Epistasis and cryptic QTL identified using modified bulk segregant analysis of copper resistance in budding yeast

Abstract

The contributions of genetic interactions to natural trait variation are challenging to estimate experimentally, as current approaches for detecting epistasis are often underpowered. Powerful mapping approaches such as bulk segregant analysis (BSA), wherein individuals with extreme phenotypes are pooled for genotyping, obscure epistasis by averaging over genotype combinations. To accurately characterize and quantify epistasis underlying natural trait variation, we have engineered strains of the budding yeast Saccharomyces cerevisiae to enable crosses where one parent's chromosome is fixed while the rest of the chromosomes segregate. These crosses allow us to use BSA to identify quantitative trait loci (QTL) whose effects depend on alleles on the fixed parental chromosome, indicating a genetic interaction with that chromosome. Our method, which we term epic-QTL (for epistatic-with-chromosome QTL) analysis, can thus identify interaction loci with high statistical power. Here, we perform epic-QTL analysis of copper resistance with chromosome I or VIII fixed in a cross between divergent naturally derived strains. We find 7 loci that interact significantly with chromosome VIII and none that interact with chromosome I, the smallest of the 16 budding yeast chromosomes. Each of the 7 interactions alters the magnitude, rather than the direction, of an additive QTL effect. We also show that fixation of one source of variation—in this case, chromosome VIII, which contains the large-effect QTL mapping to CUP1—increases power to detect the contributions of other loci to trait differences.

Introduction

Predicting phenotype from genotype is a central goal of genetics research. However, even with great advances in sequencing technology and experimental scale, accurate characterization of how genetic differences translate into trait differences remains elusive. Many genetic influences are subtle, and most traits of interest that vary in populations are determined by multiple genetic factors, as well as by environmental variation and random chance (Mackay et al. 2009; Bloom et al. 2013, 2015; Tsouris et al. 2024). Moreover, these influences may combine in complicated ways, for example, in the form of gene-by-gene (epistatic) or gene-by-environment interactions (Falconer and Mackay 1996; Boye et al. 2024; Lynch and Walsh 1998).

Epistasis is particularly challenging to detect in standard quantitative-genetic analyses because the number of possible interaction effects vastly exceeds the number of single-locus (additive) effects, leading to very low statistical power to detect the interactions (Falconer and Mackay 1996). Standard analyses fit additive effects before interaction effects, which can lead to the mistaken inference that epistasis is less salient than it actually is (Ober et al. 2015; Morgante et al. 2018). If interacting alleles are rare in a mapping population, under-detection of epistasis is even more severe. Failure to detect epistasis in turn compromises accurate prediction of an individual's phenotype from genotype, even when an additive model appears to fit well (Ober et al. 2015; Morgante et al. 2018; Mackay and Anholt 2024).

The distribution of types of epistatic effects influences both detection of loci with effects on traits and evolutionary trajectories (Phillips et al. 2000; Weinreich et al. 2005; Phillips 2008). For a given locus interacting with another locus, magnitude epistasis changes the size of an allele's effect without changing its direction (beneficial vs. detrimental), whereas sign epistasis changes the direction. Sign epistasis gives rise to peaks and valleys in fitness landscapes and can alter the order of mutations that increase fitness (Weinreich et al. 2005). Models of distribution and patterns of these effects have been postulated, with 2 extremes being global epistasis and idiosyncratic epistasis. Global epistasis indicates underlying predictability of the effects of individual alleles, perhaps based on a latent phenotype such as protein stability or physiological health (Kryazhimskiy et al. 2014; Otwinowski and Plotkin 2014). Idiosyncratic epistasis, by contrast, refers to unpredictable interaction effects that ultimately depend on details of particular alleles (Reddy and Desai 2021; Johnson et al. 2023). Although global epistasis can also refer to emergent fitness trends that can arise from idiosyncratic epistasis (Lyons et al. 2020; Reddy and Desai 2021; Diaz-Colunga et al. 2023), we use global epistasis to mean a nonlinear transformation of a latent additive trait (Otwinowski and Plotkin 2014). Data on the relative prevalences of magnitude and sign epistasis, which are currently lacking, would inform whether global or idiosyncratic is a more suitable description of epistasis patterns in nature, which in turn will inform models of the evolution of complex traits.

An ideal method for identifying and characterizing epistatic contributions to trait variation would have equal (and high) statistical power to detect additive and interaction effects. Experimental designs with extremely large sample sizes are now common (Nadeau et al. 2000; Ehrenreich et al. 2010, 2012; Matsui et al. 2022; Nguyen Ba et al. 2022), but the most powerful of these favor (or exclusively detect) additive effects. One such experimental design is bulk segregant analysis (BSA). In a typical BSA experiment, many progeny are produced from a cross between divergent parental genotypes, progeny with extreme values of a trait of interest are pooled, and high-coverage genome sequencing is used to detect loci at which the allele frequency in the selected bulk deviates significantly from the allele frequency in an unselected (or oppositely selected) bulk (Michelmore et al. 1991; Ehrenreich et al. 2010). Although BSA benefits from sampling many individuals—over 10 million in some cases (Ehrenreich et al. 2010)—it cannot detect genetic interaction effects because pooled sequencing results in an estimate of the effect of any one locus that is the average across all genotypes at other loci.

