[C01] Ecology and Enviromment

[C01-03] A mathematical model of reproductive interference between two species considering dispersal between distinct patches

*Yusuke Ikegawa^1,2,3, Atsushi Honma^1,2,3 (1. Ryukyu Sankei Co. Ltd. (Japan), 2. OPPPC (Japan), 3. University of the Ryukyus (Japan))

Keywords:

Population dynamic model,Dispersal,Spatial distribution,Species exclusion

Reproductive interference (RI) is an interspecific interaction in which one species reduces the fitness of closely related species through its reproductive behavior. Empirical studies have shown that RI might prevent sympatric coexistence of species, causing species exclusion and spatial segregation of species distributions. On the other hand, theoretical studies have examined the effects of RI on species coexistence, but those on the spatial distribution of species have not been fully investigated. In this study, we developed a population dynamic model in which males and females of two species involved in RI can disperse between two distinct patches. We assumed that female’s mating success is determined by the ratio of population densities of conspecific males to heterospecific ones in the focal patch. Then, males and females of the two species move to the different patch with inherent dispersal rates. Finally, population densities of the two species at the next time step is determined depending on mating success of females in the focal patches. We examined the effect of the dispersal rates on coexistence and spatial distribution of the two species, by running numerical simulations for 1000 unit times from the initial condition in which the two species were distributed in separate patches. We showed that if the dispersal rates of the two species were sufficiently small, each species cannot mutually invade patches dominated initially by the other species and coexisted in a spatially segregated manner. If the dispersal rate of the two species was sufficiently large, the spatial differences in population density disappeared and immediately converged to the same equilibrium states as when there was no spatial structure. Additionally, if differences in dispersal rates between the two species were sufficiently large, species with higher dispersal rates could dominate and even exclude species with low dispersal rates in both patches. It was also shown even under conditions where the effects of RI were mutually and sufficiently small enough to stabilize the two-species coexistence equilibria in the absence of the spatial structure. Such counter-intuitive species exclusions were shown if the dispersal rates of females were sufficiently large and the effect of male dispersal rates was minor. It indicates that species exclusions can more easily occur if spatial structure is taken into account, even when the effect of RI is mutually and sufficiently small.