On the Dominance Ratio. 
325 
1921-22.] 
If the selective action is sufficiently powerful, it may lead in these cases 
to the establishment of a balanced lethal system. 
2. The Survival of Individual Genes. 
If we consider the survival of an individual gene in such an organism 
as an annual plant, we may suppose that the chance of it appearing in the 
next generation in 0, 1, 2, 3 individuals to be 
where 
Po+Pi-^p2+ • • • = 1 - 
If 
f{x)=p^+p^X-\-p^X^+ . . . 
then evidently if there were two such genes in the first generation, the 
chance of occurrence in r individuals, or more strictly, in r homologous 
loci, in the second generation, will be the coefficient of x'^ in 
It follows that the chance of a single gene occurring in r homologous 
loci, in the third generation, will be coefficient of x'^ in 
The form of f(x) will vary from species to species, and in the same 
species according to the stage of development on which we fix our attention. 
For simplicity we shall suppose that the successive generations are 
enumerated at the same stage of development. For the purpose of an 
evolutionary argument it is indifferent at what stage of development the 
enumeration is made : in general it will be most convenient to fix our 
attention on that stage at which the species is least numerous. 
In certain important cases the form of f(x) may be calculated. In a 
field of cross-fertilised grain each mature and ripened plant is the mother 
of a considerable number of grains, and the father, possibly, of an almost 
unlimited number. If the number of the species is nearly constant, the 
average number of its progeny which are destined to become mature is 
very nearly 2. Or since each gene of a homologous pair occurs in half 
the gametes, the average number of mature plants in the second generation 
in which it occurs is I. Each ovule, therefore, or each pollen grain has 
individually a very small chance of surviving, and the proportions 
Pq, Pi, will be closely given by the Poisson series 
