# Pleiotropy and the evolutionary stability of plastic phenotypes: a geometric framework

## TL;DR

This paper introduces a geometric model to better understand how pleiotropy helps maintain phenotypic plasticity during evolution.

## Contribution

A novel geometric framework for modeling the evolutionary stability of conditional phenotypes with complex pleiotropy.

## Key findings

- More pleiotropic conditional phenotypes decay more slowly in fitness when not expressed.
- Pleiotropy mediates the relationship between expression patterns and decay rates of conditional phenotypes.
- Decoupling from other phenotypes can evolve during inexpression, leading to fitness decay.

## Abstract

Phenotypic plasticity allows organisms to express different traits in response to different environmental or genetic conditions. Understanding the evolution of conditional phenotypes is challenging because they are not expressed by all members of a population, which allows for the accumulation of deleterious variation due to a reduced efficacy of purifying selection. Theory suggests pleiotropic effects help prevent the decay of conditional phenotypes by exposing the variation accrued in one context to the effects of purifying selection in an alternative context. However, existing frameworks for describing the evolutionary dynamics of conditional phenotypes are limited in their ability to flexibly model the complex pleiotropic architectures that often underlie conditional phenotypes. To help improve our understanding of the evolutionary stability of conditional phenotypes, here we describe a geometric model that allows for explicit modeling of different fitness optima for conditional and alternative phenotypes, as well as their underlying pleiotropic associations. Using stochastic simulations and mathematical analyses, we show that this model recapitulates and elaborates on existing predictions regarding the role of pleiotropy in maintaining conditional phenotypes. Specifically, we found that more pleiotropic conditional phenotypes experience decreased rates of decay in fitness over periods of inexpression, the effects of which are comparable for phenotypes that are spatially and temporally conditional. Furthermore, the functional form of the relationship between conditional phenotype expression pattern and decay rate is mediated by pleiotropic effect, which provides more explicit hypotheses of when pleiotropic constraint is expected to play a significant role in the evolutionary maintenance of conditional phenotypes. Finally, we found that when pleiotropic architectures evolve over periods of conditional phenotype inexpression, decoupling from other phenotypes readily evolves and facilitates decay in fitness.