Limits to selection on standing variation in an asexual population.

Area of Science:

• Evolutionary genetics
• Population genetics
• Quantitative genetics

Background:

• Understanding the evolutionary response to selection on existing genetic variation is crucial.
• Previous models often focused on new mutations or recombination, neglecting standing variation.
• Directional selection drives adaptation by favoring specific trait values.

Purpose of the Study:

• To analyze the dynamics of directional selection on standing variation in a haploid population.
• To determine how population size (N) and initial genetic variance (V0) influence evolutionary outcomes.
• To compare evolutionary trajectories under weak versus strong selection relative to genetic drift.

Main Methods:

• Mathematical modeling of a haploid population with trait values drawn from a distribution.
• Analysis of scaling limits based on the parameter NV0.
• Application of branching processes to model allele establishment under strong selection.

Main Results:

• Under weak selection (NV0≪1), genetic variance decreases exponentially, with fitness gain matching predictions for sexual populations.
• Under strong selection (NV0≫1), allele establishment is approximated by a branching process.
• Specific formulas for ultimate fitness gain are derived for Gaussian and Laplace distributions, with variance dynamics showing a t^-3 decay.

Conclusions:

• The study provides a framework for understanding selection on standing variation without new mutations.
• Distinct regimes of weak and strong selection lead to different evolutionary dynamics and outcomes.
• The findings have implications for understanding adaptation and genetic variation maintenance in natural populations.