How does epistasis reduce phenotypic variation

This is because the number of possible multilocus genotypes, the full space of genotypic possibilities, grows exponentially with the number of loci that regulate the trait. In the presence of epistasis, each of these multilocus genotypes can in theory have its own unique phenotypic effects, giving rise to an almost infinitely complex map from genotype to phenotype.

In practice, it is difficult to characterize empirically more than a small fraction of this genotypic space. Partially for practical reasons, genetic studies therefore often either ignore genetic interactions completely to focus on the marginal effect of contributing loci, or focus on a smaller subset of the possible multilocus genotypes. The marginal additive effect of a locus is the change in the phenotype due to an allele substitution at this locus, averaged across all genetic backgrounds in the population.

It can be thought of as a projection from the multidimensional GP-space, down to one dimension. Figure 2 illustrates this for a theoretical GP-space involving only two loci, A and B. In this example, locus B capacitates turns on the effect of locus A, so that A displays a phenotypic effect only when combined with the allele B 2. The result is that under many allele frequencies, locus A will display a substantial marginal effect, but locus B will not. It might, however, still be large enough for the locus to contribute substantial additive genetic variance in a population, as there will be a mean difference in the trait between the groups of individuals that carry the alternative alleles.

It is also worth noting that while locus B does not have a measurable marginal effect on the phenotypic mean, there is a difference in variance between the genotypes. Thus, in this particular example, locus A does not display genetic variance heterogeneity, but locus B does.

As a result, locus A might be detected in a conventional genome-wide association GWA or quantitative trait locus QTL analyses for additive marginal effects, but locus B will not. Theoretical and empirical examples of pairwise capacitating epistatic gene action leading to a marginal additive effect for one, and a variance heterogeneity effect for the other, interacting locus.

A The phenotype associated with each of the four genotypes i. Locus B capacitates turns on the effect of locus A, so that A displays a phenotypic effect only when combined with the allele B 2. Because of this, locus A displays a marginal effect on the phenotypic mean, but not on the variance, when the allele frequencies are 0. Locus B displays no marginal mean effect, but an effect on the phenotypic variance i. D The genotype—phenotype map for a pairwise interaction between the two quantitative trait loci QTLs Growth4 and Growth9 detected in an F 2 intercross between two chicken lines divergently selected for 56 day body weight [ Dunnington and Siegel, ; Carlborg et al.

Figure 3 presents another theoretical GP-space involving two loci. In this example, the genotype A 2 B 2 has an effect of two on an arbitrarily chosen phenotypic scale, whereas the other three genotypes have an effect of zero. The result is that both loci display a marginal effect on both the mean and the variance. Just like in the previous example Fig. Under most allele frequencies, both loci will, however, contribute additive genetic variance.

Conventional GWA and QTL analysis methods, as well as looking for marginal effects on the phenotypic variability, might in cases such as this identify the two loci. Which of the two analysis approaches, looking for mean or variance effects, that has the best power will depend on the allele frequencies at the two loci. Theoretical and empirical examples of pairwise epistatic gene action leading to marginal additive and genetic variance heterogeneity effects at both interacting loci.

With this underlying GP-space, both loci will display both marginal additive mean and variance heterogeneity effects when the allele frequencies are 0. D The genotype—phenotype map for a pairwise interaction between two SNPs Chromosome 1, 17 bp; and Chromosome 5, 15 bp affecting mean root length in a population of wild-collected Arabidopsis thaliana accessions. The major allele at each SNP is indicated by —1 and the minor allele by 1.

This genotype—phenotype map originally published as fig. A genome-wide association analysis reveals epistatic cancellation of additive genetic variance for root length in Arabidopsis thaliana. PLoS Genetics 11, e is an empirical example of an interaction resembling that in the schematic in A , where the phenotype of one two-locus genotype class deviates from the rest.

Figure 4 illustrates a theoretical GP-space where the direction of the phenotypic effect of an allele is completely reversed depending on the genetic background at the other locus. When combined with the B 1 allele, A 1 increases and A 2 decreases the phenotype. When combined with the B 2 allele, the effects are reversed. When estimating the marginal effect of a locus in such a GP-space, the averaging across genetic backgrounds will lead to much, or all, of the phenotypic effect being canceled.

