# Quantifying the Extent of Lateral Gene Transfer Required to Avert a `Genome of Eden'

## TL;DR

This paper models and quantifies lateral gene transfer (LGT) in prokaryotes, providing mathematical bounds and computational insights to understand the evolution of genomes and the network of life.

## Contribution

It introduces a formal model for quantifying LGT, deriving exact bounds and analyzing the computational complexity using graph-theoretical methods.

## Key findings

- Exact mathematical bounds for LGT quantification
- Computational complexity analysis of LGT models
- Connections between LGT optimization and graph theory

## Abstract

The complex pattern of presence and absence of many genes across different species provides tantalising clues as to how genes evolved through the processes of gene genesis, gene loss and lateral gene transfer (LGT). The extent of LGT, particularly in prokaryotes, and its implications for creating a `network of life' rather than a `tree of life' is controversial. In this paper, we formally model the problem of quantifying LGT, and provide exact mathematical bounds, and new computational results. In particular, we investigate the computational complexity of quantifying the extent of LGT under the simple models of gene genesis, loss and transfer on which a recent heuristic analysis of biological data relied. Our approach takes advantage of a relationship between LGT optimization and graph-theoretical concepts such as tree width and network flow.