Development of associative overdominance through linkage disequilibrium in finite populations

Associative overdominance arises at an intrinsically neutral locus through its non-random association with overdominant loci. In finite populations, even if fitness is additive between loci, non-random association will be created by random genetic drift.

The magnitude of such associative overdominance is roughly proportional to the sum ofbetween the neutral and the surrounding over-dominant loci, whereis the squared standard linkage deviation, defined between any two loci by the relation

in whichpand 1 –pare frequencies of allelesA1andA2in the first locus,qand 1 –qare frequencies of allelesB1andB2in the second locus, andDis the coefficient of linkage disequilibrium. A theory was developed based on diffusion models which enables us to obtain formulae forunder various conditions, and Monte Carlo experiments were performed to check the validity of those formulae.

It was shown that ifA1andA2are strongly overdominant whileB1andB2are selectively neutral, we have approximately

provided that 4Nec≫ 1, whereNeis the effective population size andcis the recombination fraction between the two loci. This approximation formula is also valid between two strongly overdominant as well as weakly overdominant loci, if 4Nec≫ 1.

The significance of associative overdominance for the maintenance of genetic variability in natural populations was discussed, and it was shown thatNes′, that is, the product between effective population size and the coefficient of associative overdominance, remanis constant with varyingNe, if the total segregational (overdominant) load is kept constant.

The amount of linkage disequilibrium expected due to random drift in experimental populations was also discussed, and it was shown thatin the first generation, if it is produced by extractingnchromosomes from a large parental population in whichD= 0.

Genetic loads at a polymorphic locus which is maintained by frequency-dependent selection

If a polymorphic locus is maintained in finite populations by frequency-dependent selection with selective neutrality at equilibrium, it is generally accompanied by two genetic loads, i.e. the dysmetric and the drift loads. The former arises because the fitness of the population may not be at a maximum at the equilibrium gene frequency and the latter because genetic drift in small populations displaces the gene frequency from its equilibrium value.

In some simple models of frequency-dependent selection considered, the drift load is independent of selection coefficients and is approximately equal to (n−1)/(2Ne), wherenis the number of alleles andNeis the effective population size.

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.