# The evolution of queen control over worker reproduction in the social Hymenoptera

## TL;DR

This paper presents a mathematical model explaining how queen control over worker reproduction evolves and stabilizes in social Hymenoptera, highlighting conditions independent of mating frequency and emphasizing efficiency impacts.

## Contribution

It introduces a haplodiploid genetic model that defines precise conditions for the evolution and stability of queen-induced worker sterility, regardless of queen mating frequency.

## Key findings

- Queen control evolves if it increases colony efficiency.
- Queen control can evolve even if it decreases efficiency.
- Conditions for stability against worker invasion are outlined.

## Abstract

A trademark of eusocial insect species is reproductive division of labor, in which workers forego their own reproduction while the queen produces almost all offspring. The presence of the queen is key for maintaining social harmony, but the specific role of the queen in the evolution of eusociality remains unclear. A long-discussed scenario is that a queen either behaviorally or chemically sterilizes her workers. However, the demographic and ecological conditions that enable such manipulation are unknown. Accordingly, we propose a simple model of evolutionary dynamics that is based on haplodiploid genetics. We consider a mutation that acts in a queen, causing her to control the reproductive behavior of her workers. Our mathematical analysis yields precise conditions for the evolutionary emergence and stability of queen-induced worker sterility. These conditions do not depend on the queen's mating frequency. Moreover, we find that queen control is always established if it increases colony reproductive efficiency and can evolve even if it decreases colony efficiency. We further outline the conditions under which queen control is evolutionarily stable against invasion by mutant, reproductive workers.