They will therefore not be detectable by their marginal effects, regardless of whether the scan is looking for effects on the mean or the variance of the trait. In order to identify the two loci as important contributors to the phenotype, alternative analysis methods such as a two-dimensional scan for epistatic interactions Carlborg and Haley, ; Lachowiec et al.

Theoretical and empirical examples of pairwise epistatic gene action where no marginal additive or variance heterogeneity effects are observed. The direction of the phenotypic effect is completely reversed, depending on the genetic background at the other locus.

Because of this, none of the loci displays any marginal additive or variance heterogeneity effect when the allele frequencies are 0. D The genotype—phenotype map for a pairwise interaction between two QTLs Chromosome 1, peak at cM; and Chromosome 14, peak at 11 cM affecting weight at hatch in an F 2 intercross between red junglefowl and White Leghorn chickens.

A global search reveals epistatic interaction between QTL for early growth in the chicken. Genome Research 13, — is an empirical example of an interaction resembling that in the schematic in A , where effects of alleles are equal in size but opposite in direction and thereby cancel out all marginal effects. Unlike the theoretical examples in Figs 2—4 , most complex traits are affected by more than two loci. This means that even if one considers two-locus epistasis, this will in practice probably be a simplification of the true GP-space for the studied trait.

In mathematical terms, one would be studying a projection from the high dimensional GP-space, down to a lower set of dimensions. It can, for instance, facilitate the identification of causal alleles at multiple loci, as well as reveal functional dependencies between them. In a recent study, we re-analyzed a large population of haploid yeast segregants to find a strong connection between high order epistasis and variance heterogeneity at the individual interacting loci Forsberg et al.

Using these, we could evaluate how epistatic gene action contributed to the multilocus GP-space and also identify how many of the multilocus genotypes gave rise to phenotypes far from additive expectations. In particular, we identified several cases of capacitating epistasis where certain loci acted by moderating i.

Despite epistatic gene action being common in the high order GP-spaces, the additive genetic variance V A was much larger than the epistatic variance for all of the analyzed traits, illustrating how V A can be an emergent property from epistatic gene action.

These multilocus GP-spaces can also be used to illustrate how marginal additive and variance heterogeneity effects emerged from epistatic gene action. An example from the analyses of this yeast population is provided in Fig. There, we show the GP-space, the phenotype associated with every possible genotype, of six QTLs that regulate yeast growth in manganese sulfate-containing growth medium.

One of the six QTLs capacitates the effect of the other five; that is, it is an empirical multilocus example of what was theoretically illustrated in Fig. Due to this capacitating effect Fig. The other five QTLs display much lower levels of genetic variance heterogeneity Fig. High order epistasis regulating growth in yeast leads to genetic variance heterogeneity at the interacting loci.

An epistatic network involving multiple QTLs regulates the growth of yeast colonies on media containing manganese sulfate full details on the analysis done to identify this network is available in Forsberg et al. The interactions in the epistatic network are illustrated in B and D by circles corresponding to QTLs and connections to pairwise interactions. Each boxplot in A and C shows the phenotype associated with one multilocus genotype, as in Figs 2—4 , but with added information about the variability within each genotype class.

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Yoo BH. Long-term selection for a quantitative character in large replicate populations of Drosophila melanogaster. Response to selection. Genet Res 35 : 1— Download references. I am grateful to Tiago Paixao, Bill Hill, and an anonymous reviewer for their helpful comments and for support from the European Research Council Advanced Grant You can also search for this author in PubMed Google Scholar.

Correspondence to N H Barton. Suppose that a locus is initially at p 0 , and is then subject to constant selection s. It will ultimately fix one or other allele, with probabilities for the two alleles. The corresponding total variance in diploid fitness is , taking the integral over the whole time course to loss or fixation. To find this, we find t x ; p 0 , the expected time spent at x , given an initial frequency p. Two genes are responsible for the chemical reaction that produces the plant pigment anthocyanin from a precursor molecule.

