Dissecting the eQTL Micro-Architecture in Caenorhabditis elegans

The study of expression quantitative trait loci (eQTL) using natural variation in inbred populations has yielded detailed information about the transcriptional regulation of complex traits. Studies on eQTL using recombinant inbred lines (RILs) led to insights on cis and trans regulatory loci of transcript abundance. However, determining the underlying causal polymorphic genes or variants is difficult, but ultimately essential for the understanding of regulatory networks of complex traits. This requires insight into whether associated loci are single eQTL or a combination of closely linked eQTL, and how this QTL micro-architecture depends on the environment. We addressed these questions by testing for independent replication of previously mapped eQTL in Caenorhabditis elegans using new data from introgression lines (ILs). Both populations indicate that the overall heritability of gene expression, number, and position of eQTL differed among environments. Across environments we were able to replicate 70% of the cis- and 40% of the trans-eQTL using the ILs. Testing eight different simulation models, we suggest that additive effects explain up to 60–93% of RIL/IL heritability for all three environments. Closely linked eQTL explained up to 40% of RIL/IL heritability in the control environment whereas only 7% in the heat-stress and recovery environments. In conclusion, we show that reproducibility of eQTL was higher for cis vs. trans eQTL and that the environment affects the eQTL micro-architecture.


INTRODUCTION
The genetic architecture of quantitative traits in genetically segregated populations such as recombinant inbred lines (RILs) differs within and across species and strongly depends on the environment and type of trait (Fournier and Schacherer, 2017). In some cases, quantitative traits are (nearly) monogenic and display Mendelian characteristics. For instance the Kallman syndrome in humans is caused by a knockout of FGFR1 (which encodes fibroblast growth factor receptor 1) (Muenke et al., 1994), industrial melanism in British peppered moths is caused by a single gene mutation (van't Hof et al., 2011), and natural variation in the npr-1 gene in the nematode Caenorhabditis elegans is a major determinant of multiple life-history traits (Andersen et al., 2014;Sterken et al., 2015). These monogenic traits are relatively easy to detect but rather exceptions than the rule. Most quantitative traits display a complex polygenic genetic architecture, regulated by multiple QTLs, where each locus explains a proportion of the trait variation .
Studying quantitative genetics of the transcriptome has proven useful in understanding the architecture of complex traits. The transcriptional architecture can be defined as polymorphic regulators affecting the expression of genes throughout the genome. These polymorphic regulators can affect gene expression in direct ways [e.g., kinase cascades (Terpstra et al., 2010)], or indirectly [e.g., by affecting behavior (Andersen et al., 2014;Sterken et al., 2015)]. Expression quantitative trait loci (eQTL) can be measured reliably in a high-throughput fashion in many organisms like: yeast, Arabidopsis thaliana, tomato, maize, C. elegans, mice, and humans (Schadt et al., 2003;Brem and Kruglyak, 2005;Li et al., 2006;Keurentjes et al., 2007;Ranjan et al., 2016). The advantage of the eQTL-approach lies in the assessment of thousands of traits simultaneously for which the genetic architectures can be compared (Jansen and Nap, 2001;Gilad et al., 2008). First, the variance explained per underlying QTL will cover the whole range from essentially monogenic (Mendelian) to nearly undetectable. Second, correlating gene expression to loci can reveal the biological processes and phenotypes that lay downstream of (e)QTL (e.g., Jimenez-Gomez et al., 2010Terpstra et al., 2010;Andersen et al., 2014;Schmid et al., 2015;Sterken et al., 2017;Albert et al., 2018). In general, two types of eQTL can be defined: (i) trans-eQTL where a single locus affects the expression of many genes across the genome and (ii) cis-eQTL where the locus is located on or near the gene of which it affects the expression (Nica and Dermitzakis, 2013;Albert et al., 2018). Cis-eQTL can occur due to polymorphisms affecting the transcription of the gene under study, e.g., deletions or non-functional promotor regions. eQTL hotspots are loci that regulate a high abundance of transcripts. These hotspots are also called trans-bands. The occurrence of trans-bands was found to be specific for environmental conditions linked to genetic effects. Together, the cis-eQTL and trans-bands typically cover ∼75% of the mapped eQTL in any study (e.g., Snoek et al., 2017;Albert et al., 2018).
The detection of (e)QTL depends on many different factors like developmental stage, background mutations, and the ambient environment, to name a few (Li et al., 2006;Vinuela et al., 2010;Duveau and Felix, 2012;Snoek et al., 2012;Andersen et al., 2014;Francesconi and Lehner, 2014). Importantly, QTL detection is mainly determined by the number of genetically segregating RILs and the density and structure of the genetic marker map. Further characterization of QTLs often involves the identification of the underlying causal polymorphic genes in order to understand molecular mechanisms affecting complex traits and/or to facilitate breeding for selected traits. An important hallmark of QTL mapping has been the fine mapping and identification of polymorphic regulators or quantitative trait nucleotides (QTN) (Radwan and Babik, 2012;Rockman, 2012).
Fine mapping of causal variants requires determining if associated loci are single QTL or combinations of closely linked QTL, here coined the QTL micro-architecture, and how this micro-architecture depends on the environment. Apparent single QTL may be truly single QTL or a combination of closely linked QTL not segregating in the studied population. These are often hard to characterize because of a lack of resolution of the genetic map or shortage of a sufficient number of recombination events. Here, we set out to investigate the QTL micro-architecture of eQTL in the nematode C. elegans in a segregated population of RILs derived from a cross between wild-types Bristol N2 and CB4856 (Li et al., 2006;Thompson et al., 2015). Briefly, Bristol N2 and CB4856 wild types were allowed to mate after which the recombinant offspring were selfed (C. elegans is a hermaphrodite but males do occur and can be used for making crosses between strains). This yields homozygous RILs that were analyzed for their transcriptomes (Li et al., 2006). Subsequent association of polymorphic SNPs with transcriptional variation yielded eQTL. We use a set of previously detected eQTL and study their replication in a separate, independent, population of introgression lines (ILs) in this study (Doroszuk et al., 2009;Thompson et al., 2015;Snoek et al., 2017). Compared to the RILs, which are genetic mosaics of loci derived from both parents, ILs contain a single genomic segment of one parent in a genetic background of another parent. Typically, introgression lines are used to verify the existence of QTL, or to narrow down the location of a QTL in order to find the underlying causal polymorphism (e.g., see Gao et al., 2018). The RIL and IL populations are exposed to three environments: heatshock, recovery from heat-shock, and a control environment at a standard rearing temperature. We investigate three aspects of eQTL mapped in RILs: (i) we address how well eQTL are replicated in ILs, (ii) we test if the predicted numbers of eQTL agree with the observed number of differentially expressed genes in ILs, and (iii) we simulate QTL architectures explaining the relative heritability in RILs and ILs and match our data to these models. Finally, we show that the eQTL microarchitecture under ambient conditions mainly consists of closely linked eQTL.

