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<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.2d1 20170631//EN" "JATS-archivearticle1.dtd">
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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">BIORXIV</journal-id>
<journal-title-group>
<journal-title>bioRxiv</journal-title>
<abbrev-journal-title abbrev-type="publisher">bioRxiv</abbrev-journal-title>
</journal-title-group>
<publisher>
<publisher-name>Cold Spring Harbor Laboratory</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.1101/002485</article-id>
<article-version>1.1</article-version>
<article-categories>
<subj-group subj-group-type="author-type">
<subject>Regular Article</subject>
</subj-group>
<subj-group subj-group-type="heading">
<subject>New Results</subject>
</subj-group>
<subj-group subj-group-type="hwp-journal-coll">
<subject>Genomics</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Extensive epistasis within the MHC contributes to the genetic architecture of celiac disease</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name><surname>Goudey</surname><given-names>Benjamin</given-names></name>
<xref ref-type="aff" rid="a1">1</xref>
<xref ref-type="aff" rid="a2">2</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Abraham</surname><given-names>Gad</given-names></name>
<xref ref-type="aff" rid="a3">3</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Kikianty</surname><given-names>Eder</given-names></name>
<xref ref-type="aff" rid="a4">4</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Wang</surname><given-names>Qiao</given-names></name>
<xref ref-type="aff" rid="a1">1</xref>
<xref ref-type="aff" rid="a2">2</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Rawlinson</surname><given-names>Dave</given-names></name>
<xref ref-type="aff" rid="a1">1</xref>
<xref ref-type="aff" rid="a2">2</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Shi</surname><given-names>Fan</given-names></name>
<xref ref-type="aff" rid="a1">1</xref>
<xref ref-type="aff" rid="a2">2</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Haviv</surname><given-names>Izhak</given-names></name>
<xref ref-type="aff" rid="a5">5</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Stern</surname><given-names>Linda</given-names></name>
<xref ref-type="aff" rid="a2">2</xref>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name><surname>Kowalczyk</surname><given-names>Adam</given-names></name>
<xref ref-type="aff" rid="a1">1</xref>
<xref ref-type="aff" rid="a2">2</xref>
<xref ref-type="author-notes" rid="n1">*</xref>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name><surname>Inouye</surname><given-names>Michael</given-names></name>
<xref ref-type="aff" rid="a3">3</xref>
<xref ref-type="author-notes" rid="n1">*</xref>
</contrib>
<aff id="a1"><label>1</label><institution>NICTA Victoria Research Lab, The University of Melbourne</institution>, Parkville, Victoria 3010, <country>Australia</country></aff>
<aff id="a2"><label>2</label><institution>Department of Computing and Information Systems, The University of Melbourne</institution>, Parkville, Victoria 3010, <country>Australia</country></aff>
<aff id="a3"><label>3</label><institution>Medical Systems Biology, Department of Pathology and Department of Microbiology & Immunology, The University of Melbourne</institution>, Parkville, Victoria 3010, <country>Australia</country></aff>
<aff id="a4"><label>4</label><institution>Department of Mathematics, University of Johannesburg</institution>, PO Box 524, Auckland Park 2006, <country>South Africa</country></aff>
<aff id="a5"><label>5</label><institution>Bar Ilan University</institution>, Safed, <country>Israel</country></aff>
</contrib-group>
<author-notes>
<fn id="n1" fn-type="equal"><label>*</label><p>These authors contributed equally</p></fn>
<corresp>Correspondence should be addressed to Michael Inouye (<email>minouye@unimelb.edu.au</email>) and Adam Kowalczyk (<email>kowa@unimelb.edu.au</email>)</corresp>
</author-notes>
<pub-date pub-type="epub"><year>2014</year></pub-date>
<elocation-id>002485</elocation-id>
<history>
<date date-type="received">
<day>07</day>
<month>2</month>
<year>2014</year>
</date>
<date date-type="accepted">
<day>07</day>
<month>2</month>
<year>2014</year>
</date>
</history>
<permissions>
<copyright-statement>© 2014, Posted by Cold Spring Harbor Laboratory</copyright-statement>
<copyright-year>2014</copyright-year>
<license license-type="creative-commons" xlink:href="http://creativecommons.org/licenses/by/4.0/"><license-p>This pre-print is available under a Creative Commons License (Attribution 4.0 International), CC BY 4.0, as described at <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0/">http://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license>
</permissions>
<self-uri xlink:href="002485.pdf" content-type="pdf" xlink:role="full-text"/>
<abstract>
<title>Abstract</title>
<p>Epistasis has long been thought to contribute to the genetic aetiology of complex diseases, yet few robust epistatic interactions in humans have been detected. We have conducted exhaustive genome-wide scans for pairwise epistasis in five independent celiac disease (CeD) case-control studies, using a rapid model-free approach to examine over 500 billion SNP pairs in total. We found extensive epistasis within the MHC region with 7,270 statistically significant pairs achieving stringent replication criteria across multiple studies. These robust epistatic pairs partially tagged CeD risk HLA haplotypes, and replicable evidence for epistatic SNPs outside the MHC was not observed. Both within and between European populations, we observed striking consistency of epistatic models and epistatic model distribution, thus providing empirical estimates of their frequencies in a complex disease. Within the UK population, models of CeD comprised of both epistatic and additive single-SNP effects increased explained CeD variance by approximately 1% over those of single SNPs. Further analysis showed that additive SNP effects tag epistatic effects (and vice versa), sometimes involving SNPs separated by a megabase or more. These findings show that the genetic architecture of CeD consists of overlapping additive and epistatic components, indicating that the genetic architecture of CeD, and potentially other common autoimmune diseases, is more complex than previously thought.</p>
<sec>
<title>Author Summary</title>
<p>There are few bona fide examples of interactions between genetic variants (epistasis) which affect human disease risk. Here, we assess multiple genome-wide genotyped case-control datasets to investigate the role that epistasis plays in celiac disease, a common immune-mediated illness. We find thousands of replicable, statistically significant pairs of SNPs exhibiting epistasis and, interestingly, all of these fall within the well-known Major Histocompatibility Complex (MHC) region on chromosome 6. We investigate the underlying distribution of epistatic models and further assess the amount of celiac disease variance that can be explained by epistatic pairs, single SNPs and a combination thereof. Our results indicate that there is a substantial amount of shared disease variance between single SNPs and epistatic pairs, but also that a combination of the effects gives a better model of disease. These findings support powerful and routine epistasis scans for the next generation of genome-wide association studies and indicate that the genetic architecture of celiac disease, and potentially other immune-mediated diseases, is more complex than currently appreciated.</p>
</sec>
</abstract>
<counts>
<page-count count="22"/>
</counts>
</article-meta>
</front>
<body>
<sec id="s1">
<title>Introduction</title>
<p>The limited success of genome-wide association studies (GWAS) to identify common variants that substantially explain the heritability of many complex human diseases and traits has led researchers to explore other potential sources of heritability, including the low/rare allele frequency spectrum as well as epistatic interactions between genetic variants [<xref ref-type="bibr" rid="c1">1</xref>,<xref ref-type="bibr" rid="c2">2</xref>]. Many studies are now leveraging high-throughput sequencing with initial findings beginning to elucidate the effects of low frequency alleles [<xref ref-type="bibr" rid="c3">3</xref>–<xref ref-type="bibr" rid="c6">6</xref>]. However, the characterization of the epistastic component of complex human disease has been limited, despite the availability of a multitude of statistical approaches for epistasis detection [<xref ref-type="bibr" rid="c7">7</xref>–<xref ref-type="bibr" rid="c13">13</xref>]. Large-scale systematic research into epistatic interactions has been hampered by several computational and statistical challenges mainly stemming from the huge number of variables that need to be considered in the analysis (>100 billion pairs for even a small SNP array), the subsequent stringent statistical corrections necessary to avoid being swamped by large number of false positive results, and the requirement of large sample size in order to achieve adequate statistical power.</p>
