# Wanted: A population genetic theory of biological noise regulation

## TL;DR

This paper proposes a new population genetic framework to study how natural selection acts on biological noise, such as genetic or developmental variation.

## Contribution

The paper introduces a unified theoretical approach to model the evolution of biological noise regulation across different sources and timescales.

## Key findings

- A toy model predicts a selectively optimal amount of reproductive noise depending on environment change rate and population size.
- The framework connects the evolution of developmental noise to population genetic theory, resolving longstanding theoretical issues.
- Recent high-throughput assays show heritability in developmental noise, making the proposed theory timely and applicable.

## Abstract

Classical population genetics provides a robust, quantitative framework for modeling how natural selection acts on alleles that influence phenotypes with invariant fitness consequences for their carriers, such as running speed or drug resistance. By contrast, modifier theory considers the evolution of alleles that influence population genetic parameter values in their carriers, such as mutation or recombination rates. This is a more complicated problem. First, the fitness effects of modifier alleles reflect independently realized stochastic phenotype perturbations they induce in their carriers. And second, the association between modifier alleles and their induced phenotypes can decay over generations. Consequently, general results in modifier theory have been few. Here, we propose recasting modifier theory as exploring the evolution of alleles that influence the amount of stochasticity in inheritance, be it genetic, epigenetic, cytoplasmic or somatic transmission. We then present a toy model that predicts the existence of a selectively optimal amount of such “reproductive noise,” which depends on the rate of environment change, the timescale of association between noise allele and induced phenotype, and population size. Next, we suggest that the same framework can be applied to the evolution of alleles that influence “developmental noise,” i.e., the amount of stochastic phenotypic variation among genetically identical organisms reared in identical environments. This theoretical connection is timely, because high throughput assays are now demonstrating widespread heritability in the amount of developmental noise. Our approach also resolves the long-standing teleological criticism of the hypothesis that evolvability can evolve by natural selection. Taken together, this work demonstrates the opportunities for a robust, quantitative population genetic theory of alleles that influence the amount of biological noise.

Darwin’s theory of evolution describes how mean trait values change in response to natural selection over generations. But if mean trait values are subject to natural selection, what about the amount of variation (or noise) around those means? This is more than an academic question: genetic variation introduced between generations is the fuel for evolution, including the evolution of therapy resistance in pathogenic microbes and agricultural pests. And trait variation introduced within generations is essential for developmental flexibility and plasticity, but is also the basis of adaptive immunity and underlies some disease. Extending established work on the evolution of population genetic parameters like mutation and recombination rates, we propose a unified framework for studying the evolution of the amount of all sources of biological noise, whether introduced between or within generations. We present a toy model that captures both the costs and opportunities introduced by biological noise, and which suggests the existence of a selectively optimal amount of noise. Recent technological advances in our ability to characterize many sources of biological noise make this work timely, and we conclude by suggesting steps for extending and generalizing our ideas.