Using phenotypic plasticity to understand the structure and evolution of the genotype–phenotype map

Abstract

Deciphering the genotype–phenotype map necessitates relating variation at the genetic level to variation at the phenotypic level. This endeavour is inherently limited by the availability of standing genetic variation, the rate of spontaneous mutation to novo genetic variants, and possible biases associated with induced mutagenesis. An interesting alternative is to instead rely on the environment as a source of variation. Many phenotypic traits change plastically in response to the environment, and these changes are generally underlain by changes in gene expression. Relating gene expression plasticity to the phenotypic plasticity of more integrated organismal traits thus provides useful information about which genes influence the development and expression of which traits, even in the absence of genetic variation. We here appraise the prospects and limits of such an environment-for-gene substitution for investigating the genotype–phenotype map. We review models of gene regulatory networks, and discuss the different ways in which they can incorporate the environment to mechanistically model phenotypic plasticity and its evolution. We suggest that substantial progress can be made in deciphering this genotype–environment–phenotype map, by connecting theory on gene regulatory network to empirical patterns of gene co-expression, and by more explicitly relating gene expression to the expression and development of phenotypes, both theoretically and empirically.

Appendix: Model description

The model used to simulate environmental effects on gene coexpression in Fig. 2 is a version of Wagner’s (1994) model, similar to that in Siegal and Bergman (2002). The 5-gene network was encoded in a 5 × 5 matrix W, in which positive terms stand for transcription activation, and negative terms for transcription repression. Gene expression levels were stored in a vector S_t updated dynamically as

$${\mathbf{S}}_{{{\text{t}} + {1}}} = {\text{ f}}({\mathbf{W}} \, {\mathbf{S}}_{{\text{t}}} + {\mathbf{z}}_{{{\text{t}} + {1}}} ),$$

(1)

where f(x) = 1/(1+e^−4x) is a sigmoid function ensuring that gene expressions scale continuously between 0 (no expression) and 1 (maximum expression), and ζ is normally distributed noise component, with same standard deviation σ_ζ = 0.05 for all genes and no correlation among genes. The initial gene expression level was set to S₀ = 0.5 for all genes, and then updated iteratively for 20 discrete time steps according to the netword equation (1). The average expression level over the four last time steps was taken as an approximation of the equilibrium.

We allowed the environment to affect the network in three possible modes, which all involved the first gene in the network, for consistency. In mode (1), the environment modified the initial expression level of the first gene of the network, which was set to a value s₀, drawn randomly from a uniform distribution over [0,1] for each replicate simulation. In mode (2), the environment had a sustained effect on expression of the first gene of the network, which was maintained at a constant value s, also drawn randomly from a uniform distribution over [0,1] for each replicate simulation. In mode (3), the environment modified the cis-regulatory region of gene 1, therefore affecting how it was regulated by other genes. This was obtained by multiplying the first line of matrix W by (1+k), with k drawn from a normal distribution with mean zero and standard deviation σ_k = 0.1. The matrices of correlations in gene expression over simulation replicates were then computed for each mode of environmental effects, and represented in Fig. 2C–E. The model was coded in R version 4.0.3 (R core team 2020), scripts are provided as supplementary files.