<p>The strongest evidence for wide-ranging epistasis has so far come from model organisms [<xref ref-type="bibr" rid="c14">14</xref>,<xref ref-type="bibr" rid="c15">15</xref>], and recent evidence has demonstrated that epistasis is pervasive across species and is a major factor in constraining amino acid substitutions [<xref ref-type="bibr" rid="c16">16</xref>]. Motivated by the hypothesis that epistasis is commonplace in humans as well, recent studies have begun providing evidence for the existence of epistatic interactions in several human diseases, including psoriasis [<xref ref-type="bibr" rid="c17">17</xref>], multiple sclerosis [<xref ref-type="bibr" rid="c18">18</xref>], type 1 diabetes [<xref ref-type="bibr" rid="c19">19</xref>], and ankylosing spondylitis [<xref ref-type="bibr" rid="c20">20</xref>]. While these studies have been crucial in demonstrating that epistasis does indeed occur in human disease, several questions remain including how wide-ranging epistatic effects are, how well epistatic pairs replicate in other datasets, how the discovered epistatic effects can be characterized in terms of previously hypothesized models of interaction [<xref ref-type="bibr" rid="c21">21</xref>,<xref ref-type="bibr" rid="c22">22</xref>], and how much (if at all) epistasis contributes to disease heritability [<xref ref-type="bibr" rid="c23">23</xref>].</p>
<p>Celiac disease (CeD) is a complex human disease characterized by an autoimmune response to dietary gluten. CeD has a strong heritable component largely concentrated in the MHC region, due to its dependence on the HLA-DQ2/DQ8 heterodimers encoded by the HLA class II genes <italic>HLA-DQA1</italic> and <italic>HLA-DQB1</italic> [<xref ref-type="bibr" rid="c24">24</xref>]. The genetic basis of CeD in terms of individual SNP associations has been well-characterized in several GWAS [<xref ref-type="bibr" rid="c25">25</xref>–<xref ref-type="bibr" rid="c28">28</xref>], including the additional albeit smaller contribution of non-HLA variants to disease risk [<xref ref-type="bibr" rid="c29">29</xref>]. The success of GWAS for common variants in CeD has recently been emphasized by the development of a genomic risk score that could prove relevant in the diagnostic pathway of CeD [<xref ref-type="bibr" rid="c30">30</xref>]. Autoimmune diseases have so far yielded the most convincing evidence for epistatic associations, potentially due to power considerations since these diseases usually tend to depend on common variants of moderate to large effect within the MHC. Given these findings in conjunction with recent observations that rare coding variants may play only a negligible role in common autoimmune diseases [<xref ref-type="bibr" rid="c3">3</xref>], we sought to determine whether robust epistasis is detectable in CeD and whether it accounts for some of the unexplained disease heritability.</p>
<p>Here, we present the first large-scale exhaustive study of pairwise epistasis in celiac disease. Leveraging GWIS, a highly efficient approach for epistasis detection [<xref ref-type="bibr" rid="c31">31</xref>], we conduct genome-wide scans for all epistatic pairs across five separate CeD case/control datasets of European descent, finding thousands of statistically significant pairs despite stringent multiple testing corrections. Next, we show a high degree of concordance of these interactions across the datasets, demonstrating that they are highly robust and replicable. We characterize the common epistatic models found and compare them to previously proposed theoretical models. Finally, we examine the issue of whether epistasic pairs add more predictive power and explain more disease variation than do single SNPs.</p>
</sec>
<sec id="s2">
<title>Results</title>
<p>Datasets are summarized in <xref rid="tbl1" ref-type="table">Table 1</xref>, these include five independent, previously published GWAS datasets of CeD with individuals genotyped from four different European ethnicities: United Kingdom (UK1 and UK2), Finland (FIN), The Netherlands (NL) and Italy (IT) [<xref ref-type="bibr" rid="c26">26</xref>,<xref ref-type="bibr" rid="c27">27</xref>]. To limit the impact of genotyping error and other sources of non-biological variation, we implemented three stages of validation and quality control (QC): (i) standard QC within each dataset, (ii) independent exhaustive epistatic scans within each of the five datasets, and (iii) derivation of a validated list of epistatic interactions based on UK1. The study workflow is shown in <xref rid="fig1" ref-type="fig">Figure 1</xref>.</p>
<fig id="fig1" position="float" orientation="portrait" fig-type="figure">
<label>Figure 1:</label>
<caption><title>Study workflow</title></caption>
<graphic xlink:href="002485_fig1.tif"/></fig>
<table-wrap id="tbl1" orientation="portrait" position="float">
<label>Table 1:</label><caption><p>Datasets</p></caption>
<graphic xlink:href="002485_tbl1.tif"/>
</table-wrap>
<sec id="s2a">
<title>Exhaustive epistatic scans and replication</title>
<p>For each dataset, we implemented stringent sample and SNP level quality control (<bold>Methods</bold>), and then conducted an exhaustive analysis of all possible SNP pairs using the GWIS methodology [<xref ref-type="bibr" rid="c31">31</xref>]. Each pair was tested using the GSS statistic, which determines whether a pair of SNPs in combination provides significantly more discrimination of cases and controls than either SNP individually (<bold>Methods</bold>). Forty-five billion pairs were evaluated in the UK1 study (Illumina Hap300/Hap550) and 133 billion SNP pairs were evaluated in each of the four remaining cohorts (Illumina 670Quad and/or 1.2M-DuoCustom). Given this multiple testing burden, we adopted stringent Bonferroni-corrected significance levels of P = 1.1 × 10<sup>−12</sup> for the UK1 and P = 3.75 × 10<sup>−13</sup> for the remaining datasets.</p>
<p>To further ensure that the downstream results were robust to technological artefact and population stratification, we took two additional steps: (a) utilizing the raw genotype intensity data available for UK1 for independent SNP cluster plot inspection (performed by Karen A. Hunt, QMUL), and (b) replicating the epistatic interactions of the SNPs passing cluster plot inspection, where replication is defined as a SNP pair exhibiting Bonferroni-adjusted significance both in UK1 and in at least one additional study. Using these criteria, we found that 7,270 SNP pairs (654 unique SNPs) from the UK1 dataset passed both (a) and (b) above. We denote these pairs as ‘validated epistatic pairs’ (VEPs) below. <xref rid="tbl2" ref-type="table">Table 2</xref> presents the top 10 validated pairs, after pruning redundant pairs (pairs of pairs with at least two SNPs in perfect LD); the full list of VEPs is given in <bold>Supplementary Table 1</bold>. Notably, all VEPs fulfilling these robustness criteria were within the MHC.</p>
<table-wrap id="tbl2" orientation="portrait" position="float">
<label>Table 2:</label>
<caption><p>Top 10 epistatic signals detected in UK1 cohort within the extended MHC region and their properties in the remaining four cohorts</p></caption>
<graphic xlink:href="002485_tbl2.tif"/>
</table-wrap>
<p>More than 128,000 unique pairs achieved Bonferroni-adjusted significance across all five studies, with the vast majority lying within the extended MHC region of chr6 (<xref rid="fig2" ref-type="fig">Figure 2</xref> and <bold>Supplementary Table 2</bold>). Of the 131 epistatic pairs outside the MHC that were significant in at least one study, none passed Bonferroni-adjusted significance in at least one other study and were thus deemed not replicated. As expected, the number and strength of epistatic interactions increased as sample size increased. Interestingly, some of the strongest epistatic interactions tended to be in close proximity and in moderate LD, though only 1% of pairs had r<sup>2</sup> > 0.5 (<bold>Supplementary Figure 1</bold>). The heatmaps in <xref rid="fig2" ref-type="fig">Figure 2</xref> also showed that epistasis was widely distributed with distances of >1Mb common between epistatic pairs. Across all studies, epistatic interactions were consistently located in and around HLA class II genes, however further examination of the VEPs found that many of the top pairs were proximal to HLA class III genes, >1Mb upstream of <italic>HLA-DQA1</italic> and <italic>HLA-DQB1</italic>, the strongest known risk loci (<bold>Supplementary Figure 2</bold>).</p>
<fig id="fig2" position="float" orientation="portrait" fig-type="figure">
<label>Figure 2:</label>
<caption><title>Epistatic interactions within the extended MHC region</title>
<p>SNP pairs within 30KB of each other are shown as a single point on each heatmap. The colour of each point represents the most significant −log10(P-value) returned by the GSS statistic for SNPs pairs within each point. The −log10(P-value) is capped at 30 to increase contrast of lower values. The distribution of higher values in these datasets is shown in <bold>Supplementary Figure 4</bold>. The differences in the number of significant pairs detected in each cohort are clearly associated with the relative power of each study.</p></caption>
<graphic xlink:href="002485_fig2.tif"/></fig>
<p>The extent of replication of the epistatic pairs was apparent from the high degree of similarity in the rankings when pairs were sorted by GSS significance (<xref rid="fig3" ref-type="fig">Figure 3a</xref>), with ∼70–80% overlap between the UK1 and UK2 datasets extending all the way to the top 10,000 pairs, and 40-60% overlap with the pairs found in the NL and FIN datasets. Such high degrees of overlap have essentially zero probability of occurring by chance (P < 10<sup>−600</sup> for ∼80% overlap between the UK1 and UK2 top 50 pairs, hypergeometric test). The pairs found in the IT dataset showed lower levels of consistency with those detected in the UK1 dataset but overall were still much more than expected by chance with ∼30% overlap at ∼30,000 pairs (P < 10<sup>−1000</sup>).</p>
<fig id="fig3" position="float" orientation="portrait" fig-type="figure">
