54 GENETIC STOCKS AND BREEDING METHODS 



homozygosity may never be obtained. I question whether there are very many genes 

 in mammals which behave in a random fashion with no selection for either homo- 

 zygosity or heterozygosity. 



Dr. Gowen : A factor, generally ignored, is the part chance plays in any quanti- 

 tative estimates of inbreeding as measured by various coefficients. Sampled numbers of 

 genotypes are almost universally small compared to those of the total population. 

 Chance in "random selection" of parents each generation introduces so much variation 

 in the real rate changes in homozygosis that, individually, the calculated coefficients 

 may be quite misleading even though their average may measure approximately the 

 trends in infinite populations of evolutionary dimensions. 



Dr. Burdette : Dr. Pilgrim, do you wish to clarify your question ? 



Dr. Pilgrim : I wonder how many of these so-called chance elements are really 

 random. How often do we actually select a particular coat color because it happens 

 to be pleasing? There is always selection for breeding performance; otherwise it 

 would be impossible to maintain an animal colony. 



Dr. Ginsburg : The probability of mutation should also be taken into account in 

 terms of the eventual effect in stabilizing homozygosis in considering the questions 

 about selection. 



Dr. Mcintosh: In using the matrix-generation method, can repetitive multiplica- 

 tion be avoided and a final result obtained without going through all the intervening 

 steps ? 



Dr. Doolittle : In answer to Dr. Mcintosh's question, yes, one can skip a series 

 of generations in a single step, having the basic matrices. 



Dr. Burdette: Dr. Green, would you close the discussion, please? 



Dr. Green : I am intrigued by Dr. Wright's demonstration that the method of 

 path-coefficient analysis yields the same results as the matrix method in the cases 

 where the matrix method can be used. We should emphasize again that there are 

 irregular breeding systems used by breeders of laboratory animals which cannot be 

 analyzed by the matrix method but which can be analyzed by the method of path- 

 coefficients. 



I am glad that the two methods, so different in nature and approach, give 

 identical results where both methods are applicable. Each method has its limitations. 

 Dr. Wright pointed out those of path analysis. The chief limitation of the matrix 

 method is that it cannot be used with irregular systems of mating. 



With respect to the other question which was raised, we have to appreciate that 

 selection occurs whenever animals are being propagated. We cannot propagate 

 animals in a vacuum in the absence of selection nor in the absence of mutation nor in 

 the absence of chance. When it comes to dealing with actual animals, these elements 

 are ever present. On paper, a model population can be propagated with any amount of 

 selection or any amount of mutation one chooses. In the method of analysis described, 

 we made deliberate choices, namely, selection zero, mutation zero. Other choices 

 increase the complications. If there were selection for homozygotes, 100 per cent 