Genotyping and phenotyping individuals rather than pools avoids the averaging issue, but suffers from the problem that potential pairwise interactions far outnumber additive effects of single loci, resulting in greatly reduced statistical power. Two recent attempts to detect epistasis using very large sample sizes illustrate this challenge. One study, which genotyped ∼200,000 diploid progeny of a yeast cross, identified numerous interaction effects, but found a strong positive correlation between the additive effect of a locus and the number of pairwise interactions it participates in (Matsui et al. 2022). This correlation could reflect the true distribution of epistatic effects or an influence of additive-effect size on the detectability of interactions (Matsui et al. 2022). Another study genotyped ∼100,000 haploid segregants but, to maximize power, tested only interactions between pairs of additive-effect quantitative trait loci (QTL) (Nguyen Ba et al. 2022). This study found evidence of epistatic effects, but found the additive-plus-pairwise model to have only modest predictive power for the phenotypes of reconstructed genotypes, suggesting that effects remain undetected (Nguyen Ba et al. 2022). Another recent study did not genotype large numbers of segregants, but instead engineered naturally occurring gene variants into 4 divergent yeast strains to detect genetic background-dependent effects on growth. This study found a substantial fraction of variants to have background-dependent effects, but was limited to variants in and around 103 genes previously shown to be interaction hubs in genome-wide double-mutant screens (Costanzo et al. 2016; Ang et al. 2023). The results of these studies suggest that unbiased approaches are needed that equalize the power to detect additive and epistatic effects.

To identify and characterize genetic interactions with comparable statistical power to that of additive effects, we combine chromosome substitution with BSA in the genetically tractable budding yeast, Saccharomyces cerevisiae. We call this method epic-QTL (for epistatic-with-chromosome QTL) analysis. To perform epic-QTL, we cross 2 divergent natural isolates of S. cerevisiae, but before generating segregating F2 progeny from the resulting F1 diploid, we first eliminate 1 chromosome from 1 parent, fixing the remaining homologous chromosome. The result is that all surviving F2 haploids contain identical copies of 1 chromosome, but have unique combinations of the 2 parents’ alleles on all other chromosomes. We also perform the reciprocal cross, in which the other parent's chromosome is fixed. We then grow the haploid progeny in selective or nonselective conditions. Here, we use the presence or absence of copper (II) sulfate (CuSO₄) as a selective condition, with the presence of copper and subsequent oxidative stress selecting for individuals with alleles that promote survival in this environment. Standard BSA would compare the allele frequencies in bulks grown in the presence or absence of copper to identify additive QTL for the trait of copper resistance. In epic-QTL, applied to a particular fixed chromosome, there are 4 bulks rather than 2. By comparing the QTL identified in the crosses with the reciprocal fixed chromosomes, we can identify loci whose effects differ between genetic backgrounds. The loci that are dependent on parental-chromosome background for their effect are thus epistatic with that fixed chromosome and are detected with statistical power usually only afforded to additive effects. In practice, this comparison is done by including a parental-chromosome (or genetic-background) term in a logistic-regression model that is fit to the data from all 4 bulks simultaneously. An additional benefit of chromosome substitution is an increase in power for detection of additive effects by removing a source of variance in a population. With only one cross, the fixation of a chromosome containing a major QTL allows the remaining segregating sites to exert greater influence over membership in the selected bulk.

Using epic-QTL, we can determine where QTL that interact with each fixed chromosome lie relative to where additive QTL lie, and how prevalent interactions are for a given trait, in this case copper sulfate resistance. We focus on copper sulfate for 3 reasons: (1) its extensive use in prior S. cerevisiae studies, allowing comparison with previous results; (2) the potential for unexplained heritability, in that copper resistance shows a large gap in broad and narrow sense heritability compared with other traits (Bloom et al. 2015); and (3) its ecological and physiological relevance (Valentine and Gralla 1997; De Freitas et al. 2003; Rehman et al. 2019). In addition, 1 major interaction hub identified by Matsui et al. (2022) was CUP1 on chromosome VIII, which is a major driver of copper resistance, and thus a perfect candidate for chromosome fixation. We fixed chromosomes I or VIII in a cross between strains derived from an oak tree or from a wine barrel, which differ on average at 1 in 200 base pairs (Cubillos et al. 2009). The variants in these strains reflect natural genetic diversity, offering insights into genetic interactions that might occur within populations. We demonstrate that this method can be used to remove sources of trait variation to reveal additive QTL otherwise undetected at this experimental scale, as well as to identify interaction QTL with high statistical power. We find that these interactions often occur within significant additive QTL peaks, providing evidence of a lack of pervasive sign epistasis.

Materials and methods

Conditional chromosome strain construction

Two divergent haploid yeast strains, 1 oak tree-derived (NCYC3631, MATα) and 1 wine barrel-derived (NCYC3591, MATa; Cubillos et al. 2009), were each engineered for chromosome removal from diploids and later selection of haploid progeny. To facilitate crosses, strains were modified by homologous recombination at URA3, HO, and MATα using standard lithium-acetate-based transformation. URA3 prototrophy was restored (and KanMX removed) in wine-derived strains by insertion of URA3 sequence amplified from the wine-strain parent (BC187). The positive-selection marker hph, which confers resistance to hygromycin, was removed from the HO locus of each parental strain to allow the marker's use elsewhere. To remove hph, we conducted Delitto Perfetto excision (Storici and Resnick 2003) using a cassette that allows positive-selection for nourseothricin resistance (NatR) and negative-selection against HSV-TK, which encodes the thymidine kinase from herpes simplex virus and thereby confers sensitivity to the pyrimidine analogue 5-fluorodeoxyuridine (FuDR) (Alexander et al. 2014). Importantly, 2 identical sequences (cyc terminators) flank this cassette and thereby lead to spontaneous excision of the cassette by homology-based repair (Storici and Resnick 2003). Transformants were selected for the presence of NatR and checked for loss of hph. We then counter-selected using FuDR to select for removal of the cassette and resulting loss of both NatR and HSV-TK.