Strains Used
The wild-type strains N2 and CB4856 were used and 57 introgression lines (ILs) with segments of CB4856 in an N2 genetic background (Doroszuk et al., 2009). Most of the ILs have been sequenced, and the genetic map was based on the sequenced genotypes (Thompson et al., 2015), a file with the strains and the map has been included in Supplementary Table 1. The data used for the recombinant inbred lines (RILs) is accessible in .

Nematode Culturing
The strains were cultured as described previously . In short, strains were kept in maintenance at 12 • C on 6-cm Nematode Growth Medium (NGM) Petri dishes seeded with the Escherichia coli strain OP50 as food source (Brenner, 1974). Before starting the experiment, single hermaphrodites of each strain in the L2 stage were sub-cultured in 12-wells plates and grown at 20 • C. The offspring was screened for the occurrence of males by microscopy and only populations consisting solely of hermaphrodites were transferred to 9-cm NGM Petri dishes containing E. coli OP50 and grown until the bacterial food was depleted.

Treatments for the Transcriptomic Experiment
The experiment described in our previous paper was repeated on the IL population and the parental strains . We started the experiment by transferring a starved population to a new 9-cm NGM Petri dish seeded with E. coli OP50. After 60 h at 20 • C, the populations consisting of egg-laying adults were bleached to obtain the eggs, which were transferred to a new 9-cm NGM Petri dish (Brenner, 1974). Around 46 h the developmental stage of the population was assessed by microscopy, verifying that the population consisted mainly of L4 larvae. Populations not consisting of L4 larvae were not used. The strains were exposed to one of three environments: (i) a control environment; grown for 48 h at 20 • C, (ii) a heat-stress environment; grown for 46 h at 20 • C and subsequently exposed to 35 • C for 2 h, and (iii) a recovery environment; grown for 46 h at 20 • C, exposed to 35 • C for 2 h, and thereafter returned to 20 • C for 2 h. Directly after the treatment the animals were washed off the Petri dish using M9 buffer and collected in a 1.5 mL Eppendorf tube, which was centrifuged and the pellet was flash frozen in liquid nitrogen.

RNA Isolation, cDNA Synthesis, Labeling and Hybridization
The procedure was followed as described before . The RNA of the samples was isolated using the RNEasy Micro Kit from Qiagen (Hilden, Germany) following the 'Purification of Total RNA from Animal and Human Tissues.' The lysis step was modified, pellets were lysed in 150 µl RLT buffer, 295 µl RNAse-free water, 800 µg/ml proteinase K and 1% β-mercaptoethanol, which was incubated at 55 • C and 1,000 rpm in a Thermomixer (Eppendorf, Hamburg, Germany) for 30 min, where after the manufacturer's protocol was followed.
Before starting cDNA synthesis, the quality and quantity of the RNA was measured by NanoDrop-1000 spectrophotometer (Thermo Scientific, Wilmington DE, United States). The integrity of the RNA was assessed by loading 3 µL per sample on a 1% agarose gel. Samples with good quality RNA were processed following the 'Two-Color Microarray-Based Gene Expression Analysis; Low Input Quick Amp Labeling' -protocol, version 6.0 from Agilent (Agilent Technologies, Santa Clara, CA, United States). The microarrays used were Agilent C. elegans (V2) Gene Expression Microarray 4 × 44K slides. After quality control of the RNA isolation, we obtained 56/57 ILs for the control and heat-stress environment, and 55/57 ILs for the recovery environment. The parental strains were ran in four replicates, except for the CB4856 recovery experiment, which was ran in five replicates. For the parental strain N2: four control samples, four heat stress samples and three recovery samples passed quality control. For the parental strain CB4856: three control samples, three heat stress samples and five recovery samples passed quality control.

Array Scanning, Data Extraction, and Normalization
After washing, the microarrays were scanned using an Agilent High Resolution C Scanner following the recommended settings. For data extraction, Agilent Feature Extraction Software (version 10.7.1.1) was used, following manufacturer's guidelines. The extracted data was normalized together with the previously published RIL data  using the limma package in "R" (version 3.4.2, x64) (Ritchie et al., 2015). As recommended, the data was not background corrected before normalization (Zahurak et al., 2007), the within-array normalization used the 'Loess' method and between-array normalization used the Quantile method (Smyth and Speed, 2003).

eQTL Data
The eQTL data from the RILs were obtained from a previous publication  and can be explored at www.bioinformatics.nl/wormqtl2 (Snoek et al., 2020). In short, previously eQTL were mapped using a single marker model, which was conducted separately for each environment. The threshold for each of the three environments was set at −log 10 (p) > 3.9 (false discovery rate, FDR = 0.05) (see Snoek et al., 2017 for details). The cis-eQTL were defined as the gene being inside a 1 Mb window of the QTL peak or within the confidence interval of the QTL peak. The confidence interval was defined as a 1.5 drop in LOD-score from the peak.

Data Transformation
The expression data was transformed to a z-score based on the standard deviation and mean of the N2-replicates per environment, using where Z N2 is the Z-score of spot i (1, 2, . . ., 45220) of strain j (one of the RILs or ILs) and I is the normalized intensity. The µ is the mean of the intensity over the N2 strains for spot i and the σ is the standard deviation over the N2 strains for spot i. This transformation shows the effect of the CB4856 introgressions in the ILs. It should be noted that these values cannot be directly interpreted as significances.
Additionally, the expression data was transformed to a z-score based on the standard deviation and mean of the CB4856replicates per environment, using where Z CB4856 is the Z-score of spot i (1, 2,. . ., 45220) of strain j (one of the RILs or ILs) and I is the normalized intensity. The µ is the mean of the intensity over the CB4856 strains for spot i and the σ is the standard deviation over the CB4856 strains for spot i. This transformation shows the effect of the genetic background in the ILs. As for Z N2 , it should be noted that these values cannot be directly interpreted as significances.
In order to compare IL gene expression with eQTL effect sizes, another data transformation was used, as there the number of standard deviations difference with the mean is less informative than the effect in log 2 -ratio with the mean. Hence, we transformed the data by where R N2 is the log 2 -ratio with the mean of spot i of strain j, I is the normalized intensity, and µ is the mean intensity over the N2 samples.

