PLoS Genetics
Public Library of Science
Dynamic genetic architecture of yeast response to environmental perturbation shed light on origin of cryptic genetic variation
DOI 10.1371/journal.pgen.1008801, Volume: 16, Issue: 5,
•
•
• Altmetric

### Notes

Abstract

Many biological traits are polygenic, with complex interplay between underlying genes and the surrounding environment. As a result, individuals with the same allele might have distinctive phenotypes due to differences in the polygenic background and/or the environment. Such differences often create additional genetic variation that is highly relevant to quantitative and evolutionary genetics by limiting our ability to accurately predict the phenotypes in medical or agricultural applications and providing opportunities for long term evolution. Previously, yeast growth regulating genes were found to be organised in large interacting networks. Here, we found that these networks were reorganised upon environmental changes, and that this resulted in altered effect sizes of individual genes, and how the whole network contributed to growth and the level of total genetic variance, providing a basis for future studies on the genetic maintenance of trait robustness and development of genetic models for studying and predicting selection responses for quantitative traits.

Zan, Carlborg, and Copenhaver: Dynamic genetic architecture of yeast response to environmental perturbation shed light on origin of cryptic genetic variation

## Introduction

Cryptic or hidden genetic variation is a type of genetic variation normally not seen but can, as has been shown experimentally in many species, emerge from polymorphisms changing their effects upon genetic (G-by-G interaction; Epistasis) [13] or environmental (G-by-E interaction) [47] perturbations. The release of such variation could lead to the emergence of extreme phenotypes [8], modifications to the penetrance of common diseases [2], facilitation of responses to artificial selection in crops or domestic animals [3,9] and ultimately affect the capacity of populations to adapt to sudden changes in surrounding environments. It is well known that epistasis and G-by-E are important contributors to cryptic variation of continuous traits [911]. More recently empirical results from studies on microorganisms, have convincingly reported G-by-G-by-E interactions as a prevalent and potentially important phenomenon for complex trait variation [1224]. For example, by experimentally generating combinations of mutant alleles/genes, the environmental dependence of epistatic interactions between genes (G-by-G-by-E) has been shown for binary (presence/absence) phenotypes in E.coli, S. cerevisiae, D. melanogaster and A. thaliana [12,13,1719,25,26]. This environmentally dependent epistasis affected both pairwise [13,2024] and high-order [1416] interactions, and resulted in abundant changes in connectivity and output of interaction networks in response to environmental changes for interaction networks built for single nucleotide polymorphisms [1719] and genes [2729].

An alternative and complementary approach to engineering combination of alleles experimentally for studying the dynamics in environmentally dependent cryptic variation is to measure how much phenotypic variation is expressed by a segregating population of genetically identical individuals (clones or inbred lines) across multiple environments. The contributing genetic mechanisms can be identified in such populations by mapping the individual locus (G-by-E interactions) and epistatic interactions (G-by-G-by-E interactions) whose effects change across environments. Those variations in effects jointly contribute to the suppression and release of cryptic genetic variation in the population upon environmental perturbations. Understanding the link between the dynamics in the genetic architecture of a complex trait across environments, defined as which loci contribute to the trait in which environments and how their effect sizes/contributed genetic variance change, could provide insights on many aspects of evolutionary and quantitative genetics. For example, as most natural populations/species encounter both subtle and dramatic environmental changes within/across clines/generations, an improved understanding on this phenomenon is central for understanding the genetic architecture, evolution and adaptation of complex traits.

As introduced above, G-G-E interactions have been reported in several species [12,13,1719,25,26] including E.coli, S. cerevisiae, D. melanogaster and A. thaliana , however, how such interactions contribute to rudimentary concepts, such as estimates of variance, allelic effect and others, in quantitative, population and evolutionary genetics has not been explored. Further exploration on how they influence the phenotypic variance across environments, the estimates of quantitative genetic metrics, including additive/epistatic effects and variances, are central for studies aiming to dissect and predict complex traits. Here, we attempted to provide insights to these questions by reanalysing a panel of 4,390 yeast recombinant offspring (segregants) generated by crossing a laboratory strain (BY) and a vineyard strain (RM). Every segregant was genotyped and phenotyped for growth in 20 media [30]. In an earlier study, Bloom et al [30] reported large differences in the genetic and phenotypic variance of growth among the different growth environments and mapped 939 additive QTL and 330 epistatic QTL when treating growth on these media as independent traits [30]. In these analyses, most of the epistatic QTL were detected via significant pairwise statistical interactions with one or two other loci [30]. Extending this work further, Forsberg et al [31] defined multi-locus networks in the same data by connecting loci with pairwise statistical interactions. Using these networks as a basis, high-order interactions were found to be prevalent and have strong phenotypic effects that could not be predicted from the additive and pairwise epistatic effects. In particular, highly interconnected hub-loci were detected on 11 of the 20 growth media, and they regulated growth by epistatically suppressing or releasing cryptic genetic effects of multiple interactors [31]. Here, we explored how often, and which, connections in the epistatic networks change across environments and how these changes in the networks affected the level of genetic variance in growth displayed by the population (G-by-G-by-E interactions). We explored the same 330 epistatic QTL from Bloom et al [30], but instead of treating growth on each media as independent traits, we here considered growth as a single complex trait measured in different media. These growth measurements on different media then represented expression of the same phenotype in multiple environments where differences in the content of the growth media were considered as various types and strengths of environmental perturbations. Across-environment analyses were performed to explore similarities and differences of allelic effects as well as multi-locus networks across environments to reveal the dynamics in the genetic architecture of segregant growth, leading to the suppression and release of cryptic genetic variation, in response to the wide range of perturbations.

Consistent with previous studies [1224], extensive changes in the connectivity of epistatic loci were found across environments. Furthermore, our analysis found that these were often associated with changes in how the loci contributed to growth. Alterations to the growth environment often resulted in changes of output from network hubs as the number of active interactions changed, leading to altered patterns of epistatic suppression and release of genetic effects from radial loci. As a consequence, the level of suppressed or released cryptic (hidden) genetic variance changed. G-by-G-by-E interactions were thus an important mechanism by which the population modulated cryptic genetic variation by deactivating epistatic network interactions in some environments and activating them in others. The ability of a population to alter the output from epistatic network interactions to release or suppress genetic variation in response to environmental changes facilitated large phenotypic changes and could result in unforeseeable selection responses. The potential impact of these findings on the genetic maintenance of trait robustness in individuals and populations, release of selectable genetic variation by environmental perturbations, the development of genetic models for quantitative traits as well their implications in areas where this might be of practical importance, such as plant breeding and evolution, are discussed.

## Results

To illustrate the principle of our analysis approach, we provide a schematic example showing a hypothetical total interaction network with four loci (Fig 1A; locus id’s A-D). This was created by combining two smaller networks that were independently detected in their own environment (Fig 1A; Environments 1 and 2 in blue/yellow, respectively). On the left and right are the genotype-phenotype (G-P) maps for the pairwise interactions in environment 1 (left; two interactions; Fig 1A), and the G-P maps for one pairwise interaction and a single locus association in environment two (right; Fig 1A). The complete four locus network including all these loci are presented in Fig 1B together with its G-P maps in the two environments (left/right for environments 1/2; Fig 1B). The nodes in this complete network are the mapped loci (QTL) connected by their significant pairwise epistatic interactions (edges). Only loci that have a significant epistatic interaction in at least one of the environments are included. The genotype-phenotype maps (Fig 1A and 1B) illustrate how the estimates of means and variances across the 2/4/16 genotype-classes (defined by one/two/four loci) change in the population of segregants across environments as a result of the activation/deactivation of epistatic interactions in the network. This approach was extended to build a complete yeast growth interaction network (Fig 2A) from all epistatic loci detected in earlier analysis of the 20 environments separately (individually highlighted in S2 Fig) [30,31]. In the following sections, we explore how the activity of the interactions in this complete epistatic network changed across the evaluated environments and how this resulted in changes in classic quantitative genetics measures of the contributions of the involved loci to yeast growth.

