Yeast growth responses to environmental perturbations are associated with rewiring of large epistatic networks

The phenotypic effects of genetic polymorphisms often depend on the genetic and environmental context. Here, we explore how polymorphic loci in large interaction networks contribute to complex trait variation and in particular how genetic effects and network topologies are influenced by environmental perturbations. This was done by reanalysing a dataset of >4,000 haploid yeast segregants grown on 20 different media. In total, 130 epistatic loci were associated with growth in at least one environment. The across-environment interaction network defined by these loci explained 69 - 100% of the narrow sense heritability in the individual environments. Environmental changes often resulted in network hubs being connected and disconnected from their interactors, leading to changes in additive effects of individual loci, epistatic effects of multi-locus interactions and the total level of genetic variance in growth. The largest variation in genetic effects across environments was found for epistatic loci that were highly connected network hubs in some environments but not in others. In environments where loci were highly connected, the segregating alleles epistatically suppressed or released genetic effects from their interactors. In environments where they were lowly connected, the same alleles made small or no contributions to growth. Hub-loci thus often serve as modulators, influencing the phenotypic effects of environmentally specific sets of interacting effector genes, rather than being effectors themselves. These findings illustrate the importance of the interplay between large genetic interactions networks and the living environment, both for individual phenotypes and population level metrics of genetic variation.

individual loci, epistatic effects of multi-locus interactions and the total level of 23 genetic variance in growth. The largest variation in genetic effects across 24 environments was found for epistatic loci that were highly connected network hubs in 25 some environments but not in others. In environments where loci were highly 26 connected, the segregating alleles epistatically suppressed or released genetic effects 27 from their interactors. In environments where they were lowly connected, the same 28 alleles made small or no contributions to growth. Hub-loci thus often serve as 29 modulators, influencing the phenotypic effects of environmentally specific sets of 30 interacting effector genes, rather than being effectors themselves. These findings 31 illustrate the importance of the interplay between large genetic interactions networks 32 and the living environment, both for individual phenotypes and population level 33 metrics of genetic variation.

environments: effects across all environments 239
To generalize the findings from the three-environment example above, the 240 connectivity and contribution by all networks to growth across all 20 environments 241 were analysed. The results are described in detail in the sections below. 242

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Rewiring of high-order gene interaction networks in response to environmental 244 changes is common for highly connected loci In total, 13 loci with more than 4 epistatic interactors were detected in at least one of 246 the 20 environments. The networks defined by these 13 hub loci and their interactors 247 included 70% (91 of 130) of the loci in the complete network ( Figure 2A; Figure S3). 248 The connectivity of these 13 networks was highly dynamic across the 20 249 environments, with hubs being fully connected in some environments but completely 250 disconnected in others ( Figure S4A; Figure 4A). Although epistatic network 251 connectivity changed across environments, it was common that some of the Significant additive effects on growth in at least one environment were detected for 284 311 loci in the genome. Although not every locus had significant effects on growth in 285 every environment, these loci did as a group contribute significantly to growth in 286 most environments (Materials and Methods; Table S1). The effects were generally 287 stronger in one or a few of the environments ( Figure S5). For example, more than half 288 of the loci were unique to one environment and only 9 loci were associated with 289 growth in more than 10 environments. QTL by environment interactions were thus 290 abundant with 98% (307) loci displaying statistically significant QTL by environment 291 interaction after multiple testing corrections ( Figure 5; Table S2).

Variation in the non-additive genetic variance contributed by loci across 20 322 environments is correlated with the rewiring of the epistatic network 323
As reported earlier 21 , there were considerable variation in both the phenotypic and 324 genetic variation in growth ( Figure S6A), as well as broad sense (0.11 < H 2 < 0.88; 325 median 0.64) and narrow sense (0.09 < h 2 < 0.70; median 0.43) heritability between environments ( Figure S6B). The contributions from the epistatic network rewiring to 327 the differences in the non-additive genetic variances between the environments were 328 evaluated across all traits and loci. A significant positive correlation (P-value = 5.6 x 329 10 -31 ; regression; Figure 6) was detected between the differences in the levels of non- one complex trait -colony size -had been measured across many environments. In 355 this way, we could reveal that the gene-interaction networks contributing to growth, 356 and their associated high dimensional genotype to phenotype maps, were highly 357 dynamic across growth environments. Further, we also illustrated the importance of 358 these dynamics for the differences in trait expression of individual segregants, and 359 genetic variance expressed in the population, across the evaluated environments. 360 361

