1921-22.] 
On the Dominance Ratio. 
327 
Further, if a second generation of n individuals be now formed at 
random, the standard departure of p from its previous value will be 
pq 
2n 
hence. 
Ipq dO _ 1 
\ 2n dp~ 
The fact that this is independent of d makes it easy to calculate the 
changes in the distribution of d, in the absence of selection, for let y{0) dO 
represent the distribution of d in any one generation, the distribution in 
the next will be given by 
2/ + A//= 20-4^ + ?/ 3^ + ^//"+ . . . 
Jo sJ'lTTCr \ ! 
-y + pj +■ 
Now 0 -^ is very small, being — , so that measuring time in generations, we 
have 
dh/ 
Since we have drawn no distinction between the gene and its allelo- 
morph, we are only concerned with symmetrical solutions : the stationary 
case is 
A 
7T 
where A is the number of factors present. 
Besides this, we have when y is increasing 
// = — . cosh 
2 Sinn ^pir 
and when y is decreasing 
y = - 
2 sin ^pir \ 
for which 
k = ^. 
4:11 
4. Terminal Conditions. 
If we represent by the chance that a particular gene borne by a 
single individual will not be represented in the next generation, the chance 
of extinction for a factor of which h genes are in existence will be 
