# A mathematical model for gene evolution after whole genome duplication

## TL;DR

This paper introduces a mathematical model to quantify gene evolution following whole genome duplication, focusing on the balance between gene loss and functional divergence in teleost fish over 90 million years.

## Contribution

The study presents a novel equilibrium-based mathematical model to predict gene functional divergence and loss after WGD, applicable to teleosts and potentially other lineages.

## Key findings

- Estimated up to 3000 gene pairs differentiated functionally in 90 million years
- Model allows quantitative assessment of WGD impact on genomes
- Provides a framework for comparing WGD effects across lineages

## Abstract

Whole genome duplication (WGD) is one of the most important events in the molecular evolution of organisms. In fish species, a WGD is considered to have occurred in the ancestral lineage of teleosts. Recent comprehensive ortholog comparisons among teleost genomes have provided useful data and insights into the fate of redundant genes generated by WGD. Based on these data, a mathematical model is proposed to explain the evolutionary scenario of genes after WGD. The model is parameterized taking into account an equilibrium between i) rapid loss of either of the duplicate genes and ii) moderate functional differentiation of each of duplicate genes, both of which are followed by slow gene loss under purifying selection. This model predicts that, in the teleost lineage, a maximum of about 3000 gene pairs may have differentiated functionally during 90 million years after WGD. Thus, the present study provides a possibility that the whole impact of WGD can be quantitatively assessed according to the model parameters, before details of genomic structural changes or functional differentiation are investigated. If the equilibrium model is valid not only for teleosts but also for other lineages that have undergone WGDs, correlations between the assessment indices and evolutionarily significant events, such as the diversification of species or the occurrence of novel phenotypes, could be tested and compared among those lineages.