Accessory male investment can undermine the evolutionary stability of simultaneous hermaphroditism

Sex allocation (SA) models are traditionally based on the implicit assumption that hermaphroditism must meet criteria that make it stable against transition to dioecy. This, however, puts serious constraints on the adaptive values that SA can attain. A transition to gonochorism may, however, be impossible in many systems and therefore realized SA in hermaphrodites may not be limited by conditions that guarantee stability against dioecy. We here relax these conditions and explore how sexual selection on male accessory investments (e.g. a penis) that offer a paternity benefit affects the evolutionary stable strategy SA in outcrossing, simultaneous hermaphrodites. Across much of the parameter space, our model predicts male allocations well above 50 per cent. These predictions can help to explain apparently 'maladaptive' hermaphrodite systems.