<label>Figure 3:</label>
<caption><title>Replication of epistatic pairs and corresponding epistatic models between datasets and populations</title>
<p>Panel <bold>(a)</bold> shows the overlap of significant epistatic pairs as a percentage between UK1 and remaining cohorts in order of decreasing GSS significance. Vertical dotted lines indicate the Bonferroni-adjusted significance for each study. Panel <bold>(b)</bold> shows the occurrence of genotype combinations for the top pair from UK1. Colouring of cells provides an indication of the epistatic model occurring in each cohort, explained further in the Methods section. Further examples are shown in <bold>Supplementary Figure 5</bold>.</p></caption>
<graphic xlink:href="002485_fig3.tif"/></fig>
</sec>
<sec id="s2b">
<title>Empirical epistatic model distributions</title>
<p>The epistatic model provides insight into how disease risk is distributed across the nine pairwise genotype combinations. Following the conventions of Li and Reich [<xref ref-type="bibr" rid="c21">21</xref>], we discretized the models for the VEPs to use fully-penetrant values where each genotype combination implies a susceptibility or protective effect on disease (<bold>Methods</bold>), simplifying the comparison of models between different SNP pairs.</p>
<p>To establish model consistency, we first replicated the most frequent full penetrance VEP models in the other datasets (<xref rid="fig4" ref-type="fig">Figure 4</xref>). When considering the distribution of epistatic models we found striking consistency of the UK1 models with those from UK2 and the other Northern European populations (Finnish and Dutch) (<xref rid="fig4" ref-type="fig">Figure 4</xref>). Only four models from the possible 50 classes [<xref ref-type="bibr" rid="c21">21</xref>] occurred with >5% frequency in the Northern European studies, and there was substantial variation in epistatic model as a function of the strength of the interaction. Amongst all VEPs in UK1, the four models corresponded to the threshold model (T; 34.7% frequency), jointly dominant-dominant model (DD; 31.1%), jointly recessive-dominant model (RD; 17.9%), and modifying effect model (Mod; 14.73%) [<xref ref-type="bibr" rid="c21">21</xref>,<xref ref-type="bibr" rid="c32">32</xref>]. The DD and RD models are considered multiplicative, the Mod model is conditionally dominant (i.e. one variant behaves like a dominant model if the other variant takes a certain genotype), and the T model is recessive. The T model was the most frequent model, especially amongst the strongest pairs.</p>
<fig id="fig4" position="float" orientation="portrait" fig-type="figure">
<label>Figure 4:</label><caption><title>Variation in epistatic models within and between populations</title>
<p>Distribution of epistatic models in different studies as increasing less significant SNP pairs are examined, where the models were selected based on the UK1 dataset. Different colours represent a different subset of epistatic models. The “other” group represents the set of models that occur less than 5% of the time. Models have been simplified using the rules provided in (<xref ref-type="bibr" rid="c21">Li & Reich, 2000</xref>). <bold>Supplementary Figure 6</bold> examines the distribution of models for pairs where at least one genotype combination does not occur in the data.</p></caption>
<graphic xlink:href="002485_fig4.tif"/></fig>
<p>To our knowledge, the frequencies of these epistatic models have not previously been determined in a complex human disease. Interestingly, despite the consistency of MHC epistasis, the VEPs showed noticeable differences in epistatic model distribution in the IT population. This was in contrast to the other Northern European populations but consistent with the different ranking in GSS significance observed above. In the IT population, the distribution of models was altered such that there was a more even distribution. The four most frequent models were still the T model (13.6%), DD (13.45%), modifying effects (13.45%), and RD model (11.55%). But, we also observed that many of the strongest pairs within the IT cohort followed the M86 model, though M86 represented only a small proportion of models overall (0.98%). In IT, the remaining 50% of the VEP models overall consisted of many low-frequency models.</p>
<p>The cause(s) of these differences is unclear. While cryptic technical factors cannot be ruled out at this stage, it may be the case that there is population specific epistatic variation that follows the known North/South European genetic gradient [<xref ref-type="bibr" rid="c33">33</xref>].</p>
</sec>
<sec id="s2c">
<title>Contribution of epistatic pairs to celiac disease heritability</title>
<p>We next sought to estimate the CeD heritability explained by the VEPs and single SNPs. The GSS test selects each epistatic pair based on it being more predictive than either of its constituent individual SNPs. However, the procedure does not <italic>a priori</italic> guarantee that a given pair is a better predictor of disease than all other individual SNPs not included in the pair; this requires a further step to determine which pairs and/or single SNPs provide the most predictive power overall. This task is further complicated by the fact that, like linkage disequilibrium for individual SNPs, many pairs are highly correlated and thus may not add substantial predictive power after accounting for the most predictive pair. These issues can naturally be addressed within the framework of a multivariable model, accounting for all SNPs and/or pairs at once. Hence, to better assess the contribution of epistatic pairs to CeD prediction and thus heritability explained, we employed L1 penalized linear support vector machines (SVM, see <bold>Methods</bold>), an approach which models all variables concurrently (SNPs and/or pairs) and which has been previously shown to be particularly suited for maximizing predictive ability from SNPs in CeD and other autoimmune diseases [<xref ref-type="bibr" rid="c30">30</xref>,<xref ref-type="bibr" rid="c34">34</xref>]. While we find that VEPs, as expected, are associated with the <italic>HLA-DQA1</italic> and <italic>HLA-DQB1</italic> risk haplotypes (<bold>Supplementary Figure 3</bold>), we have previously found that additive models of single SNPs explain substantially more CeD variance than haplotype-based models [<xref ref-type="bibr" rid="c30">30</xref>]. We therefore employ the former to estimate the gain in heritability here.</p>
<p>We assessed CeD variance explained by constructing three separate models: (a) genome-wide single SNPs only, using the 290,277 SNPs present across all datasets, (b) the VEPs only, i.e. the 7270 VEPs encoded as 65,430 indicator variables, and (c) a ‘combined’ model of both single SNPs and VEPs together. The models were evaluated in cross-validation on the UK1 dataset, and the best models in terms of Area Under the Curve (AUC) were then taken forward for external validation in the other four datasets without further modification.</p>
<p>In UK1 cross-validation, the VEPs and combined models led to an increase in maximum AUC of 0.5% over single SNPs alone (0.883 to 0.888), corresponding to an additional ∼1.5% in explained CeD variance, from 32.6% to 34.1% (<xref rid="tbl3" ref-type="table">Table 3</xref>). External validation of these models showed that the VEPs and combined models showed similar and significant gains in AUC over the single SNPs for the UK2 and IT dataset at + 1% for IT (<italic>P</italic> = 0.0163) and + 0.9% for UK2 (<italic>P</italic> = 0.0066), but the differences in FIN and NL were smaller and not significant. In external validation, the VEPs model was highly predictive yet slightly less predictive than that based on single SNPs, with the combined model yielding the highest AUC. The increased sample size of a combined UK1 and UK2 dataset in cross-validation did not yield better AUCs nor corresponding CeD variance (<bold>Supplementary Table 3</bold>).</p>
<table-wrap id="tbl3" orientation="portrait" position="float">
<label>Table 3:</label>
<caption><p>Variance explained by models with additive and epistatic genetic effects</p></caption>
<graphic xlink:href="002485_tbl3.tif"/>
</table-wrap>
</sec>
</sec>
<sec id="s3">
<title>Discussion</title>
<p>This study has shown the robust presence of epistasis in celiac disease. Epistatic interactions were observed within the extended MHC, most strongly between neighbouring SNPs in low to moderate LD, indicating that these interactions may play a role in segregating specific haplotype classes. We have shown that these epistatic SNP pairs strongly replicate across cohorts in terms of significance, ranking, and epistatic model. To our knowledge, this level of epistatic signal strength, number of epistatic pairs, and degree of replication has not been previously shown in a complex human disease.</p>
<p>Despite observations that epistatic interactions between SNPs within a locus are enriched for batch effects and poorly clustered genotype clouds [<xref ref-type="bibr" rid="c37">37</xref>], the stringent quality control and extensive replication of the analyses in this study indicate that these SNPs are largely bona fide epistatic pairs. When considering those pairs not achieving the Bonferroni significance criteria for replication, a large number of epistatic pairs were still highly statistically associated with CeD consistently across datasets, indicating that our estimates of epistasis may be conservative. For validated epistatic pairs (VEPs), we found that much of strongest epistatic signal is over 1MB upstream of the well-known <italic>HLA-DQA1</italic> and <italic>HLA-DQB1</italic> risk loci, suggesting a potentially important contribution of HLA class III genes. We also performed a large-scale empirical characterization of the epistatic models underlying the interactions in CeD, with the majority of the VEPs approximately following the threshold model, and a smaller number following dominant-dominant, dominant-recessive, and recessive-recessive models. Further, these patterns were found to be strongly consistent across most of the datasets.</p>
