# Dual genetic mechanisms of heterosis: population structure and gene action

## TL;DR

This paper explains how hybrid vigor (heterosis) arises from population structure and gene action, using maize to show how inbreeding and genetic diversity affect hybrid performance.

## Contribution

The paper introduces a new theoretical model that integrates population-level inbreeding and gene action to explain heterosis.

## Key findings

- Heterosis and inbreeding depression are linear functions of inbreeding and genetic diversity under directional dominance.
- Midparent value and parental inbreeding depression strongly predict heterosis in maize grain yield.
- Heterosis results from two independent mechanisms: population structure and gene action.

## Abstract

Heterosis refers to the superiority of a hybrid over its parents. Existing heterosis theory has not sufficiently addressed the contribution of inbreeding at both population level and the level of individual lines within populations. The objectives of the present paper were to formalize theoretical extensions of heterosis theory to address inbreeding at multiple levels, to empirically test the theory in maize, and to provide greater clarity in the quantitative genetic interpretation of heterosis as a function of independent genetic principles of population structure and gene action.

Existing heterosis theory for biparental crosses was extended by adding terms for inbreeding within panmictic parent populations. The theory was tested with an experiment in maize with a diverse set of panmictic and inbred parents.

Extended theory demonstrated that both heterosis and inbreeding depression are linear functions of inbreeding, FST at the population level, and f at the individual level, under a model of directional dominance. The model demonstrates that heterosis is expected to be negatively related to both midparent value and inbreeding depression within parent populations, i.e., heterosis increases as midparent value decreases and as inbreeding depression within parent populations decreases. Consistent with theoretical predictions we found that that for maize grain yield midparent value predicted 86% of heterosis in a set of crosses and parental inbreeding depression predicted 70% of variation in heterosis among crosses.

Model extensions presented here illustrate the excess and transient nature of heterozygosity in the F1 generation that is partially responsible for the unique performance benefit of F1 hybrids. Mechanistically, the theory illustrates that heterosis is a function of two separate and independent mechanisms, population structure and gene action, both of which need to be considered in understanding the mechanisms of heterosis.