The effects of genotype-by-environment interactions on yeast growth 362
The studied dataset did not allow direct estimation of the contribution by systematic 363 environmental (i.e. growth medium) effects on the phenotypes as the available growth 364 measurements were pre-normalised against growth in a control medium 21 . However, 365 estimates of the contributions by direct genetic (G) and genotype-by-environment (G-366 by-E) effects showed that direct genetic effects only contributed about 1/3 as much to 367 the variance in growth compared to contributions by G-by-E. Consistent with the 368 large contributions from G-by-E, we found large differences in the genetic 369 architecture of growth (defined as associated loci and their genetic effects) across 370 environments. The wiring into interaction networks, as well as marginal additive 371 effects, of many growth loci were highly environmentally specific. Likely as a 372 consequence of this, the phenotype changed across environments with the rewiring of 373 the genetic growth network. The same polymorphisms thus contributed to growth in 374 different ways across the environments, regardless of whether their effects were 375 quantified via marginal additive effects or variance explained by the complete 376 network. In the following sections we discuss these findings in more detail as well as 377 their implications for the mapping, and understanding the evolution of complex traits.

Connections to available knowledge 442
Our reanalyses of experimental data show that G-by-G-by-E interactions were 443 generally important for the variation in growth across environments. This extends and connects earlier results from numerous studies in multiple species illustrating the 445 importance of G-by-G and G-by-E for complex trait variation 1-7 . For example, many 446 yeast genes are known to be nonessential in one genetic background, but essential in 447 another, with the essential genes often being highly connected hubs in interaction 448

Potential implications for modelling of quantitative traits 489
The studies of this yeast population here, and earlier 1 , illustrate that the most highly 490 connected loci in the interaction networks (the hubs) often serve as modulators. They 491 have little, or no, individual effects but rather influence the phenotype by releasing the 492 effects of environmentally specific sets of interacting effector genes. This is an 493 opposite scenario to that assumed in the recently proposed Omnigenetic model for quantitative traits 39 , where it is postulated that the highly connected loci in the 495 networks are effectors that are modulated by many other genes. One consequence of 496 this is that results from association studies where loci are detected based on their 497 marginal additive effects need to be interpreted with caution. This is because it might 498 be incorrect to assume that such effects suggest that the locus has a direct (effector) 499 influence on the trait or disease, while it in fact could be entirely a composite effect of 500 contributions by multiple other effector loci. Another potential modelling challenge 501 highlighted here is the potentially large influence by epistasis by environment 502 interactions. We find that they might not only influence the variation in quantitative 503 traits by modulating the effects of individual genes, but also in defining which sets of 504 interactors that are under genetic control by capacitor loci. Further theoretical, and 505 empirical, work is needed to explore the potential implications of these findings for 506 modelling of quantitative trait variation from molecular data in, for example, genome-507 wide association studies and studies on the basis for, maintenance of and utilization of 508 genetic variation in short-and long-term adaptations to natural and artificial selection.

Estimating the contributions by genotype and genotype-by-environment 533 interactions to the phenotypic variance 534
The phenotypic variance was partitioned into contributions from genotype (G), 535 genotype-by-environment (G-by-E) and residual (environmental; E) effects by fitting 536 model (1) to the data: 537 y !" is the mean growth for the replicates of individual i in environment j (j = 1..n; n is 539 the number of growth conditions); id i is the individual segregant (genotype) coded as 540 a factor and ! ! is a dummy variable representing the growth condition (environment). 541 !" ! *! ! is the interaction (G-by-E) between a particular segregant (genotype) and 542 growth condition (environment). Since the available data was normalised against a 543 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 545 estimated by their respective sum of squares (Sum of Square for id is calculated as 546 (!" ! − !") ! ! 2 and Sum of Square for the interaction id * ! is calculated as

