Models of Fluctuating Selection Between Generations: A Solution for the Theoretical Inconsistency.

The theory of selection fluctuation between generations has been a topic with much activities in population genetics and molecular evolution in 1970's. Most studies suggested that, as the result of fluctuating selection between generations, the frequency of an (on average) neutral mutation may fluctuate around 0.5 during the long-term evolution before it was ultimately fixed or lost. However, this pattern can only be derived from a specific type Wright-Fisher additive model, coined by the Nei-Yokoyama puzzle. In this commentary, I revisited this issue and figured out a theoretical assumption that has never been claimed explicitly, the notion of reference phenotype. Consider one locus with two-alleles: A is the wildtype allele and A' is the mutation. The fluctuating selection model actually requires a constraint that one of three genotypes (AA, AA', or A'A') must maintain a constant fitness without fluctuating between generations. It appears that the balancing selection at a frequency of 0.5 emerges only when the heterozygote (AA') is the reference genotype. Because it is difficult to determine which genotype could be the reference genotype in a real population, a desirable population genetics model should take all three possibilities into account. To this end, I propose a mixture model, where each genotype has a certain chance to be the reference genotype. My analysis showed that the emergence of balancing selection depends on the relative proportions of three different reference genotypes.