Fig 1
Epistatic networks are constructed based on results from association analyses modelling two-locus interactions. The circles represent QTL (A-D) involved in significant pairwise interactions contributing to growth (A; blue/yellow in environment 1/2, respectively). Interaction networks are first constructed for the environments separately by connecting significantly interacting loci (A; blue/yellow lines). The complete set of loci and pairwise interactions are next used to define a complete across environment growth interaction network (B). All the within-environment networks are therefore sub-networks. The multi-locus genotype-phenotype maps for the within-environment (A) and across environment (B) networks are illustrated using box-plots where the growth of the segregants relative to that in a standard environment (y-axis) are given for the evaluated single- or multi-locus genotypes (x-axis). Two networks are evaluated in (A) showing how loci contribute to growth in each of the two environments, resembling the results reported in earlier studies of this population [31]. In B) the additional analyses performed here to explore the dynamics in the genetic regulation of yeast growth in response to environmental perturbations are illustrated. Here, the complete across-environment interaction network is used as basis and its multi-locus genotype-phenotype maps explored across all environments. This facilitated both the identification of how the contributions by individual interactions in the network changed across environments (overlaps of loci/interactions across environments), and what the associated changes are in the genetic effects of individual and combination of alleles (differences in the genotype-phenotype maps).A schematic illustration of how an epistatic, across environment QTL network is defined and its phenotypic effects in response to environmental perturbations are evaluated.
Fig 2
(A) The complete across-environment interaction network includes 130 loci contributing epistatically to growth in at least one environment. Each node represents a locus, and its colour shows in how many environments it was involved in significant epistatic interactions. The edges represent significant pairwise interactions between loci, with the number of edges connecting pairs of loci corresponding to the number of times this pair was detected across the 20 environments. (B/C) Histograms showing the number of environments in which the 130 loci were involved in at least one significant epistatic interaction/ additive effect. D) Histogram showing the number environments in which each of the 212 pairwise interactions were significant. E) Histogram showing how much of the additive variance for growth in the 20 environments that was explained by the 130 loci in the network.Summary of the features of the complete interaction network for yeast growth across the 20 studied environments.

### Defining the complete across environment epistatic network of growth loci

The complete across environment growth interaction network included 130 loci, each detected with significant epistatic effect on growth for at least one environment in earlier analyses of this population [31] (Fig 2A, S2 Fig; Materials and Methods details how these networks were constructed; S1 Note). Among them, 69 (53%) were detected in only one environment by their epistatic effects, while the remaining loci were detected with significant epistatic interactions for more than one environment (Fig 2B; S3 Fig). In addition to their epistatic effect, 102 (78%) of the loci were also detected with significant additive effects for at least one of the 20 environments (Fig 2C). It should thus be noted, that some of the 130 loci were earlier only considered as additive loci in one or more of the environments as they only had significant additive effects in them [30]. In total, across all 20 environments, 212 pairwise interactions were detected among the 130 loci. The majority of the interactions (75%, 160) were unique to one environment, while the remaining 25% (52) were detected in at least 2 environments (Fig 2D). When fitting an additive-only model to the 130 loci, one environment at a time, these loci altogether explained between 69–100% of the additive genetic variance for growth in the 20 environments (Fig 2E). This indicates that epistatic interaction and allelic effects are highly dynamic with loci turning on/off their additive/epistatic effects or alter their epistatic connectors across environments.

### The dynamics in the genotype-to-phenotype maps for growth are associated with environmentally induced changes in activity of epistatic network interactions: An example across three environments

We explored the association between changes in the activity of epistatic network interactions and the phenotypic output of additive and epistatic effects of loci, across environments. To achieve this goal, we first present a sub-network built from 3 selected media, where either Indoleacetic acid (IAA) or Formamide had been added, or the carbon source had been changed from Glucose to Raffinose. Segregant growths were, overall, more similar on the media containing IAA and Formamide than in the medium with Raffinose as carbon source (PCA in Fig 3A; pairwise correlations S4 Fig). These media were selected to allow an evaluation of the relationship between degree of similarity of growth environment (measured by the phenotypic correlations in growth) and the resemblance of the underlying genetic architecture (as dissected in the following section). A 28-locus interaction network was defined from the epistatic loci detected for growth on the 3 selected media/environments (as described above and in Materials and Methods). Out of the 28 loci originally detected for their epistatic effect on at least one of the environments, 6 loci have significant additive effects in all 3 environments while another 7 loci have significant additive effects in 2 environments. Similarly, 6 loci have significant epistatic effects in all 3 environments while another 9 loci have significant epistatic effects in 2 environments (Fig 3C). Out of the 42 pairwise interactions detected in the 3 environments, only 1 pairwise interaction is shared across all 3 environments, with another 9 interactions being shared across 2 environments. This changes in activity of the epistatic interactions in the network when the environment changes thus involved (Fig 3E–3G) i) loci that were epistatic in all environments but with changes in the set of loci they interacted with, ii) loci that were epistatic in one environment, but contributed by additive effects only to growth in another or iii) loci that were epistatic in one environment and did not contribute to growth at all in the other.

Fig 3
A) A two-dimensional PCA plot illustrating the resemblance in growths of yeast segregants across the 20 environments (media). Open squares represent a medium and the filled dots media with added IAA or Formamide or the medium where Raffinose was the carbon source. B/C) Histograms showing the number of environments in which the 28 loci had at least one significant epistatic interaction/additive effect. D) Histogram showing the number environments in which each of the 42 pairwise interactions were significant. E-G) Illustrations of differences and similarities in types of genetic effects (epistatic, additive or none) and activity of the interactions in the epistatic growth network on IAA, Formamide and Raffinose, containing media, respectively. The hub and radial loci in the IAA epistatic network studied earlier [31] are highlighted with red/black arrows. The red lines connects significant pairwise interactions reported in Bloom et al [30]. The grey lines indicate epistatic interaction detected in other media. Panes H-J) Each box plot represents a group of segregants with the same number of growth-decreasing alleles at the five radial QTLs, separated and colored based on the genotype at the hub QTL. The x axis gives the number of growth-decreasing alleles at the radial QTLs and the colour of the box indicates the genotype at the hub QTL (chrVIII: 98,622 bp; tomato/ blue corresponds to BY/ RM alleles).Illustrations of the relationships between environmental perturbations and contributions by high-order interactions contribute to yeast segregant growth.

### Loci with variable contributions to growth across environments display extensive changes in activity of network interactions: Evaluating effects across all environments

To generalize the findings from the three-environment example above, the contribution by all networks to growth and the associated changes in activity of the epistatic interactions were analysed across all 20 environments. The results are described in detail in the sections below.

#### Change in output of high-order gene interaction networks in response to environmental changes is common for highly connected loci

In total, 13 loci with more than 4 epistatic interactors were detected in at least one of the 20 environments. The networks defined by these 13 hub loci and their interactors included 70% (91 of 130) of the loci in the complete network (Fig 2A; S7 Fig). The activity of the interactions of these 13 networks was highly dynamic across the 20 environments, with all interactions to hubs being active in some environments but completely inactive in others (S6A Fig; Fig 4A). Although epistatic network activity changed across environments, it was common that some of the interactors (0–83%; median 30%) that were inactivated still had detectable additive effects in other environments (Fig 4B; S6B Fig). The power to detect epistatic effects is lower than that for additive effects, making direct comparisons between the number of epistatic interactions and additive effects inappropriate. However, the common observation that epistatic interactions are more frequently inactivated when the environment changes suggests them to be more sensitive to environmental perturbations than additive effects (Fig 5A and 5B; S6A and S6B Fig). In addition, when the interactions between hub and radial loci were active in one environment and not in another, the total contribution by the whole network to the growth variation decreased (Fig 4C). The change of the epistatic networks in response to environment changes was thus associated with their contribution to growth.

Fig 4
A) Histogram illustrating the changes in activity of network interactions in 13 epistatic networks, with more than 4 interactors, across the 20 environments. For each network, a set of interactors was defined to include the radial loci in the most highly activated environment. The percentage of these interactors that were epistatically active with the hub in each of the remaining 19 environments was calculated (x-axis). The overlap of interactors in the 13 networks across the 20 environments was summarized as the counts of environments with similar percentages of shared active interactors (y-axis). B) Histogram illustrating the percentage of interactors (defined as in A above) that have significant additive effects across the 13 networks and 20 environments. The x-axis shows the percentage of these interactors that have additive effects across the other 19 environments. The y-axis summarizes these percentages across the 13 networks. C) In each environment, adjusted r2 values are calculated for all networks and ranks of these model fits were assigned. The association between the connectivity of the epistatic networks (x-axis; number of loci connected to the hub), and their contributions to the variance in growth (y-axis; rank of adjusted r2 values) across the 13 networks and 20 environments, is illustrated as box-plots of these ranks grouped by the number of interactors.Illustrations of the dynamics of the interactions in the largest mapped epistatic networks, and their contribution to growth variation, across all tested environments.
Fig 5
A) 311 loci had significant additive genetic effects on growth in at least one of the 20 environments. The estimated additive effects (y-axis) for each locus (x-axis) in the 20 studied environments are illustrated using dots in different colours. The loci (represented by the most significant SNPs) are sorted from left to right by the variance of the estimated additive effects across the environments. All additive effects estimates were obtained by fitting all 311 loci jointly in a linear model. The 4 loci without significant genotype by environment interactions are indicated with black arrows below the x-axis. Out of the 13 highly activated loci (interacting with more than 4 other loci), 11 had significant additive effects in at least one environment [31] and they are highlighted with red arrows on the top. B) An illustration of the relationship between the maximum number of active epistatic interactions (x-axis) and the variance in their estimated additive effects across the 20 media. Each blue dot represents a locus with a significant additive effect. The red dashed line is the regression line (P value = 7.1 x 10−39).The variations in additive effects on segregant growth and their associations with network activity.

