New PDF release: A Mathematical Theory of Natural and Artificial Selection

By John Burdon Sanderson Haldane

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Additional info for A Mathematical Theory of Natural and Artificial Selection

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Acud. Sci. 7,168. An Introduction to the Theory of Statistics,p. 38. (4) JONES (1920). Biol. Bull. 38,251. (I) ~ (2) Mr Haldane, A mathematical theory, etc. 363 A mathematical theory of natural and artificial selection. Part in. By Mr J. B. S. HALDANE, Trinity College. ] In this part the cases of a single but incompletely dominant factor, and of several interacting factors are considered. Mating is supposed to be at random, populations to be very large, and generations not to overlap. The notation is, so far as possible, that of Part I (1): Selection of an incompletely dominant autosomal character.

But JV = D (t) = f " F (t - x) S (x) dx = FS, Jo _r Jo - *) ' + K'LYsN Hence selection proceeds at the same rate as when generations are separate, with a selection coefficient equal to + kL l • Haldane, Trans. Camb. Phil. Soe. 23, p. 19, 1924. 612 Mr Haldane, A mathematical theory When dominants are rare, f(w) is large and equal to a constant / , K = 1 + k, and F(x) is small. Therefore (l+kL)(c-t) = e'L>+K'L , where c is a constant of integration. D(t)=[*>2F(t-x) S (x) dx = 2SF (t) J 0o

S(x) be the probability of a female dominant reaching the age x. s (x) be the probability of a female recessive reaching the age x. K{x)Sx be the probability of a female dominant (alive or dead, as above) producing a female offspring between the ages x and x + Sx. [K (x) — k (x)] Sx be the same probability for a female recessive. L (x) Sx be the same probability for a male dominant. [L (x) — I (#)] Sx be the same probability for a male recessive. S = I S (x) dx, s = / $ (x) dx. Jo Jo K=\ Jo K{x)dx, K'= I xK(x)dx, Jo L = { L (x) dx, L ' = ( Jo J (i k=\ xL (x) dx, 1 = 1 - II k(x)dx.

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