To select for haploids of 1 mating-type in bulks to be sequenced, we engineered the MATα locus to contain the HSV-TK negative-selection marker for removal of any cell that is not a mating-type α haploid. MATα contains a bidirectional promoter driving the expression of the α1 and α2 genes, both of which must be active for the cell to sporulate (Haber 2012). The negative-selection marker was inserted upstream of α1 and its promoter, and the STE3 promoter (pSTE3), which is activated by the transcriptional co-activator encoded by α1, was placed upstream of α2 (Sprague et al. 1983). Thus, the selection cassette was placed in a way that maintains expression of both α1 and α2 in mating-type α haploids and in diploids. As a result, the engineered MATα cells retain the ability to mate with mating-type a cells as haploids and to sporulate as diploids, but both diploids and haploid mating-type α haploids are sensitive to FuDR. For this transformation, we used the positive-selection marker hph. We transformed a cassette containing MATα homology and the positive- and negative-selection markers into the Oak α strain and then replaced hph with NatR using lithium-acetate homology-directed transformation, allowing use of hph in later transformations.

For chromosome elimination by driving transcription through the centromere, we constructed an inducible-promoter cassette by using overlapping PCR to combine the HSV-TK and hph markers from Alexander et al. (2014), the GAL1 promoter (pGAL1), and regions homologous to the yeast genome adjacent to the centromere. The centromere-region primers matched the primers used by Reid et al. (2008) or matched sequences very close nearby. These cassettes were transformed into either chromosome I or chromosome VIII in either the Oak α or Wine a strains. All strains are detailed in Supplementary data (Supplementary Table 4). These haploid strains are referred to as the background (Wine a or Oak α) plus [I] or [VIII] to indicate the chromosome that can be eliminated.

Wine a[I] and Oak α were mated to produce diploids, and Wine a and Oak α[I] were mated to produce diploids capable of producing the reciprocal chromosome fixation (Fig. 1a). Diploids were selected by ability to grow in both the absence of uracil and the presence of nourseothricin, and ploidy was confirmed by flow cytometry using DNA staining with propidium iodide on the Cytek Aurora. To fix chromosome I, diploids were then plated onto medium containing 2% D-Galactose (and lacking glucose) to induce the GAL1 promoter's transcription through the centromere of the conditional chromosome. Although we did not use markers to select for the loss of a chromosome, plating on galactose and restreaking from single colonies was effective for yielding chromosome loss. Colonies from the restreaked plate were checked by Sanger sequencing to identify a loss of the conditional chromosome (i.e. by loss of heterozygosity on that chromosome), then grown in liquid media and frozen as clonal aneuploid (2N–1) strains, which we term Oak I or Wine I to indicate the parent of origin of the remaining chromosome I in these otherwise hybrid strains. Populations of ∼10⁷ clonal aneuploids were sporulated using 2% potassium acetate for ∼10 days at room temperature (25°C) to produce ∼4 × 10⁷ segregants with identical chromosome I of either Oak or Wine background but segregating parental genotypes at all other loci. To select for haploids above and beyond the MATα selection, spores were vortexed for 10 min in 50% diethyl ether to kill unsporulated diploids (Dawes and Hardie 1974). Surviving spores were rinsed twice in sterile water, then germinated by incubation in 1 mg/mL Zymolyase (Z100T) for 12 min before culturing in each experiment. The process was completed identically for the reciprocal fixations of chromosome VIII.

Fig. 1.

Insertion of GAL1 promoter allows for fixed chromosomes. a) Matings to produce reciprocal diploids with single conditional chromosomes for chromosome I. b) Induction of the GAL1 promoter adjacent to the centromere destabilizes the chromosome's kinetochore, leading to loss of that chromosome in diploids and fixation of the homologous chromosome in F2 haploid progeny. One representative cross of the 4 (Oak I) is shown. Spores missing chromosome I are desaturated to indicate their inability to grow. c) BSA experiment for interactions with chromosome I, allowing detection of additive effects by comparison of selected (shaded blue) and unselected (unshaded) bulks and of interactions with chromosome I background (orange or purple). d) Schematic diagram of sign epistasis (left) and magnitude epistasis (right) based on the log odds of alleles at a single position. Thin turquoise lines and arrows represent the average selection effect, whereas thicker red arrows represent the differences that result from that parental background. No parental effect is shown.

Concentration determination for selection

We tested approximate concentrations of copper for selection by growing cells in media of different concentrations for 24 h (matching the experiment time) and then counting the cells either by automatic cell counter (ThermoFisher Countess II) or by manual counting on a hemocytometer. From there, we chose narrower ranges of doses that would provide between 1% and 10% survival. After conducting experiments, cell counts in some experiments were checked by hemocytometer to confirm that experimental treatments were achieving the intended amount of selection.

