96 I The Process of Evolution 



size N, defined as the number of parents responsible for the 

 genetic composition of the next generation. That the breeding size 

 of a population may be considerably smaller than the overall size of 

 a population should be obvious from the situation of man, where 

 individuals under 10 years of age and over 60 years of age are gen- 

 erally excluded from the breeding population. 



Effective Breeding Size 



Most important evolutionarily is what is known as the elective 

 breeding size Np. This is equivalent to the breeding size N only in 

 an "ideal" population of continuing large size in which there are 

 equal numbers of the two sexes, mating is at random, and the 

 gametes are drawn at random from the parents. This ideal popula- 

 tion is an abstraction; for practical purposes the eflFective breeding 

 size is alivatjs smaller than the breeding size. In some cases, how- 

 ever, the difference may be quite small. Uneven sex ratios, inbreed- 

 ing, cyclic reduction of breeding size, and nonrandom sampling of 

 the gametes all depress the effective breeding size. As an example, 

 consider a population of N breeding individuals, mating at random, 

 not fluctuating in size, and having the gametes drawn at random 

 from the parents. Table 6.4 shows the effects of different sex ratios 

 on the effective breeding size, where Ne = 4NcfN9/(IVcf ~\-N 9 ), 

 and N d -\-N 9 = 400. The derivation for this formula is given in Li. 

 Similarly, if the effective size for four successive generations is 10, 

 100, 10,000, and 100, the average eflFective size (which is the har- 

 monic mean, the reciprocal of the mean of the reciprocals, of the 

 sizes at each generation) over those generations is approximately 

 33. Note that this is much closer to the minimum number in the 

 series than to the maximum. EflFective breeding size indicates the 

 size of the "ideal" population whose genetic behavior would be the 

 same as that of the population under consideration. This permits 

 valid comparisons of population size. To equate two populations 

 with 400 breeding individuals, one with 200 males and 200 females, 

 and the other with 5 males and 395 females, would be to ignore the 

 genetic consequences of the sex-ratio inequality of the latter popu- 

 lation. (For example, all other factors being equal, it would lose its 

 variability much more rapidly than the former because the males, in 

 essence, would become a bottleneck in the transfer of genetic vari- 

 ability from generation to generation. ) One sometimes can point out 

 the individuals that are members of a breeding population, but one 

 cannot segregate a group and label it the "eflFective population." 

 Unless otherwise specified, population size will refer in what follows 

 to the eflFective population size and will be designated simply by N. 



