| 3 AB + | Ab + | aB + | 3 | ab |
| 7 AB + | Ab + | aB + | 7 | ab |
| 15 AB + | Ab + | aB + | 15 | ab, etc., etc. |
In such a series the number of gametes containing A is equal to the number lacking A, and the same is true for B. Consequently the number of zygotes formed containing A is three times as great as the number of zygotes which do not contain A; and similarly for B. The proportion of dominants to recessives in each case is 3 : 1. It is only in the distribution of the characters with relation to one another that these cases differ from a simple Mendelian case.
As the study of these series presents another feature of some interest, we may consider it in a little more detail. In the accompanying table are set out the results produced by these different series of gametes. The series marked by an asterisk have already been demonstrated experimentally. The first term in the series,
in which all the four kinds of gametes are produced in equal numbers is, of course, that of a simple Mendelian case where no coupling occurs.
| No. of Gametes in series. | Distribution of Factors in Gametic Series | No. of Zygotes produced. | Form of F2 Generation. | |||
| AB. Ab. aB. ab. | AB. | Ab. | aB. | ab. | ||
| 4 | 1 : 1 : 1 : 1 | 16 | 9 | 3 | 3 | 1 |
| 8 | 3 : 1 : 1 : 3 | 64 | 49 | 7 | 7 | 9 |
| 16 | 7 : 1 : 1 : 7 | 256 | 177 | 15 | 15 | 49* |
| 32 | 15 : 1 : 1 : 15 | 1024 | 737 | 31 | 31 | 225* |
| 64 | 31 : 1 : 1 : 31 | 4096 | 3009 | 63 | 63 | 961 |
| 128 | 63 : 1 : 1 : 63 | 16384 | 12161 | 127 | 127 | 3969* |
| 2n | (n-1) : 1 : 1 : (n-1) | 4n2 | 3n2-(2n-1) | (2n-1) | (2n-1) | n2-(2n-1) |
Now, as the table shows, it is possible to express the gametic series by a general formula (n + 1) AB + Ab + aB + (n - 1) ab, where 2n is the total number of the gametes in the series. A plant producing such a series of gametes gives rise to a family of zygotes in which 3n2 - (2n - 1) show both of the dominant characters and n2 - (2n - 1) show both of the recessive characters, while the number of the two classes which each show one of the two dominants is (2n - 1). When in such a series the coupling becomes closer the value of n increases, but in comparison with n2 its value becomes less and less. The larger n becomes the more negligible is its value relatively to n2. If, therefore, the coupling were very close, the series 3n2 - (2n - 1) : (2n - 1) : (2n - 1) : n2 - (2n - 1) would approximate more and more to the series 3n2 : n2, i.e. to a simple 3 : 1 ratio. Though the point is probably of more theoretical than practical interest, it is not impossible that some of the cases which have hitherto been regarded as following a simple 3 : 1 ratio will turn out on further analysis to belong to this more complicated scheme.
CHAPTER X
SEX