Power-laws in phylogenetic trees and the preferential coalescent

Area of Science:

• Evolutionary Biology
• Phylogenetics
• Computational Biology

Background:

• Phylogenetic trees map evolutionary relationships, with topology (imbalance) offering insights into evolutionary dynamics, especially when temporal data is scarce.
• Classical metrics like Colless and Sackin indices quantify tree imbalance, which typically falls between balanced and skewed states in empirical phylogenies.
• A power-law relationship between subtree sizes and cumulative sizes characterizes this intermediate imbalance, but its origin and exponent remain unclear.

Purpose of the Study:

• To develop a generative model for phylogenetic trees that explains the observed power-law scaling in tree imbalance.
• To elucidate the mathematical basis of this scaling and the characteristic exponent.
• To provide new tools for interpreting tree imbalance in evolutionary studies.

Main Methods:

• Developed a generative model inspired by Kingman's coalescent, incorporating niche-like dynamics via preferential node coalescence.
• Mapped this process to Smoluchowski's coagulation kinetics, described by a generalized Smoluchowski equation.
• Analyzed the resulting tree structures to identify power-law exponents.

Main Results:

• The proposed model successfully generates imbalanced phylogenetic trees exhibiting power-law scaling.
• The model's exponents align with empirical and numerical observations of tree imbalance.
• This work reveals the mathematical foundation underlying the observed scaling laws in phylogenetic tree topology.

Conclusions:

• The coalescent-inspired model with preferential coalescence provides a mechanistic explanation for power-law scaling in phylogenetic tree imbalance.
• This framework clarifies the mathematical origin of observed scaling exponents.
• The findings offer novel approaches for inferring evolutionary processes from phylogenetic tree imbalance.