PG-SCUnK: measuring pangenome graph representativeness using single-copy and universal K-mers

PG-SCUnK: measuring pangenome graph representativeness using single-copy and universal K-mers | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results PG-SCUnK: measuring pangenome graph representativeness using single-copy and universal K-mers View ORCID Profile Cumer Tristan , View ORCID Profile Milia Sotiria , View ORCID Profile Alexander S. Leonard , View ORCID Profile Pausch Hubert doi: https://doi.org/10.1101/2025.04.03.646777 Cumer Tristan 1 Animal Genomics, ETH Zurich , Zurich, Switzerland Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Cumer Tristan For correspondence: t.cumer.sci{at}gmail.com Milia Sotiria 1 Animal Genomics, ETH Zurich , Zurich, Switzerland Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Milia Sotiria Alexander S. Leonard 1 Animal Genomics, ETH Zurich , Zurich, Switzerland Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Alexander S. Leonard Pausch Hubert 1 Animal Genomics, ETH Zurich , Zurich, Switzerland Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Pausch Hubert Abstract Full Text Info/History Metrics Supplementary material Preview PDF Abstract Background Pangenome graphs integrate multiple assemblies to represent non-redundant genetic diversity. However, current evaluations of pangenome graphs rely primarily on technical parameters (e.g., total length, number of nodes/edges, growth curves), which fail to assess how effectively the graph represents homologous stretches across the integrated assemblies. Results We introduce a novel method to quantitatively assess how well a pangenome graph represents its integrated assemblies. Our method quantifies how many single-copy and universal k-mers from the source assemblies are uniquely and completely represented within the graph nodes. Implemented in the open-source tool PG-SCUnK, this approach identifies the fractions of unique, duplicated, and split k-mers, which correlate with short read mapping rates to the pangenome graph. Conclusions Insights provided by PG-SCUnK facilitate the selection of appropriate parameters to build optimal pangenome graphs. Availability and implementation A bash implementation of the PG-SCUnK workflow is freely available under the GNU GPLv3 license at https://github.com/cumtr/PG-SCUnK/ . 1. background Pangenome graphs have emerged as a promising data structure to overcome the limitations of linear reference genomes, which fail to capture genetic diversity thereby introducing mapping biases particularly for diverged genomes ( Günther and Nettelblad 2019 ; Martiniano et al . 2020; Lin et al . 2024 ). Pangenome graphs integrate multiple assemblies and represent their diversity in a single graph ( Abel et al . 2020 ). In such a graph, each node corresponds to a DNA sequence, with input assemblies represented as paths and edges connecting nodes along these paths. Conserved sequences appear as nodes shared across all paths, while variant sites form bubbles or snarls composed of different nodes and edges ( Paten et al . 2018 ). Pangenome graph references can reduce read mapping and variant genotyping biases ( Garrison et al . 2018 ; Sirén et al . 2021 ). Consequently, these graphs enable accurate genotyping across a wide range of variant types, from single nucleotide polymorphisms to large structural variants (SVs) ( Hickey et al . 2020 ). Various statistics are available to assess the quality, contiguity and completeness of linear assemblies ( Li and Durbin 2024 ). Assembly contiguity is often evaluated with technical metrics like total length or contig L50 and N50, while assembly completeness is commonly assessed through the presence (complete or fragmented), absence, or duplication of highly conserved genes (i.e. using BUSCO scores ( Simão et al . 2015 )). For pangenome graphs, existing metrics primarily describe the graph’s structure without addressing its biological relevance. Widely used summary statistics report the total nucleotide length, the number of nodes, edges or paths ( Guarracino et al . 2022 ), as well as node coverage and pangenome growth ( Parmigiani et al . 2024 ). Complex genomic regions (such as centromeres) are often poorly represented in pangenome assemblies and can disproportionately inflate these metrics, thereby complicating their biological interpretation (Milia et al . 2024). Recent work evaluated graph quality by re-aligning either the original long read sequences ( Liao et al . 