<p>We have previously found that penalized predictive models based on individuals SNPs similar to those used here are able to extract more predictive ability from the MHC region than models based on coarse-grain HLA types [<xref ref-type="bibr" rid="c30">30</xref>]. Here, we have found that combined models of both epistatic SNP pairs and single SNPs achieve slightly improved accuracy over models created with single SNPs alone, and that models of only epistatic SNP pairs explained similar amounts of CeD variance as single SNPs. Examining this redundancy more closely, the epistatic SNP pairs are highly correlated with single SNPs that are usually located near one of the pair (see <bold>Supplementary Figure 7).</bold> This correlation between single SNPs and combinations of SNPs appears to have been previously hinted at in a study by de Bakker et al examining the effectiveness of SNPs to tag HLA genotypes, where groups of SNPs were found to be more highly correlated with HLA genes than single SNPs [<xref ref-type="bibr" rid="c38">38</xref>]. The shared information between these single SNP and epistatic effects implies that determining the causal signal will be more difficult than previously thought. Just as the redundancy between single SNPs in LD has affected the resolution of causal genetic variants, our findings indicate that a similar, though currently unexplored, sharing of information may exist between epistatic variants and single variants. Such an observation is supported by previous literature [<xref ref-type="bibr" rid="c39">39</xref>] and may help to explain some of the controversy around epistatic versus additive genetic effects.</p>
<p>Celiac disease has a strong HLA signal, is highly heritable and is thought to conform to the Common-Disease, Common-Variant (CDCV) model [<xref ref-type="bibr" rid="c24">24</xref>]. Yet within this ‘model disease’ [<xref ref-type="bibr" rid="c25">25</xref>], our results suggest the presence of a previously unexplored level of complexity. Given their similar disease etiologies [<xref ref-type="bibr" rid="c40">40</xref>], we predict that these observations may hold true for other autoimmune/inflammatory diseases and other diseases that approximate the CDCV model. It is less likely that these observations affect our understanding of complex diseases that are unlikely to approximate CDCV, such as coronary artery disease, though it has been proposed that epistasis plays a role for these types of conditions as well [<xref ref-type="bibr" rid="c1">1</xref>].</p>
<p>The limitations of the first generation GWAS approach to explain missing heritability has led to the development and application of more complex approaches to resolve this problem, yet success has been elusive. Recent results suggest that rare variants add little to known heritability for a number of autoimmune diseases including celiac disease [<xref ref-type="bibr" rid="c26">26</xref>]. The predictive models generated in this work indicate that while epistatic pairs have substantial predictive power, their overall explained heritability is not substantially more than that for additive effects. Combined models of epistatic and additive effects are likely to constitute the best solution, however it is unlikely that these alone with resolve missing heritability.</p>
<p>These findings have implications for how next generation GWAS should be analysed and interpreted. While epistatic analyses have increasingly been advocated [<xref ref-type="bibr" rid="c27">27</xref>], this study demonstrates the usefulness of such an approach alongside that of traditional genome-wide analysis of additive effects. Many challenges remain in conducting this type of analysis. While we found strong epistasis within the MHC, future advances in statistical methods could uncover additional epistasis with weaker effects or involving rare variants, and it is currently unknown how weaker and rare variant epistatic effects interact with additive effects in humans. A main challenge of genetic association studies, the inference of genetic architecture, may very well be complicated by the shared information between epistatic and additive effects and it may be that targeted perturbation experiments will be required to identify the true causal signal.</p>
</sec>
<sec id="s4">
<title>Methods</title>
<sec id="s4a">
<title>Quality control</title>
<p>A range of quality control measures were applied to all datasets to limit the impact of genotyping error. For all datasets, we removed non-autosomal SNPs, SNPs with MAF <1%, missingness >1% and those deviating from Hardy Weinberg Equilibrium in controls with <italic>P</italic> < 5 × 10<sup>−6</sup>. Samples were removed if data missingness was >1%. Cryptic relatedness was also stringently assessed by examining all pairs of samples using identity-by-descent in PLINK, and removing one of the samples if <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="002485_inline1.gif"/></alternatives></inline-formula>. The cryptic relatedness filter removed 17 samples within the UK1 cohort that related to other UK1 samples, and 1208 samples from the UK2 cohort which were either related to other UK2 samples or UK1 samples. Dataset sizes in <xref rid="tbl1" ref-type="table">Table 1</xref> are reported after the quality control steps above. Significant epistatic SNP pairs were further assessed by manually inspecting the genotyping cluster plots of both SNPs in the UK1 cohort. Intensity data for the other studies was not available thus epistatic pairs discovered in these datasets were not classified as robust and were not used in heritability estimates, however the consistency of the statistics and epistatic model across independent datasets indicated that many likely represent bona fide epistasis. Cluster plot inspection removed 115 SNPs with poor genotyping assays.</p>
</sec>
<sec id="s4b">
<title>Statistical tests for epistasis</title>
<p>Here, we briefly describe the intuition behind the Gain in Sensitivity and Specificity (GSS) test we employ to detect epistasis, and later we present several approximations we employ in analyzing epistasis across datasets. The test has been presented in detail in [<xref ref-type="bibr" rid="c31">31</xref>] and, currently, a web server implementing the GSS test is at <ext-link ext-link-type="uri" xlink:href="http://bioinformatics.research.nicta.com.au/software/gwis/">http://bioinformatics.research.nicta.com.au/software/gwis/</ext-link>.</p>
<p>There is a long history of discussion around the exact definition of epistasis, or gene-gene interaction [<xref ref-type="bibr" rid="c41">41</xref>]. Here, we use a definition that is closely aligned with the multifactor dimensionality reduction (MDR) family of gene-gene interaction methods [<xref ref-type="bibr" rid="c42">42</xref>]: an epistatic interaction is defined as a significant improvement of a SNP-pair in classifying cases from controls over what is possible using each SNP individually. There are two main differences between our approach and similar approaches for detecting epistasis [<xref ref-type="bibr" rid="c8">8</xref>,<xref ref-type="bibr" rid="c22">22</xref>]. First, our approach is “model-free”, as it makes no assumptions about the way in which genotypes combine to affect the phenotype [<xref ref-type="bibr" rid="c7">7</xref>,<xref ref-type="bibr" rid="c43">43</xref>], but considers all possible pairwise interactions for each pair, making it potentially more powerful to detect unknown epistatic forms, as empirical knowledge about epistasis in humans is currently lacking. Second, instead of measuring the deviation from additive effects (for example, using a likelihood ratio test), our approach focuses on the utility of the test in case/control classification, quantified using the receiver-operating characteristic (ROC) curve, and measuring the deviation in the curve from that induced by the additive model.</p>
<p>The main principle behind the GSS is quantification of the gain in predictive power afforded by a putative epistatic pair over and above the predictive power due to each of its constituent SNPs. The difference in predictive power is assessed in terms of the ROC curves induced by the pair and each of the SNPs. The ROC curve is formed by considering each possible genotype (or pair of genotypes), and measuring the sensitivity (true positive rate, TPR) and specificity (1 – false positive rate, FPR) at that point, and ordering them in decreasing order by the ratio TPR/FPR; hence the curve is piecewise linear. Since the two ROC curves induced by the individual SNPs may intersect, we represent them using a convex hull, which is the best ROC curve that can be produced by any linear combination of the two individual SNPs, and represents a conservative estimate of the predictive power of the individual SNPs. The GSS then assigns a p-value to each point in the pair’s ROC curve, based on the probability of observing a combination of genotypes with a higher or equal TPR and a lower or equal FPR, under the null hypothesis that the true TPR and FPR reside below the convex hull. We employ a highly efficient minimax-based implementation, maximizing the probability for each point on the ROC curve (worst case scenario) against all points of the convex hull, and returning the minimum probability over all points [<xref ref-type="bibr" rid="c31">31</xref>]; this is done using an exact procedure rather than relying on approximations based on the normal distribution. Finally, the best p-value is assigned as the overall p-value for the pair, allowing the pairs to be ranked and corrected for multiple testing as is standard practice in GWAS. Those SNPs that are significant after multiple testing correction are deemed significant epistatic pairs.</p>
