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

1.对于具有时间间歇竞争关系的Lotka-Volterra竞争两种群系统，时间间歇竞争可以实现共存或强化竞争.本文还介绍了这两种物种的空间分布，建立了一个反应扩散系统的数学模型，并将空间分布的扩张或收缩作为行波问题进行了讨论。到目前为止，我们发现，时间间歇的竞争可能会导致两个物种在同一地点共存，其空间分布重叠。在数学上，这种共址共存的条件将与不考虑空间分布的种群动态情况下的共存条件密切相关。此外，在空间共位共存的情况下，每个空间分布侵入另一个物种的栖息地。数值计算表明， ...更多信息 h空间侵入可以被视为具有恒定速度的静止行波2。对于Lotka-Volterra捕食-食饵系统，我们研究了食饵与竞争共存的可能性，其中竞争是由一个共同的捕食者介导的表观竞争.我们可以证明，即使当一个猎物由于捕食者的捕食而趋于灭绝时，如果它与另一个猎物有适当的竞争关系，无论捕食者是否灭绝，猎物都可以生存。这意味着，随着食物网中猎物之间竞争关系的消除，一些猎物可能会因这种间接影响而灭绝。这表明，竞争关系可以促进这些竞争物种之间的共存。因此，在一个稳定的生态系统中，竞争关系可以使系统稳定。另一方面，新物种的入侵可能会大大破坏系统的稳定性，这取决于入侵物种可能的捕食行为。

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