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Accounting for genetic interactions improves modeling of individual quantitative trait phenotypes in yeast

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Abstract

Experiments in model organisms report abundant genetic interactions underlying biologically important traits, whereas quantitative genetics theory predicts, and data support, the notion that most genetic variance in populations is additive. Here we describe networks of capacitating genetic interactions that contribute to quantitative trait variation in a large yeast intercross population. The additive variance explained by individual loci in a network is highly dependent on the allele frequencies of the interacting loci. Modeling of phenotypes for multilocus genotype classes in the epistatic networks is often improved by accounting for the interactions. We discuss the implications of these results for attempts to dissect genetic architectures and to predict individual phenotypes and long-term responses to selection.

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Figure 1: Many QTLs involved in pairwise interactions are part of highly interconnected epistatic networks.
Figure 2: Epistatic network regulating growth on IAA-containing medium.
Figure 3: Epistatic networks contain hub QTL capacitor alleles of both BY and RM origin that moderate growth-increasing or growth-decreasing effects of segregating alleles at radial QTLs.
Figure 4: Biases in additive-model-based estimates of phenotypes are largest in the genotype classes with the greatest or poorest expected growth.
Figure 5: Simulations show that the additive genetic variances contributed by the loci in the epistatic network regulating growth on IAA-containing medium are highly dependent on the allele frequencies at the other loci in the same network.

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Acknowledgements

Funding was provided by the Howard Hughes Medical Institute and by NIH grants R01 GM102308 (L.K.) and F32 GM116318 (M.J.S.) and Swedish Research Council grant 621-2012-4632 (Ö.C.).

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Authors and Affiliations

Authors

Contributions

Analyses were designed by S.K.G.F., J.S.B., M.J.S., L.K. and Ö.C. Analyses were conducted by S.K.G.F. and Ö.C. The manuscript was written by S.K.G.F. and Ö.C. and incorporates comments by J.S.B., M.J.S. and L.K.

Corresponding author

Correspondence to Örjan Carlborg.

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The authors declare no competing financial interests.

Integrated supplementary information

Supplementary Figure 1 LOD scores for all significant genetic interactions (n = 266) involving the 330 epistatic QTLs detected in this population.

The left box plot displays the LOD scores for the genetic interactions between hubs (involved in more than four interactions) and radial loci. The right box plot displays the LOD scores for the genetic interactions that do not involve a hub. The p-value is from a two-sided, non-parametric Wilcoxon test.

Supplementary Figure 2 The correlations between the number of genetic interactions that a locus is involved in and its marginal additive and variance heterogeneity effects.

The x axis shows the number of pairwise genetic interactions each locus is involved in. The left y axis shows the marginal additive and the right y axis shows the marginal variance heterogeneity effect on the phenotype. Each dot in the figure represents a locus. The red dots show the marginal effect on the mean of the phenotype (r = 0.42; P < 1 × 10–12), whereas the blue dots show the effect on the phenotypic variability (r = 0.64; P < 1 × 10–12).

Supplementary Figure 3 Phenotypic distributions in segregants with different combinations of alleles across the six loci in 14 epistatic networks affecting growth in different media.

The networks are divided depending on whether the hub QTL is a significant capacitor or not. A Tukey box plot (the bottom/top of the box are the first/third quartiles, the band is the median and the ends of whiskers extend to the lowest/highest data point within 1.5 times the interquartile range) is plotted for each of the 64 genotype classes in every network. Color indicates the genotype at the hub QTL (green/gray boxes for BY/RM alleles, respectively). The x axis represents the six-locus genotype class, where blue/orange dots indicate growth-increasing/growth-decreasing alleles at the five radial QTLs in the network. The black lines through the boxes illustrate the additive-model-based estimates of the phenotypes for the 64 genotype classes. The number above the x axis is the number of segregants in each genotype class.

Supplementary Figure 4 Phenotypic distributions in segregants with a varying number of growth-decreasing alleles at the radial loci across the six loci in 14 epistatic networks affecting growth in different media.

The networks are divided depending on whether the hub QTL is a significant capacitor or not. Each Tukey box plot (the bottom/top of the box are the first/third quartiles, the band is the median and the whiskers extend to the lowest/highest data point within 1.5 times the interquartile range) represents a group of segregants that share the same number of growth-decreasing alleles at the five radial QTLs in the respective networks. The segregants are divided and colored based on the genotype at the hub QTL (green/gray boxes for BY/RM alleles, respectively). The x axis gives the number of growth-decreasing alleles at the radial QTLs and the number of segregants in each group. The regression lines illustrate the fit of linear additive models to segregants with alternative genotypes at the hub QTL.

Supplementary Figure 5 Phenotype estimation bias for the individual multilocus genotype classes in 15 epistatic networks.

The networks are divided depending on whether the hub QTL is a significant capacitor or not. Each y axis gives the cross-validated estimation error (bias) for the six-locus additive model representation of the genotype value of each individual multilocus genotype class as compared to the actual phenotype (yŷ). Each Tukey box plot (the bottom/top of the box are the first/third quartiles, the band is the median and the whiskers extend to the lowest/highest data point within 1.5 times the interquartile range) shows the distribution of prediction errors in 1 of the 64 genotype classes in the network. The 32 leftmost box plots represent the genotype classes with the capacitor hub QTL allele (or with the highest h2 in the case of a non-significant capacitor hub). Significant biases, i.e., where the estimation errors deviate significantly from zero, are colored in yellow.

Supplementary Figure 6 Difference in estimation accuracy between additive and epistatic models illustrated as the cross-validation results from the ten epistatic networks where the hub QTL is a significant capacitor.

The y axis gives the difference in cross-validated mean squared error (MSE) between an additive model (MSEadd) and a model including pairwise interactions (MSEepi2). Each dot corresponds to the difference in MSE for one genotype class. The difference is measured as MSEadd – MSEepi2, meaning that positive values correspond to genotype classes where the estimation accuracy is improved when using an epistatic model.

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Supplementary Figures 1–6 and Supplementary Note. (PDF 1887 kb)

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Forsberg, S., Bloom, J., Sadhu, M. et al. Accounting for genetic interactions improves modeling of individual quantitative trait phenotypes in yeast. Nat Genet 49, 497–503 (2017). https://doi.org/10.1038/ng.3800

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