The multilocus multiplicative selection equilibria

The concept of monomial selection is introduced as a natural generalization of the multiplicative selection. It is proven that the equilibrium set of the multilocus multiallele population under monomial selection is generically finite. The result is new even in the multiplicative case. An upper bound for the number of equilibria is given. @ 2003 Elsevier Science Ltd. All rights reserved. In particular, gi = a& (1 5 i < 1). Obviously, g = gugv, where V is the subset of those loci which do not belong to U. The partitions U 1 V can be identified with all formally possible crossing-overs. If a crossing-over U 1 V occurs in meiosis then every gamete pair (g, h) produces the recombinant gametes guhv and hugv with equal probabilities r(U 1 V)/2, where r is the linkage distribution. The latter is supposed to be fixed in what follows. By definition, A state p of the population on the gamete level is a probability distribution p(g) on the set P of all gametes: p(g) 2 0, Cp(g) = 1, where g runs over P. Given some fitness values X(g, h) = X(h,g) 2 0, X(g,g) > 0, the evolutionary equations under the corresponding selection and random mating are where .