#### Variations in marginal additive effects across environments associated with the activity of interactions in the epistatic networks

Significant additive effects on growth in at least one environment were detected for 311 loci in the genome. Although not every locus had significant effects on growth in every environment, these loci did as a group contribute significantly to growth in most environments (Materials and Methods; S1 Table). The effects were generally stronger in one or a few of the environments (S7 Fig). For example, more than half of the loci were unique to one environment and only 9 loci were associated with growth in more than 10 environments. QTL by environment interactions were thus abundant with 98% (307) loci displaying statistically significant QTL by environment interaction after multiple testing corrections (Fig 5; S2 Table; see details in Materials and Methods).

All 11 QTL that were highly active (> 4 epistatic interactors; S2 Table) in at least one environment displayed large variations in the marginal additive effects across the environments (Fig 5A; P-value = 6.1 x 10−8 ; Wilcoxon rank sum test). As the network activity of these loci also changed much between environments, we hypothesised that the additive effects in the different environments were associated with changes in the number of active G-by-G interactions of the locus. To test this, we estimated the correlation between the variations in the number of active epistatic interactors and variance in the additive effects across the 20 environments. This correlation was highly significant (Fig 5B; P value = 7.1x10-39; linear regression), suggesting that the variation in additive effects of polymorphisms across the 20 environments, rather than the effect size, was associated with the changes in activity of interactions in the epistatic network.

### Across environment variation in total genetic variance is correlated with changes of the epistatic network

As has been reported earlier in Bloom et al [30], there were considerable variation in both the phenotypic and genetic variance in growth (S8A Fig), indicated by the variation in broad sense (0.11 < H2 < 0.88; median 0.64 [30]) and narrow sense (0.09 < h2 < 0.70; median 0.43 [30]) heritability across environments (S8B Fig). Here, we evaluated whether the changes in the total genetic variance across environments (considered as hidden/cryptic genetic variance) is associated with changes in the underlying epistatic genetic architecture (number of active G-G-E interactions). When studying the changes in the complete 130-locus interaction network across the 20 environments, there are simultaneous forming and collapsing of active sub-networks. Instead of focusing on changes for individual interactions, we instead compared the total number of significantly active epistatic interactions in the environments as a proxy for the total changes in the epistatic genetic architecture. A significant positive correlation (P-value = 5.6 x 10−31 ; regression; Fig 6) was detected between the pairwise differences in i) the levels of total genetic variance (Vtotal1 -Vtotal2; where total genetic variance is estimated as phenotypic variance times broad sense heritability) and ii) differences in the number of total active epistatic connections (nep1 -nep2) across all pairs of environments. This, together with the results described above, highlights that the dynamics in the underlying genetic architecture, i.e. changes in G-by-G-by-E interactions across environments, is likely to involved in the suppression and release of cryptic genetic variance upon environmental perturbation.

Fig 6
A significant correlation (P-value = 5.6 x 10−31 from regression) was detected between the pairwise differences in the number of active epistatic interactions (x-axis) and the total genetic variances (Vtotal1 –Vtotal2; Vtotal = H2; y-axis) for the loci in the complete interaction network across the 20 environments.Illustration of the relationship between the activity of interactions in the epistatic network and amount of total genetic variance explained by the epistatic network across the growth environments.

## Discussion

### Approaches to study genotype by environment interactions

One intriguing question in biology is how living organisms cope with changes in living conditions throughout their lifetime. One potential mechanism is Gene x Environment interactions, achieved by gradually modify the effects of common genes, mechanisms or networks that are more or less active across environments. Another form is the recruitment of condition specific mechanisms that are inactive under most of the circumstances. Here, we study this phenomenon by reanalysing a publicly available haploid segregant yeast dataset where growth was measured as colony radius after 48 h growth on various media.

In our study, colony radius was considered as one trait and measurements from the various media were considered realizations of this same traits across multiple environments. A forward genetics screen was first used to identify loci affecting this common growth-measurement across all environments. Subsequently analyses were performed to evaluate where the identified additive/non-additive loci fell on the sliding scale from being common contributors with significant effects in many environments to be loci with more specific in only a few environments. Similar with colony radius, most quantitative traits are likely to be influenced by a variety of mechanisms especially when studied across a range of environments. Hence, rather than studying growth as a complex phenotype resulting from multiple cell biological and physiological processes as in the forward genetic screens, sub-phenotypes that could better reflect the output of the specifically targeted biological process can be assayed separately. Therefore, an alternative reverse genetics approach could be applied to study Gene x Environment by focusing on polymorphisms in these sub-phenotypes targeting specific genes/pathways/networks.

One advantage of the adopted forward genetic approach is that it does not require any prior assumptions about which biological mechanisms are expected to contribute to trait variation, or limit explorations to a set of known genes/pathways/networks. This makes it possible to dissect the genetic basis of quantitative traits using assays that are not specifically targeting the output of individual biological mechanisms and obtain a complete overview of the composite phenotype. In contrast, the reverse genetic approach will provide more detailed insights to specific biological mechanisms beyond what can be achieved in a forward genetics screen. It is, however, difficult to obtain the same general overview of how loci/pathways/networks combine their effects as in a forward genetics screen. Hence, it will likely be a combination of both that gives the direct the future development.

Unfortunately, the reverse genetic approach requires in-depth prior biological assumptions to decompose and measure the composite phenotype as sub-components which are not always available, affordable or even feasible to collect, quantify or pre-define. This hampers the broad application of this approach in quantitative genetics. Another possibility is to use statistics to partition the variance of a complex quantitative phenotype into components aiming at representing common and specific genetic contributions in the studied environments. Separate genome scans could then be performed for these components as independent phenotypes to reveal loci contributing to these. However, such analyses assume that that these statistically inferred components of the phenotypes are biologically independent and further analyses are thus required to obtain a complete view of how they jointly contribute to the composite phenotype.

Despite the large differences in growth environments, high genetic correlations, and considerable overlaps of both additive loci and active epistatic network interactions (S1S3 Figs) were found. This was common even for growth conditions expected to require distinctive physiological responses, suggesting that underlying signalling and regulatory networks are shared. The forward genetics approach chosen here to analyse the data will not be able to specifically quantify the contributions by defined signalling and regulatory pathways across environments. However, by considering segregant growth as a composite model complex trait resembling those used in quantitative genetic studies in animals, plants and humans, it could provide novel insights to the link between genetic and phenotypic variation in this segregating population. Further methodological development and molecular work is, however, needed to more completely explore and define the roles of individual biological mechanisms in the common and specific genetic contributions to growth in the different environments.

### The effects of genotype-by-environment interactions on yeast growth

The studied dataset did not allow direct estimation of the contribution from environmental (i.e. growth medium) effects to the phenotypes as the available growth measurements were pre-normalised against growth in a control medium [30]. However, estimates of the contributions by direct genetic (G) and genotype-by-environment (G-by-E) effects showed that direct genetic effects only contributed about 1/3 (estimated using ANOVA by fitting the replicate growth measures for the individual segregants across the 20 environments as response variable with the segregant ID and environment as factorial explanatory variables in a linear model) as much to the variance in growth compared to contributions from G-by-E. Consistent with the large contributions from G-by-E, we found large differences in the genetic architecture of growth (defined as associated loci and their genetic effects) across environments. In the following sections we discuss these findings in more detail as well as their implications for the mapping, and understanding the evolution of complex traits.

### High environmental specificity for both additive and epistatic genetic effects

Most of the detected loci, regardless of mapped via their additive effects or epistatic interactions, only contributed to growth in one or a few environments. This in itself indicates extensive G-by-E interactions. However, loci mapped by their additive effects replicated to a greater extent across environments than loci mapped via their epistatic effects (Fig 2, S2 Fig). Epistatic loci were thus highly environmentally specific, suggesting a connection between G-by-G and G-by-E in this population. This is consistent with previous analysis on a similar yeast cross, where cryptic genetic variation is released under rare allelic combinations in specific environmental conditions [19]. The environmentally induced changes in the activity of network interactions influencing the phenotypic output of individual and combinations of loci, altering the level of genetic variance of the population in the environments. Such variations in the allelic effects across environments is thus likely important in many studies of complex traits, for example when aiming to understand the processes allowing individuals and populations respond to changes in the surrounding environments.

