From adaptive dynamics to adaptive walks.

Area of Science:

• Evolutionary Biology
• Mathematical Biology
• Population Genetics

Background:

• Asexual population dynamics are often modeled using measure-valued Markov processes.
• Previous studies focused on large populations with rare, separated mutations.
• The impact of high mutation rates on evolutionary trajectories remains less understood.

Purpose of the Study:

• To analyze the deterministic system of asexual populations under a high mutation rate regime.
• To investigate the resulting evolutionary dynamics, including adaptive walks and type coexistence.
• To explore how the type space structure and fitness landscape shape evolutionary jumps.

Main Methods:

• Derivation of a deterministic model from a measure-valued Markov process in the large population limit.
• Analysis of the system as mutation probability tends to zero, increasing mutation frequency.
• Examination of a modified model with limited mutant spread to study fitness landscape traversal.

Main Results:

• The limiting process exhibits adaptive walks and jumps between equilibria of coexisting types.
• The graph structure of the type space significantly influences the jump dynamics.
• Limited spread of mutants can enable crossing of fitness valleys, leading to distinct limiting walks.

Conclusions:

• High mutation rates drive populations through adaptive walks and jumps, influenced by type space connectivity.
• The model provides insights into evolutionary trajectories in complex fitness landscapes.
• Understanding these dynamics is crucial for predicting population evolution under varying mutation pressures.