Confirmation of IL Genotype
Before mapping, we assured that samples were labeled correctly by applying a cis-eQTL based analysis of gene expression compared to the genetic map of the IL population, for details and explanation, see (Zych et al., 2017). Samples of three strains were removed (WN263, WN264, and WN284), as the strains did not match the genotypes in the IL population (Doroszuk et al., 2009;Thompson et al., 2015).

Confirmation of eQTL in Introgression Lines
The differential expression per IL was calculated based on the Z-score calculated using the N2 parental strains (Z N2 ). As each IL was measured once, we estimated the significance assuming a normal distribution based on the genetic-background parent. These significances were corrected for multiple testing by the Benjamini-Hochberg method, as applied by the p.adjust function in R (Benjamini and Hochberg, 1995). As a control and benchmark, the same procedure was applied to the individual RILs. The number of differentially expressed genes with an expected eQTL per CB4856 locus were counted for both the ILs and the RILs. These were expressed as a percentage of the expected eQTL in that locus (separately for cis-and trans-eQTL).
Another method of confirming eQTL is by correlating the differential expression per inbred line compared to the genetic background-parent (R N2 ) with the QTL effect. By calculating the Pearson correlation of R N2 with the eQTL effect per IL or RIL separately for the cis-and trans-eQTL, it can be assessed how well the overall QTL patterns were recapitulated per strain. These correlations were calculated using the cor function and the significances of correlation were calculated using the cor.test function.

Confirmation of Trans-bands Using ILs
In the eQTL study on the RILs , 19 transbands were identified (Supplementary Table 3). For each transband 2 to 6 ILs covering or flanking the locus were tested by correlating the trans-eQTL effect with the R N2 in the individual ILs. Significance was determined based on the correlation values in the N2 samples. Only if the correlation was stronger than the highest-correlating N2 sample, it was called as significant. Only significant positive correlations (effect direction matches the eQTL model) were scored as confirming the trans-band.
To determine the overall false-positive rate of this analysis, we determined the correlation of the ILs that were not in or near the trans-band region. These correlations were compared to the correlation value at which the trans-band was called confirmed. This resulted in an overall false positive rate of 0.11. It should be noted that this approach assumes that trans-bands stem from a single location and that these locations were accurately pinpointed in the RIL mapping. Hence, the derived threshold can be considered strict.

Expectation of Differential Expressed Genes Based on eQTL
First, the number of differentially expressed genes in each RIL and IL was calculated using the contrast with either of the ancestral strains, Z N2 and Z CB4856 , at an estimated significance of p < 1 × 10 −5 to apply a strickt threshold for declaring significance as the Z-scores were based on the variance of a few samples. Second, the expected number of differentially expressed genes was estimated for each RIL and IL based on the eQTL architecture in the RIL population [eQTL threshold, −log 10 (p) > 3.9; FDR = 0.05] . These values were normalized to the RIL population (the RIL population average was set to 1), to compare the relative number of differentially expressed genes expected versus observed in the ILs.

Differential Gene-Expression in N2 and CB4856
Differential gene expression between the two parental strains was independently calculated for each environment using a linear model where I is the normalized intensity of spot i (1, 2,. . ., 45220) of strain j (CB4956 or N2) is explained over genotype G and residual variance e. For the parental strain N2: n = 4 in control and heat-stress environments, n = 3 in recovery environment. For the parental strain CB4856: n = 3 in control and heat stress environments and n = 5 recovery in recovery environment. The obtained significances were corrected for multiple testing using the Benjamini-Hochberg method implemented in the p.adjust function in R (Benjamini and Hochberg, 1995). A threshold of FDR = 0.1 was taken as requirement for differential expression.

Estimation of Trait Genetic Architecture
Two approaches were taken to determine trait architectures using both RIL and IL population: heritability calculations and directly testing the amount of variance between both populations. Both approaches are based on the notion that the trait variance in the populations scale with trait complexity, where here σ 2 is the trait variance, proportional to the variance captured by n QTL (which can be multiple loci interacting; epistasis) and the measurement error. The contrast between the RIL and the IL population is that the QTL segregating in the IL population will affect fewer strains per QTL, whereas in the RIL population each QTL will segregate on average in 50% of the strains. In other words, the IL population shares most QTL effects because the genetic background is the same, whereas in the RIL population most QTL segregate. Heritability was calculated as in (Brem and Kruglyak, 2005;Keurentjes et al., 2007), where where H 2 was the heritability of spot i (1, 2,. . ., 45220) of population F (either RIL or IL) within one of the three environments. The σ 2 indicated the trait variance of spot i. Here the pooled trait variance of the parental lines N2 and CB4856 (denoted with P) was used as an estimate of the measurement error, which was subtracted from the trait variance of either the RIL or IL population. We used a permutation approach to determine the threshold for significant heritability (Brem and Kruglyak, 2005;Vinuela et al., 2012). Thereto, the gene expression values per spot per environment were randomized over the strains (RIL and IL separately, but together with the same parental lines) and recalculated the heritability as described above. This was repeated 1,000 times, and the 5% highest value for each spot was taken as the FDR = 0.05 threshold. Negative heritabilities (variance in the parental strains larger than in the RIL or IL populations were not taken along in the analysis). The second measure was by determining the ratio of trait variance between the IL and the RIL population. The assumption was that the variance contributed by random sources (σ 2 e ) was equal in both populations. Hence, this is a measure of relative heritability and was calculated as where R H was the heritability ratio of spot i (1, 2,. . ., 45220), and σ 2 was the trait variance in either the IL or the RIL population within one of the tree environments. We took the log 2 ratio, meaning that traits with a higher heritability in the IL population resulted in a positive number, and traits with a higher heritability in the RIL population with a negative number. We performed two tests to place the relative heritability in perspective. First, we took the spots showing significant heritability (FDR = 0.05). Second, to test whether variance was significantly different between the two populations, we used the non-parametric Fligner-Killeen test for homogeneity of variances, this we corrected for multiple testing using the Benjamini-Hochberg method (FDR = 0.05) (Conover et al., 1981;Benjamini and Hochberg, 1995).
Simulating Trait Architecture Impact on Relative Heritability To determine how the trait variance behaves proportionally in each population, we simulated different trait architectures in both the IL and RIL population. First, all QTL effect sizes were simulated by random drawing from a standard normal distribution (µ = 0, σ = 1). These QTL were simulated in trait architectures containing 1 to 100 QTL (or 1 to 100 clusters of closely linked QTL, each 33331 times). To recapitulate the observed QTL distribution in C. elegans, we distributed these QTL along the informative markers in our IL and RIL population. This assured an enrichment of QTL on the chromosome arms compared to the chromosome tips and centers (Rockman et al., 2010;Snoek et al., 2017). To approach the residual variance (σ 2 e ) in our data, we added random variation based on a normal distribution (rnorm) such that the average heritability of each simulated trait was 0.85 The following eight architectures were simulated: (i) randomly distributed additive QTL, (ii) randomly distributed additive QTL that only show their effect in one genotype, (iii) clusters of closely linked QTL with random effects, (iv) clusters of closely linked QTL that only show their effect in one genotype, (v) clusters of closely linked QTL that are balanced within the ancestral genotypes, (vi) clusters of closely linked QTL that are balanced within the ancestral genotypes and only show their effect in one genotype, (vii) randomly distributed interacting QTL, (viii) clusters of closely linked interacting QTL. The number of closely linked QTL per cluster was simulated from two to five. The additive and closely-linked model were similar in essence, but differ in the architecture, where we modeled the closely-linked QTL such that these were not segregated in the population used. The simulation functions can be found at the git archive: https: //git.wur.nl/published_papers/sterken_2019_closely_linked_qtl. The distribution of traits over a balanced closely-linked architecture and additive architecture was done by measuring the number of heritable traits with a heritability ratio between −3 and −2 (peak) and between 0.5 and 1.5 (intersect). These intervals were chosen as they represent areas where the distributions of these models differ. The number of expected traits per interval were counted as the median of all simulated architectures (so 1 to 100 QTL, and 2 to 5 QTL per closely-linked locus) in order to get an estimation that is less dependent on the chosen simulation parameters. The predicted number of traits at the peak and the intersect for the additive model (a) and the balanced closelylinked model (b) were used to solve the true distribution based on the real number of heritable traits in these heritability ratio intervals (c). This was done by solving the equations a peak × x 1 + b peak × x 2 = c peak and a intercept × x 1 + b intercept × x 2 = c intercept for x 1 and x 2 using the solve function in R. This led to the estimated number of additive traits (x 1 ) and balanced closely linked traits (x 2 ).

