Beyond two alleles: multiallelic genotypic selection and its estimation from time-series data.

Genetic diversity is central to evolutionary change, with both natural selection and random genetic drift depending on variation within a population. An individual in a diploid population carries two alleles per locus, yet the population as a whole can harbour many alleles, giving rise to a rich spectrum of homozygous and heterozygous genotypes. Such multiallelic variation is common at biologically and medically important loci such as the major histocompatibility complex, the ABO blood group system, and genes underlying monogenic diseases. However, much of population genetic theory and data analysis has focussed on biallelic loci. Here, we introduce a matrix representation of the genotypic selection acting at a multiallelic locus. This exploits the common mathematical structure underlying selection and drift, and separates the effects of genetic diversity and fitness. The representation accommodates diverse selection regimes, including additive, multiplicative, frequency-dependent, and temporally varying selection, as well as heterozygote advantage. We show how, under specific assumptions, genotype-specific fitness-effects can be estimated from allele frequency trajectories over microevolutionary timescales. Applying this estimation procedure to time-series data from experimental yeast evolution illustrates how multiallelic fitness interactions, including heterozygote advantage, may be characterised from haplotype frequency data. More broadly, this work provides a practical foundation for analysing evolutionary dynamics at multiallelic loci in experimental and natural populations.