Genetic benefits are potentially the most robust explanation of the controversial issue of evolutionary maintenance of polyandry, but the unambiguous demonstration of such benefits has been hindered by the possibility of their confusion with maternal effects. Previous research has shown that polyandrous bulb mite females produce daughters with higher fecundity than monandrous females. Here, we investigate whether this effect arises because polyandrous females invest more in their offspring, or because their offspring inherit 'good genes' from their fathers. Females were mated with either one or four (different) males. However, by sterilizing three of the four males with ionizing radiation, we eliminated any chance of sexual selection (in the polyandrous treatment) so that any differences in the female mating regimes must have been owing to maternal effects. Polyandry had no significant effect on daughter fecundity, thus indicating that any previously documented effects must have been genetic. This was further supported by a significant association between fathers' offensive sperm-competitive ability and the fecundity of their daughters. The association with fathers' sperm defensive ability was not significant, and neither was the association between fathers' sperm competitiveness and sons' reproductive success. However, sons of polyandrous females had lower reproductive success than sons of monandrous females. This shows that the maternal effects of polyandry should be taken into account whenever its costs and benefits are being considered.