2023 ) or source assemblies ( Leonard et al . 2023 ) to the pangenome graph. However, none of these approaches comprehensively evaluate how accurately and efficiently the pangenome graph represents the underlying assemblies. Here, we use single-copy and universal sequences to measure how well a graph represents homologous sequences of the source assemblies. We assume that k-mers found exactly once in an assembly (referred to as single copy) and present across all source assemblies of a pangenome (thus universal) are orthologous, thereby should be integrated uniquely in the nodes of the graph. Single-copy and universal k-mers (SCUnKs) from the source assemblies are classified as unique if they appear only once in full length, duplicated if they occur multiple times, and split if they are fragmented across different nodes in the evaluated pangenome graph. We have developed a tool to calculate these three metrics and demonstrated their utility in constructing pangenome graphs that achieve high mapping rates. 2. Implementation We developed PG-SCUnK, a workflow designed to assess pangenome graph quality using SCUnKs derived from the input assemblies. PG-SCUnK categorizes these k-mers into three types depending on their frequency in the pangenome graph nodes: Unique: K-mer present only once and in full within the nodes. Duplicated: K-mer present multiple dmes in full within the nodes. Split: K-mer absent from the nodes, thus fragmented across nodes. The PG-SCUnK workflow is as follows ( Fig. 1 ): Download figure Open in new tab Figure 1. PG-SCUnK workflow. Grey shaded boxes represent the three main steps of the workflow. Captions on the right depict how PG-SCUnK results for a pangenome graph can be represented on a ternary plot, where each point represents the three metrics calculated by PG-SCUnk that sum to 100%. This example graph has 98.5% of the SCUnKs identified as unique, 0.5% identified as duplicated and 1% as split. Graph extraction Sequences are extracted from all nodes in the pangenome graph and every k-mer is identified and its frequency of occurrence counted. Assemblies processing K-mers present only once within each assembly used to construct the graph (single-copy k-mers) are identified. Single-copy k-mers that are present in all the input assemblies are referred to as SCUnKs. Comparison The set of SCUnKs from the input assemblies is compared with those integrated into the graph to identify unique, duplicated, or split k-mers. The PG-SCUnK workflow is implemented as a Bash script that automates these three steps, leveraging the KMC software ( Kokot, Długosz and Deorowicz 2017 ) for efficient k-mer extraction and comparison. 3. Results and discussion We evaluated the performance and output produced by PG-SCUnK on pangenome graphs built for different species using two widely used construction methods. Our evaluation included a cattle pangenome graph generated for this study (initially published by Milia et al . 2024; see supplementary material for details) and four previously published pangenome graphs: two human pangenome graphs ( Liao et al . 2023 ) that were constructed using either PGGB ( Garrison et al . 2023 ) or Minigraph-Cactus ( Hickey et al . 2024 ), a pangenome graph for finches ( Fang and Edwards 2024 ) and one for grapevine ( Liu et al . 2024 ). See Supplemental Table S1 for detailed information about the graphs. Runtime and performances The analysis of k-mer profiles of pangenome graphs with PG-SCUnK is both time- and memory-efficient ( Table 1 ). For example, processing a graph containing 90 haplotype assemblies of a single human chromosome on a single thread required between 19 and 138 minutes per chromosome. Runtime scaled linearly with chromosome size (Fig. S1). Maximum memory usage ranged from 3.6 to 22.1 GB and significantly correlated with graph complexity (Fig. S1). View this table: View inline View popup Download powerpoint Table 1. Computational performance of PG-SCUnK. For each pangenome graph considered, the number in brackets reports the number of haplotypes included in the graph. For CPU time and peak memory usage, the number represents the median value across the different chromosomes while the number in brackets reports the minimum and maximum. All results presented here are for a k-mer size of 100. PG-SCUnK across diverse taxa PG-SCUnK categorizes the SCUnKs into unique, duplicated, and split, thereby revealing apparent differences among the evaluated pangenome graphs ( Fig. 2 & S2). We observed a high proportion of unique SCUnKs ranging from 97.93 to 99.04 in the human pangenome graph built with PGGB , and from 99.11 to 99.42% in the cattle graph. Only a small fraction of the SCUnKs were either duplicated (duplication rates of 0.03-0.94% and 0.06-0.34% for humans and cattle respectively) or split (split rates of 0.89-1.47% and 0.49-0.65%). Human chromosomes displayed some heterogeneity in the PG-SCUnK scores, and this pattern was consistent across both construction methods (i.e. PGGB and Minigraph-Cactus , Fig. S3). Much greater PG-SCUnK scores variability was observed for the finch and grapevine graphs; the finch chromosomal graphs showed a wide range in unique and duplication rates (43.6 to 95.08% for unique and 2.32 to 55.90% for duplicated) coupled with low split rates (0.41 to 2.88%). The grapevine graphs exhibited variable unique and split rates (79.92 to 96.39% and 3.42 to 20.08% respectively) with low duplication levels (0 to 0.52%). Further research is needed to explore if technical factors (e.g., differences in graph construction parameters) or biological factors (e.g., assembly characteristics such as GC content, repeat regions or completeness) contribute to the observed heterogeneity between and within pangenomes. While exploring the reason behind the variability of each specific case is beyond the scope of this study, we provide a companion script (FindSCUnKsRegions.bash) to map unique, duplicated, and split SCUnKs back to the genome. This allows users to identify the genomic regions where these SCUnKs occur which may provide useful to investigate why certain SCUnKs are duplicated or split (Figure S4-S7). Nevertheless, our results demonstrate that PG-SCUnK efficiently exposes how well pangenome graphs represent homologous sequences from the assemblies across the tree of life. Download figure Open in new tab Figure 2. PG-SCUnK scores for various pangenome graphs. The ternary plot presents the PG-SCUnK scores for publicly available pangenome graphs of four species (cattle, human, finch and grapevine). The right panel depicts a detailed view of the top corner of the main ternary plot. Effects of k-mer size We investigated how k-mer size (31, 51, 71, 100 [default], 111, and 211) affects the portion of the genome considered by PG-SCUnK and the inferred scores. Our results revealed striking differences in the absolute proportion of k-mers identified as SCUnKs, ranging for example from 69.3% (-k 31) to 19.7% (-k 211) in humans and from 8.8% % (-k 31) to 0.1% (-k 211) in finches (Fig. S8). This variation may be driven by species-specific heterozygosity, as greater genetic diversity reduces the likelihood of a k-mer being universal (genome wide heterozygosity between 0.0013 to 0.0016 in humans ( Auton et al . 2015 ) and 0.003 to 0.005 in finches ( Shultz et al . 2016 )). Across all tested graphs, the proportion of SCUnKs decreased with increasing k (Fig. S8), likely because larger k-mers are more prone to disruptions by polymorphisms. Despite these variations, k-mer size has little to no effect on PG-SCUnK scores for k ≤ 111 (Fig. S9 - S12): the correlation between PG-SCUnK scores ranged from 0.935 to 0.999 in cattle, 0.992 to 1 in humans, 0.974 to 1 in finches and 0.967 to 0.998 in grapevine. These findings indicate that while k-mer size influences the fraction of the genome considered, its impact on PG-SCUnK scores remains minimal. PG-SCUnK score varies depending on the construction parameters We explored the usefulness of PG-SCUnK for optimizing graph construction assuming that SCUnKs should be found in their full length and unique in an optimally built graph (i.e. maximizing the rate of unique SCUnK). We generated multiple graphs with PGGB for bovine chromosome 13 using varying parameter sets and calculated PG-SCUnK scores for the resulting graphs ( Fig. 3A ). Adjustments to the segment-length parameter (-s) produced distinct effects: low values increased the split rate (indicative of an overly compact graph), intermediate values maximized uniqueness (with a maximum value obtained for -s 10k), and higher values led to increased duplication rates. A similar pattern was observed for the percent-identity parameter (-p), with an optimization of the unique rate at intermediate values. The minimum match length parameter (-k) has no impact on the PG-SCUnK scores at low values but results in a sharp increase in duplication and split rates at higher values. These results demonstrate that PG-SCUnK