<p>Analogously to odds ratios used for analyses of single SNPs, we can estimate odds ratios for epistatic pairs based on the GSS statistic
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="002485_ueqn1.gif"/></alternatives>
</disp-formula>
where π<sub>{<italic>i</italic>,<italic>j</italic>}</sub> denotes the proportion of samples with phenotype <italic>i</italic>, 0 for cases and 1 for controls, and carrying genotype combinations which are marked as <italic>j</italic> with <italic>HR</italic>(high risk) indicating genotypes which are associated by GSS with cases and <italic>LR</italic> (low risk) indicating genotypes which are associated with controls. By relying on the model-free GSS approach, this odds ratio can be seen as deriving the specific model maximizing the level of improvement over that of the individual SNPs in the pair.</p>
</sec>
<sec id="s4c">
<title>Approximate representation of the epistatic models</title>
<p>While the GSS approach is the basis for detecting epistatic pairs, the models it produces can be hard to visually interpret and categorize into broad groups. To simplify interpretation, we approximate the models for the statistically significant pairs found via GSS using two representations: balanced penetrance models and full penetrance models.</p>
<sec id="s4d">
<title>Balanced penetrance models</title>
<p>Following Li and Reich [<xref ref-type="bibr" rid="c21">21</xref>] we employ the penetrance, that is, the probability of disease given the genotype, estimated from the data for each of the nine genotype combinations as (number of cases with combination)/(number of individuals with combination). Representing the epistatic model in terms of penetrance allows us to clearly see which genotype combinations contribute more to disease risk (or conversely, may be protective).</p>
<p>One limitation of the penetrance is that it is typically considered in isolation of the disease background rate (the prevalence), which may be misleading when comparing penetrance levels across datasets with widely varying proportions of cases. For example, a penetrance of 50% for a given SNP would be considered very high in a dataset consisting of 1% cases and 99% controls, but no better than random guessing in datasets with 50%/50% cases and controls. Hence, we employ a standardization to ensure that the penetrance is comparable across datasets, termed <italic>balanced sample penetrance</italic>, and defined as
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="002485_ueqn2.gif"/></alternatives>
</disp-formula>
where <italic>p</italic><sub><italic>iv</italic></sub> refers to the proportional frequency of genotype <italic>v</italic> in class <italic>i</italic>, where controls are 0 and cases are 1 (0 = controls, 1 = cases). The balanced sample penetrance ranges between 0 and 1, where 0 means that the genotype only occurs in controls, 1 means that the genotype only occurs in cases and 0.5 means the genotype occurs evenly between the two classes. Balanced penetrance can be related to either standard penetrance or relative risk in the data via monotonic transformations. The definition is easily extended to the case of pair of SNPs. The only difference is the use of the 3 × 3 = 9 possible genotype combinations from each SNP-pair rather than the 3-value set of genotypes from an individual SNP.</p>
</sec>
<sec id="s4e">
<title>Simplification to full penetrance models</title>
<p>The balanced-penetrance epistatic models provide fine-grained insight into the relative effects of each genotype combination. In addition, we employ a coarse-grain approach where these values are discretized into binary values (0/1), so called “fully penetrant” models, an approach analogous to that of Li and Reich [<xref ref-type="bibr" rid="c21">21</xref>]. These binary models forgo some detail but make it easier to categorize epistatic models into broad classes based on their patterns of interaction, such as the classic XOR pattern [<xref ref-type="bibr" rid="c8">8</xref>] or the threshold model [<xref ref-type="bibr" rid="c22">22</xref>]. Swapping major and minor alleles, and swapping the SNP ordering in the contingency table, can reduce the number of fully penetrant models. Unlike Li and Reich, we do not swap the high and low risk status, as we are interested in distinguishing between protective and deleterious combinations. Furthermore, Li and Reich also excluded models with all high or low risk genotypes. Such models can not exist within the set we are analyzing as they would show no association with disease. Li and Reich were able to show that there are only 51 possible fully penetrant disease models after accounting for symmetries. However, as we do not swap risk status, there will be 100 possible full-penetrance models that can appear within the analysis conducted here [<xref ref-type="bibr" rid="c22">22</xref>].</p>
<p>Given that some genotype combinations in certain SNP pairs are rare, there may be insufficient evidence to determine whether they have a substantial effect on disease risk. As such, we have used a simple heuristic for such entries, denoting all cells with a frequency below 2% in both cases and controls as ‘low risk’. Experiments with this threshold revealed that altering this cutoff between 0% and 7% made little difference to the overall distribution of our models.</p>
</sec>
</sec>
<sec id="s4f">
<title>The predictive models</title>
<p>We employed a sparse support vector machine (SVM) implemented in SparSNP [<xref ref-type="bibr" rid="c44">44</xref>]. This is a multivariable linear model where the degree of sparsity (number of variables being assigned a non-zero weight) is tuned via penalization. The model is induced by minimizing the L1-penalized squared hinge loss
<disp-formula>
<alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="002485_ueqn3.gif"/></alternatives>
</disp-formula>
where β and β<sub>0</sub> are the model weights and the intercept, respectively, <italic>N</italic> is the number of samples, <italic>p</italic> is the number of variables (SNPs and/or encoded pairs), <italic>x</italic><sub><italic>i</italic></sub> is the <italic>i</italic>th vector of <italic>p</italic> variables (genotypes and/or encoded pairs), <italic>y</italic><sub><italic>i</italic></sub> is the <italic>i</italic>th case/control status {+1, −1}, and λ ≥ 0 is the L1 penalty. To find the optimal penalty, we used a grid of 100 penalty values within 10 replications of 10-fold cross-validation, and found the model/s that maximized the average area under the receiver-operating characteristic curve (AUC). For models based on single SNPs, we used minor allele dosage {0, 1, 2} encoding of the genotypes. For models based on SNP pairs, the standard dosage model is not applicable; hence, we transformed the variable representing each pair (encoded by integers 1 to 9) to 9 indicator variables using the Python library scikit-learn [<xref ref-type="bibr" rid="c45">45</xref>], using a consistent encoding scheme across all datasets. The indicator variables were then analyzed in the same way as single SNPs. Results were analyzed in R [<xref ref-type="bibr" rid="c46">46</xref>] with the packages ROCR [<xref ref-type="bibr" rid="c47">47</xref>] and pROC [<xref ref-type="bibr" rid="c48">48</xref>], and plotted using the ggplot2 [<xref ref-type="bibr" rid="c49">49</xref>] package.</p>
</sec>
<sec id="s4g">
<title>Evaluation of predictive ability and explained disease variance</title>
<p>To maximize the number of SNPs available for analysis, we imputed SNPs in the UK2, FIN, NL, and IT dataset to match those that were in the UK1 dataset but not in former, using IMPUTE v2.3.0 [<xref ref-type="bibr" rid="c50">50</xref>]. Post QC this left 290,277 SNPs common to all five datasets. Together with 9 × 7270 pairs = 65,430 indicator variables, this led to a total of 355,707 variables in the combined singles + pairs dataset. Models trained in cross-validation on the UK1 dataset were then applied without any further tuning to the four other datasets, and the external-validation AUC for these models was then estimated within the validation datasets. To derive the proportion of phenotypic variance explained by the model (on the liability scale), we used the method of Wray et al. [<xref ref-type="bibr" rid="c51">51</xref>], assuming a population prevalence of 1%.</p>
</sec>
</sec>
</body>
<back>
<ack>
<title>Acknowledgements</title>
<p>MI was supported by an NHMRC early career fellowship 637400. MI and GA were supported by University of Melbourne funding. BG, EK, QW, DR, FS, IH and AK were supported by National ICT Australia (NICTA). NICTA is funded by the Australian Government’s Department of Communications, Information Technology and the Arts, the Australian Research Council through Backing Australia’s Ability, and the ICT Centre of Excellence programs.</p>