BSA

Pools of segregants with reciprocal fixed chromosomes (Oak I and Wine I, or Oak VIII and Wine VIII) were grown in parallel for 24 h in either YPD or YPD + copper sulfate at doses determined in each chromosome-fixed bulk population to produce between 1% and 10% survival. The control cultures grown in YPD were seeded at 10% of the starting density for the selected group. Each of the 4 bulk categories per chromosome-fixation experiment was grown at least in triplicate. After 24 h, each of these bulks was separately harvested by spinning down cells and extracting DNA either by phenol-chloroform-isoamyl alcohol extraction and ethanol precipitation (Green and Sambrook 2018), or by Qiagen DNeasy Blood and Tissue Extraction Kit 69506.

Sequencing

After DNA was harvested, single-end libraries for DNA sequencing were prepared according to Baym et al. (2015) protocol using Illumina kit FC-131-2001 and KAPA HiFi amplification kit KK2612. Fragments were selected to be 200–600 bp by AMPure XP bead cleanup (Fisher NC9959336) and pooled based on concentrations determined by LifeTechnologies Qubit 3.0 and Roche 480 LightCycler qPCR. Libraries were then sequenced on an Illumina NovaSeq 6000, with an average per-bulk depth of ∼70×. Reads were basecalled using Picard IlluminaBasecallsToFastq version 2.23.81, with APPLY_EAMSS_FILTER set to false (Broad Institute 2024), then demultiplexed using Pheniqs version 2.1.02, allowing for 1 mismatch in sample index sequences (Galanti et al. 2021), with both steps executed using a custom nextflow pipeline, GENEFLOW3 (NYU Center for Genomics and System Biology Genomics Core 2023). Reads were aligned to the S288C reference genome R64 using BWA-MEM (Li and Durbin 2010), sorted using PicardTools (Broad Institute 2024), and then underwent quality control using Genome Analysis Toolkit (Van Der Auwera et al. 2013) command BQSR. Variants were called using GATK HaplotypeCaller (Poplin et al. 2017) as described by Mansfeld and Grumet (2018).

epic-QTL analysis

VCFs were converted to tables of reads to analyze in R using GATK's VariantsToTable function. We first removed all loci with >2 alternate alleles to control for mapping quality issues, then assigned each alternate allele to the corresponding parent based on SNP location from whole genome sequencing of the parent strains (Ziv et al. 2017). To increase our signal-to-noise ratio and take advantage of the inherent correlation of nearby genomic positions in a single F2 cross, we smoothed the read counts in rolling windows of 200 SNPs using a Gaussian-weighted mean, which corresponds on average to 40 kb or ∼15 cM.

To partition the effects of fixed-chromosome parent of origin, selection, and their interaction, we performed logistic regression on these counts for each smoothed position using the following formula:

$$\begin{array}{rl}\log (& \mathrm{allele}\mathrm{odds})=\beta 0+\beta 1\cdot \mathrm{selection}+\beta 2\cdot \mathrm{background}+\\ & \beta 3\cdot (\mathrm{selection}\times \mathrm{background})+ϵ\end{array}$$

where selection is the presence or absence of copper sulfate in the culture media, background is the parent of origin of the fixed chromosome, and the selection × background term captures the dependence on background of the selection effect, i.e. epistasis. At each position, there are at least 24 counts that are the data: 2 alleles × 2 selection conditions × 2 chromosome-parent backgrounds × at least 3 replicates. We then used the z-scores of each effect to identify additive (selection) and epistatic (selection × background) QTL. Absent any effects of the fixed chromosome's parent of origin on segregation of the other chromosomes or on growth in the absence of copper sulfate, we do not expect to see a significant background effect. For this reason, we set the contrasts of the selection variable to 0 (copper absent) and 1 (copper present), and for the background variable to −0.5 (Wine) and 0.5 (Oak). An interactive schematic of how different forms of epistasis are revealed by the logistic-regression model is available at http://shiny.bio.nyu.edu/ms4131/epistasisBSA/.

To establish our statistical threshold for interactions, we conducted permutations of allele frequency ratios by shuffling positions within each parent and replicate in the nonselected bulks. This permutation approach is based on the assumption that, in the absence of selection, there would be no loci associated with the trait. For the permutations, we excluded chromosomes I and VIII from all experiments to remove the effect of the fixed chromosomes, and removed chromosomes III and V, which contained engineered regions not identical in the 2 parents. We then assigned bulks randomly to these permuted values according to the structure of the original dataset (the same number of replicates in each group) and calculated our selection, background, and interaction effects for each. These effects drawn from the bulks of 2 different parents form the null distribution of z-scores of interaction effects for each experiment. All analyses employ a false discovery rate (FDR) threshold of 5%.

Peaks of absolute z-score (QTL locations) were called by identifying the maximum points within-chromosome segments bounded by chromosome ends or local minima, defined as positions where the local slope of the absolute z-score trace shifted from negative to positive. The local slope was calculated within sliding windows of 700 SNPs by linear regression within the window. The highest point in that segment, if above the 5% FDR, was then called as the peak. Additive and interaction peak locations are available in Supplementary data (Supplementary Tables 2 and 3).

