Complex dynamics occur in a single-locus, multiallelic model of general frequency-dependent selection.

Area of Science:

• Evolutionary biology
• Population genetics
• Theoretical ecology

Background:

• Frequency-dependent selection is a key driver of evolutionary dynamics.
• Understanding non-equilibrium dynamics is crucial for predicting evolutionary trajectories.
• The pairwise-interaction model (PIM) provides a framework for studying these dynamics.

Purpose of the Study:

• To investigate the non-equilibrium dynamics generated by a simple model of frequency-dependent selection.
• To characterize allele-frequency cycling and aperiodic trajectories in systems with varying numbers of alleles.
• To analyze the properties of attractors, including cycle length and domains of attraction.

Main Methods:

• Examination of the parameter space of the pairwise-interaction model (PIM).
• Analysis of systems with 3, 4, and 5 alleles under frequency-dependent selection.
• Measurement of attractor characteristics: number, cycle length, and domains of attraction.

Main Results:

• Non-equilibrium dynamics, including allele-frequency cycling and aperiodic trajectories, were detected for 3-5 allele polymorphisms.
• Larger numbers of alleles resulted in smaller domains of attraction and longer cycles.
• Negative frequency-dependent selection favored cycling with larger domains of attraction.
• Aperiodic trajectories were observed only in systems with 4 or 5 alleles.

Conclusions:

• The PIM generates complex genetic cycles and aperiodic dynamics under frequency-dependent selection.
• Observed genetic cycles have longer periods than those in ecological models, potentially making them difficult to distinguish from stable equilibria in short-term observations.
• These findings highlight the intricate evolutionary pathways possible even in simple genetic models.