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

Area of Science:

• Ecology
• Theoretical Ecology
• Mathematical Biology

Background:

• The colonization model explains species coexistence through competition for sites.
• Traditional models assume mass action encounters, leading to stable equilibrium in constant environments.
• The impact of different encounter modes on species diversity and community dynamics remains underexplored.

Purpose of the Study:

• To investigate the effects of varying encounter processes on species diversity within the colonization model.
• To analyze community dynamics under different encounter modes, particularly focusing on ratio-dependent encounters.

Main Methods:

• Analysis of community dynamics within the colonization model.
• Systematic variation of encounter processes between propagules and habitable sites.
• Mathematical analysis of species frequency trajectories and stability under different encounter conditions.

Main Results:

• Perfect ratio-dependent encounters lead to approximate neutral stability, disrupting traditional equilibrium.
• Species frequencies exhibit continuous, irregular temporal variations, termed 'strange nonchaotic attractors' (SNAs).
• Trajectories are highly dependent on initial conditions, with an infinite number of unique SNAs existing.

Conclusions:

• Encounter mode is a critical factor influencing species diversity and community stability.
• Ratio-dependent encounters provide a novel mechanism for generating complex transient dynamics, distinct from chaos.
• The findings challenge assumptions of stable equilibrium in ecological models and highlight the importance of initial conditions.