Results

Implementation of epic-QTL for copper resistance

Our method to identify QTL interacting with a fixed chromosome, or epic-QTL, combines chromosome substitution with BSA in a cross of 2 parental yeast strains. For the parental strains, we used divergent natural isolates of S. cerevisiae: NCYC3631 and NCYC3591 (hereafter “Oak” and “Wine”, respectively). Before crossing the 2 strains, we engineered 1 strain of each parent to contain the inducible GAL1 promoter (pGAL1) adjacent to the centromere of 1 chromosome. Inducing a high level of transcription through the centromere destabilizes the kinetochore, resulting in missegregation of the chromosome during mitosis so that a strain with only the homologous chromosome remaining can be isolated (Reid et al. 2008). By this method, we fixed chromosome I in each background (Fig. 1a) and, separately, chromosome VIII in each background. We then mated the Wine pGAL1 strain with the Oak non-pGAL1 strain (Fig. 1b), and vice versa, to produce diploids with reciprocal conditional chromosomes. Each diploid strain was then plated on galactose to induce pGAL1. After re-plating colonies from the galactose-containing media to ensure clonality, individual colonies were checked by Sanger sequencing at biallelic regions to confirm loss of the conditional chromosome. Each of these aneuploid (2N–1) strains was then sporulated to produce an F2 population of haploid segregants fixed for a single parent's chromosome (Fig. 1b), which could then be used for selection × background BSA (Fig. 1c and d).

Before proceeding to BSA, we demonstrated that the Oak and Wine parental strains, which have been shown to differ phenotypically in multiple traits (Gerke et al. 2006; Clowers et al. 2015), indeed differ in the phenotype of copper sulfate resistance. We grew populations of haploids of each parental strain in an array of doses of CuSO₄ in rich media (YPD) and compared the cell counts of each population to a control of the same seed culture. The wine haploid strain showed higher resistance to CuSO₄, surviving at almost double the percentage at which the oak haploid strain survived in mid-range doses of CuSO₄ (Supplementary Fig. 1).

Due to chromosome fixation, the relative intensity of selection varied at the same doses of CuSO₄ between crosses. Specifically, as shown below, Wine chromosome VIII has a strongly advantageous allele, so the same dose of CuSO₄ produces more survivors in the Wine VIII cross than in the Oak VIII cross. We therefore tested multiple doses of CuSO₄ to determine the dose that produced 1–10% survival of the population. This range of selection optimizes BSA by balancing detectable effects and retention of causative genetic variation in the surviving population (Magwene et al. 2011). Unselected bulks from each cross were seeded in YPD at 10% of the cell number at which selected bulks were seeded so that their final cell densities were approximately the same as those in the selected bulks.

Known drivers of resistance are identified as additive QTL

Previous studies have identified additive QTL for the trait of copper sulfate resistance in a variety of S. cerevisiae strains (Ehrenreich et al. 2010; Bloom et al. 2013, 2015; She and Jarosz 2018). In addition, multiple studies have identified mechanistic drivers of copper resistance, including certain alleles of the FRE1 gene and copy number amplification of the CUP1 locus (Welch et al. 1989; Jungmann et al. 1993; De Freitas et al. 2003). Because there is overlap across strains for identification of some QTL (Taylor and Ehrenreich 2015), one form of validation of epic-QTL would be for previously known resistance loci to be detected by epic-QTL as additive effects (that is, effects that do not depend on the parental origin of the fixed chromosome).

In epic-QTL, as in standard BSA, allele frequency differences between bulks at a given genomic site indicate a contribution of variation at that site to bulk membership. For the reciprocal chromosome I crosses and, separately, for the reciprocal chromosome VIII crosses, we sequenced the 4 bulks (selected vs. unselected for each Oak or Wine fixed chromosome) at a high depth of coverage (average ∼70× per site per bulk) to estimate allele frequencies. We partitioned the effects of selection, parental-chromosome background (hereafter “background”), and their interaction using a logistic regression model as described in Materials and methods. The selection term's coefficient reflects the additive effect on CuSO₄ survival regardless of parental-chromosome background, whereas the interaction term reflects epistasis with the fixed chromosome (Fig. 1d). To visualize significant effects across the genome, we use the z-score of each coefficient. The z-score is advantageous over the parametric P-value to which it corresponds because its sign indicates the direction of effect of the fixed chromosome, and because we use permutations of it to determine a threshold of FDR, detailed in Materials and methods. To compare significance regardless of effect direction, the majority of plots display absolute values of z-scores. Signed z-scores for each coefficient and position are included in Supplementary data (Supplementary Table 1).

The additive (selection) peaks on chromosomes VIII and XII are very close to the known copper-resistance genes, CUP1 and FRE1, respectively (Fig. 2). These genes are well documented to play critical roles in copper detoxification in yeast. CUP1 encodes a metallothionein involved in sequestering copper ions, thereby mitigating copper toxicity within the cell (Adamo et al. 2012). FRE1 encodes a ferric reductase enzyme that contributes to iron uptake and detoxification of copper (Hassett and Kosman 1995; Georgatsou and Alexandraki 1999). In both fixed-chromosome backgrounds, we identify FRE1 as a major driver of resistance, with peak maxima <6 kb away from the coding region (Fig. 2). The crosses for the 2 fixed-chromosome backgrounds are independent, so the agreement between the 2 crosses further validates the method. In the strains fixed for chromosome I, the peak on chromosome VIII is upstream of the CUP1 coding sequence. CUP1 has 2 paralogs, CUP1-1 and CUP1-2, within a larger tandemly duplicated region in the reference genome of the laboratory strain S288C. We found that the region surrounding these paralogs had poor mapping quality, likely due to repetitive sequences and potential CUP1 copy-number variation, which is a known mechanism of resistance (Adamo et al. 2012). These regions were therefore excluded from our variant calling, and so the peak upstream of the coding sequence is as close as can be to this known driver of copper resistance.

