Vol.. 6, 1920 GENETICS: S. WRIGHT 331 
of each other in a population which is mating at random. They are of 
equal importance, as indicated by the equality of inheritance from sire 
and dam. The degree of determination in each case must, therefore, be 
one-half. 
a = VV2 
The relation between the germ-cells and the genetic constitution of one 
of the parents is not quite so obvious. It is well known that in a popula- 
tion which is mating at random, the proportion of homozygous and hetero- 
zygous classes come to an equilibrium such that the number of those hetero- 
zygous in a given factor equals twice the square root of the product of 
the numbers in the two homozygous classes. For factors A and a, the 
proportion in the three classes can be expressed in the following form : 
x^AA + 2xyAa + y^aa 
In the production of this population by the preceding generation, there 
were + y"^ cases in which similar germ-cells united at fertilization and 
2^1!;^ cases in which the egg and sperm were dissimilar. 
When this population produces germ-cells, there are -|- cases in 
which gametogenesis results in similar ones, and 2xy cases in which they 
are dissimilar. 
Thus in a population of this kind, the correlation between the germ-cells 
produced by gametogenesis is exactly the same as that between two germ- 
cells which unite at fertilization, the correlation in which case, of course, is 
zero. Consequently, the relation between a germ-cell and the genetic 
constitution of the parent is the same as its relation to that of the offspring. 
Thus we may look upon the constitution of the germ-cell as half determined 
by that of the parent and half by chance at segregation. 
Th^g = h = a = (9) 
In considering the genetic constitution of the fertilized egg as simply 
the sum of the constitutions of the egg and sperm, each heterozygous 
class is rated as if exactly intermediate between the two corresponding 
homozygous classes. This is not, however, the correct way to grade the 
genetic constitution as a factor in development, unless dominance is lack- 
ing. The correlation between the two methods of grading depends on the 
degree of dominance and on the ratio of dominant to recessive factors in 
the population. For perfect dominance and a distribution of all pairs of 
allelomorphs according to the proportion lAA : 2Aa : laa, the correla- 
tion is V^/s- 'I^he correlation between the genetic constitution of parent 
and offspring is thus about Vs if there is perfect dominance, instead of 
As already noted, the progeny of a cross between two grades of piebald 
are almost exactly intermediate on the average and the second generation 
is only slightly more variable than the first. These results might be due 
to two groups of dominant factors with opposed effects. The most prob- 