Genome-Wide Confirmation of eQTL Effects and Location Using Introgression Lines
Analysis of differential expression showed that introgression lines (ILs) could confirm both cis-and trans-eQTL that were previously mapped in the recombinant inbred line (RIL) population . A population of 48 RILs, 56 ILs (Doroszuk et al., 2009;Supplementary Table 1), and at least three replicates of the ancestral strains N2 and CB4856 were exposed to the three environments ( Figure 1A). Based on the number of eQTL expected in the CB4856 locus of each IL, we found that on average 69.5% (FDR = 0.05) of the cis-eQTL found using the RILs could be confirmed using the ILs over all three environments (FDR = 0.05). The trans-eQTL found in the RILs, were confirmed on average 42.2% (FDR = 0.05) in the ILs (Figure 1 and Supplementary Table 2). Note that the tiling structure of the ILs meant that each QTL location was covered by 0-5 (5-95% quantiles) ILs (Supplementary Figure 1). The percentage of confirmed eQTL was positively correlated with the RIL significance threshold (Supplementary Figure 2A). Furthermore, correlation analysis of the log 2 ratio with the N2 ancestor in the ILs versus the eQTL effect measured by RILs showed that eQTL effects in the CB4856 locus of each strain were well approximated in the ILs (average Pearson correlation, rho = 0.661; Supplementary Figure 2B and Supplementary Table 2). Together, over all three environments, the analyses confirmed eQTL occurrence and effect sizes in the RIL population in independent experiments using an IL population.
Next, we investigated the trans-bands identified in the RIL population more closely. The trans-bands were described in a previous study . For each trans-band, we took 2 to 6 ILs covering and flanking the locus and tested if the trans-eQTL effects correlated significantly with differentially expressed genes in the ILs compared to N2. We found supporting evidence for 14 out of 19 trans-bands at an overall falsepositive rate of 0.11; see Section "Materials and Methods." Furthermore, we narrowed down the location for some of these trans-bands (Supplementary File 1 and Supplementary Table 3).
In particular the trans-bands in the control and heat-stress environment were well supported (5/5 and 6/7, respectively), whereas those in the recovery environment were less (3/7). The poor support in the recovery environment is likely due to the few trans-eQTL per trans-band in that environment (median of 25 genes in recovery versus 51 in control and 125 in heat stress). Altogether, we conclude that trans-bands were highly replicable, to a higher extent than individual trans-eQTL.
Next, we asked if the number of differentially expressed genes in the IL population could be predicted from the RIL population. Therefore we compared the gene expression in both populations to the CB4856 ancestor to measure the effect of the N2 loci and to the N2 ancestor to measure the effect of the CB4856 loci. The effect of CB4856 introgressions in an N2 genetic background on gene expression was negatively correlated with the expectations based on the RIL population. In other words, in the RIL population the number of genes differentially expressed due to the introgression was under-estimated and the number of genes differentially expressed due to the genetic background was over-estimated (Figure 2). In the ILs we found that the relative number of differentially expressed genes compared to N2 was 6.7-fold higher than expected based on the differentially expressed genes found in the RILs (paired t-test, p < 1 × 10 −54 ). Furthermore, when compared to CB4856, the number of differentially expressed genes in the ILs was 3.3-fold lower than expected from the RILs (paired t-test, p < 1 × 10 −128 ). The differences between RILs and ILs were consistent when changing both the threshold for differential expression and the threshold for eQTL-based expectations (Supplementary Figure 3). These results show that the expectations from a single marker model are a poor predictor for differentially expressed genes in ILs. Importantly, a single marker model under-estimates the impact of small introgressions and over-estimates the impact of the genetic background.

