Ongoing evolution of polyandry, and consequent extra-pair reproduction in socially monogamous systems, is hypothesised to be facilitated by indirect selection stemming from cross-sex genetic covariances with components of male fitness. Specifically, polyandry is hypothesised to create positive genetic covariance with male paternity success due to inevitable assortative reproduction, driving ongoing coevolution. However, it remains unclear whether such covariances could or do emerge within complex polyandrous systems. First, we illustrate that genetic covariances between female extra-pair reproduction and male within-pair paternity success might be constrained in socially monogamous systems where female and male additive genetic effects can have opposing impacts on the paternity of jointly reared offspring. Second, we demonstrate non-zero additive genetic variance in female liability for extra-pair reproduction and male liability for within-pair paternity success, modelled as direct and associative genetic effects on offspring paternity respectively, in free-living song sparrows (Melospiza melodia). The posterior mean additive genetic covariance between these liabilities was slightly positive, but the credible interval was wide and overlapped zero. Therefore, while substantial total additive genetic variance exists, the hypothesis that ongoing evolution of female extra-pair reproduction is facilitated by genetic covariance with male within-pair paternity success cannot yet be definitively supported or rejected either conceptually or empirically.

female.data.dryad.finalPhenotypic data for quantitative genetic analysis of female liability for extra-pair reproductionfemale.Ainv.finalInverse A matrix for quantitative genetic analysis of female liability for extra-pair reproductionmale.data.dryad.finalPhenotypic data for quantitative genetic analysis of male liability for within-pair paternity successmale.Ainv.finalInverse A matrix for quantitative genetic analysis of male liability for within-pair paternity successmale.female.data.dryad.finalPhenotypic data for joint quantitative genetic analysis of female liability for extra-pair reproduction and male liability for within-pair paternity successmale.female.Ainv.finalInverse A matrix for joint quantitative genetic analysis of female liability for extra-pair reproduction and male liability for within-pair paternity success