Fig. 2.

Consistent additive peaks, including known drivers of copper resistance, were identified in each fixed parental-chromosome experiment. (Top) Traces represent absolute z-scores of additive (selection) coefficients. Dashed line corresponds to the experiment with chromosome I fixed, and solid line corresponds to the experiment with chromosome VIII fixed. Horizontal lines indicate the 5% FDR threshold for each experiment. The only trace for chromosome I is solid, and the only trace for chromosome VIII is dashed, because of the fixed chromosome in each experiment. Significant peaks for each experiment are denoted as points on the traces as well as vertical lines below (fixed chromosome I as lighter blue shade, top strip, and fixed chromosome VIII as darker blue shade, bottom strip). In these strips, regions of significant z-scores are shown in gray, with intensities proportional to absolute z-score. (Bottom) Zoomed-in traces of chromosomes VIII and XII, which each contain large additive QTL. Vertical pink bars represent the locations of CUP1 and FRE1, both of which fall under large-effect additive peaks as expected.

Fixing large-effect QTL increases power for detection of additive effects

The resolution and reproducibility of epic-QTL are further supported by additive QTL that do not map to known copper-resistance loci. Between the experiment with fixed chromosome I and the experiment with fixed chromosome VIII, we identified many overlapping selection-QTL peaks with locations of highest absolute z-scores within 1.5 kb of one another, indicating not only that there is high resolution and reproducibility but also that the underlying mechanisms of resistance do not strongly differ in the presence of one or the other fixed chromosome (Fig. 2, Supplementary Table 2).

Having established that our method identifies additive QTL, we next investigated the result of chromosome fixation on additive effects. Removal of a major-effect QTL is expected to increase the power to detect QTL of lesser effect (Sinha et al. 2008), so we investigated whether epic-QTL has an added benefit of increasing power when a major-effect QTL exists on a fixed chromosome. We found that indeed the majority of peaks in the fixed chromosome VIII experiment had z-scores of greater magnitude than the corresponding peaks in the fixed chromosome I experiment and that several additional peaks were detected that were not called when chromosome I was fixed, despite controlling for strength of selection and reducing the impact of any random differences in selection strength by having biological replicate experiments (Fig. 2, Supplementary Fig. 3). On chromosome XII in particular, only a single peak is obvious in the fixed chromosome I experiment, whereas in the fixed chromosome VIII experiment, 2 peaks can clearly be differentiated (Fig. 2). Taken together, our results for additive QTL demonstrate that epic-QTL has the potential for high power, resolution and reproducibility; that copper resistance in the Oak × Wine cross progeny shares at least some underlying mechanisms with other S. cerevisiae strains; and that removal of a major source of variance can increase power to detect other additive QTL.

Magnitude epistasis is identified with chromosome VIII but not chromosome I

Reciprocal chromosome fixation effectively converts effects that are epistatic with that chromosome into additive effects that can be detected with high power by BSA. In the context of the epic-QTL logistic-regression model, these epistatic effects are identified as significant selection-by-background interactions.

We identify 7 interactions with chromosome VIII: one each on chromosomes VII, X, XII, XIV, and XV, and 2 on chromosome XI (Fig. 3, Supplementary Table 3). The z-score of each interaction peak is less extreme than that of its corresponding additive effect but not always in the same direction as the additive effect, indicating that there is no consistent interaction effect (such as the Oak chromosome always amplifying Oak alleles’ selection effects). We did not identify any interactions at a 5% FDR with chromosome I (Fig. 3a), despite observing >10 additive QTL. As chromosome I is the smallest of the S. cerevisiae chromosomes, it is plausible that there would not be any interactions with the entire chromosome. This result suggests that epic-QTL does not generate spurious interactions, and that interactions are specific and not widespread across the genome.

Fig. 3.

Interaction effects indicate magnitude epistasis. a) Fixed chromosome I (top) and fixed chromosome VIII (bottom) absolute z-scores for CuSO₄ experiments, with traces indicating additive (black, as shown in Fig. 2) and interaction (red) effects. Vertical red lines indicate where an interaction peak has been called, with solid lines indicating the highest peak on a chromosome and dashed lines indicating a second significant peak. b) Allele frequencies of the Oak allele at the maximum point of each interaction QTL per chromosome (indicated by solid lines in 3A and triangles in 3C), in each population. Oak (O) and Wine (W) fixed chromosome VIII backgrounds are on the horizontal axis, and the allele frequency of the Wine allele is on the vertical axis. Line-crossing of selected (blue) and nonselected (gray) would indicate sign epistasis. c) Comparisons of z-scores at interaction peaks (red triangles) with z-scores at corresponding additive peaks (black triangles).

