Persistence conditions of symmetric social hybridogenesis in haplo-diploid hymenoptera

In eusocial Hymenoptera species, females variably develop into either alate females (queens) or workers, and in most cases, caste differentiation is determined environmentally. Recently, however, female castes in two harvester ant species, Pogonomyrmex rugosus and P. barbatus, were found to be determined genetically in hybrid zones of these two species. In the hybrid populations, homozygous females (e.g. AA or BB) and heterozygous females (AB) develop into alate females and workers, respectively. This genetic caste determination system is called symmetric social hybridogenesis (SSH). It is clear that populations with SSH can persist only if all four genotypes (AA and BB females, and A and B males) coexist simultaneously. However, it is not obvious that these populations are always persistent when the four genotypes simultaneously exist. Here, we examined the stability and persistence of an SSH population using a simple mathematical model. According to the analysis of the model, the SSH population persists only when some conditions are satisfied: (1) each female mates with more than two males, and (2) male production increases less steeply than linearly with increasing numbers of workers in a colony, and alate female production increases more steeply than linearly with increasing numbers of workers, or (2′) male production increases more steeply than linearly with increasing numbers of workers in a colony, and alate female production increases much more steeply than male production. Therefore, it is not obvious that SSH populations are maintained and are stable for long periods. We discuss whether these conditions are satisfied in real SSH populations.