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Large-scale Gene Knockdown in C. elegans Using dsRNA Feeding Libraries to Generate Robust Loss-of-function Phenotypes

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Symmetric replicator dynamics with depletable resources.

W Garrett Mitchener¹

¹College of Charleston, 66 George St., Charleston, South Carolina 29407, USA.

Chaos (Woodbury, N.Y.)

|April 30, 2022

Summary

This summary is machine-generated.

This study modifies evolutionary game dynamics by incorporating resource depletion, showing that overuse leads to chaotic behavior and complex orbital patterns. Resource-dependent payoffs in replicator dynamics can generate rich, unpredictable population behaviors.

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Area of Science:

Evolutionary Game Theory
Population Dynamics
Mathematical Biology

Background:

The standard replicator equation models evolutionary population game dynamics.
This study introduces resource depletion into the replicator dynamics framework.
Payoffs are now dependent on resource availability, which replenishes over time.

Purpose of the Study:

To analyze the impact of resource depletion on evolutionary game dynamics.
To investigate the transition from stable equilibria to chaotic behavior.
To explore the topological complexity of population trajectories.

Main Methods:

Modification of the standard replicator equation to include resource dynamics.
Analysis of system stability through bifurcations and phase space exploration.
Numerical solutions and Poincaré maps to identify chaotic dynamics and orbital structures.

Main Results:

Low depletion rates lead to stable equilibria with equally popular strategies.
Increasing depletion rates cause bifurcations, vanishing stable points, and complex orbital topologies.
High depletion rates induce immediate chaotic dynamics, characterized by horseshoes in Poincaré maps, without period-doubling cascades.

Conclusions:

Resource depletion significantly alters population game dynamics, introducing complexity and chaos.
The variety of orbital types preceding chaos appears to generate the chaotic behavior.
Symmetries can reveal periodic orbits, with their manifolds potentially forming homoclinic tangles.