44 GENETIC STOCKS AND BREEDING METHODS 



but 



2 2 Vftfv = 22 VftPqa + 2 *7»(i - P)q t 

 = P(2 v igi ) 2 + (i - P) 2 vfa 



thus 



f = r os = [(i -P)2 v? qi - (i - P)(2 v^yv* 2 

 = 1 - p 



= (h - h)\h . 



Thus the inbreeding coefficient, F, can be looked upon either as the correlation 

 between uniting gametes or as a measure of the relative decrease in heterozygosis 

 irrespective of numbers or relative frequencies of alleles or any values that may be 



Fig. 13. Brother-sister mating, zygote diagram. 



assigned them. This, of course, includes the assumption that there is no disturbance 

 from assortative mating if there are three or more alleles or from selection. The 

 correlation between any two gametes with designated roles in the system of mating is 

 similarly related to the decrease in heterallelism in the designated pairs. 



It will be convenient to illustrate the method first by the simple case of brother- 

 sister mating. 1443 Figure 13 shows the system of mating diagrammatically. The 

 analysis is reduced to its simplest form, however, by considering only the gametes. The 

 compound path coefficients relating a gamete produced by an individual to those that 

 united to produce that individual have the value 1/2, since there is a probability of 

 1/2 that the allele in the former is derived from that in the latter (tending to give a 

 correlation of 1) and a probability of 1/2 that it is not (tending to give a correlation of 

 as far as the path in question is concerned). Since it is assumed that the variance of the 

 allelic array is constant, the path coefficient is merely the average, 1/2. 



In the gametic diagram, figure 14, there are two kinds of correlations in each 

 generation, that between any random gametes from the two parents (r os = F) and 

 that between two random gametes from the same individual (r ss = r 00 by symmetry). 



