Two-Locus Local Adaptation by Additive or Epistatic Gene Combinations in Autotetraploids Versus Diploids

In this article, we present a theoretical comparison of local adaptation between diploid and autotetraploid populations when fitness is determined by either additive or epistatic interactions between alleles at 2 loci. A continent-island model of local adaptation is derived, with 1-way migration from the continent to the island and distinct genotypes adaptive on the continent versus the island. The meiotic component of the model accounts for multivalent formation and the processes of chromosomal gametic disequilibrium and double reduction, which are unique to autotetraploids. Both the adaptability and efficiency of adaptation are investigated, where adaptability asks whether a population adapts and efficiency is the rate of adaptation. With an additive genetic basis to fitness, diploids experience better adaptability and efficiency than autotetraploids. With epistasis, our results indicate a limited parameter space in which autotetraploids have greater adaptability than diploids, but results indicate an interesting difference between adaptability and efficiency of adaptation. Oftentimes, diploids exhibit greater adaptability whereas autotetraploids exhibit greater efficiency of adaptation. These findings provide evidence for the advantage of epistasis within autotetraploids when efficiency of adaptation is of interest. Although autotetraploids are more efficient, under the same conditions and at equilibrium, diploid populations often have higher mean local fitness. Overall, the most ideal situation for autotetraploid local adaptation compared to diploids is when epistasis is strong, mutation is weak, recombination is high, selection is strong, deleterious selection is additive, chromosomal gametic disequilibrium is present, and double reduction is absent.