100 I The Process of Evolution 



The rate of this decay is intimately tied to the population size. 

 Genes are lost at a rate of 1/4N per generation and fixed at a rate of 

 1/4N per generation. Thus this decay of variability takes place at the 

 rate of l/2iV genes per generation. Consider some extreme examples. 

 If p has a value of .125 in a breeding population of only 4 individuals, 

 1 individual has the only gene representing p, and only one-eighth 

 of the gametes have that gene. If that single individual fails to re- 

 produce, the gene is lost. If the individual does reproduce, the 

 chance of loss of the gene is Y2 when it leaves only 1 offspring, Y^ 

 when it leaves 2 offspring, Vs when it leaves 3 offspring, etc. How- 

 ever, in a population of 4,000 breeding individuals, an absolute mini- 

 mum of 500 individuals carry the gene in question if the gene fre- 

 quency is .125. All these individuals would then be homozygous for 

 the gene in question, and all must fail to reproduce to cause loss of 

 the gene. Drift (sampling error) is a mathematical fact. How- 

 ever, the significance of drift as opposed to selection has been widely 

 debated. It seems certain that drift is of very little importance in 

 large populations ( say N greater than 500 ) , but in small populations 

 drift may be an active evolutionary factor. 



Loss of Mutations 



An additional aspect of loss of variability through sampling error 

 concerns the probability of loss of a mutant gene. Imagine a men- 

 delian population in which N is constant (a pair of adults produce, 

 on an average, two offspring) and in which a certain locus is at 

 fixation (all individuals homozygous AA). If, in a single individual, 

 A mutates A^ a producing a single heterozygote Aa, this hetero- 

 zygote must, if it breeds, backcross with an AA individual ( no others 

 being available). The offspring of this backcross will consist, on an 

 average, of 50 percent AA and 50 percent Aa. Owing to chance, this 

 mating may produce 0, 1, 2, 3, • • •, r offspring, the probability of 

 each family size following a Poisson distribution with a mean of 2 

 (the average number of offspring). If no offspring are produced, the 

 gene is lost; if 1 offspring is produced, the probability of loss is .50; 

 if 2 offspring are produced, the probability of loss is .25; and if r 

 offspring are produced, the probability of loss equals 2"''. Using the 

 coefficients from the Poisson distribution, one can calculate the limit 

 of the aggregate probability of loss to be equal to .3679. Fisher has 

 calculated the probabilities of extinction for a mutation appearing 

 in a single individual under the condition that the mutation is of no 

 selective value and also under the condition that the mutant has a 



