B: Where the new variety is recessive +-----------+-----------+----------+------------------------------------+ | | | | Number of generations taken | |Percentage |Percentage |Percentage| to pass from one position | |of total |of total |of total | to another as indicated | |population |population |population| in the percentages of different | |formed by |formed by |formed by | individuals in left-hand column. | |old variety|the hybrids|the new +--------+--------+--------+---------+ | | |variety | 100/50 | 100/75 | 100/90 | 100/99 | +-----------+-----------+----------+--------+--------+--------+---------+ | 99.9 | .09 | .000 | | | | | | 98.0 | 1.96 | .008 | 1920 | 5740 | 17,200 | 189,092 | | 90.7 | 9.0 | .03 | 85 | 250 | 744 | 8,160 | | 69.0 | 27.7 | 2.8 | 18 | 51 | 149 | 1,615 | | 44.4 | 44.4 | 11.1 | 5 | 13 | 36 | 389 | | 25. | 50. | 25. | 2 | 6 | 16 | 169 | | 11.1 | 44.4 | 44.4 | 2 | 4 | 11 | 118 | | 2.8 | 27.7 | 69.0 | 2 | 4 | 11 | 120 | | .03 | 9.0 | 90.7 | 2 | 6 | 14 | 152 | | .008 | 1.96 | 98.0 | 2 | 6 | 16 | 165 | | .000 | .09 | 99.9 | 4 | 10 | 28 | 299 | +-----------+-----------+----------+--------+--------+--------+---------+ {156} If the favoured variety is dominant it must be borne in mind that it can be either homozygous or heterozygous--that for these purposes it is represented in the left-hand column by the hybrids as well as by the homozygous dominant. In a population in equilibrium which contains about 2% of a dominant form, the great bulk of these dominants will be heterozygous, and the relative proportion of recessives, heterozygous, and homozygous dominants is given in the second line of the left-hand column. Let us suppose now that we want to know what will be the percentage of dominants after 1000 generations if they form 2% of the population to start with, and if, during this period, they have been favoured with a 1% selection advantage. After 165 generations the proportion of recessives is 90.7, so that the proportion of dominants has risen to over 9%; after 153 further generations the percentage of dominants becomes 27.7 + 2.8 = 30.5; after 739 generations it is 88.8%, and after 1122 generations it is 69.0 + 27.7 = 96.7. Hence the answer to our question will be between 89% and 97%, but nearer to the latter figure than the former. Mr Norton has informed me that the figures in the table are accurate to within about 5%. * * * * * {157} APPENDIX II