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Investigation of Plant Interactions Across Common Mycorrhizal Networks Using Rotated Cores

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Intraspecific interactions facilitate mutualism across multilayer networks under weak selection.

Yihe Ma¹, Hui Zhang^2,3,4, Chaoqian Wang⁵

¹School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, 710072, Shaanxi, China.

Journal of Mathematical Biology

|June 23, 2026

Summary

Evolution favors mutualism in structured populations when strong intraspecific interactions outweigh interspecific ones. This theoretical model reveals how population structure and game parameters influence the evolution of cooperation.

Keywords:

Fixation probability Interdependent populations Mutualism

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Area of Science:

Evolutionary Biology
Theoretical Ecology
Game Theory

Background:

Interspecific mutualism, a common phenomenon in biological and social systems, is a key area of study in evolutionary biology.
Understanding the evolutionary drivers and maintenance mechanisms of mutualism, especially in structured populations, remains a significant research challenge.

Purpose of the Study:

To theoretically investigate the evolution of mutualism in arbitrary interdependent populations.
To derive conditions favoring mutualism under weak selection using coalescent random walk theory.

Main Methods:

Development of an evolutionary model for interdependent populations.
Application of coalescent random walk theory to analyze conditions for mutualism.
Derivation of conditions for mutualism under weak selection.

Main Results:

Evolution favors mutualism when the strength of intraspecific interactions surpasses a specific threshold.
This threshold is contingent upon the population structure and game parameters.
Intraspecific interactions play a crucial positive role in the evolution of mutualism.

Conclusions:

The study highlights the importance of intraspecific interactions in promoting the evolution of interspecific mutualism.
Findings extend previous research by incorporating the influence of population structure and intraspecific effects.
Provides a theoretical framework for understanding mutualism in complex, structured populations.