The developmental-genetics of canalization

Abstract

Canalization, or robustness to genetic or environmental perturbations, is fundamental to complex organisms. While there is strong evidence for canalization as an evolved property that varies among genotypes, the developmental and genetic mechanisms that produce this phenomenon are very poorly understood. For evolutionary biology, understanding how canalization arises is important because, by modulating the phenotypic variation that arises in response to genetic differences, canalization is a determinant of evolvability. For genetics of disease in humans and for economically important traits in agriculture, this subject is important because canalization is a potentially significant cause of missing heritability that confounds genomic prediction of phenotypes. We review the major lines of thought on the developmental-genetic basis for canalization. These fall into two groups. One proposes specific evolved molecular mechanisms while the other deals with robustness or canalization as a more general feature of development. These explanations for canalization are not mutually exclusive and they overlap in several ways. General explanations for canalization are more likely to involve emergent features of development than specific molecular mechanisms. Disentangling these explanations is also complicated by differences in perspectives between genetics and developmental biology. Understanding canalization at a mechanistic level will require conceptual and methodological approaches that integrate quantitative genetics and developmental biology.

Keywords: Canalization; Epistasis; Genotype-phenotype maps; Nonlinearity; Robustness.

Figure 1. Environmental canalization and phenotypic plasticity

To illustrate the relationship between phenotypic plasticity and environmental canalization, we simulated a trait varying across a norm of reaction in response to an environmental effect. In each case, the phenotypic value is a function of the deterministic environmental effect plus an random term that is isotropic and normally distributed. In A, the variance of the random term is constant across the norm of reaction. However, a nonlinear relationship between the environmental effect and the phenotypic outcome generates variance heterogeneity across the norm of reaction. The downward modulation of variance across the middle of the range is the canalization effect. In B, two genotypes are shown that differ in the shape of the relationship between the environmental factor and the phenotypic outcome. This also generates a differential modulation of phenotypic variance. In this case, there is genetic variation in environmental canalization. In C, variance (the random term) increases away from the mean environmental value. This might occur, for example, if the more extreme environmental conditions are increasingly stressful, resulting in less stable development. In all cases, the entire range of phenotypic effects possible under different environmental conditions is the phenotypic plasticity. The shape of the curve that relates the phenotype to the environmental condition is the norm of reaction. The differential modulation of variance along and across these curves is environmental canalization. Environmental canalization can vary due to genotype or environment.

Figure 2. Variation among isogenic mutant mice with the same genotype

MicroCT scans showing the front of the face of two different genotypes of embryos in comparison to controls. A) 10.5 day Wildtype C57BL6J mouse embryos. B) Fgf8neo/− (~80% loss) embryonic day 10.5 embryos (Green et al 2017). C) Examples of B9d1−/− (null) 11.5 day embryos.

Figure 3. Developmental nonlinearity and variance heterogeneity and epistasis

This schematic shows how additive variation in a developmental process produces non-additive variation when that process has a nonlinear relationship to phenotypic outcomes. The first column shows genotype-phenotype maps while the second column shows phenotypic distributions by genotype. B and C show two of many possible two locus models. Both generate variance heterogeneity and epistasis.

Figure 4. Redundancy or Multiple Inputs and Canalization

In A, variation in a hypothetical trait is determined by variation in three processes that vary independently of each other. The variance of the trait is lower than the variance of the component processes because of the averaging effect of multiple inputs. If any of the component processes are eliminated, such as might occur in a loss of function mutation for a redundant gene, the variance of the trait is increased.

Figure 5. Developmental nonlinearity and phenotypic robustness

A) A nonlinear curve relating variation in a mechanism (e.g. gene expression) to phenotypic outcome. The amount of phenotypic variation that corresponds to a constant amount of variation in the mechanism is dependent on the slope at each point along the curve. B shows an expansion of Lewontin’s Genotype-phenotype map in the first column and hypothetical gene expression to process and gene-expression to phenotype curves in the second. The number of levels is arbitrary in this example.

Figure 6. The Fgf8 gene-expression phenotype map and robustness

A) Gene-expression to phenotype map for an allelic series of E10.5 mouse embryos that vary in level of Fgf8 expression. The hypothetical genotypes are null, loss of function (LF), wildtype (WT) and overexpression (OE). This example shows a buffered range around the wildtype although many shapes of such curves are possible.