The presence of an interaction can indicate different forms of epistasis. One possibility is sign epistasis, which in the case of epic-QTL would mean that changing the parent of the fixed chromosome changes the direction of the QTL effect at the interacting locus. An alternative possibility is magnitude epistasis, in which the QTL effect size at the interacting locus changes but the direction of the effect remains the same. In experimental designs such as standard BSA, where effects at any locus are averaged across a population, sign epistasis obscures phenotypic effects as the effects of allele pairs cancel each other out. Perfect sign epistasis, in which effect magnitude is equal but effect direction is opposite, is therefore impossible to detect by BSA without fixation of 1 allele in the pair to isolate the effect. In contrast, magnitude epistasis still produces an additive effect, although the effect size will be the average of that of each allele combination. To characterize our interaction QTL as exhibiting sign or magnitude epistasis with the fixed chromosome, we (1) compared the allele frequencies of the highest points of the interaction peak (Fig. 3c) and (2) scanned for loci above the 5% FDR threshold where the interaction z-score was more extreme than its corresponding additive z-score. Sign epistasis would require line-crossing of allele frequencies between parental backgrounds in the selected bulks, which we do not observe at interaction peaks (Fig. 3b). We also do not find any significant interaction z-scores that are greater in magnitude than their selection effect (Fig. 3c), which would indicate that the interaction obscures the additive effect through averaging. We therefore conclude that epistasis with chromosome VIII is magnitude and not sign epistasis.

Prior studies have identified interaction QTL for copper resistance in S. cerevisiae either by testing for interactions between additives QTL (Bloom et al. 2015) or by barcoding combinations of alleles in natural variants (Matsui et al. 2022; Nguyen Ba et al. 2022). We compared interactions identified with chromosome VIII in our study with those identified in these other studies, which utilized strains other than the Oak and Wine strains used here. We find that there is little overlap between identified loci (Supplementary Fig. 2). There are, however, consistent additive effects at specific loci such as CUP1, and indeed most interactions with chromosome VIII from the other studies did involve the CUP1 locus. These results suggest that interactions are between specific alleles not necessarily present in all crosses, which could be corroborated with additional epic-QTL experiments with different parental strains.

Further evidence that interaction effects are idiosyncratic is that not every additive locus interacts with the fixed chromosome (Fig. 3c), and there is no correlation in the direction or magnitude of effect of the interaction compared with additive effect. The majority of interaction peaks (4 of 7) were within 6 kb of the additive peak maxima, indicating that the interactions with chromosome VIII are likely with the same loci that produce additive effects. Of the remaining interaction peaks, two (the one on chromosome VII and the lesser one on XI) overlap with what appear as shoulders of additive peaks, suggesting that multiple QTL occur within that peak, and that the second largest is interacting with chromosome VIII. The peak on chromosome XV might also correspond more with the shoulder of the additive peak. The interaction peak and corresponding additive peak shoulder on chromosome VII are close to the CUP2 gene, which induces transcription of CUP1 (Welch et al. 1989). CUP2 could thus be a candidate for allele substitution to confirm the interaction with CUP1 on chromosome VIII. Overall, the co-occurrences of interaction peaks with additive peaks indicate that interactions occur primarily with loci that have an additive effect, and the lack of interactions at every additive peak, or even the most significant additive peaks, suggests that interactions are specific and idiosyncratic rather than the result of a global transformation of additive effects.

Discussion

Identifying epistatic contributions to trait variation presents challenges caused by the combinatorial nature of interactions and their potential to obscure effects of individual alleles. Methods to detect pairwise interaction effects suffer from low statistical power due to the number of pairwise comparisons across the genome to test. High power can be achieved by BSA experiments, but averaging over combinations of alleles precludes analysis of interactions. Because of these challenges, approaches for predicting the effect of genotype often minimize the contribution of epistasis to phenotypic variance, by first (or only) fitting additive effects (Ober et al. 2015). However, although the effects of epistasis might be statistically underestimated, specific examples of epistasis have been observed across species and traits, such as in tomato size and fruit number (Eshed and Zamir 1996; Aguirre et al. 2023), corn kernel coloration (Ford 2000), and mouse coat color (Bennett and Lamoreux 2003, reviewed in Phillips 2008). In nonnatural variants such as deletion mutations or engineered hypomorphs, interactions have also been quantified; using high-throughput approaches, Costanzo et al. (2016) found ∼900,000 interactions among 23 million double mutants representing nearly every pair of genes in the yeast genome and Hale et al. (2024) found that over one quarter of 1,721 CRISPR-interference perturbations showed growth effects that depend on genetic background. We developed epic-QTL with the aim of bringing the power of a high-throughput, DNA sequencing-based approach to the identification of interactions between natural genetic variants. Specifically, we circumvented the statistical problem of pairwise testing of natural variants by reciprocally fixing a single chromosome from each of 2 genetic backgrounds in a cross between divergent yeast strains. With the high power afforded by BSA, we observe magnitude epistasis with additive QTL but no evidence of cryptic sign epistasis.

We first verified our method by comparing additive QTL identified by epic-QTL, both between experiments with chromosome I or chromosome VIII fixed and between our study and those conducted on copper resistance in other strains. Known drivers of copper resistance, CUP1 and FRE1, were identified as additive QTL in all experiments where the loci were allowed to segregate. Additive peaks colocalized between the experiment with chromosome I fixed and the experiment with chromosome VIII fixed, but on average those identified in the experiment with fixed chromosome VIII were stronger, very likely due to the fixation of a major QTL. In comparison with other studies of copper sulfate resistance, several additive QTL were found in common, but many were not, suggesting strain-specific differences in which alleles are present that impact resistance.

