Adaptive mutations are historically considered to be dominant. This notion derives from Haldane (1927) who showed that when a mutation is rare, as it is the case of new mutations, it is more likely to be fixed if it is dominant. This is so because selection has little chance of acting on recessive mutations as most of the mutants alleles are found in heterozygous and recessive mutations are phenotypically expressed only in homozygotes.

However, it has been recently shown that a substantial proportion of adaptive mutations should be overdominant. In the recent publication in Genome Biology and Evolution by González and Guio, they experimentally test the dominance effect of an adaptive transposable element insertion. They have found that the dominance effect of this mutation is background specific: while the mutation is dominant in some genetic backgrounds, it is overdominant in others. Elucidating whether changes in dominance effect due to alleles at linked or unlinked loci is a common phenomenon should be the subject of future research.

These results add to the limited number of studies in which the dominance effect of adaptive mutations has been empirically estimated.

Reference article: The dominance effect of the adaptive transposable element insertion Bari-Jheh depends on the genetic background. Guio L, González J.  Genome Biol Evol. 2015 Apr 24;7(5):1260-6. doi: 10.1093/gbe/evv071.