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Phylogenetic comparative studies suggest that the direction of deviation from bilateral symmetry (sidedness) might evolve through genetic assimilation; however, the changes in sidedness inheritance remain largely unknown. We investigated the evolution of genital asymmetry in fish of the family Anablepidae, in which males' intromittent organ (the gonopodium, a modified anal fin) bends asymmetrically to the left or the right. In most species, males show a 1 : 1 ratio of left-to-right-sided gonopodia. However, we found that in three species left-sided males are significantly more abundant than right-sided ones. We mapped sidedness onto a new molecular phylogeny, finding that this left-sided bias likely evolved independently three times. Our breeding experiment in a species with an excess of left-sided males showed that sires produced more left-sided offspring independently of their own sidedness. We propose that sidedness might be inherited as a threshold trait, with different thresholds across species. This resolves the apparent paradox that, while there is evidence for the evolution of sidedness, commonly there is a lack of support for its heritability and no response to artificial selection. Focusing on the heritability of the left : right ratio of offspring, rather than on individual sidedness, is key for understanding how the direction of asymmetry becomes genetically assimilated.

Animal genitalia vary considerably across taxa, with divergence in many morphological traits, including striking departures from symmetry. Different mechanisms have been proposed to explain this diversity, mostly assuming that at least some of the phenotypic variation is heritable. However, heritability of the direction of genital asymmetry has been rarely determined. Anablepidae are internally fertilizing fish where the anal fin of males has been modified into an intromittent organ that transfers sperm into the gonopore of females. Males of anablepid fishes exhibit asymmetric genitalia, and both left- and right-sided individuals are commonly found at similar proportions within populations (i.e. antisymmetry). Although this polymorphism was described over a century ago, there have been no attempts to determine if genital asymmetry has a genetic basis and whether the different morphs are accumulating genetic differences, as might be expected since in some species females have also asymmetric gonopores and thereby can only be fertilized by compatible asymmetric males. We address this issue by combining breeding experiments with genome-wide data (ddRAD markers) in representative species of the two anablepid genera with asymmetric genitalia:AnablepsandJenynsia. Breeding experiments showed that all offspring were asymmetric, but their morphotype (i.e. right- or left-sided) was independent of parental morphotype, implying that the direction of asymmetry does not have a strong genetic component. Consistent with this conclusion, association analyses based on approximately 25 000 SNPs did not identify markers significantly associated with the direction of genital asymmetry and there was no evidence of population structure between left- and right-sided individuals. These results suggest that the direction of genital asymmetry in anablepid fishes might be stochastic, a commonly observed pattern in species with antisymmetry in morphological traits.