderson Haldane

By John Burdon Sanderson Haldane

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Carn. Inst. Wash. , 237. Pearl. 1907. Biometrika 5, 213. Pearl. 1912. Am Nat. 46, 130. Pearson. 1904. Phil. Trans. R. Soc. A203, 53. Pearson. 1908. Proc. R. Soc. 54, 72. Pearson and Lee. 1903. Biometrika 2, 371. Punnett. Mimicry in Butterflies, 154. Punnett. 1917. J. Hered. 8, 464. Renner. 1917. Z. indukt. -u. Verblehre 18, 121. Schimidt. 1920. C. r. Tray. Lab. Carlsberg, 14. Warren. 19t7. Genetics 2, 305. Wood. 1905. J. Agric. Science 1,364. A MATHERJATICAL THEORY OF NATURAL AND ARTIFICIAL SELECTION.

Bateson. MendeFs Principles of Heredity, p. 221. Crozier and Snyder. 1922. Proc. Soc. Exp. Biol. Med. 19, 327. Detlefsen. 1915. Genetics 3, 573. Durham. 19il. J. Genetics 1, 107. Goldschmidt. 1920. Z. indukt. -u. Verblehre 23, 1. Hardy. 1908. Science 28, 49. Heribert-Nilsson. 1920. Hereditas 1, 41. Ibsen and Steigleder. 1917. Am. Nat. 51,740. Jennings. 1915. Genetics 1, 53. Jones. 1920. Biol. Bull. 311,251. Morgan and Bridges. 1916. Carn. Inst. Wash. , 237. Pearl. 1907. Biometrika 5, 213. Pearl.

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'. Hence if either I or I' is larger than k the effects of linkage are unimportant.

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