How often do duplicated genes evolve new functions?

A recently duplicated gene can either fix a null allele (becoming a pseudogene) or fix an (advantageous) allele giving a slightly different function, starting it on the road to evolving a new function. Here we examine the relative probabilities of these two events under a simple model. Null alleles are assumed to be neutral; linkage effects are ignored, as are unequal crossing over and gene conversion. These assumptions likely make our results underestimates for the probability that an advantageous allele is fixed first. When new advantageous mutations are additive with selection coefficient s and the ratio of advantageous to null mutations is rho, the probability an advantageous allele is fixed first is (1 - e-s/rho S + 1)-1, where S = 4Nes with Ne the effective population size. The probability that a duplicate locus becomes a pseudogene, as opposed to evolving a new gene function, is high unless rhoS >> 1. However, even if advantageous mutations are very rare relative to null mutations, for sufficiently large populations rhoS >> 1 and new gene function, rather than pseudogene formation, is the expected fate of most duplicated genes.