Gene C controls the first step in the reaction to produce the step 1 product, and gene P controls the second step in the reaction to produce anthocyanin. Primula Petal Color. Figure 3: Malvidin production. Production of the petal pigment malvidin is controlled by one gene, but its synthesis can be suppressed by another gene at a different locus. Wheat Kernel Color. Figure 4: Colored kernel production. Wheat kernel color is determined by the action of two genes: gene A and gene B.

If either gene is functional, a colored kernel will result. If both genes are not functional, the kernel will be colorless. Coat Color in Horses. Other Types of Epistatic Interactions. References and Recommended Reading Bateson, W. Human Molecular Genetics 11 , — Dooner, H. Article History Close.

Share Cancel. Revoke Cancel. Keywords Keywords for this Article. Save Cancel. Flag Inappropriate The Content is: Objectionable. Flag Content Cancel. Email your Friend. Submit Cancel. This content is currently under construction. Explore This Subject. Gene Linkage. The Foundation of Inheritance Studies. Methods for Studying Inheritance Patterns. Variation in Gene Expression. Topic rooms within Gene Inheritance and Transmission Close. No topic rooms are there. Or Browse Visually. Other Topic Rooms Genetics.

Student Voices. Creature Cast. Simply Science. Green Screen. Green Science. Bio 2. The Success Code. Why Science Matters. The Beyond. Plant ChemCast. Postcards from the Universe. Brain Metrics. Fig 1. Table 1. Model comparison for models with Full and without Reduced epistasis terms included. Pleiotropy and correlation among traits Pleiotropy is common for both single-locus and epistatic effects S2 Table and S3 Table.

Fig 2. Density plots of bias-corrected V A calculated with and without epistasis for each trait. Table 2. Mean and standard deviation in parentheses for additive and total genetic variance calculated with and without bias-correction above and below the line, respectively , as well as with and without epistasis for both of the allele frequency distributions.

Table 3. Standardized mean square error MSE and standardized bias for corrected Corr. Fig 3. Discussion Epistasis is often a major factor in the mapping from genotype to phenotype [ 2 , 5 , 29 , 30 ], but its relevance to heritability and evolution remains contentious [ 9 , 10 ].

Conclusion The results of this study, documenting the role of variable epistasis in determining genetic variance components are timely given the renewed interest and debate on the subject [ 9 , 10 ]. Supporting Information. S1 Data. Phenotype date used for estimation of genetic effects as well as sampling co variance matrices. S1 Code. C code used to calculate variance components. S1 Table. S2 Table. Single-locus effect estimates for each QTL on each trait.

S3 Table. Epistatic effect estimates for all DNILs. S4 Table. Pairwise correlations between the effect estimates for the different traits.

S5 Table. Pairwise correlations between traits. S1 Fig. Genotypic means and non-epistatic values for DNILs. S2 Fig. S3 Fig. S4 Fig. Distributions for corrected additive genetic variance for the U-shaped distribution of allele frequencies.

S5 Fig. Distributions for corrected genetic variance for the Uniform distribution of allele frequencies. S6 Fig. Distributions for corrected genetic variance for the U-shaped distribution of allele frequencies. S7 Fig. Distributions for uncorrected genetic variance for the Uniform distribution of allele frequencies. S8 Fig.

Distributions for uncorrected genetic variance for the U-shaped distribution of allele frequencies. S9 Fig. Distributions for uncorrected additive genetic variance for the Uniform distribution of allele frequencies. S10 Fig. Distributions for uncorrected additive genetic variance for the U-shaped distribution of allele frequencies. S11 Fig. Distributions for additive genetic variances calculated with and without bias-correction for the bias-correction simulations.

S12 Fig. Distributions for genetic variances calculated with and without bias-correction for the bias-correction simulations.

Acknowledgments The authors thank S. Macdonald and M. Orive for comments on the manuscript. References 1. Genome research, Huang W. Proceedings of the National Academy of Sciences, Kelly J. Genetics, Moore J. Human heredity, Shimomura K. Zuk O. Bloom J. Nature, Crow J. Hansen T.

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