Escape from parsimony of a double-cut-and-join genome evolution process

TL;DR

This paper investigates genome evolution models using double-cut-and-join operations, analyzing when the evolutionary process diverges from the most parsimonious path by comparing actual operations to the DCJ distance.

Contribution

It adapts a method to estimate the number of cycles in the breakpoint graph, revealing when the evolution process escapes from parsimony in DCJ models.

Findings

Process remains close to parsimonious up to about half the genome size in steps.

The method estimates the number of cycles using Erdős-Rényi graph models.

Evolution diverges from parsimony beyond approximately n/2 steps.

Abstract

We analyze models of genome evolution based on both restricted and unrestricted double-cut-and-join (DCJ) operations. We compare the number of operations along the evolutionary trajectory to the DCJ distance of the genome from its ancestor at each step, and determine at what point they diverge: the process escapes from parsimony. Adapting the method developed by Berestycki and Durret (2006), we estimate the number of cycles in the breakpoint graph of a random genome at time $t$ and its ancestral genome by the number of tree components of an Erd\"os-R\'enyi random graph constructed from the model of evolution. In both models, the process on a genome of size $n$ is bound to its parsimonious estimate up to $t\approx n/2$ steps.