Quasispecies dynamics with time lags and periodic fluctuations in replication

Area of Science:

• Evolutionary dynamics
• Theoretical biology
• Mathematical modeling

Background:

• Quasispecies theory explains biological information dynamics in high-mutation-rate replicators.
• It is applied to prebiotic evolution, RNA viruses, and cancer cell populations.
• Real-world scenarios require extensions to the basic quasispecies model, including time lags and fluctuations.

Purpose of the Study:

• To investigate the impact of time lags and periodic fluctuations on quasispecies dynamics.
• To analyze the classical quasispecies model in a single-peak fitness landscape.
• To examine the error threshold hypothesis under these conditions.

Main Methods:

• Combining delayed ordinary differential equations and topological Leray-Schauder degree.
• Analyzing the quasispecies model with constant population constraint.
• Investigating scenarios with and without backward mutation and periodic fluctuations.

Main Results:

• Time lags with constant population constraint keep dynamics within the simplex.
• Periodic orbits exist with backward mutation and periodic fluctuations, irrespective of time lags.
• Without backward mutation, periodic fluctuations or time lags alone do not create periodic orbits, but solutions may oscillate.
• The error threshold hypothesis is supported for periodic fitness/time lags with constant fitness, but not with backward mutations.

Conclusions:

• Time lags and periodic fluctuations significantly alter quasispecies dynamics, influencing the existence of periodic orbits.
• The error threshold remains valid under specific conditions but is disrupted by backward mutations.
• These findings offer a more nuanced understanding of evolutionary dynamics in systems with high mutation rates.