A mathematical formalism for natural selection with arbitrary spatial and genetic structure.

Area of Science:

• Evolutionary biology
• Population genetics
• Mathematical modeling

Background:

• Natural selection models often have limitations in scope.
• A unified framework is needed to handle diverse genetic and population structures.

Purpose of the Study:

• To develop a general mathematical formalism for natural selection.
• To define and relate key evolutionary concepts within this framework.
• To demonstrate its applicability to complex scenarios.

Main Methods:

• Formalism based on 'genetic sites' within individuals.
• Modeling biological events as stochastic replacement events.
• Representing natural selection as a Markov chain.

Main Results:

• Defined reproductive value, fitness, neutral drift, and fixation probability.
• Identified criteria for allele selection, showing equivalence under low mutation.
• Formalized the method of weak selection.

Conclusions:

• The proposed formalism offers a powerful and versatile approach to studying natural selection.
• It successfully models evolutionary games on graphs and haplodiploid selection.
• Provides a unified theoretical basis for diverse evolutionary scenarios.