Population dynamics of a species with two or three types of males on a lattice

In any biological population, the individuals with low reproductive success appear recursively at every generation. This phenomenon is prominent in rearing animals and insects, such as aquaculture. We consider the variation in the fitness of male and assume that all individuals live on a lattice. Recently, lattice models have been applied to sexual populations. In these cases, simulations have been carried out by two methods: local and global interactions. In the former, birth process occurs between neighboring sites, whereas in the latter it occurs between any pair of lattice sites. In the present paper, we deal with the population dynamics of a single species that contains two or three types of males and one female. Our attention is paid on the conditions of both “stability” and “sustainability”. Here the stability means that the system reaches a surviving equilibrium in population dynamics. In contrast, the sustainability denotes that the population size at the equilibrium is sufficiently high. Simulation for two-male system exhibits the Allee effect: the population goes extinct, unless both densities of male and female are substantially high. For the stability, the high-fitness male is more important than the subordinate male. However, for the sustainability, our results shows that the low-fitness male plays more important role than high-fitness male. Especially if the low-fitness male is not reproductive, the population tends to go extinct. This tendency is conspicuous, when we consider the local interaction. Moreover, simulations are carried out for three-male system. It is found that the sustainability is influenced not by the fitness variation in male but the average of male fitness. Our results suggest that fitness reductions in individuals can become very critical for maintaining artificially breeding populations.