Is the term 'allele' specific to sexual populations?

Question

I had always thought that 'allele' simply meant a variant of a gene and thus could be used in the context of either asexual or sexual populations. With it only being slightly less useful as a concept in asex because of the lack of recombination and thus no reshuffling of allele among offspring. Recently, I was reading a paper that wrote:

In the asexual and sexual populations mentioned earlier, the implicit model space is simply a point in genotype frequency space or allele frequency space, respectively.

Suggesting that alleles should primarily be used in the context of sexual populations. Wikipedia gives a general definition consistent with both asex and sex use, but all examples listed are sexual.

Hence my terminology question:

Should I use the word 'allele' for variants of genes only in the case of sexual populations? Or is it alright to use 'allele' in populations of obligate asexuals?

I realize why recombination forces us to represent a whole population as allelic frequency instead of talking about individual genotypes, and why asex lets us focus on just the latter. In this question, I am not curious about this distinction, just the purely terminological question.

Answer 1

No, it's fine to use for asexuals too. There's an ambiguity in the term "locus" for asexuals, but "allele" is fine, and "gene" is not much more ambiguous than it is for sexuals (which isn't saying much).

Your final paragraph seems confused though, and I think it's related to your main question. When recombination is sufficiently frequent to keep the population in linkage equilibrium, it allows us to represent the population simply as a point in allele frequency space, rather than in the full, exponentially-larger genotype space. So Watson and Szathmary are using different terms for the two cases not because they can't use "allele" in an asexual context, but because alleles are not sufficient to describe an asexual population.

In general sexual populations are not in linkage equilibrium and cannot be simply described by allele frequencies either, as W&S note later in that paragraph.