<p>We thank the investigators of the van Heel et al., 2007 and Dubois et al., 2010 papers (David van Heel and Cisca Wijmenga) for providing the celiac disease data. We thank Karen A. Hunt (QMUL) for performing cluster plot inspection on the UK1 data. We also thank Rami Mukhtar for useful technical advice regarding implementation of algorithms used here and Andrew Kowalczyk and Leon Gor for assistance with development of software utilised for this work. We also thank Armita Zarnegar for assistance with processing of data and John Markham, Justin Bedo and Geoff Macintyre for insightful discussions and comments.</p>
</ack>
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</ref-list>
</back>
</article> |
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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">BIORXIV</journal-id>
<journal-title-group>
<journal-title>bioRxiv</journal-title>
<abbrev-journal-title abbrev-type="publisher">bioRxiv</abbrev-journal-title>
</journal-title-group>
<publisher>
<publisher-name>Cold Spring Harbor Laboratory</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.1101/002634</article-id>
<article-version>1.1</article-version>
<article-categories>
<subj-group subj-group-type="author-type">
<subject>Regular Article</subject>
</subj-group>
<subj-group subj-group-type="heading">
<subject>New Results</subject>
</subj-group>
<subj-group subj-group-type="hwp-journal-coll">
<subject>Ecology</subject>
</subj-group>
</article-categories>
<title-group>
<article-title><monospace>mangal</monospace> – making complex ecological network analysis simpler</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<contrib-id contrib-id-type="orcid">http://orcid.org/0000-0002-0735-5184</contrib-id>
<name><surname>Poisot</surname><given-names>Timothée</given-names></name>
<xref ref-type="aff" rid="a1">1</xref>
<xref ref-type="aff" rid="a2">2</xref>
<xref ref-type="corresp" rid="cor1">*</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Baiser</surname><given-names>Benjamin</given-names></name>
<xref ref-type="aff" rid="a3">3</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Dunne</surname><given-names>Jennifer A.</given-names></name>
<xref ref-type="aff" rid="a4">4</xref>
<xref ref-type="aff" rid="a5">5</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Kéfi</surname><given-names>Sonia</given-names></name>
<xref ref-type="aff" rid="a6">6</xref>
</contrib>
<contrib contrib-type="author">
<contrib-id contrib-id-type="orcid">http://orcid.org/0000-0002-4098-955X</contrib-id>
<name><surname>Massol</surname><given-names>François</given-names></name>
<xref ref-type="aff" rid="a7">7</xref>
<xref ref-type="aff" rid="a8">8</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Mouquet</surname><given-names>Nicolas</given-names></name>
<xref ref-type="aff" rid="a6">6</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Romanuk</surname><given-names>Tamara N.</given-names></name>
<xref ref-type="aff" rid="a9">9</xref>
</contrib>
<contrib contrib-type="author">
<contrib-id contrib-id-type="orcid">http://orcid.org/0000-0001-9436-9674</contrib-id>
<name><surname>Stouffer</surname><given-names>Daniel B.</given-names></name>
<xref ref-type="aff" rid="a10">10</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Wood</surname><given-names>Spencer A.</given-names></name>
<xref ref-type="aff" rid="a11">11</xref>
<xref ref-type="aff" rid="a12">12</xref>
</contrib>
<contrib contrib-type="author">
<contrib-id contrib-id-type="orcid">http://orcid.org/0000-0002-4498-7076</contrib-id>
<name><surname>Gravel</surname><given-names>Dominique</given-names></name>
<xref ref-type="aff" rid="a1">1</xref>
<xref ref-type="aff" rid="a2">2</xref>
</contrib>
<aff id="a1"><label>1</label><institution>Université du Québec à Rimouski, Département de Biologie</institution>, 300 Allées des Ursulines, Rimouski (QC) G5L 3A1, <country>Canada</country></aff>
<aff id="a2"><label>2</label><institution>Québec Centre for Biodiversity Sciences, Montréal (QC)</institution>, <country>Canada</country></aff>
<aff id="a3"><label>3</label><institution>Department of Wildlife Ecology and Conservation, University of Florida</institution>, Gainesville</aff>
<aff id="a4"><label>4</label><institution>Sante Fe Institute</institution>, 1399 Hyde Park Road, Santa Fe NM 87501</aff>
<aff id="a5"><label>5</label><institution>Pacific Ecoinformatics and Computational Ecology Lab</institution>, 1604 McGee Ave., Berkeley, CA 94703</aff>
<aff id="a6"><label>6</label><institution>Institut des Sciences de l’Évolution</institution>, UMR CRNS 5554, Université Montpellier 2, 3405 Montpellier, <country>France</country></aff>
<aff id="a7"><label>7</label><institution>Laboratoire Génétique et Evolution des Populations Végétales</institution>, CNRS UMR 8198, Université Lille 1, Bâtiment SN2, F-59655 Villeneuve d’Ascq cedex, <country>France</country></aff>
<aff id="a8"><label>8</label><institution>UMR 5175 CEFE – Centre d’Ecologie Fonctionnelle et Evolutive (CNRS)</institution>, 1919 Route de Mende, F-34293 Mont-pellier cedex 05, <country>France</country></aff>
<aff id="a9"><label>9</label><institution>Department of Biology, Dalhousie University</institution></aff>
<aff id="a10"><label>10</label><institution>University of Canterbury, School of Biological Sciences</institution>, Christchurch, <country>New Zealand</country></aff>
<aff id="a11"><label>11</label><institution>Natural Capital Project, School of Environmental and Forest Sciences, University of Washington</institution>, Seattle, WA 98195, <country>USA</country></aff>
<aff id="a12"><label>12</label><institution>Department of Biological Sciences, Idaho State University</institution>, Pocatello, ID 83209, <country>USA</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>*</label>Author for correspondence: <email>t.poisot@gmail.com</email>.</corresp>
</author-notes>
<pub-date pub-type="epub">
<year>2014</year>
</pub-date>
<elocation-id>002634</elocation-id>
<history>
<date date-type="received">
<day>12</day>
<month>2</month>
<year>2014</year>
</date>
<date date-type="accepted">
<day>12</day>
<month>2</month>
<year>2014</year>
</date>
</history>
<permissions>
<copyright-statement>© 2014, Posted by Cold Spring Harbor Laboratory</copyright-statement>
<copyright-year>2014</copyright-year>
<license license-type="creative-commons" xlink:href="http://creativecommons.org/licenses/by/4.0/"><license-p>This pre-print is available under a Creative Commons License (Attribution 4.0 International), CC BY 4.0, as described at <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0/">http://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license>
</permissions>
<self-uri xlink:href="002634.pdf" content-type="pdf" xlink:role="full-text"/>
<abstract>
<p>The study of ecological networks is severely limited by (i) the difficulty to access data, (ii) the lack of a standardized way to link meta-data with interactions, and (iii) the disparity of formats in which ecological networks themselves are represented. To overcome these limitations, we conceived a data specification for ecological networks. We implemented a database respecting this standard, and released a R package (<monospace>rmangal</monospace>) allowing users to programmatically access, curate, and deposit data on ecological interactions. In this article, we show how these tools, in conjunctions with other frameworks for the programmatic manipulation of open ecological data, streamlines the analysis process, and improves eplicability and reproducibility of ecological networks studies.</p>
</abstract>
<kwd-group kwd-group-type="author">
<title>Keywords</title>
<kwd>R</kwd>
<kwd>API</kwd>
<kwd>database</kwd>
<kwd>open data</kwd>
<kwd>ecological networks</kwd>
<kwd>species interactions</kwd>
</kwd-group>
<counts>
<page-count count="14"/>
</counts>
</article-meta>
</front>
<body>
<sec id="s1">
<title>Introduction</title>
<p>Ecological networks enable ecologists to accommodate the complexity of natural communities, and to discover mechanisms contributing to their persistence, stability, resilience, and functioning. Most of the “early” studies of ecological networks were focused on understanding how the structure of interactions within one location affected the ecological properties of this local community. Such analyses revealed the contribution of ‘average’ network properties, such as the buffering impact of modularity on species loss (<xref ref-type="bibr" rid="c7">Pimm <italic>et al</italic>. 1991</xref>,), the increase in robustness to extinctions along with increases in connectance (<xref ref-type="bibr" rid="c4">Dunne <italic>et al</italic>. 2002</xref>), and the fact that organization of interactions maximizes biodiversity (<xref ref-type="bibr" rid="c2">Bastolla <italic>et al</italic>. 2009</xref>). More recently, new studies introduced the idea that networks can vary from one realization to another. They can be meaningfully compared, either to understand the importance of environmental gradients on the realization of ecological interactions [@tylianakis_habitat_2007], or to understand the mechanisms behind variation in the structure of ecological networks (<xref ref-type="bibr" rid="c10">Poisot <italic>et al</italic>. 2012</xref>). Yet, meta-analyses of a large number of ecological networks are still extremely rare, and most of the studies comparing several networks do so within the limit of particular systems (<xref ref-type="bibr" rid="c14">Schleuning <italic>et al</italic>. 2011</xref>; <xref ref-type="bibr" rid="c3">Dalsgaard <italic>et al</italic>. 2013</xref>). The severe shortage of data in the field also restricts the scope of large-scale analyses.</p>
