LECTURES IN BIOLOGICAL SCIENCES 



higher phases of human evolution fortunately retain intact the 

 basic biologically determined hereditary potentialities, which 

 can become fully realized as soon as the cultural conditions per- 

 mit. It is only because biological heredity is relatively stable 

 and is not easily changed by the environment that we can 

 escape from the conclusion that the backward races of mankind 

 are really inferior. By the recognition that man has two systems 

 of transmitting information from one generation to the next— 

 the biological system and a socio-cultural system as well— the 

 study of continuous variation in man and the influence of the 

 environment on it becomes liberated from considerations of a 

 political nature. 



The formulation of the theory that continuous variation de- 

 pends on the joint action of many genes, each with small effect, 

 allowed an extremely rapid development of our understanding 

 of the genetical situation within sub-human populations which 

 are involved in evolutionary change. As a first step, the proc- 

 esses of natural selection were expressed in mathematical terms 

 by authors such as Sewall Wright (1931), Haldane (1932), and 

 Fisher (1930). The fundamental advance in understanding 

 which was involved in these developments was the change from 

 the consideration of evolution in terms of the genetics of indi- 

 viduals to a consideration in terms of populations. The basic 

 unit considered by the mathematician was not the individual 

 organism but a population of interbreeding organisms. Within 

 such a population there will be different alleles of very many 

 genes, and the mathematical formulae express the ways in which 

 the frequency of the different alleles change as natural selection 

 or other processes operate on the population. The development 

 of this point of view began about 1930, and by now the theory 

 of population genetics has become a large and elaborate sub- 

 ject. It is only possible to mention one or two of the major 

 advances. 



Perhaps the most interesting question that has arisen from 

 the theoretical investigations is the possibility that populations 

 may sometimes be reduced to such small numbers that purely 

 stochastic fluctuations in the frequency of alleles may result in 

 evolutionary changes, which will then not be strictly controlled 

 by natural selection. The importance of this phenomenon, 



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