The Theory of Population Genetics ; 95 



Note that there is no change whatsoever in the gene frequency, 

 which can be determined after the first generation by taking the 

 square root of the frequency of the proper homozygote. Under the 

 conditions described, there is a genetic inertia in mendehan popu- 

 lations. Unless mutation, selection, differential migration, certain 

 changes in the mating pattern, or a drop in population size disturbs 

 the equilibrium, there is no change in the genetic structure of the 

 population. To a very large degree, overcoming this inertia (espe- 

 cially changing of the gene frequency) is what is described as 

 "evolution." 



The ideas associated with the Hardy-Weinberg law are basic to 

 any consideration of evolutionary processes, and it is essential that 

 the reader become thoroughly familiar with them. For a discussion 

 of extensions of the Hardy-Weinberg law and properties of equi- 

 librium populations, the reader is referred to the excellent book on 

 population genetics by Li (1955). 



Although populations in equilibrium are rare (or nonexistent) in 

 nature, the law is of great value in describing a situation in which 

 there is no evolution, as it provides a base line for measuring evolu- 

 tionary change. Now some ways in which populations deviate from 

 Hardy-Weinberg ecjuilibrium are considered. 



POPULATION SIZE 



In all populations there are some random fluctuations in gene fre- 

 quency. Because of sampling error, no set of gametes drawn from a 

 parental population will have exactly the same gene frequency as 

 the parental population. In addition, because of chance occurrences 

 in the union of gametes, the population of zygotes formed will 

 not have precisely the same gene frequency as the population of 

 gametes. Finally, even if the deaths among maturing indixiduals 

 are completely random, sampling error will intervene to produce a 

 filial breeding population in which the gene and genotvpe fre- 

 quencies once again deviate from the gene and genotype frequencies 

 of the original population of zygotes. In large populations these 

 sampling errors tend to balance each other, since they are different 

 in different areas and at different stages in the reproductive process. 

 Changes in gene frequency because of sampling error are therefore 

 usually negligible. However, in small populations these random 

 fluctuations take on considerable importance. 



Thus the size of a population may have a considerable effect on 

 its genetic structure. Biological populations are always finite in size. 

 The gross population size is simply the number of individuals in a 

 population at a given time. Of greater significance is the breeding 