Micro-Architecture of eQTL
The distribution and differences of genetic recombination over ILs and RILs allowed studying the architecture of eQTL in C. elegans. We hypothesized that different underlying trait architectures would leave different trait-variance distributions in the IL and RIL population. For example, a simple trait architecture dominated by one major QTL would only lead to an effect on trait levels in a single or a few ILs, but in ∼50% of the RILs. Hence, resulting in a low trait variance over the genome-wide IL population compared to the RIL population. As heritability was a straightforward way to interpret trait variance, we estimated the broad-sense heritability (H 2 ) in both populations (Supplementary Table 4). In general, heritability was higher in the RIL population. In total, over all conditions, we found 10673 unique genes that showed significant heritability in the RIL population, whereas we found 2,952 unique genes that showed significant heritability in the IL population (permutation, FDR = 0.05; Supplementary Figure 4A). Only 929 genes in the RILs and 8 genes in the ILs showed heritable gene expression variation over all three environments (Supplementary Figures 4B,C). The reason for the difference between populations was partly due to 534 out of 929 genes having an eQTL in the RILs (of which 354 had a cis-eQTL), which captured little heritable variation in the whole IL population. From the heritability analysis, we conclude that, as expected, heritability was higher in the RIL population, and that heritability is highly environment dependent.
To gain insight in the impact of different trait architectures, we simulated eight distinct architectures, including additive and epistatic architectures (see section "Materials and Methods, " Supplementary Figures 5, 6) and measured trait variance ratios between the IL and RIL population. Subsequently, we FIGURE 1 | Experimental setup and eQTL confirmation. (A) The four types of populations used in the experiment: recombinant inbred lines (RILs), the ancestral strain CB4856, the ancestral strain N2, and introgression lines (ILs). These were exposed to three separate treatments: control (48 h at 20 • C), heat-stress (46 h at 20 • C followed by 2 h at 35 • C), and recovery (as heat-stress, followed by an additional 2 h at 20 • C). After the experiment, populations of the strains were harvested and used for transcriptome measurement by microarray. (B) the percentage of eQTL confirmed based on differentially expressed genes per IL and per RIL (FDR = 0.05). The percentages are split-out over the three environments, and the two eQTL type (cis or trans). The eQTL were mapped using the RIL population, hence that population is expected to confirm the eQTL to a high degree. (C) An example of one cis-eQTL (for gene F26E4.1) and one trans-eQTL (for gene K06H6.1) in the IL population. On the x-axis the genotype at the QTL locus is plotted, and on the y-axis the expression (R N2 ).
assumed that the measurement error (σ 2 e ) was similar for both populations and calculated the heritability ratio between both populations ( Figure 3A). Based on the additive simulation, we expected 95% of the variance ratios to fall between −3.6 and −1.7, whereas under a model with closely-linked QTL that cancel each other out in the same genetic background (balanced), the 95% interval falls between −24.9 and 4.9. The balanced closely-linked QTL architecture was modeled such that QTL within such a cluster would only separate occasionally by a recombination in the RIL and IL population. The shape of the distribution of genes with significant heritability seems to form a combination of additive and balanced closely linked QTL (Figure 3A). To get an estimate of the contribution of the two models, we used the difference in the additive and balanced closely linked distributions from the simulation to estimate how the traits are divided over the two QTL models (Figure 3B). Analysis of the two distributions revealed that in all three environments additivity was the most likely QTL model (60-93% of genes with significant H 2 ). Balanced closely linked QTL explained up to 40% of relative heritability in the control environment, but only 7% in the heat stress and recovery environments (Supplementary Table 5). Therefore, we hypothesize that the balanced closely linked QTL model is an important eQTL architecture in the nematode C. elegans.

Two Predictions From the Balanced Closely Linked eQTL Microarchitecture
The balanced closely linked QTL model comes with two testable predictions: (i) the genes with heritable variation in gene expression were not differentially expressed in the parental FIGURE 2 | Number of differentially expressed genes (DEG) expected (exp.) from eQTL mapping and observed experimentally (obs.). On the x-axis, the population type is shown and on the y-axis, the expected and observed ratio of differentially expressed genes is shown, both normalized for the expectation in the RILs [eQTL threshold, -log 10 (p) > 3.9; DEG threshold, -log 10 (p) > 5]. In the left panel the effect compared to N2 is shown (effect of the CB4856 loci; introgressions in the IL panel) and in the right panel the effect compared to CB4856 is shown (effect of the N2 loci; genetic background in the IL panel).

FIGURE 3 | Balanced closely linked QTL can explain heritability ratios between the RIL and IL populations. (A)
Histogram of the heritability ratio in the IL versus the RIL population of genes with significant gene expression heritability (permutation, FDR = 0.05). The light orange surface indicates microarray spots of genes with heritable variation in gene expression only in the RIL population (3,262 in control, 7,545 in heat-stress, and 12,176 in recovery), the pink surface microarray spots of genes with only heritable variation in gene expression in the IL population (145, 59, and 71, respectively) and the orange color microarray spots of genes with heritable variation in gene expression in both populations (1,216, 1,588, and 1,507 respectively). (B) The density distribution of the heritability ratios of genes with heritable gene expression variation over the balanced closely linked (green) and the additive (purple) QTL model. Trait models consist only of additive or balanced closely linked QTL. (C) Overlap in differentially expressed genes between ILs [threshold -log 10 (p) > 5]. The comparisons are grouped per chromosome (x-axis): the intra-chromosomal comparisons and all other chromosomes versus chromosome I, II, III, IV, V, or X. On the y-axis the fraction overlap is shown. The dots represent one IL versus IL comparison the size corresponds to the number of overlapping differentially expressed genes.
strains, (ii) differential expression of genes was not only linked to one location in ILs but to clusters of ILs perturbing distant loci (multiple balanced clusters).
First, we calculated the number of genes with significant heritabilities. For the RILs, 4,478 spots (2,910 genes) displayed significant heritability (FDR = 0.05) in control environment FIGURE 4 | Three genes with high heritability in gene expression variation in the IL population compared to the RIL population. (A) Comparison in expression between IL and RIL population for clec-62, mtl-2, and npp-1. On the x-axis, the population type and on the y-axis, the z-score with the N2 parental lines. The dashed horizontal lines indicate the significance threshold [z-score, -log 10 (p) > 5]. (B) The expression per introgression. On the x-axis, the introgression location is shown per chromosome. On the y-axis, the z-score with the N2 parental line is shown. The dashed horizontal lines indicate the significance threshold [z-score, -log 10 (p) > 5]. The colors indicate the environments (blue for control, red for heat-stress, and green for recovery).
(H 2 ≥ 0.68), 9,133 spots (5,072 genes) in heat-shock environment (H 2 ≥ 0.70), and 13,683 spots (7,537 genes) in recovery environment (H 2 ≥ 0.62). For the ILs, 1,361 spots (1,012 genes) displayed significant heritability (FDR = 0.05) in control environment (H 2 ≥ 0.70), 1,647 spots (1,123 genes) in heatshock environment (H 2 ≥ 0.71), and 1,578 spots (1,092 genes) in recovery environment (H 2 ≥ 0.64). Then, we compared these with differential expression in the parental strains. Indeed, only 9.1-15.4% of the genes with heritable variation in gene expression were differentially expressed when comparing the two parental strains (FDR = 0.1; Supplementary Table 6). Also, the second prediction was found to be correct, on average 21.9% of the differentially expressed genes were shared between IL strains covering loci on different chromosomes, which was only slightly less than the average of 25.1% between ILs covering the same chromosome ( Figure 3C and Supplementary Figure 7, and for examples Figure 4). Therefore, we concluded that localized genetic complexity was a major part of the eQTL architecture. Furthermore, differences in heritability between the RIL and IL populations over environments indicated that the control environment was different from heat-shock and recovery. The balanced closely linked architecture, which predicted a broad range of relative heritability, seemed to be most prominent in the control environment. It could be that these complex architectures were more important for the developmental process. This environmental effect could be illustrated by the expression variation of the genes: mtl-2, npp-1, and clec-62. Of which mtl-2 and npp-1 showed an interaction with the environment. The gene npp-1 only showed this interaction in the control environments, environment where ILs on multiple chromosomes showed differential expression of this gene, yet for mtl-2 ILs with differential expression on different chromosomes were found during recovery conditions, whereas clec-62 shows ILs with differential expression on different chromosomes in control and heat stress conditions (Figure 4). The nuclear core complex protein NPP-1 is involved in spindle formation and important for oogenesis, a process that was interrupted during heat-shock (Schetter et al., 2006;Jovic et al., 2017). MTL-2, one of two metallothioneins in C. elegans, was expressed in the intestine and was induced after heat-shock (Freedman et al., 1993). The pattern observed for clec-62 was exceptional as it showed a consistent response over all three environments where IL strains with an introgression on chromosome I, chromosome IV, and chromosome X showed much lower expression compared to the N2 ancestor. Furthermore, also an IL strain with an introgression on chromosome II and one with an introgression on chromosome V displayed this phenotype. C-type lectin 62 is a gene belonging to the extensive clec-family, which is thought to be involved in C. elegans immunity (Schulenburg et al., 2008) although its exact function is not known.

