Dynamics of Lotka-Volterra Competition Patch Models in Streams with Two Branches

Area of Science:

• Ecology
• Mathematical Biology
• Theoretical Ecology

Background:

• River networks exhibit complex branching patterns, influencing ecological dynamics.
• Species competition models are crucial for understanding biodiversity in fragmented habitats.

Purpose of the Study:

• To investigate species competition in two distinct river network modules: distributary and tributary streams.
• To analyze the conditions for mutant species invasion based on dispersal strategies.
• To compare the global dynamics of these two river network models.

Main Methods:

• Development of two competition patch models for distributary and tributary river networks.
• Analysis of mutant species invasion criteria using invasion curves.
• Comparison of global dynamics under varying drift rates.

Main Results:

• For both models, mutant invasion occurs if dispersal strategy is below a specific invasion curve, though curve shapes differ.
• Global dynamics can be similar or distinct based on river network structure.
• When drift rates are equal, dynamics align for small rates but diverge for large rates.

Conclusions:

• River network topology significantly influences species competition outcomes.
• The study confirms a previously stated conjecture regarding species invasion in riverine systems.
• Dispersal strategies and drift rates are key factors determining species coexistence and dynamics in river networks.