### Environmental specificity of high-order interaction effects facilitates buffering of genetic effects in populations

Here, it was shown that the connectivity of the interaction networks, as well as the capacitation effects of the hub-loci, generally were environment specific: the capacitors released the large phenotypic effects of its interactors in some environments, whereas they were often unaffected by them in others. Together with previous findings where yeast growth plasticity was found to be regulated by environment-specific multi-QTL interaction [17], G-by-G-by-E interactions are thus likely to be a buffering mechanism allowing populations to accumulate cryptic genetic variation in a wide range of environments, for later release in response to environmental perturbations facilitating large and rapid responses.

### Network capacitation influences individual robustness to environmental perturbations

Our results suggest that the interplay between network interactions and environmental factors are important also for individual robustness. Individuals with more non-capacitation hub alleles perform better, on an average (S9 Fig), and tend to show less variability across environments. This might be of relevance to, for example, plant breeding where one of the key challenges is to minimise the impact of genotype by environment interactions on production. Interactions in large gene interaction networks, buffered by environmental factors, might thus be an important driver of observed G-by-E interactions in populations. Targeted breeding for particular alleles at central network hubs might provide routes to genotypes that are either robust performers when challenged by environmental changes or high performers in more defined environments. In addition, G-by-G-by-E might provide multiple routes for populations and individuals to adapt to environmental changes. With the presence of environmentally independent additive effects, it is likely that alleles can be accumulated to intermediate frequencies in populations with small or no fitness costs in many environments. Upon rapid environmental change, the G-by-G-by-E interactions studied here can suppress or release large amounts of selectable genetic variation at a considerably higher rate [3234], facilitating more rapid and larger selection responses beyond predictions obtained based on the levels of additive variance, or heritability, in the populations.

### Connections to available knowledge

Our study confirms the importance of G-by-G and G-by-E for complex trait variation [913,17,31]. For example, many yeast genes are known to be nonessential in one genetic background, but essential in another, with the essential genes often being highly connected hubs in interaction networks [28]. Similar mechanisms have been studied also in bacteria where, for example, evaluations of the effects of 18 randomly selected mutations in E.coli in two environments and five genetic backgrounds illustrate that all of them have genetic background dependent effect on phenotypic plasticity [23]. Capacitation is also a well-known mechanisms studied in detail in several species, including the heat shock protein HSP90 [35,36] in Arabidopsis thaliana and EGFR in Drosophila melanogaster [37]. A limitation of this study is that it is based on one particular cross, making it difficult to know whether the results are specific to this data or generally applicable. Further work in other crosses, different environments and ultimately natural populations is thus needed to evaluate this. The work, however, provides a strategy for how to design and analyse such new data. Further, given that there is evidence from multiple other species that G by G by E interactions contributes to complex trait variation also present, such work is motivated to more completely dissect also the biological mechanisms underlying such interactions.

### Hypothetical molecular mechanisms underlying the observed effects

A number of the mapped hub-QTL harbour candidate genes with known biological functions, including GPA1 [38], HAP1 [3941], KRE33 [42], MKT1 [43] and IRA2 [44] (S5 Fig). Although they are obvious positional, further work is required to validate the functional candidate genes, in particular if and how they might contribute to the dynamic changes across environments. Not only because earlier work focussed on marginal genetic effects, rather than network effects, but also as the studies were performed in the environments where the effects were most prominent. Some earlier findings, however, allows us to present hypotheses about ways that they might contribute to the effects discovered here. For example, several hub-QTL were also epistatic hubs for expression QTLs [45] where interactions between HAP1KRE33 and between HAP1MKT1 contributed to variations in the expression levels of many genes [45]. These studies were, however, performed in a single environment and expression QTL are known to often be environmentally dependent [46,47]. Further studies of transcriptomic and metabolic data across multiple environments would therefore be a possible route to explore whether changes in the connectivity of the genetic networks around these loci across environments results in associated changes also at transcriptomic and metabolic levels.

### Potential implications for modelling of quantitative traits

The studies of this yeast population here, and earlier [31], illustrate that the most highly connected loci in the interaction networks (the hubs) often serve as modulators. They have little, or no, individual effects but rather influence the phenotype by releasing the effects of environmentally specific sets of interacting effector genes. This is an opposite scenario to that assumed in the recently proposed Omnigenetic model for quantitative traits [48], where it is postulated that the highly connected loci in the networks are effectors that are modulated by many other genes. One consequence of this is that results from association studies where loci are detected based on their marginal additive effects need to be interpreted with caution. This is because it might be incorrect to assume that such effects suggest that the locus has a direct (effector) influence on the trait or disease, while it in fact could be entirely a composite effect of contributions by multiple other effector loci. Another potential modelling challenge highlighted here is the potentially large influence from epistasis by environment interactions. We find that they might not only influence the variation in quantitative traits by modulating the effects of individual genes, but also in defining which sets of interactors that are under genetic control by capacitor loci. Further theoretical, and empirical, work is needed to explore the potential implications of these findings for modelling of quantitative trait variation from molecular data in, for example, genome-wide association studies and studies on the basis for, maintenance of and utilization of genetic variation in short- and long-term adaptations to natural and artificial selection. For example, an interesting implication of our findings is that they suggest not only to screen for large effect alleles amongst rare variants [49], but to broaden screens further to facilitate detection of variants that display variable effects across genetic backgrounds (populations) and environments.

### Conclusions

In summary, we show that epistatic networks respond dynamically to environmental perturbations. The dynamics in the network connectivity across environments were connected to changes in allelic effects of individual loci, epistatic effects of multi-locus interactions and the genetic variance contributed by these on the population level. These findings illustrated how G-by-G-by-E interactions influences both individual phenotypes and population level genetic variation. Our results provide novel insights on the fundamental mechanisms contributing to variation in complex traits with practical implications to, in particular, fields where the genetic mechanisms facilitating responses to variations in the environment are central, including evolutionary biology and breeding.

## Methods

### Downloaded data for the BY x RM haploid segregant yeast population

A detailed description of the generation of the 4,390 BY × RM strains, as well as the genotyping, phenotyping, quality control of genotypes, filtering and normalization of growth measurements is available in Bloom et al [30]. All the data analysed here was downloaded from the supplements of that paper. The previously detected additive and epistatic QTLs, as well as their connectivity into within-environment interaction networks, are available in the supplementary information of Forsberg et al [31]. The downloaded significant QTL-QTL interaction pairs were originally mapped in a two-locus interaction analysis across all possible combination of genome wide polymorphisms [30]. The within environment interaction networks were constructed by [31], providing input for the definition of a complete across-environment epistatic network.

### Estimating the contributions by genotype and genotype-by-environment interactions to the phenotypic variance

The phenotypic variance was partitioned into contributions from genotype (G), genotype-by-environment (G-by-E) and residual (environmental; E) effects by fitting model (1) to the data:

${\overline{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}=\mathrm{u}+{id}_{i}+{\mathrm{E}}_{\mathrm{j}}+{id}_{i}*{\mathrm{E}}_{j}+\mathrm{e}$
${\overline{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}$ is the mean growth for the replicates of individual i in environment j (j = 1..n; n is the number of growth conditions); idi is the individual segregant (genotype) coded as a factor and Ej is a dummy variable representing the growth condition (environment). idi*Ej is the interaction (G-by-E) between a particular segregant (genotype) and growth condition (environment). Since the available data was normalised against a control medium, there was (as expected) no significant contrition by E. The relative contributions to the total growth (phenotypic) variance from G and G-by-E were estimated by their respective sum of squares (Sum of Square for id is calculated as ${\sum }_{1}^{p}\left({id}_{i}-\overline{id}{\right)}^{2}$ and Sum of Square for the interaction id*E is calculated as ${\sum }_{1}^{p}\left({id}_{i}*{\mathrm{E}}_{j}-\overline{{id}_{i}*{\mathrm{E}}_{j}}{\right)}^{2}$)

### Defining a set of independently associated additive growth loci

A set of across-environment growth loci was defined. First, QTLs detected in the earlier environment-separate analyses with peak associations within 20kb and in pairwise r2 > 0.9 were selected. Second, all the loci selected in step 1 were subjected to a multi-locus polygenic association analysis [50,51] to identify a final set of statistically independent loci (FDR < 0.05) with additive effects on growth in each tested environment [30]. Alternative definitions ranging from physical distance < 20 kb and r2 > 0.6 to physical distance < 10 kb and r2 > 0.9 were evaluated and found to result in very similar results in practice.

### Across environment evaluation of the additive growth loci

Several growth loci in the final set defined above only had significant individual associations in one growth environment. To test if they, as a group, contributed to the polygenic inheritance of growth also in other environments we compared the fit of the following models to the data (models 2 and 3) using a likelihood ratio test.

