Whether partially recessive deleterious mutations should favor the spread of chromosomal inversions extending permanently heterozygous sex determining regions (SDR) has led to some debate. In this article, we use individual-based simulations to estimate fixation probabilities of inversions arising on autosomes and sex chromosomes under a wide range of parameter values. As shown previously, ‘lucky’ inversions carrying a lower-than-average mutation load are initially favored and tend to spread. Our results show that linkage to a permanently heterozygous SDR (on a Y or W chromosome) or to a mating-type locus hinders the spread of inversions when Ns is high (where N is population size and s the strength of selection against deleterious alleles), as the absence of recombination leads to mutation accumulation. However, it may help the spread of inversions when Ns is lower and/or when the dominance coefficient of deleterious alleles is low, by allowing the fixation of inversions that initially carry deleterious alleles, despite the fact that they eventually become deleterious (‘sheltering’ effect). Finally, we show that partial selfing may either help or hinder the spread of inversions capturing a mating-type locus, as they benefit from the masking of deleterious alleles, but also suffer from a higher equilibrium mutation load. ### Competing Interest Statement The authors have declared no competing interest.
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