The key strength of epic-QTL is the identification of interactions with fixed chromosomes at high statistical power. We next compared interactions found by epic-QTL to those identified for copper resistance using different strains, different methods, and smaller sample sizes (Ehrenreich et al. 2012; Bloom et al. 2013; Matsui et al. 2022; Nguyen Ba et al. 2022), finding that although there is some overlap in regions containing additive QTL, the majority of interactions are not common between studies. This finding speaks to the importance of more high-powered studies of interactions and potentially also suggests that interactions are idiosyncratic in that they are dependent on the specific alleles found in divergent strains. Because we detected more additive than interaction QTL, not every detected additive QTL in our study contained interaction QTL. Moreover, interactions did not necessarily cluster only under the highest additive peaks. This finding further supports that the interactions are idiosyncratic and do not reflect a consistent nonlinear transformation of additive effects, which would be the case for global epistasis (Otwinowski and Plotkin 2014). One key overlap with another study to note, however, is CUP1 as a hub for interactions on chromosome VIII (Matsui et al. 2022). That interactions occur with chromosome VIII but not chromosome I, and that interactions occur primarily with additive QTL, suggests that our interactions might be with CUP1. The logical next step would be to fix the chromosomes found to interact with fixed chromosome VIII, allowing chromosome VIII to segregate, and thereby to identify the interaction partner(s) on this chromosome.

The interaction QTL identified here provides evidence of 3 compelling trends that imply a middle ground between completely idiosyncratic epistasis and highly predictable global epistasis: (1) interaction peaks commonly colocalized with additive peaks, (2) magnitude epistasis was observed whereas sign epistasis was notably absent, and (3) interaction peaks differ between studies and are not driven by strength of an additive peak. Sign epistasis has the potential to completely obscure additive effects, and thus the lack of sign epistasis implies that interactions occur primarily with loci that already have an effect. Precise colocalization of additive and interaction maxima suggests that the additive QTL interacts with the fixed chromosome. These trends corroborate the conclusion by Bloom et al. (2015) that interactions occur primarily between additive QTL, and they validate the approach of reducing the search space by only looking at interactions between additives QTL as done by Nguyen Ba et al. (2022).

Sign but not magnitude epistasis can influence available evolutionary trajectories by creating valleys between peaks on a fitness landscape (Phillips et al. 2000; Weinreich et al. 2005). Examples of specific reciprocal sign epistasis, for example, mutually exclusive adaptive mutations in the HXT6/7 and MTH1 genes during experimental evolution under glucose limitation, have been shown to cause fitness valleys (Kvitek and Sherlock 2011). Sign epistasis involving mutations in specific interaction hubs has also been observed (Ang et al. 2023), but the general prevalence of sign epistasis is yet to be determined. epic-QTL offers an unbiased, powerful method for detecting sign epistasis. The lack of sign epistasis detected here, therefore, indicates that it is relatively rare, at least for the trait, fixed chromosomes, and parental strains we studied.

It will be important to see whether the trends we observed generalize to other fixed chromosomes and other complex traits. A complete set of fixed-chromosome strains would yield an additional benefit of very rapid assessment of the extent to which epistasis impacts variation in a trait, in that a completely additive genetic architecture would mean that the sum of chromosome effects should equal the difference between the parental strains. Such a test only requires chromosome-substituted strains, not segregants from them. This chromosome-based test would not rule out epistasis between loci within a chromosome and therefore could underestimate the extent of epistasis. Nonetheless, when this kind of test was applied in mice and rats to a large number of anatomical and physiological traits, the sum of chromosome effects far exceeded the parental difference, revealing ample evidence of epistasis (Shao et al. 2008). Moreover, the epic-QTL approach need not be limited to fixation of entire chromosomes. Reciprocal fixations of regions of chromosomes or individual genes or even individual nucleotides could be engineered and used for BSA to achieve within-chromosome resolution.

A widespread lack of sign epistasis would greatly aid in identifying interactions in studies where experimental manipulations of genotypes are not possible. Genome-wide association studies in particular face challenges with respect to the number of subjects relative to the number of possible interactions between markers, and so a variety of methods have been proposed to avoid exhaustively searching all possible pairs of polymorphisms (Van Steen and Moore 2019). Prioritizing interactions between additive loci rather than every possible combination could therefore be a principled approach to increase the power to detect interaction effects. Characterizing interaction effects in humans should in turn allow for greater precision in predicting response to medication and susceptibility to disease, as well as facilitate further understanding of the molecular mechanisms of complex traits. In all, our characterization of epistasis not only enhances our understanding of genetic interactions in model organisms but also has implications for improvement of applications in personalized medicine and trait prediction across diverse species.

Data availability

All data is available in the Supplemental Information or deposited on github at https://github.com/Siegallab/epicQTL. Raw sequencing data is publicly available from the NCBI Sequence Read Archive (PRJNA1175662). Supplementary Table 1 is available on GSA FigShare: https://doi.org/10.25386/genetics.28355381.

Supplemental material available at GENETICS online.

Funding

This work was supported by National Institutes of Health grant R35GM148344 (to M.L.S.).