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.
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