$\overline{Y}={X}_{1}{\beta }_{1}+\mathrm{e}$
$\overline{Y}={X}_{1}{\beta }_{1}+{X}_{2}{\beta }_{2}+\mathrm{e}$

Here, $\overline{Y}$ is a vector of the average growth of each segregant (genotype) in a particular environment and e is the normally distributed residual. The joint contributions by the individually significant/non-significant loci in a specific environment was modelled in X1β1/X2β2, respectively. X1 includes a column vector of 1’s for the population mean and column vectors with the genotype of each significantly associated SNP in the environment with the two homozygous genotypes coded as 0/2, respectively. X2 includes column vectors with genotypes of all loci in the set defined above that was not individually significant in the tested environment. β1/β2 are vectors including the estimated additive effects for the two sets of loci. A likelihood ratio test was used to compare the fit of the two models using the lrtest function in R package lmtest [52].

### Detect individual loci involved in genotype by environment interactions

All growth loci defined in the polygenic analysis were evaluated for genotype by environment interactions. This by fitting the following two models to the data:

${y}_{ijk}=\mathrm{u}+{\mathrm{E}}_{\mathrm{j}}{+\mathrm{a}}_{1}{\mathrm{b}}_{1}+{\mathrm{a}}_{2}{\mathrm{b}}_{2}+\cdots {\mathrm{a}}_{\mathrm{n}}{\mathrm{b}}_{\mathrm{n}}+\mathrm{e}$
${y}_{ijk}=\mathrm{u}+{\mathrm{E}}_{\mathrm{j}}+{\mathrm{a}}_{1}{\mathrm{b}}_{1}+{\mathrm{a}}_{2}{\mathrm{b}}_{2}+\cdots {\mathrm{a}}_{\mathrm{n}}{\mathrm{b}}_{\mathrm{n}}+{\mathrm{E}}_{\mathrm{j}}{\mathrm{a}}_{\mathrm{x}}{\mathrm{B}}_{\mathrm{x}}+\mathrm{e}$

In both models, yijk is the growth of replicate k for segregant i in environment j (j = 1..20 environments; k = 1..nij; nij is the number of replicates for individual i in environment j); ax is the indicator regression variable for the genotype of QTL x coded as 0 and 2 for the homozygous minor and major alleles; bx are the corresponding estimated additive effects; u is the population mean and Ej is the effect of environment j (j = 1…20) on growth. Model 5 also includes an interaction term EjaxBx between one of the QTL and the environment. Model 5 was fitted for each QTL one at a time to test for its interaction with the 20 growth environments. The significance of each QTL by environment interaction was evaluated using a likelihood ratio test between models 4 and 5. Polygenicity was accounted for by the simultaneous fitting of all mapped loci in the two models. The analyses were performed using custom R scripts [53].

### Estimating the additive effects of QTL in different growth environments

A linear model (model 6) was used to estimate the additive effects of all the additive loci selected in the polygenic analysis in each tested environment.

$\overline{Y}=\mathrm{X}\mathrm{\beta }+\mathrm{e}$

Here, $\overline{Y}$ is the average growth of the replicates for each segregant (genotype) in each tested condition. e is the normally distributed residual. X includes a column vector of 1’s for the population mean and additional column vectors with the indicator regression variables for all the SNPs included in the model (coded as 0/2 for the two homozygous genotypes, respectively). β is a column vector with the corresponding additive effects. This model was fitted for each environment independently to obtain estimates of the additive effects for each locus in each environment.

### Construction of an across-environment epistatic interaction network

A complete across-environment epistatic growth interaction network was constructed from the environment specific networks reported in Forsberg et al [31]. First, the environment specific networks inferred for each growth environment were extracted from the results of Forsberg et al [31]. Second, we evaluated whether any of the pairwise interactions detected for a specific environment made significant contribution to growth at the remaining environments under a more lenient significant threshold only correcting for the total number of pairwise interactions detected across all environments. This was performed using a likelihood ratio test between models with and without the pairwise interaction for a particular pair of epistatic loci as described in detail by Bloom et al [30]. Then, the across-environment network was constructed by connecting the loci display pairwise interaction in any of the 20 environments using igraph [54] as descried in Forsberg et al [31]. These analyses were performed using custom scripts implemented in R [53] [will be made available upon publication or by request during review]. The raw data from which these were constructed are avaiable as supplement 5 in Bloom et al [30]; The analysis scripts/results from these earlier analyses are available at https://github.com/simfor/yeast-epistasis-paper and are described in detail by Forsberg et al [31]).

### Evaluation of the G-by-G-by-E interaction for a six-locus interaction network

The effects of a six locus interaction network, originally detected and explored for growth in IAA containing growth medium in Forsberg et al [31], were here evaluated across multiple environments. This analysis was performed to explore the association between the changes in activity of interactions of the epistatic genetic network and its contribution to growth in the different environments. To quantify the effects of G-by-G-by-E interactions, models 4 and 5 were fitted to the data with ax (x = n = 1) used as the indicator variable for each of the 64-genotype classes defined by the genotypes at the 6 loci. All other parameters, and the likelihood ratio test used to obtain the P-values for comparing the models, were the same as described above.

## Acknowledgements

We thank Simon Forsberg, Tilman Rönneburg and Thibaut Payen for discussions and comments on the manuscripts and figures.

## References

1

TFC Mackay. . Epistasis and quantitative traits: using model organisms to study gene–gene interactions. Nat Rev Genet. 2014;15: , pp.22–33. , doi: 10.1038/nrg3627

2

HJ Cordell. . Epistasis: what it means, what it doesn’t mean, and statistical methods to detect it in humans. Hum Mol Genet. 2002; , doi: 10.1093/hmg/11.20.2463

3

Ö Carlborg, CS Haley. . Epistasis: Too often neglected in complex trait studies?Nature Reviews Genetics. 2004 pp. , pp.618–625. , doi: 10.1038/nrg1407

4

G Gibson, I Dworkin. . Uncovering cryptic genetic variation. Nat Rev Genet. 2004;5: , pp.681–690. , doi: 10.1038/nrg1426

5

DL Des Marais, KM Hernandez, TE Juenger. . Genotype-by-Environment Interaction and Plasticity: Exploring Genomic Responses of Plants to the Abiotic Environment.Annu Rev Ecol Evol Syst.2013;44: , pp.5–29. , doi: 10.1146/annurev-ecolsys-110512-135806

6

D. Thomas. Gene–environment-wide association studies: emerging approaches. Nat Rev Genet. 2010;11: , pp.259–272. , doi: 10.1038/nrg2764

7

AA Elias, KR Robbins, RW Doerge, MR Tuinstra. . Half a Century of Studying Genotype × Environment Interactions in Plant Breeding Experiments. Crop Sci. 2016;56: , pp.2090, doi: 10.2135/cropsci2015.01.0061

8

SKG Forsberg, Ö Carlborg. . On the relationship between epistasis and genetic variance heterogeneity. J Exp Bot. Oxford University Press; 2017;68: , pp.5431–5438. , doi: 10.1093/jxb/erx283

9

O Carlborg, L Jacobsson, P Ahgren, P Siegel, L Andersson. . Epistasis and the release of genetic variation during long-term selection. Nat Genet. 2006;38: , pp.418–420. , doi: 10.1038/ng1761

10

TE Juenger, S Sen, KA Stowe, EL Simms. . Epistasis and genotype-environment interaction for quantitative trait loci affecting flowering time in Arabidopsis thaliana. Genetica. 2005;123: , pp.87–105. , doi: 10.1007/s10709-003-2717-1

11

E Sasaki, P Zhang, S Atwell, D Meng, M Nordborg. . Missing G x E Variation Controls Flowering Time in Arabidopsis thaliana.PLOS Genet.2015;11: , pp.e1005597, doi: 10.1371/journal.pgen.1005597

12

AN Smith, L-A Miller, G Radice, R Ashery-Padan, RA Lang. . Stage-dependent modes of Pax6-Sox2 epistasis regulate lens development and eye morphogenesis. Development. 2009;136: , pp.3377–3377. , doi: 10.1242/dev.043802

13

RE Kerwin, J Feusier, A Muok, C Lin, B Larson, D Copeland, et al. Epistasis × environment interactions among Arabidopsis thaliana glucosinolate genes impact complex traits and fitness in the field. New Phytol. 2017;215: , pp.1249–1263. , doi: 10.1111/nph.14646

14

J Hou, J van Leeuwen, BJ Andrews, C Boone. . Genetic Network Complexity Shapes Background-Dependent Phenotypic Expression. Trends Genet. 2018;34: , pp.578–586. , doi: 10.1016/j.tig.2018.05.006

