Establishment of new mutations in changing environments.

Area of Science:

• Evolutionary genetics
• Population genetics
• Mathematical biology

Background:

• Understanding adaptation is key in evolutionary genetics, particularly with ongoing environmental and climatic changes.
• The establishment of new beneficial mutations is a fundamental process in adaptation.

Purpose of the Study:

• To develop a generalized method for calculating the probability of new beneficial mutations establishing in changing environments.
• To extend classical models of mutation fixation to scenarios with time-varying selection coefficients.

Main Methods:

• Utilized time-dependent branching processes to approximate mutation establishment probability.
• Assumed small temporal changes in offspring distribution for simplification.
• Generalized Haldane's classic fixation probability result for constant environments.

Main Results:

• Derived simple approximations for establishment probability under temporally changing selection.
• Showed that under weak selection, establishment probability depends on a weighted average of selection coefficients.
• Weights indicate the contribution of different generations to the establishment probability.

Conclusions:

• The derived approximation accurately predicts mutation establishment probability across various temporal changes in selection.
• The findings offer a generalized framework for studying adaptation in dynamic environments.
• Applicable to scenarios with consistent, periodic, or random changes in selection and population size.