Fixation probabilities in graph-structured populations under weak selection.

Area of Science:

• Evolutionary biology
• Mathematical modeling
• Population genetics

Background:

• Spatial structure influences evolutionary dynamics.
• The Birth-death process on graphs models population structure and selection.
• Calculating fixation probabilities on arbitrary graphs is computationally challenging.

Purpose of the Study:

• To derive a computable expression for the fixation probability of weakly-selected mutations on arbitrary weighted graphs.
• To explore the impact of graph structure on natural selection, genetic drift, and their balance.
• To identify specific graph structures that amplify or dampen selection.

Main Methods:

• Derivation of fixation probability using lineage coalescence time.
• Application of the derived expression to arbitrary weighted graphs.
• Computational analysis of small graphs and use of a genetic search algorithm.

Main Results:

• An efficient method to compute weak-selection fixation probabilities for any graph.
• Identification of graph families with significant effects on fixation probabilities.
• Demonstration of how graph structure modulates natural selection and neutral drift.

Conclusions:

• Graph structure plays a critical role in evolutionary processes.
• The derived method allows for precise quantification of selection's influence based on spatial organization.
• Understanding mutation processes is key to interpreting evolutionary outcomes in structured populations.