Modeling diploid male dynamics in Hymenoptera: Effects of the number of alleles, dispersal by random walk and simple spatial structuring

Insects in the order Hymenoptera such as wasps, ants and bees exhibit a haplodiploid system of sexual determination in which females result from fertilized eggs and males from unfertilized eggs. Genetic information for sex determination is contained in a single multiallelic locus, so that the heterozygous individuals become females, and the hemizygous or homozygous individuals, haploid or diploid males, respectively. This mechanism is called single locus complementary sex determination (sl-CSD). While females and haploid males are regarded to be fertile, the opposite occurs for diploid males, so the significant production of diploid males (DM) may lead a population to an extinction scenario called the “diploid male vortex”. In the present work, we investigate the dynamics of populations of an organism with sl-CSD under various combinations of three parameters: male flight skills, number of sexual alleles and concentration of prohibited zones in a terrain represented by a square lattice. Sites of this lattice were randomly chosen as prohibited, where individuals could not pass, so the terrain was divided into islands of various sizes where individuals were confined. After a given simulation, the number of DM was measured. The main results that come from our simulations are: (i) the DM number depends more on the number of random steps in the male flight than on the number of alleles; (ii) the DM frequency in the small fragments becomes the same as the entire network when the limit of percolation is reached; (iii) the number of random steps explains the difference between the DM number found in the largest fragment and in the small fragments when the limit of percolation is reached.