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Dimorphism by Singularity Theory in a Model for River Ecology
Martin Golubitsky1, Wenrui Hao2, King-Yeung Lam3
1Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA.
Bulletin of Mathematical Biology
|March 31, 2017
Summary
Two similar species can coexist in more ways than previously thought. This study expands understanding of the dimorphism region using advanced mathematical theory and a river species model.
Area of Science:
- Evolutionary biology
- Mathematical biology
- Theoretical ecology
Background:
- Coexistence of similar species is a fundamental question in evolutionary biology.
- Previous models suggested coexistence requires strategies near nondegenerate evolutionarily singular strategies.
- Adaptive dynamics theory provides a framework for studying evolutionary processes.
Purpose of the Study:
- To investigate the generality of the dimorphism region for species coexistence.
- To explore coexistence conditions beyond nondegenerate evolutionarily singular strategies.
- To apply unfolding theory to understand complex evolutionary dynamics.
Main Methods:
- Utilizing unfolding theory near degenerate evolutionarily singular strategies.
- Applying the theory to a partial differential equation (PDE) model of river species.
- Analyzing the structure of the dimorphism region.
Main Results:
- Demonstrated that the dimorphism region can be more general than previously described.
- Identified novel forms of the dimorphism region using unfolding theory.
- Showcased the applicability of the approach with a riverine ecosystem model.
Conclusions:
- The conditions for species coexistence are more varied than previously understood.
- Degenerate evolutionarily singular strategies offer a richer landscape for evolutionary dynamics.
- This work provides new insights into the complex patterns of adaptive dynamics.
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