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Population evolution on a multiplicative single-peak fitness landscape
1Department of Physics, University of Sheffield, U.K.
Journal of Theoretical Biology
|March 7, 1996
Summary
Finite populations evolve differently than infinite ones. This study models sequence evolution, showing populations balance mutation and selection, leading to stable evolution rates independent of selection strength.
Area of Science:
- Evolutionary biology
- Population genetics
- Molecular evolution
Background:
- Evolutionary models often assume infinite populations, neglecting finite size effects.
- Adaptive walk models simplify populations to single sequences, which is unrealistic.
- Finite populations with related sequences exhibit unique evolutionary dynamics.
Purpose of the Study:
- To develop and analyze a model for population evolution in a fitness landscape with a single peak, considering finite population size.
- To investigate the balance between mutation and selection in finite populations.
- To understand how sequence evolution rate depends on population size, sequence length, selection strength, and mutation rate.
Main Methods:
- Developed a model representing each individual by a sequence of L genes with fitness Wk = (1-s)k.
- Analyzed the model in the limit of infinite sequence length (L-->infinity), relating it to Muller's Ratchet.
- Used numerical simulations and approximate theory to study finite length sequences and their evolution.
- Investigated the mean overlap between gene sequences over time (Q(t)) and analyzed a simplified solvable model.
Main Results:
- Finite populations evolve away from the fitness peak until a mutation-selection balance is reached.
- Populations wander in sequence space at a constant mean Hamming distance from the optimum.
- Evolutionary rate within this 'spherical shell' is independent of selection strength, depending only on mutation rate (u).
- Selection is less effective in smaller populations (N), increasing the mean Hamming distance (
). - In a model with favorable/unfavorable mutations, an optimal non-zero mutation rate (U) maximizes fitness increase.
Conclusions:
- Finite population size significantly impacts evolutionary trajectories compared to infinite population models.
- A balance between mutation and selection leads to a stable, albeit evolving, population state in sequence space.
- The rate of molecular evolution can be independent of selection strength, primarily driven by mutation.
- Natural selection may favor non-zero mutation rates under certain conditions, optimizing evolutionary potential.
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