15

MN Mullis, T Matsui, R Schell, R Foree, IM Ehrenreich. . The complex underpinnings of genetic background effects.Nat Commun. 2018;9: , pp.3548, doi: 10.1038/s41467-018-06023-5

16

JT Lee, MB Taylor, A Shen, IM Ehrenreich. . Multi-locus Genotypes Underlying Temperature Sensitivity in a Mutationally Induced Trait.ML Siegal, editor. PLOS Genet.2016;12: , pp.e1005929, doi: 10.1371/journal.pgen.1005929

17

A Bhatia, A Yadav, C Zhu, J Gagneur, A Radhakrishnan, LM Steinmetz, et al. Yeast Growth Plasticity Is Regulated by Environment-Specific Multi-QTL Interactions.G3 Genes|Genomes|Genetics.2014;4: , pp.769–777. , doi: 10.1534/g3.113.009142

18

A Yadav, H Sinha. . Gene-gene and gene-environment interactions in complex traits in yeast. Yeast. 2018;35: , pp.403–416. , doi: 10.1002/yea.3304

19

A Yadav, K Dhole, H Sinha. . Differential regulation of cryptic genetic variation shapes the genetic interactome underlying complex traits. Genome Biol Evol. 2016;8: , pp.3559–3573. , doi: 10.1093/gbe/evw258

20

KM Flynn, TF Cooper, FBG Moore, VS Cooper. . The Environment Affects Epistatic Interactions to Alter the Topology of an Empirical Fitness Landscape.JC Fay, editor. PLoS Genet.2013;9: , pp.e1003426, doi: 10.1371/journal.pgen.1003426

21

C Li, J Zhang. . Multi-environment fitness landscapes of a tRNA gene. Nat Ecol Evol. 2018;2: , pp.1025–1032. , doi: 10.1038/s41559-018-0549-8

22

MGJ de Vos, FJ Poelwijk, N Battich, JDT Ndika, SJ Tans. . Environmental Dependence of Genetic Constraint.HE Hoekstra, editor. PLoS Genet.2013;9: , pp.e1003580, doi: 10.1371/journal.pgen.1003580

23

SK Remold, RE Lenski. . Pervasive joint influence of epistasis and plasticity on mutational effects in Escherichia coli. Nat Genet. 2004;36: , pp.423–426. , doi: 10.1038/ng1324

24

JT Lee, AL V Coradini., A Shen, IM Ehrenreich. . Layers of Cryptic Genetic Variation Underlie a Yeast Complex Trait. Genetics. 2019;211: , pp.1469–1482. , doi: 10.1534/genetics.119.301907

25

C-T Zhu, P Ingelmo, DM Rand. . G×G×E for Lifespan in Drosophila: Mitochondrial, Nuclear, and Dietary Interactions that Modify Longevity.N-G Larsson, editor. PLoS Genet.2014;10: , pp.e1004354, doi: 10.1371/journal.pgen.1004354

26

PJ Freda, ZM Ali, N Heter, GJ Ragland, TJ Morgan. . Stage-specific genotype-by-environment interactions for cold and heat hardiness in Drosophila melanogaster. Heredity. 2019;123: , pp.479–491. , doi: 10.1038/s41437-019-0236-9

27

S Bandyopadhyay, M Mehta, D Kuo, M-K Sung, R Chuang, EJ Jaehnig, et al. Rewiring of Genetic Networks in Response to DNA Damage. Science. 2010;330: , pp.1385–1389. , doi: 10.1126/science.1195618

28

E Kuzmin, B VanderSluis, W Wang, G Tan, R Deshpande, Y Chen, et al. Systematic analysis of complex genetic interactions. Science. 2018;360: , pp.eaao1729, doi: 10.1126/science.aao1729

29

GP Leung, MJ Aristizabal, NJ Krogan, MS Kobor. . Conditional Genetic Interactions of RTT107, SLX4, and HRQ1 Reveal Dynamic Networks upon DNA Damage in S. cerevisiae.G3 Genes|Genomes|Genetics.2014;4: , pp.1059–1069. , doi: 10.1534/g3.114.011205

30

JS Bloom, I Kotenko, MJ Sadhu, S Treusch, FW Albert, L Kruglyak. . Genetic interactions contribute less than additive effects to quantitative trait variation in yeast. Nat Commun. 2015;6: , pp.8712, doi: 10.1038/ncomms9712

31

SKG Forsberg, JS Bloom, MJ Sadhu, L Kruglyak, Ö Carlborg. . Accounting for genetic interactions improves modeling of individual quantitative trait phenotypes in yeast. Nat Genet. Nature Research; 2017;49: , pp.497–503. , doi: 10.1038/ng.3800

32

G Gibson. . Decanalization and the origin of complex disease. Nat Rev Genet. 2009;10: , pp.134–140. , doi: 10.1038/nrg2502

33

AB Paaby, M V Rockman. . Cryptic genetic variation: evolution’s hidden substrate. Nat Rev Genet. Nature Research; 2014;15: , pp.247–258. , doi: 10.1038/nrg3688

34

EJ Hayden, E Ferrada, A Wagner. . Cryptic genetic variation promotes rapid evolutionary adaptation in an RNA enzyme. Nature. 2011;474: , pp.92–95. , doi: 10.1038/nature10083

35

C Queitsch, TA Sangster, S Lindquist. . Hsp90 as a capacitor of phenotypic variation. Nature. 2002;417: , pp.618–624. , doi: 10.1038/nature749

36

SL Rutherford, S Lindquist. . Hsp90 as a capacitor for morphological evolution. Nature. 1998;396: , pp.336–342. , doi: 10.1038/24550

37

I Dworkin, A Palsson, K Birdsall, G Gibson. . Evidence that Egfr contributes to cryptic genetic variation for photoreceptor determination in natural populations of Drosophila melanogaster. Curr Biol. 2003;13: , pp.1888–93. , doi: 10.1016/j.cub.2003.10.001

38

I Miyajima, M Nakafuku, N Nakayama, C Brenner, A Miyajima, K Kaibuchi, et al. GPA1, a haploid-specific essential gene, encodes a yeast homolog of mammalian G protein which may be involved in mating factor signal transduction. Cell. 1987;50: , pp.1011–1019. , doi: 10.1016/0092-8674(87)90167-x

39

D Bourgarel, C-C Nguyen, M Bolotin-Fukuhara. . HAP4, the glucose-repressed regulated subunit of the HAP transcriptional complex involved in the fermentation-respiration shift, has a functional homologue in the respiratory yeast Kluyveromyces lactis. Mol Microbiol. 1999;31: , pp.1205–1215. , doi: 10.1046/j.1365-2958.1999.01263.x

40

L Zhang, A Hach. . Molecular mechanism of heme signaling in yeast: the transcriptional activator Hap1 serves as the key mediator. Cell Mol Life Sci. 1999;56: , pp.415–426. , doi: 10.1007/s000180050442

41

F Creusot, J Verdière, M Gaisne, PP Slonimski. . CYP1 (HAP1) regulator of oxygen-dependent gene expression in yeast.J Mol Biol. 1988;204: , pp.263–276. , doi: 10.1016/0022-2836(88)90574-8

42

S Sharma, J-L Langhendries, P Watzinger, P Kötter, K-D Entian, DLJ Lafontaine. . Yeast Kre33 and human NAT10 are conserved 18S rRNA cytosine acetyltransferases that modify tRNAs assisted by the adaptor Tan1/THUMPD1. Nucleic Acids Res. Oxford University Press; 2015;43: , pp.2242–58. , doi: 10.1093/nar/gkv075

43

RB Wickner. . MKT1, a nonessential Saccharomyces cerevisiae gene with a temperature-dependent effect on replication of M2 double-stranded RNA. J Bacteriol. 1987;169: , pp.4941–4945. , doi: 10.1128/jb.169.11.4941-4945.1987

44

K Tanaka, BK Lin, DR Wood, F Tamanoi. . IRA2, an upstream negative regulator of RAS in yeast, is a RAS GTPase-activating protein. Proc Natl Acad Sci. 1991;88: , pp.468–472. , doi: 10.1073/pnas.88.2.468

45

FW Albert, JS Bloom, J Siegel, L Day, L Kruglyak. . Genetics of trans-regulatory variation in gene expression. Elife. 2018;7: , pp.e35471, doi: 10.7554/eLife.35471

46

EN Smith, L Kruglyak. . Gene–Environment Interaction in Yeast Gene Expression. T Mackay, editor. PLoS Biol. 2008;6: , pp.e83, doi: 10.1371/journal.pbio.0060083

47

JA Lewis, AT Broman, J Will, AP Gasch. . Genetic architecture of ethanol-responsive transcriptome variation in Saccharomyces cerevisiae strains. Genetics. Genetics Society of America; 2014;198: , pp.369–82. , doi: 10.1534/genetics.114.167429