Most eQTL Mapped in RILs Are Replicable in ILs
Here, we show that eQTL mapped in a RIL population can be confirmed in an IL population. We found that the majority of cis-eQTL are replicable in the IL population (on average 69.5% per IL), whereas trans-eQTL are less replicable in ILs (on average 42.2% per IL). This likely reflects the mainly monogenic architecture of cis-eQTL, versus the more polygenic and environment-dependent trans-eQTL (Li et al., 2006;Keurentjes et al., 2007;Rockman et al., 2010;Snoek et al., 2017;Albert et al., 2018). Especially the confirmation of trans-bands by ILs shows that these regulatory hot-spots are robust regardless of genetic background. It should be noted that this study does have limited power per introgression line as each line was only measured once per condition. Hence we avoid conclusions based on a single ILs throughout this paper. However, the tiling nature of the population does mean that each locus is covered by multiple ILs (Doroszuk et al., 2009). Furthermore, the RIL and IL experiment were separated in time, which could lead to unexpected effects influencing the replication. This study helps the search for candidate genes underlying these trans-bands, by narrowing-down the regions. However, additional experiments and replicates are recommendable and currently being pursued for the heat-stress trans-band on chromosome IV. Furthermore, it shows how ILs can be used to narrow-down these eQTL hotspots , using correlation analysis previously used to link trans-bands to genes and biological processes (Andersen et al., 2014;Sterken et al., 2017). These findings show on a large scale that QTL mapped using a single marker model in a moderately sized RIL population are reliably replicable in a population with a different genetic structure, which confirms findings for single traits reported in C. elegans and beyond [for example, see Andersen et al., 2014;Gao et al., 2018)].

Introgression Lines Indicate the Presence of Parental-Balanced, Polygenic, Traits
The difference in genetic complexity between RILs and ILs can be leveraged to understand trait architectures. Despite confirming many QTL, it has been noted that ILs often tell a different story than RILs, implying abundant genetic interactions, not uncovered by RILs [as reviewed by Mackay (2014)]. In this study, we also show that the number of differentially expressed genes in the N2 genetic background of the ILs is lower than expected compared to RIL-based estimations. Furthermore, eQTL mapped in the RIL population also led to an underestimation of the number of differentially expressed genes due to the introgressions in the ILs. To summarize, the introgressions display more-thanadditive effects, whereas the genetic background shows less-thanadditive effects.
Our findings are in line with observations in introgression lines in C. elegans, showing that for some traits more and different QTL than expected from RILs can be found (e.g., Gaertner et al., 2012;Glater et al., 2014;Snoek et al., 2014a). Additionally, our findings are also in line with findings in other organisms, where such effects have been reported for different types of traits (Shao et al., 2008;Gale et al., 2009;Spiezio et al., 2012). In this study, we show this effect in general, over many gene expression traits. Moreover, a direct comparison of trait mapping in a genome-wide IL population versus a RIL population has only been conducted in a few studies, as far as we are aware (Glater et al., 2014;Snoek et al., 2014a). It has been argued that ILs showing more-or less-than-additive effects compared to the parental strains is a hallmark of epistasis [as reviewed by Mackay (2014)]. However, recent studies in yeast show that additivity underlies most of the heritable trait variation among inbred lines, where epistasis accounts for phenotypic extremes (Bloom et al., 2015;Forsberg et al., 2017;Albert et al., 2018). Thus remains the question, what kind of trait architecture drives our observations: pervasive epistasis or widespread additivity?
The Developmental Trait Architecture Consists of Balanced Closely Linked QTL Trait architectures underlying natural variation in C. elegans differ strongly over traits. For example, currently 25 quantitative trait nucleotides (QTNs) are known in C. elegans, capturing a majority of the heritable variation for particular traits [reviewed by Gaertner and Phillips (2010) and Rockman (2012) Hahnel et al. (2018)]. However, there are also examples of traits that are highly heritable but have only yielded complex or few QTL (let alone QTNs). For example, a study on bacterial preference of C. elegans noted a relatively high heritability (0.46) for Serratia marcescens over E. coli, yet uncovered only a single QTL in the RILs used for mapping whereas multiple were expected (Glater et al., 2014). Furthermore, recent work from our group, studying metabolite abundances showed high heritability (from 0.32 up to 0.82) corresponding to a few uncovered QTL (Gao et al., 2018). Intriguingly, several studies imply trait architectures consisting of closely linked QTL that are balanced in the parental strains (Gaertner et al., 2012;Glater et al., 2014;Bernstein et al., 2019). By simulation, we obtained evidence that some trait architectures can be differentiated by relative heritability between IL and RIL populations which is a property we can reliably measure in our two populations, as it only relies on determining trait variance. In this way, we found that for genes without an eQTL, but showing high heritability, the most parsimonious explanation lies in an architecture comprised of (multiple) closely linked QTL clusters. This type of architecture seems especially prominent during normal development where it could affect approximately 40% of genes with heritable expression variation. It should be noted that only strictly balanced closely linked and strictly additive QTL distributions were modeled. Furthermore, a study containing more replication to take in account intra-strain variance should be conducted to confirm this hypothesis. This would also benefit from a better knowledge on the trait architecture based on RILs, as in Bernstein et al. (2019). We think the observed distribution suggests that a combination of (both or multiple) types of QTL make up the complete genetic architecture of a trait.
In recent years, the number of parameters known to affect gene expression variation in the context of natural variation has steadily grown. It is currently clear that environment (Li et al., 2006;Snoek et al., 2017), age (Vinuela et al., 2010), development (Francesconi and Lehner, 2014), and background mutations  affect gene expression variation and eQTL distribution in C. elegans. These factors could also contribute to the observed heritability differences between ILs and RILs. For environment, we can confirm that it plays an important role: the heritability ratio is strongly dependent on environment. This is in line with effects observed for trans-eQTL, which are also strongly environment dependent, implying heritability is as well (Li et al., 2006;Snoek et al., 2017). Developmental differences between the strains in each population could also drive some of the observed heritability ratios. For example, ILs could be developmentally more homogenous than RILs, which could result in lower levels of trait variance in ILs. It is clear that age affects trans-eQTL and heritability (Vinuela et al., 2010(Vinuela et al., , 2012. However, it is unclear how that would affect the heritability ratios we measure in general; it seems unlikely that developmental differences result in a specific variance signature as changes occur in both populations. More specific, in this experiment strains are tightly synchronized and developmental stage is observed to be L4 before isolation, therefore we expect that these potential sources of increased variance are controlled. Hence, the relative heritabilities under normal development imply clusters of closely linked QTL.

