The Theory of Population Genetics | 115 



distributions. Each curve in the figure represents a probabiHty den- 

 sity function of the form 



where C is a constant making the function integrate to 1, and the 

 other notation is as above. Such a function may represent the man- 

 ner in which the probabihty is distributed over the possible events. 

 The area under each curve is unitv, and the area between the curve 

 and each section of the abscissa (q axis) is the probabihty that the 

 gene frequency will lie along that stretch of the q axis. Thus in Fig. 

 6.4 one can see at a glance that, under the given conditions, there 

 is a much smaller probability that q will lie between .4 and .6 when 

 m = 1/4N than when m = 4/N. Stationary frequency distributions 

 are a very convenient way of illustrating the effects of various evo- 

 lutionary forces on different kinds of populations and are widely 

 used for this purpose. Readers interested in further information on 

 probability density functions and other subjects relating to the 

 mathematical treatment of probabilities are referred to any intro- 

 ductory text on probability theory. 



Stationary frequency distributions may be used to represent the 

 distribution of the gene frequency under consideration in a large 

 number of populations under the same evolutionary conditions, the 



Fig. 6.4 j Distribution of fre- 

 quencies of a gene among sub- 

 divisions of a population, where 

 the gene frequency of the migrants 

 is p = q = .50. For further ex- 

 planation of this type of diagram 

 see text. {From Wright, 1931, 

 Genetics 16.) 



9 = 