48

EA Boyle, YI Li, JK Pritchard. . An Expanded View of Complex Traits: From Polygenic to Omnigenic. Cell. 2017 pp. , pp.1177–1186. , doi: 10.1016/j.cell.2017.05.038

49

TA Manolio, FS Collins, NJ Cox, DB Goldstein, LA Hindorff, DJ Hunter, et al. Finding the missing heritability of complex diseases. Nature. 2009;461: , pp.747–753. , doi: 10.1038/nature08494

50

Y Zan, Z Sheng, M Lillie, L Rönnegård, CF Honaker, PB Siegel, et al. Artificial Selection Response due to Polygenic Adaptation from a Multilocus, Multiallelic Genetic Architecture. Mol Biol Evol. R Found. Stat. Comput, Vienna; 2017;2: , pp.7–10. , doi: 10.1093/molbev/msx194

51

Z Sheng, ME Pettersson, CF Honaker, PB Siegel, Ö Carlborg. . Standing genetic variation as a major contributor to adaptation in the Virginia chicken lines selection experiment. Genome Biol. 2015;16: , pp.219, doi: 10.1186/s13059-015-0785-z

52

A Zeileis, T Hothorn. . Diagnostic checking in regression relationships.R News. 2002;2: , pp.7–10.

53

R Core Team. R Core Team, 2015 R: A Language and Environment for Statistical Computing. R Found. Stat. ComputVienna Austria URL: https://www.R-project.org/. R Foundation for Statistical Computing Vienna Austria. 2015. ISBN 3-900051-07-0

54

G YU, Y CHEN, Y GUO. . Design of integrated system for heterogeneous network query terminal. J Comput Appl. 2009;29: , pp.2191–2193. , doi: 10.3724/SP.J.1087.2009.02191

17 Feb 2020

* Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out. *

Dear Dr zan,

Thank you very much for submitting your Research Article entitled 'Dynamic genetic architecture of yeast growth response to environmental perturbation shed light on origin of hidden genetic variation' to PLOS Genetics. Your manuscript was fully evaluated at the editorial level and by independent peer reviewers. The reviewers appreciated the attention to an important topic but identified some aspects of the manuscript that should be improved.

All three reviewers are highly qualified to evaluate the manuscript.  Nonetheless, whereas Reviewers #1 and #3 were quite positive, Reviewer #2 was significantly more skeptical.  Reviewer #2’s primary concern is that growth was measured by colony radius which is a phenotype that may have multiple confounding inputs.  This is a reasonable question.  As an aside, the editors noted that the tone of these comments was at times overly-aggressive, but that tone did not influence our assessment of the underlying scientific/technical issues. Can you use an independent measurement to validate the robustness of colony radius as a measure of growth in your experiments?  Barring that, I think it would be important to explicitly discuss this caveat when discussing the conclusions of the manuscript.

We therefore ask you to modify the manuscript according to the review recommendations before we can consider your manuscript for acceptance. Your revisions should address the specific points made by each reviewer.

1) Provide a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript.

2) Upload a Striking Image with a corresponding caption to accompany your manuscript if one is available (either a new image or an existing one from within your manuscript). If this image is judged to be suitable, it may be featured on our website. Images should ideally be high resolution, eye-catching, single panel square images. For examples, please browse our archive. If your image is from someone other than yourself, please ensure that the artist has read and agreed to the terms and conditions of the Creative Commons Attribution License. Note: we cannot publish copyrighted images.

We hope to receive your revised manuscript within the next 30 days. If you anticipate any delay in its return, we would ask you to let us know the expected resubmission date by email to plosgenetics@plos.org.

If present, accompanying reviewer attachments should be included with this email; please notify the journal office if any appear to be missing. They will also be available for download from the link below. You can use this link to log into the system when you are ready to submit a revised version, having first consulted our Submission Checklist.

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org.

Please be aware that our data availability policy requires that all numerical data underlying graphs or summary statistics are included with the submission, and you will need to provide this upon resubmission if not already present. In addition, we do not permit the inclusion of phrases such as "data not shown" or "unpublished results" in manuscripts. All points should be backed up by data provided with the submission.

PLOS has incorporated Similarity Check, powered by iThenticate, into its journal-wide submission system in order to screen submitted content for originality before publication. Each PLOS journal undertakes screening on a proportion of submitted articles. You will be contacted if needed following the screening process.

To resubmit, you will need to go to the link below and 'Revise Submission' in the 'Submissions Needing Revision' folder.

Please let us know if you have any questions while making these revisions.

Yours sincerely,

Gregory P. Copenhaver

Editor-in-Chief

PLOS Genetics

Reviewer's Responses to Questions

Reviewer #1: In this manuscript, the authors reanalyze a large existing dataset to work to better understand the potential role of epistasis in influence quantitative genetic variation in growth across a number of environments in yeast. This contributes to the growing level of data showing that GxGxE has an underappreciated contribution to quantitative traits. I only have a few suggestions.

In Figure 2E, do the authors have an estimate on how the additive variance explained responds to decreasing the number of loci? I ask because with 130 loci and the number of progeny utilized, the loci may have lost their independence and the fraction of additive variance may have asymptoted with a smaller collection of loci. Essentially, using 130 loci may be the equivalent of bar coding each individual and thus the additive estimate is functioning as a broad sense estimate at this level. Some discussion on this possibility would help the reader who is disinclined from epistasis to get past a high additive explanatory potential.

Is it that the environment is rewiring the network or altering how the output of the network is displayed? Rewiring implies (not inherently the authors intended implication) that the molecular connections are changing. I might suggest a different non-molecular wording.

Am I correct in interpreting Figure 5A as implying that the idea of rare alleles tending to have large effects needs to be tempered to say that they might also tend to be more environmentally and epistatically dependent? If that is correct, is there a reason to at best only provide veiled allusions to this outcome?

As a personal thought, I tend to prefer cryptic genetic variance as crypsis can be a passive process while hidden implies effort/mechanism to hide. I know that the community has not settled on a nomenclature so I won’t attempt to enforce one.

Line 67, I believe the authors mean E. coli, S. cerevisiae and A. thaliana as at least one of the ensuing manuscripts is in Arabidopsis. And I do believe that the plant citation works to investigate some of the quant gen parameters discussed in line 91-94. Albeit in far narrower GxGxE collection.

If I’m reading correctly, all the multi-locus epistasis citations are in yeast. There are some papers on higher order epistasis in Plants and Drosophila that would help to move the conclusions beyond yeast.

In Line 420, I’m struggling with this equation Vtotal= H2 *Vp = H2. Is this correct as it seems odd to say broad sense heritability times Vp is equal to broad sense heritability. What am I missing?

Reviewer #2: This ms. aims to examine epistatic (GxG) and genotype-by-environment (GxE) interactions using a previously published data set (Bloom et al. 2015) consisting of large mapping population of segregants in the budding yeast S. cerevisiae whose growth was measured under a large number of environmental conditions and stressors.

The novel angle the authors employ, relative to two earlier studies using the same dataset (Bloom et al., Forsberg et al. 2017), is to treat growth as a single complex trait, rather than distinct traits for each environment, and use this single trait to compare "reorganization" of epistatic interactions across environments.

Unfortunately, while this is a clever idea in the abstract, the biological reality of endpoint growth measures (the trait measured in the original Bloom et al. study) makes this highly questionable in practice, and calls into question whether any useful biological insights are likely to emerge from such an analysis. Bloom and co-authors simply measured colony radii for each segregants after 48 hrs of growth on various agar plates. Colony radius reflects a mix of various cell biological and physiological traits -- division rate, cell size and cell shape, cell-cell interactions, etc. While various measures of growth on agar plates is often the microbiologists primary screening tool, no careful microbial geneticist would presume a priori that growth under neomycin stress is comparable to growth in xylose (to take as an example two of the more physiologically distinct conditions in the Bloom et al. data). While I don't doubt that some of the subsets of environments in the data affect underlying signaling and regulatory networks in similar ways, and hence would in some sense be comparable traits, this seems like a hypothesis to be tested not taken a priori to be true.

The difficulty of biological interpretability of the analyses is apparent from the discussion section -- little biological insight emerges about genetic networks in yeast, nor is there concrete new understanding the reader can take away about the genetic features that may shape GxGxE interactions in yeast or other organisms.

Reviewer #3: In this manuscript, the authors investigated and evaluated the role of G-by-G-by-E interaction on the complex traits. To explore the role of environment influencing epistatis that can lead to the expression of cryptic variation, the authors reanalyzed a dataset of 4,390 yeast genotyped segregants, which were phenotyped in 20 different conditions. As previously shown, they found that genetic interaction networks are contributing to complex traits. But more interesting, they highlighted and illustrated the importance of dynamics in epistatic network, genetic effects of individual alleles and genetic variance expressed across environments.

