HALDANE ON SELECTION 



Z53 



as to the stability of normal age distribu- 

 tion. Consideration of the effect of 

 generations that overlap to the extent 

 that they do in mankind shows that the 

 changes due to slow selection are very 

 similar to those which occur when 

 generations are separate. 



The last paper of the series, Part V (5), 

 considers the subject of mutation. The 

 frequency of occurrence of mutations is 

 generally small, and on the whole, 

 mutants recessive to the normal type 

 occur more commonly than dominants. 

 A consideration of selection in this case 

 shows that if it acts against mutation it 

 is ineffective, provided that the rate of 

 mutation is greater than the coefficient of 

 selection. Moreover, mutation is quite 

 effective where selection is not: namely, 



in causing an increase of recessives where 

 these are rare. It is also more effective 

 than selection in weeding out rare reces- 

 sives, provided it is not balanced by 

 back-mutation of dominants. Mutation, 

 therefore, determines the course of evo- 

 lution as regards factors of negligible 

 advantage or disadvantage to the species, 

 but it can lead to results of impor- 

 tance only when its frequency becomes 

 large. 



This series of papers is not only valuable 

 for the large number of cases treated, but 

 it is extremely fertile in suggestions for 

 possible extensions of the analysis. As 

 it stands, it constitutes the most complete 

 mathematical treatment of the effect of 

 natural and artificial selection which has 

 appeared. 



LIST OF LITERATURE 



(1) Pearson, K. 1896. Contributions to the 

 mathematical theory of evolution. Note on 

 reproductive selection. Proc. Roy. Soc., 

 59: 301-305. 



(z) Warren, H. C. 1917. Numerical effects of 

 natural selection acting upon Mendelian 

 characters. Genetics, z: 305-31Z. 



(3) Norton, H. T. J. Work quoted by Punnett. 



See 8. 



(4) Jennings, H. S. 1916-17. The numerical 



results of diverse systems of breeding. Ge- 

 netics, 1: 53-89;!: 97-154. 



(5) Haldane, J. B. S. 1914-17. A mathematical 



theory of natural and artificial selection. 

 Part I. Trans. Cambridge Phil. Soc, 23 : 19-41. 

 Part II. Proc. Cambridge Phil. Soc. (Biol. 

 Sci.), 1: 158-163. Part III. Proc. Cam- 

 bridge Phil. Soc, Z3: 363-371. Part IV. 

 Ibid., 607-615. Part V. Ibid., 838-844. 



(6) Pearson, K. 1904. Mathematical contribu- 



tions to the theory of evolution. XII. On 

 a generalized theory of alternative inheritance, 



with special reference to Mendel's laws. 

 Phil. Trans. Roy. Soc. A, 103: 53-86. 



(7) Hardy, G. H. 1908. Mendelian proportions 



in a mixed population. Science N. S., z8: 

 49-50. 



(8) Punnett, R. C. 1915. Mimicry in Butterflies. 



Cambridge University Press, vi + 188 pp. 

 16 plates. 



(9) Wood, T. B. 1905. Note on the inheritance 



of horns and face colour in sheep. Journ. 

 Agric Science, 1: 364-365. 



(10) Morgan, T. H., and Bridges, C. B. 1916. 



Sex-linked inheritance in Drosopbila. Car- 

 negie Inst. Wash. Publ. 137. 87 pp. z plates. 



(11) Pearl, R. 1911. The Mendelian inheritance, 



of fecundity in the domestic fowl. Amer. 

 Nat., 46: 697-711. 



(iz) Pearson, K., and Lee, A. 1903. On the laws 

 of inheritance in man. I. Inheritance of 

 physical characters. Biometrika, z: 357-46Z. 



(13) Lotka, A. J. 19ZZ. The stability of the nor- 

 mal age distribution. Proc. Nat. Acad. Sci., 

 8: 339-345- 