<p>An increasing number of approaches are being put forth to <italic>predict</italic> the structure of ecological networks, either relying on latent variables (<xref ref-type="bibr" rid="c13">Rohr <italic>et al</italic>. 2010</xref>) or actual traits (<xref ref-type="bibr" rid="c5">Gravel <italic>et al</italic>. 2013</xref>). Such approaches, so as to be adequately calibrated, require easily accessible data. Comparing the efficiency of different methods is also facilitated if there is an homogeneous way of representing ecological interactions, and the associated metadata. In this paper, we (i) establish the need of a data specification serving as a <italic>lingua franca</italic> among network ecologists, (ii) describe this data specification, and (iii) describe <monospace>rmangal</monospace>, a <monospace>R</monospace> package and companion database relying on this data specification. The <monospace>rmangal</monospace> package allows to easily retrieve, but also deposit, ecological interaction networks data from a database. We provide some use cases showing how this new approach makes complex analyzes simpler, and allows for the integration of new tools to manipulate biodiversity resources.</p>
</sec>
<sec id="s2">
<title>Networks need a data specification</title>
<p>Ecological networks are (often) stored as an <italic>adjacency matrix</italic> (or as the quantitative link matrix), that is a series of 0 and 1 indicating, respectively, the absence and presence of an interaction. This format is extremely convenient for <italic>use</italic> (as most network analysis packages, <italic>e.g.</italic> <monospace>bipartite, betalink, foodweb</monospace>, require data to be presented this way), but is extremely inefficient at <italic>storing</italic> meta-data. In most cases, an adjacency matrix informs on the identity of species (in cases where rows and columns headers are present), and the presence or absence of interactions. If other data about the environment (<italic>e.g.</italic> where the network was sampled) or the species (<italic>e.g.</italic> the population size, trait distribution, or other observations) are available, they are most either given in other files, or as accompanying text. In both cases, making a programmatic link between interaction data and relevant meta-data is difficult and error-prone.</p>
<p>By contrast, a data specification (<italic>i.e.</italic> a set of precise instructions detailing how each object should be represented) provides a common language for network ecologists to interact, and ensure that, regardless of their source, data can be used in a shared workflow. Most importantly, a data specification describes how data are <italic>exchanged</italic>. Each group retains the ability to store the data in the format that is most convenient for in-house use, and only needs to provide export options (<italic>e.g.</italic> through an API, <italic>i.e.</italic> a programmatic interface running on a webserver, returning data in response to queries in a predetermined language) respecting the data specification. This approach ensures that <italic>all</italic> data can be used in meta-analyses, and increases the impact of data (<xref ref-type="bibr" rid="c9">Piwowar <italic>et al</italic>. 2007</xref>; <xref ref-type="bibr" rid="c8">Piwowar & Vision 2013</xref>).</p>
</sec>
<sec id="s3">
<title>Elements of the data specification</title>
<p>The data specification (<xref ref-type="fig" rid="fig1">Fig. 1</xref>) is built around the idea that (ecological) networks are collections of relationships between ecological objects, each element having particular meta-data associated. In this section, we detail the way networks are represented in the <monospace>mangal</monospace> specification. An interactive webpage with the elements of the data specification can be found online at <ext-link ext-link-type="uri" xlink:href="http://mangal.uqar.ca./doc/spec/">http://mangal.uqar.ca./doc/spec/</ext-link>. The data specification is available either at the API root (<italic>e.g.</italic> <ext-link ext-link-type="uri" xlink:href="http://mangal.uqar.ca/api/v1/?format=json">http://mangal.uqar.ca/api/v1/?format=json</ext-link>), or can be viewed using the <monospace>whatIs</monospace> function from the R package (see <italic>Supp. Mat. 1</italic>). Rather than giving an exhaustive list of the data specification (which is available online at the aforementioned URL), this section serves as an overview of each element, and how they interact.</p>
<fig id="fig1" position="float" orientation="portrait" fig-type="figure">
<label>Fig. 1:</label>
<caption><p>An overview of the data specification, and the hierarchy between objects. Each box correspond to a level of the data specification. Grey boxes are nodes, blue boxes are interactions and networks, and green boxes are meta­ data. The <bold>bold</bold> boxes (<monospace>dataset, network, interaction, taxa</monospace>) are the minimal elements needed to represent a network.</p></caption>
<graphic xlink:href="002634_fig1.tif"/>
</fig>
<fig id="fig2" position="float" orientation="portrait" fig-type="figure">
<label>Fig. 2:</label>
<caption><p>Relationship between the number of species and number of interactions in the anemonefish-fish dataset.</p></caption>
<graphic xlink:href="002634_fig2.tif"/>
</fig>
<fig id="fig3" position="float" orientation="portrait" fig-type="figure">
<label>Fig. 3:</label>
<caption><p>Relationships between the geographic distance between two sites, and the species dissimilarity, network dissimilarity with all, and only shared, species.</p></caption>
<graphic xlink:href="002634_fig3.tif"/>
</fig>
<fig id="fig4" position="float" orientation="portrait" fig-type="figure">
<label>Fig. 4:</label>
<caption><p>Spatial plot of a network, using the maps and <monospace>rmangal</monospace> packages. The circle in the inset map show the location of the sites. Each dot in the main map represents a species, with interactions drawn between them.</p></caption>
<graphic xlink:href="002634_fig4.tif"/>
</fig>
<p>We propose <monospace>JSON</monospace>, a format equivalent to <monospace>XML</monospace>, as an efficient way to uniformise data representation for two main reasons. First, it has emerged as a <italic>de facto</italic> standard for web platform serving data, and accepting data from users. Second, it allows <italic>validation</italic> of the data: a <monospace>JSON</monospace> file can be matched against a scheme, and one can verify that it is correctly formatted (this includes the possibility that not all fields are filled, as will depend on available data). Finally, <monospace>JSON</monospace> objects are easily and cheaply (memory-wise) parsed in the most common programming languages, notably R (equivalent to list) and <monospace>python</monospace> (equivalent to <monospace>dict</monospace>). For most users, the format in which data are transmitted is unimportant, as the interaction happens within <monospace>R</monospace> – as such, knowing how <monospace>JSON</monospace> objects are organized is only useful for those who want to interact with the API directly. The <monospace>rmangal</monospace> package takes care of converting the data into the correct <monospace>JSON</monospace> format to upload them in the database.</p>
</sec>
<sec id="s4">
<title>Node information</title>
<sec id="s4a">
<title>Taxa</title>
<p>Taxa are a taxonomic entity of any level, identified by their name, vernacular name, and their identifiers in a variety of taxonomic services. Associating the identifiers of each taxa is important to leverage the power of the new generation of open data tools, such as <monospace>taxize</monospace> [@chamberlain_taxize_2013]. The data specification currently has fields for <monospace>ncbi, gbif, itis, eol</monospace> and <monospace>bold</monospace> identifiers. We also provide the taxonomic status, <italic>i.e.</italic> whether a taxa is a true taxonomic entity, a “trophic species”, or a morphospecies.</p>
</sec>
<sec id="s4b">
<title>Population</title>
<p>A <monospace>population</monospace> is one observed instance of a <monospace>taxa</monospace> object. If your experimental design is replicated through space, then each taxa have a <monospace>population</monospace> object corresponding to each locality. Populations do not have associated meta-data, but serve as “containers” for <monospace>item</monospace> objects.</p>
</sec>
<sec id="s4c">
<title>Item</title>
<p>An <monospace>item</monospace> is an instance of a population. Items have a <monospace>level</monospace> argument, which can be either <monospace>individual</monospace> or <monospace>population</monospace>; this allows to represent both individual-level networks (<italic>i.e.</italic> there are as many items attached to a <monospace>population</monospace> than there were individuals of this <monospace>population</monospace> sampled), and population-level networks. When <monospace>item</monospace> represents a population, it is possible to give a measure of the size of this population. The notion of item is particularly useful for time-replicated designs: each observation of a population at a time-point is an <monospace>item</monospace> with associated <monospace>trait</monospace> values, and possibly population size.</p>
</sec>
</sec>
<sec id="s5">
<title>Network information</title>
<sec id="s5a">
<title>Interaction</title>