can be used to guide parameter selection during pangenome graph construction and can aid building high quality reference graphs. Download figure Open in new tab Figure 3. PG-SCUnK scores varies depending on parameter choice and predict the mappability of the graph. (A) PG-SCUnK scores across a wide range of parameters used during the building of a cattle pangenome graph for chromosome 13. For each varying parameter, the two others were fixed to the values used for the entire genome (fixed parameters: -s 75k, -p 98, k 31). (B) Relation between the duplication rate of the SCUnKs identified by PG-SCUnK and the proportion of reads with secondary alignments with a mapping quality of 60 across the range of the graph presented in (A). PG-SCUnK scores predict the mappability of a graph We evaluated the ability of PG-SCUnK to predict the mappability of a pangenome graph, based on the hypothesis that elevated levels of duplicated or split SCUnKs would compromise read mapping accuracy. Using the bovine pangenome graph constructed with various parameters, we simulated short reads from the source assemblies, mapped them to the graph, and assessed two key metrics: (i) the proportion of reads mapping with a perfect score (mapping quality of 60), and (ii) the proportion of those reads with a secondary mapping of equivalent quality. A high proportion of perfectly mapped reads supports the graph’s utility as an unbiased reference. As expected, across all parameter settings, the proportion of simulated reads mapping with a quality score of 60 remained consistently high. For the segment-length parameter (-s), the mean proportion ranged from 92.4% to 93%, except at a segment length of 1 kbp, where it dropped to 83.7% (Fig. S13). For the percent-identity parameter (-p), values ranged from 92.2% to 93.6%, with a notable increase to 98.2% at 99.9% identity (Fig. S13). For the minimum match length parameter (-k), the mapping rate varied between 92.6% and 96.2%, with the lowest rate observed at k = 51 (Fig. S13). Additionally, we observed a negative relationship between the proportion of split SCUnKs and mapping rate: graphs with the highest mapping rates had the lowest split SCUnK proportions (Fig. S14). To assess mapping confidence, we examined the proportion of reads with a secondary alignment of equivalent quality (i.e., both primary and secondary mapping quality = 60). A low rate indicates confident, unique mapping, while a high rate suggests ambiguity. This metric revealed substantial differences across graph-building parameters. The proportion of duplicated mappings increased from 1.4% to 4.6% with varying segment-length values (-s; Fig. 3B , S13), ranged from 3.9% to 6.7% for percent-identity (-p), and spiked to 80.5% at p = 99.9 ( Fig. 3B , S13). For minimum match length (-k), the proportion ranged from 4.1% to 8.5%, with a steep rise at higher values ( Fig. 3B , S13). These trends mirrored the duplication rates captured by PG-SCUnK scores, confirming a clear relationship between duplicated SCUnKs and secondary mapping rates ( Fig. 3B ). Consistent with our single-chromosome observations, a high proportion of reads mapped perfectly across all chromosomes in each organism: 98.6% for humans, 99.1% for cattle, 99.2% for finches, and 97.4% for grapevine (Fig. S15). This proportion was negatively correlated with the fraction of split SCUnKs across organisms (Fig. S16), though intra-organism chromosomal comparisons showed more variability (Fig. S17). The rate of secondary alignments of equivalent quality revealed marked differences between species, with mean values of 0.023 for humans, 0.025 for cattle, 0.15 for finches, and 0.027 for grapevine (Fig. S18), alongside some heterogeneity within each species’ chromosomal graphs. Across all organisms, the fraction of duplicated SCUnKs was positively correlated with the rate of perfect secondary alignments (Fig. S19), a trend largely driven by the finch pangenome but consistently observed across species (Fig. S20). Taken together, these results demonstrate that PG-SCUnK scores predict graph mappability and offer a practical framework for selecting optimal reference graphs for accurate short-read mapping. PG-SCUnK scores outperform existing metrics To the best of our knowledge, there are currently no methods or metrics that formally assess how well a graph reflects its constituent assemblies. However, some existing technical metrics can still be useful to assess the properties of pangenome