The Role of Cryptic Genetic Variation on Trait Complexity
We used the contrast in genetic complexity of the RIL and IL population to investigate trait complexity. The relative heritabilities between these populations differed over the three environments. In our previous study on the RILs, we show that the trans-eQTL architecture is different over the three environments, showing that trans-eQTL contribute most to cryptic genetic variation. Here, we find that the microarchitectures is more complex in an ambient environment.
Development of an organism is a tightly regulated process and completion of development into a reproducing adult is essential for reproduction, hence fitness. The nematode C. elegans experiences outbreeding depression (Dolgin et al., 2007), given the strains N2 and CB4856 are genetically distinct, it is likely that inbred lines constructed from these two strains disrupt some linked loci involved in this process (Seidel et al., 2008;Snoek et al., 2014a). We hypothesize that especially the ambient environment stimulating normal development is prone to accentuate the effects of genetic 'mismatches' resulting in trait variation. First, local sites are expected to co-segregate over many generations in C. elegans, making it likely that they are filled with compensatory mutations (Rockman et al., 2010). Second, development is a polygenic, tightly regulated, process. On the level of gene expression, there are strong changes over the entire development from egg to adult, and during the last juvenile stage (L4) especially (Francesconi and Lehner, 2014;Hendriks et al., 2014;Snoek et al., 2014b;Jovic et al., 2019b). Together, these two effects may cause the C. elegans populations in ambient environments to show micro-architectures that are more complex.
On the other hand, stress responses are also tightly regulated, but initially aimed at reaching a stress-survival mode, which is a process that involves fewer genes than development. The heat-shock response in C. elegans starts by de-phosphorylation of HSF-1 and DAF-16 and entry of these transcription factors into the nucleus [as reviewed by Rodriguez et al. (2013)]. Once there, they regulate the expression of chaperones that function to minimize cellular damage. The physiological effects of heat-shock exposure are duration dependent, where a 2h exposure in our setup does not result in severe phenotypic effects (Jovic et al., 2017). However, longer exposures lead to less movement, delayed egg-laying, and early death. Between N2 and CB4856, there are x temperature related traits mapped: thermal preference (mapping to the left of chromosome X) (Gaertner et al., 2012), recovery from heat-stress (mapping to the centerright of chromosome II) (Rodriguez et al., 2012), reproduction after heat-stress (mapping to the center-right of chromosome II and the left of chromosome IV) (Rodriguez et al., 2012), and temperature-related size differences (mapping to tra-3 on chromosome IV) (Kammenga et al., 2007). The chromosome II region associated with recovery from heat-stress was confirmed by ILs WN225 and WN226 in the original paper, and falls under a heat-stress trans-band . Here, we find that both ILs confirm the existence of the trans-band. Hence, the gene expression affected by a polymorphic gene on chromosome II could be linked to recovery from heat-stress.
Overall, our results show that populations in both the heatshock and recovery from heat-shock environments show fewer QTL with complex micro-architectures. We hypothesize that this is due to the effect of the strong transcriptional response induced by heat shock (Brunquell et al., 2016;Jovic et al., 2017). It is possible that this abrupt disturbance emphasizes regulatory variation in only a few key response pathways compared to the more subtle and complex process of development.

Implications for Understanding Life-History Adaptations
Our data facilitate exploring the functional implications of gene transcriptional changes following heat-shock and recovery. The gene transcriptional landscape consists of multiple gene networks underlying different traits, including life-history traits (Valba et al., 2015). Gene transcriptional response to stress and subsequent recovery are likely to shape life-histories given that many of the involved polymorphic genes may have clear functionalities. For instance, polymorphic regulators in genes affecting thermo-sensation may be important for controlling locomotor behavior induced by thermal stress via control neural decision-making (Stegeman et al., 2019). C. elegans is ectothermal and inhabits ecological niches that are prone to rapid temperature fluctuations in Europa (N2), but stable temperatures in Hawaii (CB4856) (Crombie et al., 2019). Hence, in Europe it needs to cope with these sudden temperature changes. Jiang et al. (2018) studied the genetics of cold-warm changes in C. elegans and detected ISY-1 and ZIP-10 as major gate keepers of temperature change responses (Jiang et al., 2018). It would be interesting to investigate if polymorphic gene expression regulators in this warm-cold switch are likely to underlie these temperature switches. Moreover, more variable alleles affecting gene expression could be detected using the recently developed multi parental RIL populations as they show variation in life history traits (Noble et al., 2017;Snoek et al., 2019). We recently showed that thermotolerance in C. elegans could be predicted from the gene expression resilience patterns in worms exposed to heat stress (Jovic et al., 2019a,b). It was found that the predictive outcomes also hold up across different genotypes, suggesting that polymorphic regulators play an important role in thermotolerance.

