PROCESS LEADING TO QUASI-FIXATION OF GENES IN NATURAL POPULATIONS DUE TO RANDOM FLUCTUATION OF SELECTION INTENSITIES

Abstract

MONG factors that may produce random fluctuation of A in natural populations,random sampling of gametes an d greanned ofrmeq fuluenctcuieastionof selection intensities may be especially important in relationto evolution. On the process of " random drift " that will be realizedin finite populations due to the random sampling of gametes in reproduction,not only precise mathematical studies have been carried out (WRIGHT1931, 1945 ; FISHER 1930 ; HALDAN19E3 9 ; FELLE1R9 50) but also severalmodel experiments have been undertaken (cf. HOUSE1 953). Since 1931,WRIGHTh as repeatedly emphasized the evolutionary significance ofrandom drift in a natural population which is subdivided into manypartially isolated sub-groups. His theory is now accepted by manyevolutionists such as HALDAN(E19 49), MULLER (1949), DOBZHANSK(1Y951) and others. On the other hand, no special attention seems tohave been paid to the random fluctuation of gene frequencies dueto the random fluctuation in the selection intensities until FISHEaRnd FORD( 1 947) emphasized its prevalence in natural populations andchallenged the theory of Wright by denying any significance of randomdrift due to small population number in evolution. This led to apolemic (cf. WRIGHT1 948; FISHERan d FORD19 50; WRIGHT1 951). Experimentalstudies on natural populations have been carried out by the schoolof FISHERan d FORD(e .g., SHEPPAR1D95 1 ; DOWDESWELanLd FORD 1952)and by LAMOTT(1E9 52). In spite of these, no mathematical investigationsseem to have been worked up on the process of change due to the randomfluctuation of selection intensities, except a short article reportedby the present author (KIMURA19 52a), though WRIGHT(1 948) gave adistribution of gene frequencies in steady state for a special case.In his report, the present author proved, using a method of transformationand approximation, that the process can be regarded as a deformedGaussian process. In the present paper, a pair of alleles lackingdominance will be assumed.