graphs. One of these metrics is total inflation, which is defined as the ratio of the graph’s total nucleotide length to that of a single assembly (typically the highest-quality or reference assembly). We evaluated how the total inflation score can predict graph mappability and compared it with the PG-SCUnK score (Figure S21). Our results show that, within each organism, inflation correlates with the relative mappability of the chromosomal graph; specifically, higher inflation scores are associated with increased duplication rates. However, absolute inflation values varied substantially across organisms. For instance, certain cattle graphs exhibited inflation scores twice as high as the maximum observed in finches, despite having less than a third of the duplication rate. In contrast, the PG-SCUnK score provides a more absolute measure of mappability by relating the SCUnK duplication rate to the probability of a read having a secondary hit with a mapping quality of 60. Overall, these findings suggest that while total inflation may serve as a quick indicator of problematic graphs within a species, PG-SCUnK offers a more detailed and standardizable alternative. It delivers both a score and an analytical framework, even when evaluating a single graph. 4. Conclusion PG-SCUnK assesses pangenome graph quality through quantifying the representation of single-copy and universal k-mers. This method compares and benchmarks pangenome graphs independently from the source assemblies, thereby enabling to evaluate how well a graph captures the underlying assemblies. PG-SCUnK introduces intuitive metrics that complement traditional graph-level summaries by focusing on sequence representativeness rather than structural properties alone, thereby enhancing the interpretability and utility of graphs for downstream analyses. Availability and requirements Project name: PG-SCUnK Project home page: https://github.com/cumtr/PG-SCUnK Operating system(s): Linux, MacOS Programming language: Shell, R Other requirements: KMC v3 License: GNU GPL 3. Any restrictions to use by non-academics: see License Ethics approval and consent to participate Not applicable Consent for publication Not applicable Availability of data and materials Supplementary data are available online. The PG-SCUnK workflow is freely available at https://github.com/cumtr/PG-SCUnK . Code used in this article is available at https://github.com/cumtr/PG-SCUnK_paper . The bovine graph produced in this study is available on Zenodo at https://zenodo.org/records/15097551 . Other pangenome graphs used in this study are available at: https://s3-us-west-2.amazonaws-.com/human-pangenomics/index.html?prefix=pangenomes/freeze/freeze1/pggb/chroms/ and https:-//s3-us-west-2.amazonaws.com/human-pangenomics/index.html?prefix=pangenomes/freeze/-freeze1/minigraph-cactus/hprc-v1.1-mc-grch38/hprc-v1.1-mc-grch38.chroms/ for the human pan-genome graphs, https://datadryad.org/stash/dataset/doi:10.5061/dryad.hhmgqnkqb for the finch pangenome graphs, and https://zenodo.org/records/10851548 for the grapevine pangenome graphs. Competing interests The authors declare that they have no competing interests Funding This study was supported by a grant from the Swiss National Science Foundation (SNSF; grant ID 204654). Authors’ contributions TC conceptualized and designed the study with input from HP. TC implemented the method with assistance from ASL. TC conducted the analyses with support from SM and ASL. 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Bioinformatics 2015 ; 31 : 3210 – 2 . OpenUrl CrossRef PubMed ↵ Sirén J , Monlong J , Chang X et al. Pangenomics enables genotyping of known structural variants in 5202 diverse genomes . Science 2021 ; 374 : abg8871 . OpenUrl CrossRef PubMed View the discussion thread. Back to top Previous Next Posted September 03, 2025. Download PDF Supplementary Material Email Thank you for your interest in spreading the word about bioRxiv. NOTE: Your email address is requested solely to identify you as the sender of this article. Your Email * Your Name * Send To * Enter multiple addresses on separate lines or separate them with commas. You are going to email the following PG-SCUnK: measuring pangenome graph representativeness using single-copy and universal K-mers Message Subject (Your Name) has forwarded a page to you from bioRxiv Message Body (Your Name) thought you would like to see this page from the bioRxiv website. 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