Continuous irregular dynamics with multiple neutral trajectories permit species coexistence in competitive communities.

The colonization model formulates competition among propagules for habitable sites to colonize, which serves as a mechanism enabling coexistence of multiple species. This model traditionally assumes that encounters between propagules and sites occur as mass action events, under which species distribution can eventually reach an equilibrium state with multiple species in a constant environment. To investigate the effects of encounter mode on species diversity, we analyzed community dynamics in the colonization model by varying encounter processes. The analysis indicated that equilibrium is approximately neutrally-stable under perfect ratio-dependent encounter, resulting in temporally continuous variation of species' frequencies with irregular trajectories even under a constant environment. Although the trajectories significantly depend on initial conditions, they are considered to be "strange nonchaotic attractors" (SNAs) rather than chaos from the asymptotic growth rates of displacement. In addition, trajectories with different initial conditions remain different through time, indicating that the system involves an infinite number of SNAs. This analysis presents a novel mechanism for transient dynamics under competition.

Effects of generalized and specialized adaptive defense by shared prey on intra-guild predation.

Intra-guild predation (IGP), predation on consumers which share common prey with the predators, is an important community module to understand a mechanism for persistence of complex food webs. However, classical theory suggests that persistence of an IGP system is unlikely particularly at high productivity, while empirical data do not support the prediction. Recently, adaptive defense by shared prey has been recognized to enhance coexistence of species and stability of the system. Some organisms having multiple predators in IGP systems employ two types of defenses; generalized defense that is effective against multiple predators and specialized one that is effective against only a specific predator species. We consider an IGP model including shared prey that can use the two types of defenses in combination against the consumer or omnivore. Assuming that the shared prey can change the allocation of defensive effort to increase its fitness, we show that the joint use of two types of adaptive defenses promotes three species coexistence and enhances stability of the IGP system when the specialized defense is more effective than the generalized one. When the system is unstable, a variety of oscillations appear and both the population densities and defensive efforts or only the population densities oscillate. Joint use of defenses against the consumer tends to increase the equilibrium population density of the shared prey with the defense efficiencies. In contrast, efficient generalized and specialized defenses against the omnivore often decrease the prey population. Consequently, adaptive defense by shared prey may not necessarily heighten the population size of the defender but sometimes increases densities of both the attackers and defender in IGP systems.

Dispersal-mediated coexistence of competing predators.

Models of metapopulations have often ignored local community dynamics and spatial heterogeneity among patches. However, persistence of a community as a whole depends both on the local interactions and the rates of dispersal between patches. We study a mathematical model of a metacommunity with two consumers exploiting a resource in a habitat of two different patches. They are the exploitative competitors or the competing predators indirectly competing through depletion of the shared resource. We show that they can potentially coexist, even if one species is sufficiently inferior to be driven extinct in both patches in isolation, when these patches are connected through diffusive dispersal. Thus, dispersal can mediate coexistence of competitors, even if both patches are local sinks for one species because of the interactions with the other species. The spatial asynchrony and the competition-colonization trade-off are usual mechanisms to facilitate regional coexistence. However, in our case, two consumers can coexist either in synchronous oscillation between patches or in equilibrium. The higher dispersal rate of the superior prompts rather than suppresses the inferior. Since differences in the carrying capacity between two patches generate flows from the more productive patch to the less productive, loss of the superior by emigration relaxes competition in the former, and depletion of the resource by subsidized consumers decouples the local community in the latter.