Mathematical Model Analysis for the Stability Change of Ecosystem by Elimination of Interspecific Relationship

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1. As for Lotka-Volterra competing two species system with temporally intermittent competitive relationship, the temporally intermittent competition could realize the coexistence or emphasize the competition as a result. We introduce in addition the spatial distribution of those two species, making a mathematical model with reaction-diffusion system, and discuss the expansion or the shrinking of spatial distribution as a travelling wave problem. Until now we find that the temporally intermittent competition could cause the coexistence of two species at the same site, with their spatially overlapping distributions. Mathematically the conditions for such co-location coexistence would be closely related to the condition for coexistence in case of population dynamics without taking account of spatial distribution. Moreover, in case of spatial co-location coexistence, each spatial distribution invades into the habitat of another species. Numerical calculations indicate that the front of suc … More h spatial invasion can be treated as a stationary travelling wave with a constant speed2. As for Lotka-Volterra predator-prey system, we investigate the possibility of coexistence of preys with competition which mediates the apparent competition by a common predator. We can show that, even when a prey tends to go extinct due to predation by a predator that feeds another preys, the prey could survive if it has an appropriate competitive relationship with another prey(s), with or without predators extinction. This implies that, with an elimination of competitive relationship between preys within a food web, some preys could go extinct due to such indirect effect. Consequently it is indicated that the competitive relationship could promote the coexistence between those competing species. Therefore, the competitive relationship within a stable ecosystem may stabilize the system. On the other hand, the invasion of new species may considerably destabilize the system, depending on the possible predation for the invading species Less