It is well known that some species produce offspring carrying only female chromosomes by processes such as apomixis and parthenogenesis (generically termed "gynogenesis"). There are also several cases of natural reproduction by androgenesis in which diploid offspring carry nuclear chromosomes from only the male parent. We used population genetics models to investigate the conditions for invasion of rare androgenesis alleles and the consequences of their spread. Our models predict that androgenesis alleles often spread to fixation. If fixation causes the loss of females or female function in the population, population extinction occurs. Therefore, androgenesis alleles represent a new class of selfish genetic elements. Extinction is more likely in dioecious species than in hermaphrodites. Within dioecious species, extinction is more likely when androgenesis occurs via paternal apomixis (vs. fusion or doubling of haploid nuclei) and when females are the heterogametic sex (vs. male heterogamety). The apparent rarity of androgenesis compared to gynogenesis could be because androgenesis is harder to detect and more often leads to population extinction. Also, there could be greater evolutionary constraints on the origin of mutations for androgenesis. We suggest characteristics of groups in which further cases of androgenesis are more likely to be found.