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

By John Burdon Sanderson Haldane

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Additional resources for A Mathematical Theory of Natural and Artificial Selection

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23, p. 363, 192(1. e. selection is confined to females, then (2K'L+L')F (333) Hence the proportion of recessive males is (L' + 2K'L)v 2kLV{t~Q' of recessive females When dominants are rare, (l+ikL)(t-t0) The number of male dominants is proportional to F (t), that of females being double that of males. When the intensity of selection is equal in both sexes, these equations simplify to u(t) dtU{t)~ u(t)] W[l + u(t)] (35) ' ) F(t) = e K< analogous to equation (7*2) of Part I. (3-7), DISCUSSION. The most satisfactory table of K (x) known to me is that given by Dublin and Lotka* for certain American women.

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. We consider a series of cases, in each of which a new form is favoured in a limited area, the coefficient of selection being k. In each generation a number of migrants of the original type, equal to the whole population of the limited area multiplied by a constant I, migrate into it.

Recessives nearly disappear. If p be of the same order of magnitude as the larger of k and q, u has a moderate value and the population is dimorphic. e. dominants are rare. If k be negative all the roots are positive if they are real, provided q > 2p and — k (1 - q) > 2q —p. e. is positive, that is to say, when q is small, if 4pAa + ( - 8p" + 20p q + 9') k + 4 (p + q)* is positive. All these three conditions can rarely be fulfilled, but such cases may presumably occur. Thus if p = "000,001, q = "0004, k = -008; u'-398u> + 7197-8U-4Q3-2 = 0.