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While sex can be advantageous for a lineage in the long term, we still lack an explanation for its maintenance with the twofold cost per generation. Here we model an infinite diploid population where two autosomal loci determine, respectively, the reproductive mode, sexual versus asexual and the mating system, polygynous (costly sex) versus monogamous (assuming equal contribution of parents to offspring, i.e. non-costly sex). We show that alleles for costly sex can spread when non-costly sexual modes buffer the interaction between asexual and costly sexual strategies, even without twofold benefit of recombination with respect to asexuality. The three interacting strategies have intransitive fitness relationships leading to a rock–paper–scissors dynamics, so that alleles for costly sex cannot be eliminated by asexuals in most situations throughout the parameter space. Our results indicate that sexual lineages with variable mating systems can resist the invasion of asexuals and allow for long-term effects to accumulate, thus providing a solution to the persisting theoretical question of why sex was not displaced by asexuality along evolution.

Sexual reproduction with variable mating systems can resist asexuality in a rock–paper–scissors dynamics