CONCLUSION
We present an eQTL experiment conducted with ILs in three environments covering the same conditions as a RIL experiment published previously . We show that ILs can replicate both cis-and trans-eQTL; furthermore, we present evidence supporting 14 eQTL hot spots (trans-bands). Yet, eQTL mapped in the RIL population systematically under-estimate the impact of a single introgression on the transcriptome and over-estimate the impact of the genetic background, suggesting additional genetic complexity. We present evidence that during normal growth multiple clusters of closely linked QTL could underly additional genetic complexity.
Further understanding of this phenomenon requires systematic dissection of many QTL -a process that in this study was only undertaken for trans-bands -using introgression lines. It remains to be determined what kind of role epistasis plays in trait variation. Currently, RIL populations in most species are typically of insufficient size to detect any epistasis beyond two loci interactions. Careful crosses with ILs to generate double-loci ILs might be a way forward to further our understanding of trait regulation in the context of natural genetic variation.

DATA AVAILABILITY STATEMENT
The transcriptome datasets used in the analysis are deposited at ArrayExpress E-MTAB-5779 and E-MTAB-7424.    (Seidel et al., 2008). (B). A histogram of the number of CB4856 loci covering an eQTL. Typically, an eQTL is covered by CB4856 loci of 2 ILs and 23 RILs (median).

AUTHOR CONTRIBUTIONS
Supplementary Figure 2 | Confirmation of eQTL by significance thresholds and correlation analysis. (A) The percentage of confirmed eQTL per population per eQTL-type. On the x-axis, the −log 10 (p) significance threshold in the RILs is shown (binned per 0.5 in the analysis) and on the y-axis the percentage of confirmed eQTL per bin per strain is shown (at least five confirmable eQTL required per bin). For example, for the RIL WN98 under recovery conditions there were 115 cis-eQTL with a significance between 4.0 and 4.5 in its CB4856 regions, 91 of these were confirmed based on the z-score (79.1%). This example results in a dot where the size corresponds to the number of eQTL and the color indicates the environments. The line shown is a linear regression curve, where the surrounding gray area is the confidence interval. (B) The Pearson correlation of eQTL effects with gene expression in the ILs and the RILs. On the x-axis the population type is plotted and on the y-axis the Pearson correlation. The correlations are split-out over the three environments (control, heat stress, and recovery) and over eQTL type (cis or trans). The arrows indicate QTL effect sizes as found in the N2 genotype (orange) and the CB4856 genotype (blue). Perfectly opposed arrows, one of which orange and the other blue, indicate that the same QTL has an opposite effect in the two genotypes (e.g., as seen for Additive random distribution). When an arrow lacks a perfectly opposed arrow of another color, it means that the QTL is only found in that particular genotype. Epistatic interactions are indicated as a line connecting two rectangles.

Supplementary
Supplementary Figure 6 | Variance ratios between IL and RIL population for the simulated trait architectures (Supplementary Figure 5). The density of occurrence of variance ratios per simulation is given. The color scale indicates how many QTL for a trait were simulated.
Supplementary Figure 7 | Overlap in differentially expressed genes between ILs [threshold −log 10 (p) > 5]. The ILs are ordered based on introgression on the xand y-axis. The location of the CB4856 segment is indicated behind the IL strain-code. The fraction overlap shown is calculated as the percentage of unique differentially expressed genes in the two compared ILs. The overlap is shown for the control environment (A), the heat-stress environment (B), and the recovery environment (C).
Supplementary Table 1 | The genotypes of the strains used in this study, −1 denotes a CB4856 genotype, a 1 denotes an N2 genotype. The genotypes are given per chromosome and per position (based on WormBase version WS258).  The table lists the strain name, strain type and the comparisons are split out for the cis-and trans-eQTL. The correlation reported is the Pearson correlation and its significance. The number of eQTL present in the CB4856 loci is given, as is the percentage that is also differentially expressed (FDR = 0.05).

Supplementary
Supplementary Table 3 | Summary of the comparison of gene expression in the ILs with the trans-bands identified previously . The location of the trans-band and the number of genes and microarray spots affected are listed. The genotypes of the ILs with an introgression adjacent to -or covering the trans-band are listed. The genotypes of the ILs that confirm the trans-band and the trans-band locus that these ILs imply are also given.
Supplementary Table 4 | Table with the heritabilities per spot per environment per population. The estimated genetic variance (V g ) and the technical variance (measured from the replicated parental lines -measurement error -V e ) are given, as is the heritability (H 2 ). The FDR0.05 column indicates the threshold of significance based on permutation.
Supplementary Table 5 | A table with the estimated fraction and amount of traits for an additive QTL architecture and a balanced closely-linked QTL architecture. The numbers are calculated based on only a single type of QTL occurring for a particular architecture. For example, additive means n QTL that display an additive effect, without any other type of effect for that simulated trait.
Supplementary Table 6 | Differentially expressed genes between N2 and CB4856 for the three environments: control, heat-stress, and recovery from heat stress. The columns in the table: SpotID, the Agilent spot identifier, the information on the gene expression detected by that spot is given [chromosome, location (start/stop), strand, and three identifiers]. Two columns show if genes are significantly heritable; general (in any population) and specific (which population, or both). The significance and effect columns give the output of the linear model when comparing CB4856 versus N2 (positive effect indicates the gene is higher expressed in N2). The last column gives the significance as corrected for multiple testing (FDR).
Supplementary File 1 | Comparison of gene expression in ILs with eQTL in trans-bands identified in the RIL population. Per trans-band, a figure was constructed. In (A) the name of the trans-band is given at the top of the panel (e.g., chromosome I, 3.5-4 million bases) the correlation of the relative gene expression (R N2 ) was correlated with the eQTL effect for the ILs covering or nearby the trans-band. Significance was determined based on the highest correlation in the N2 strains, only strains with a stronger correlation than N2 were scored as significant. In (B) the genetic map of the ILs of the trans-band chromosome is shown. On the x-axis the genomic location (in million bases) is shown and on the y-axis the ILs. In (C) the actual correlation between expression in the ILs and eQTL effect in the RILs is shown. With on the x-axis the eQTL effect and on the y-axis R N2 . Each dot represents a spot on the microarray with an eQTL in the trans-band investigated. The line indicates the estimated slope and the pale blue area around the line indicates the confidence interval of the fit.