Effect of initial linkage disequilibrium and epistasis on fixation probability in a small population, with two segregating loci.

The probability of ultimate fixation was studied for 2 loci small populations by the method of Monte Carlo simulation and also partly by analytical treatment. The analytical solutions for fixation probability known at present and the difficulty of their application to more complex situations were discussed. Monte Carlo experiments were carried out for large values ofN e s 1,N e s 2 andN e ε, for which the analytical solutions have not been obtained.One of the main purposes was to investigate the effect of initial linkage disequilibrium (D) on fixation probability. Whens 1,s 2 and ε are 0, the effect of disequilibrium is given by {1-2N e c/(2N e c+1)}D withKIMURA'S model and {1-2N e c/(2 N e c-c+1)}D with the model ofKARLIN andMCGREGOR. When |N e s 1| and |N e s 2| were small and ε=0, the effect of disequilibrium was shown to be almost the same as in the selectively neutral case (formulas 8). When those parameters are not small, the effect of disequilibrium is larger because of the rapid approach to fixation.Another purpose of this study was to investigate the effect of epistasis on fixation probability.KIMURA obtained the solution for joint fixation ofA andB when the selective advantage is given to genotypeAB as the joint effect ofA andB. The present study has verified his formula and showed that linkage does not affectu(AB) under initial linkage equilibrium. Also some cases of additive × additive epistasis were studied.