Overall, the manuscript is very interesting and bring a new insights into the mechanisms involved in the variation of complex traits.

I only have a couple of points that need to be addressed:

The authors use one cross between two given isolates, namely BY and RM. It is always difficult to know if the obtained results are not specific to the studied cross. This is something that should be discussed in the manuscript.

As the phenotypes are pre-normalized growth measurements (against growth in a control medium), the authors do not have a direct estimation of G-by-E. Did they try to run the same analysis on the non-normalized dataset? What are the results?

In the author summary, the word ‘gene’ is misused –

e.g. ‘individual with the same gene might have distinctive phenotypes’.

The discussion is very long and wordy. It could be shortened.

**********

Have all data underlying the figures and results presented in the manuscript been provided?

Large-scale datasets should be made available via a public repository as described in the PLOS Geneticsdata availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

1 Mar 2020

13 Apr 2020

* Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out. *

Dear Dr zan,

Thank you very much for submitting your Research Article entitled 'Dynamic genetic architecture of yeast response to environmental perturbation shed light on origin of cryptic genetic variation' to PLOS Genetics. Your manuscript was fully evaluated at the editorial level and by two of the original three independent peer reviewers. The reviewers appreciated the attention to an important topic but identified some aspects of the manuscript that should be improved.

The reviewers are split in their opinion.  Reviewer #2 still thinks that treating growth under all conditions as a single phenotype misses critical underlying complexity and in doing so renders the analysis flawed.  Reviewer #1 is less concerned by this limitation and acknowledges that you aren't trying to explain all of what is happening but rather you're trying to use a single measurable trait to study complex genetics in a way that it not well represented in the literature. It is important to note that both reviewers are exceptionally qualified experts in the field, so I can appreciate both of their perspectives. As a way of threading the needle I think it will be critical to fully acknowledge the limitations described by Reviewer #2 in the text of the article and explain, at least by fully discussing if not by revising the analysis, how the system would be structured if individual growth components were accounted for.

We therefore ask you to modify the manuscript according to the review recommendations before we can consider your manuscript for acceptance. Your revisions should address the specific points made by each reviewer.

1) Provide a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript.

2) Upload a Striking Image with a corresponding caption to accompany your manuscript if one is available (either a new image or an existing one from within your manuscript). If this image is judged to be suitable, it may be featured on our website. Images should ideally be high resolution, eye-catching, single panel square images. For examples, please browse our archive. If your image is from someone other than yourself, please ensure that the artist has read and agreed to the terms and conditions of the Creative Commons Attribution License. Note: we cannot publish copyrighted images.

We hope to receive your revised manuscript within the next 30 days. If you anticipate any delay in its return, we would ask you to let us know the expected resubmission date by email to plosgenetics@plos.org.

If present, accompanying reviewer attachments should be included with this email; please notify the journal office if any appear to be missing. They will also be available for download from the link below. You can use this link to log into the system when you are ready to submit a revised version, having first consulted our Submission Checklist.

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org.

Please be aware that our data availability policy requires that all numerical data underlying graphs or summary statistics are included with the submission, and you will need to provide this upon resubmission if not already present. In addition, we do not permit the inclusion of phrases such as "data not shown" or "unpublished results" in manuscripts. All points should be backed up by data provided with the submission.

PLOS has incorporated Similarity Check, powered by iThenticate, into its journal-wide submission system in order to screen submitted content for originality before publication. Each PLOS journal undertakes screening on a proportion of submitted articles. You will be contacted if needed following the screening process.

To resubmit, you will need to go to the link below and 'Revise Submission' in the 'Submissions Needing Revision' folder.

Please let us know if you have any questions while making these revisions.

Yours sincerely,

Gregory P. Copenhaver

Editor-in-Chief

PLOS Genetics

Reviewer's Responses to Questions

Reviewer #1: The authors have responded to and clarified my concerns from the previous version.

I have one suggestion, would it be possible to include the additivity and barcoding/independence analysis as a supplemental section. This analysis will be very helpful for the community when considering population size and locus independence when creating future populations or analyzing existing populations. I personally had not expected the role of environment in structuring the asymptote. This would be very useful for citations and guiding grant proposals.

Reviewer #2: Please see review in attachment.

**********

Have all data underlying the figures and results presented in the manuscript been provided?

Large-scale datasets should be made available via a public repository as described in the PLOS Geneticsdata availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.

Reviewer #1: Yes

Reviewer #2: None

**********

PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Reviewer #1: No

Reviewer #2: No

23 Apr 2020

27 Apr 2020

Dear Dr zan,

We are pleased to inform you that your manuscript entitled "Dynamic genetic architecture of yeast response to environmental perturbation shed light on origin of cryptic genetic variation" has been editorially accepted for publication in PLOS Genetics. Congratulations!

Before your submission can be formally accepted and sent to production you will need to complete our formatting changes, which you will receive in a follow up email. Please be aware that it may take several days for you to receive this email; during this time no action is required by you. Please note: the accept date on your published article will reflect the date of this provisional accept, but your manuscript will not be scheduled for publication until the required changes have been made.

Once your paper is formally accepted, an uncorrected proof of your manuscript will be published online ahead of the final version, unless you’ve already opted out via the online submission form. If, for any reason, you do not want an earlier version of your manuscript published online or are unsure if you have already indicated as such, please let the journal staff know immediately at plosgenetics@plos.org.

In the meantime, please log into Editorial Manager at https://www.editorialmanager.com/pgenetics/, click the "Update My Information" link at the top of the page, and update your user information to ensure an efficient production and billing process. Note that PLOS requires an ORCID iD for all corresponding authors. Therefore, please ensure that you have an ORCID iD and that it is validated in Editorial Manager. To do this, go to ‘Update my Information’ (in the upper left-hand corner of the main menu), and click on the Fetch/Validate link next to the ORCID field.  This will take you to the ORCID site and allow you to create a new iD or authenticate a pre-existing iD in Editorial Manager.

If you have a press-related query, or would like to know about one way to make your underlying data available (as you will be aware, this is required for publication), please see the end of this email. If your institution or institutions have a press office, please notify them about your upcoming article at this point, to enable them to help maximise its impact. Inform journal staff as soon as possible if you are preparing a press release for your article and need a publication date.

Thank you again for supporting open-access publishing; we are looking forward to publishing your work in PLOS Genetics!

Yours sincerely,

Gregory P. Copenhaver

Editor-in-Chief

PLOS Genetics

www.plosgenetics.org

----------------------------------------------------

Comments from the reviewers (if applicable):

----------------------------------------------------

Data Deposition

If you have submitted a Research Article or Front Matter that has associated data that are not suitable for deposition in a subject-specific public repository (such as GenBank or ArrayExpress), one way to make that data available is to deposit it in the Dryad Digital Repository. As you may recall, we ask all authors to agree to make data available; this is one way to achieve that. A full list of recommended repositories can be found on our website.

The following link will take you to the Dryad record for your article, so you won't have to re‐enter its bibliographic information, and can upload your files directly:

Additionally, please be aware that our data availability policy requires that all numerical data underlying display items are included with the submission, and you will need to provide this before we can formally accept your manuscript, if not already present.

----------------------------------------------------

Press Queries

1 May 2020

PGENETICS-D-19-02048R2

Dynamic genetic architecture of yeast response to environmental perturbation shed light on origin of cryptic genetic variation

Dear Dr Zan,

We are pleased to inform you that your manuscript entitled "Dynamic genetic architecture of yeast response to environmental perturbation shed light on origin of cryptic genetic variation" has been formally accepted for publication in PLOS Genetics! Your manuscript is now with our production department and you will be notified of the publication date in due course.

The corresponding author will soon be receiving a typeset proof for review, to ensure errors have not been introduced during production. Please review the PDF proof of your manuscript carefully, as this is the last chance to correct any errors. Please note that major changes, or those which affect the scientific understanding of the work, will likely cause delays to the publication date of your manuscript.

Soon after your final files are uploaded, unless you have opted out or your manuscript is a front-matter piece, the early version of your manuscript will be published online. The date of the early version will be your article's publication date. The final article will be published to the same URL, and all versions of the paper will be accessible to readers.

Thank you again for supporting PLOS Genetics and open-access publishing. We are looking forward to publishing your work!

With kind regards,

Matt Lyles

PLOS Genetics

On behalf of:

The PLOS Genetics Team

Carlyle House, Carlyle Road, Cambridge CB4 3DN | United Kingdom

plosgenetics@plos.org | +44 (0) 1223-442823