<p>An <monospace>interaction</monospace> links, <italic>a minima</italic>, two <monospace>taxa</monospace> objects (but can also link pairs of <monospace>populations</monospace> or <monospace>items</monospace>). The most important attributes of <monospace>interactions</monospace> are the type of interaction (of which we provide a list of possible values, see <italic>Supp. Mat. 1</italic>), and its <monospace>nature</monospace>, <italic>i.e.</italic> how it was observed. This field help differentiate direct observations, text mining, and inference. Note that the <monospace>nature</monospace> field can also take <monospace>absence</monospace> as a value; this is useful for, <italic>e.g.</italic>, “cafeteria” experiments in which there is high confidence that the interaction did not happen.</p>
</sec>
<sec id="s5b">
<title>Network</title>
<p>A <monospace>network</monospace> is a series of <monospace>interaction</monospace> object, along with (i) informations on its spatial position (provided at the latitude and longitude), (ii) the date of sampling, and (iii) references to measures of environmental conditions.</p>
</sec>
<sec id="s5c">
<title>Dataset</title>
<p>A <monospace>dataset</monospace> is a collection of one or several <monospace>network</monospace>(s). Datasets also have a field for <monospace>data</monospace> and <monospace>papers</monospace>, both of which are references to bibliographic or web resources describing, respectively, the source of the data, and the papers in which these data have been significantly used. Datasets are the preferred entry point in the resources.</p>
</sec>
</sec>
<sec id="s6">
<title>Meta-data</title>
<sec id="s6a">
<title>Trait value</title>
<p>Objects of <monospace>type</monospace> item can have associated <monospace>trait</monospace> values. These consist in the description of the trait being measured, the value, and the units in which the measure was taken.</p>
</sec>
<sec id="s6b">
<title>Environmental condition</title>
<p>Environmental conditions are associated to datasets, networks, and interactions objects, to allow for both macro and micro environmental conditions. These are defined by the environmental property measured, its value, and the units.</p>
</sec>
<sec id="s6c">
<title>References</title>
<p>References are associated to datasets. They accommodate the DOI, JSON or PubMed identifiers, or a URL. When possible, the DOI should be preferred as it offers more potential to interact with other on-line tools, such as the <italic>CrossRef</italic> API.</p>
</sec>
<sec id="s6d">
<title>Use cases</title>
<p>In this section, we present use cases using the <monospace>rmangal</monospace> package for R, to interact with a database implementing this data specification, and serving data through an API (<ext-link ext-link-type="uri" xlink:href="http://mangal.uqar.ca/api/v1/">http://mangal.uqar.ca/api/v1/</ext-link>). It is possible for users to deposit data into this database, through the <monospace>R</monospace> package. Data are made available under a <italic>CC-0 Waiver</italic> (<xref ref-type="bibr" rid="c11">Poisot <italic>et al</italic>. 2013</xref>). Detailed informations about how to upload data are given in the vignettes and manual of the <monospace>rmangal</monospace> package. So as to save room in the manuscript, we source each example; the complete <monospace>r</monospace> files to reproduce the examples of this section are attached as <italic>Suppl. Mat.</italic>. In addition, the <monospace>rmangal</monospace> package comes with vignettes explaining how users can upload their data into the database, through <monospace>R</monospace>.</p>
<p>The data we use for this example come from <xref ref-type="bibr" rid="c12">Ricciardi et al. (2010)</xref>. These were previously available on the <italic>Interaction-Web DataBase</italic> as a single <monospace>xls</monospace> file. We uploaded them in the <monospace>mangal</monospace> database at <ext-link ext-link-type="uri" xlink:href="http://mangal.uqar.ca/api/v1/dataset/1">http://mangal.uqar.ca/api/v1/dataset/1</ext-link>.</p>
</sec>
</sec>
<sec id="s7">
<title>Link-species relationships</title>
<p>In the first example, we visualize the relationship between the number of species and the number of interactions, which <xref ref-type="bibr" rid="c6">Martinez (1992)</xref> propose to be linear (in food webs).</p>
<p><preformat>source("usecases/1_ls.r")</preformat></p>
<p>Producing this figure requires less than 10 lines of code. The only information needed is the identifier of the network or dataset, which we suggest should be reported in publications as: “These data were deposited in the <monospace>mangal</monospace> format at <monospace><URL>/api/v1/dataset/<ID></monospace>”, possibly in the acknowledgements. So as to encourage data sharing, we encourage users of the database to cite the original dataset or publication.</p>
</sec>
<sec id="s8">
<title>Network beta-diversity</title>
<p>In the second example, we use the framework of network <italic>β</italic>-diversity (<xref ref-type="bibr" rid="c10">Poisot <italic>et al</italic>. 2012</xref>) to measure the extent to which networks that are far apart in space have different interactions. Each network in the dataset has a latitude and longitude, meaning that it is possible to measure the geographic distance between two networks.</p>
<p>For each pair of network, we measure the geographic distance (in km.), the species dissimilarity (<italic>β<sub>S</sub></italic>), the network dissimilarity when all species are present (<italic>β<sub>W</sub> <sub>N</sub></italic>), and finally, the network dissimilarity when only shared species are considered (<italic>β<sub>OS</sub></italic>).</p>
<p><preformat>source("usecases/2_beta.r")</preformat></p>
<p>As shown in <italic>Fig. XX</italic>, while species dissimilarity and overall network dissimilarity increase when two networks are far apart, this is not the case for the way common species interact. This suggests that in this system, network dissimilarity over space is primarily driven by species turnover. The ease to gather both raw interaction data and associated meta-data make producing this analysis extremely straightforward.</p>
</sec>
<sec id="s9">
<title>Spatial visualization of networks</title>
<p><xref ref-type="bibr" rid="c1">Bascompte (2009)</xref> uses an interesting visualization for spatial networks, in which each species is laid out on a map at the center of mass of its distribution; interactions are then drawn between species to show how species distribution determines biotic interactions. In this final use case, we propose to reproduce a similar figure.</p>
<p><preformat>source("usecases/3_spatial.r")</preformat></p>
</sec>
<sec id="s10">
<title>Conclusions</title>
<p>In this contribution, we presented <monospace>mangal</monospace>, a data format for the exchange of ecological networks and associated meta-data. We deployed an online database with an associated API, relying on this data specification. Finally, we introduced <monospace>rmangal</monospace>, a R package designed to interact with APIs using the <monospace>mangal</monospace> format. We expect that the data specification will evolve based on the needs of the community. At the moment, users are welcome to propose such changes on the project issue page: <ext-link ext-link-type="uri" xlink:href="https://github.com/mangal-wg/mangal-schemes/issues">https://github.com/mangal-wg/mangal-schemes/issues</ext-link>. A python wrapper for the API is also available at <ext-link ext-link-type="uri" xlink:href="http://github.com/mangal-wg/pymangal/">http://github.com/mangal-wg/pymangal/</ext-link>.</p>
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in Data Studio
Grobid End 2 End evaluation dataset
https://grobid.readthedocs.io/en/latest/End-to-end-evaluation/
Official URL: https://zenodo.org/record/7708580
Here are the datasets used for GROBID end-to-end benchmarking covering:
metadata extraction,
bibliographical reference extraction, parsing and citation context identification, and
full text body structuring.
The following collections are included:
a PubMedCentral gold-standard dataset called PMC_sample_1943, compiled by Alexandru Constantin. The dataset, around 1.5GB in size, contains 1943 articles from 1943 different journals corresponding to the publications from a 2011 snapshot. For each article, we have a PDF file and a NLM XML file.
a bioRxiv dataset called biorxiv-10k-test-2000 of 2000 preprint articles originally compiled with care and published by Daniel Ecer, available on Zenodo. The dataset contains for each article a PDF file and the corresponding reference NLM file (manually created by bioRxiv). The NLM files have been further systematically reviewed and annotated with additional markup corresponding to data and code availability statements and funding statements by the Grobid team. Around 5.4G in size.
a set of 1000 PLOS articles, called PLOS_1000, randomly selected from the full PLOS Open Access collection. Again, for each article, the published PDF is available with the corresponding publisher JATS XML file, around 1.3GB total size.
a set of 984 articles from eLife, called eLife_984, randomly selected from their open collection available on GitHub. Every articles come with the published PDF, the publisher JATS XML file and the eLife public HTML file (as bonus, not used), all in their latest version, around 4.5G total.
For each of these datasets, the directory structure is the same and documented here.
Further information on Grobid benchmarking and how to run it: https://grobid.readthedocs.io/en/latest/End-to-end-evaluation/. Latest benchmarking scores are also available in the Grobid documentation: https://grobid.readthedocs.io/en/latest/Benchmarking/
These resources are originally published under CC-BY license. Our additional annotations are similarly under CC-BY.
We thank NIH, bioRxiv, PLOS and eLife for making these resources Open Access and reusable.
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