Defining a set of independently associated additive growth loci 550
A set of across-environment growth loci was defined. First, QTLs detected in the 551 earlier environment-separate analyses with peak associations within 20kb and in 552 pairwise r 2 > 0.9 were selected. Second, all the loci selected in step 1 were subjected 553 to a multi-locus polygenic association analysis 40,41 to identify a final set of 554 statistically independent loci (FDR < 0.05) with additive effects on growth in each 555 tested environment 21 . Alternative definitions ranging from physical distance < 20 kb 556 and r 2 > 0.6 to physical distance < 10 kb and r 2 > 0.9 were evaluated and found to 557 result in very similar results in practice (result not shown). 558 559

Across environment evaluation of the additive growth loci 560
Several growth loci in the final set defined above only had significant individual 561 associations in one growth environment. To test if they, as a group, contributed to the 562 polygenic inheritance of growth also in other environments we compared the fit of the 563 following models to the data (models 2 and 3) using a likelihood ratio test. 564 Here, ! is a vector of the average growth of each segregant (genotype) in a particular 567 environment and e is the norsmally distributed residual. The joint contributions by the 568 individually significant/non-significant loci in a specific environment was modelled in ! ! ! ! /! ! ! ! , respectively. X 1 includes a column vector of 1's for the population mean 570 and column vectors with the genotype of each significantly associated SNP in the 571 environment with the two homozygous genotypes coded as 0/2, respectively. ! ! 572 includes column vectors with genotypes of all loci in the set defined above that was 573 not individually significant in the tested environment. ! ! / ! ! are vectors including the 574 estimated additive effects for the two sets of loci. A likelihood ratio test was used to 575 compare the fit of the two models using the lrtest function in R package lmtest 42 . 576 577

Detect individual loci involved in genotype by environment interactions 578
All growth loci defined in the polygenic analysis were evaluated for genotype by 579 environment interactions. This by fitting the following two models to the data: 580 In both models, ! !"# is the growth of replicate k for segregant i in environment j (j = 583 1..20 environments; k = 1..n ij ; n ij is the number of replicates for individual i in 584 environment j); ! ! is the indicator regression variable for the genotype of QTL x 585 coded as 0 and 2 for the homozygous minor and major alleles; b x are the 586 corresponding estimated additive effects; u is the population mean and ! ! is the effect 587 of environment j (j = 1…20) on growth. Model 5 also includes an interaction term 588 E ! a ! B ! between one of the QTL and the environment. Model 5 was fitted for each 589 QTL one at a time to test for its interaction with the 20 growth environments. The 590 significance of each QTL by environment interaction was evaluated using a likelihood 591 ratio test between models 4 and 5. Polygenicity was accounted for by the 592 simultaneous fitting of all mapped loci in the two models. The analyses were 593 performed using custom R scripts 43 . 594

Estimating the additive effects of QTL in different growth environments 596
A linear model (model 6) was used to estimate the additive effects of all the additive 597 loci selected in the polygenic analysis in each tested environment. 598 Here, ! is the average growth of the replicates for each segregant (genotype) in each 600

Evaluation of the G-by-G-by-E interaction for a six-locus interaction network 627
The effects of a six locus interaction network, originally detected and explored for 628 growth in IAA containing growth medium in Forsberg et al 1 , were here evaluated 629 across multiple environments. This analysis was performed to explore the association 630 between the rewiring of the epistatic genetic network and its contribution to growth in 631 the different environments. To quantify the effects of G-by-G-by-E interactions, 632 models 4 and 5 were fitted to the data with a ! (x = n =1) used as the indicator variable 633 for each of the 64-genotype classes defined by the genotypes at the 6 loci. All other 634 parameters, and the likelihood ratio test used to obtain the P-values for comparing the 635 models, were the same as described above.   X-axis is the number of non-compacitated alleles across 13 hubs detected in our study, and y-axis is the mean growth rank obtained by first rank the growth measurements across 20 enviroemtns and then taking the artihma tical mean.