A pan-genome data structure induced by pooled sequencing facilitates variant mining in heterogeneous germplasm

Valuable genetic variation lies unused in gene banks due to the difficulty of exploiting heterogeneous germplasm accessions. Advances in molecular breeding, including transgenics and genome editing, present the opportunity to exploit hidden sequence variation directly. Here we describe the pan-genome data structure induced by whole-genome sequencing of pooled individuals from wild populations of Patellifolia spp., a source of disease resistance genes for the related crop species sugar beet (Beta vulgaris). We represent the pan-genome as a map of reads from pooled sequencing of a heterogeneous population sample to a reference genome, plus a BLAST data base of the mapped reads. We show that this basic data structure can be queried by reference genome position or homology to identify sequence variants present in the wild relative, at genes of agronomic interest in the crop, a process known as allele or variant mining. Further we demonstrate the possibility of cataloging variants in all Patellifolia genomic regions that have corresponding single copy orthologous regions in sugar beet. The data structure, termed a “pooled read archive,” can be produced, altered, and queried using standard tools to facilitate discovery of agronomically-important sequence variation.


Introduction
Germplasm collections are a source of novel genetic variants for crop improvement. Within a breeding program, if donor parent germplasm from a gene bank accession is unimproved, many cycles of backcrossing to the elite parent are necessary to mitigate the inevitable introduction of undesirable traits genetically linked to the variant of interest. When donor parent germplasm is heterogeneous, isogenic lines may need to be produced prior to introgressive breeding to limit the scope of linkage drag and increase phenotypic uniformity. Recurrent backcrossing and production of isogenic lines is laborious and timeconsuming, sometimes requiring many years (Rojas et al. 2009;Biancardi et al. 2010;McCouch et al. 2012). In some species, the production of isogenic lines may be precluded by inbreeding depression (Li and Brummer 2009;Lindhout et al. 2011).
Abstract Valuable genetic variation lies unused in gene banks due to the difficulty of exploiting heterogeneous germplasm accessions. Advances in molecular breeding, including transgenics and genome editing, present the opportunity to exploit hidden sequence variation directly. Here we describe the pan-genome data structure induced by wholegenome sequencing of pooled individuals from wild populations of Patellifolia spp., a source of disease resistance genes for the related crop species sugar beet (Beta vulgaris). We represent the pan-genome as a map of reads from pooled sequencing of a heterogeneous population sample to a reference genome, plus a BLAST data base of the mapped reads. We show that this basic data structure can be queried by reference genome position or homology to identify sequence variants present in the wild relative, at genes of agronomic interest in the crop, a process known as allele or variant mining. Further we demonstrate the possibility of cataloging variants in all Patellifolia genomic regions that have corresponding Supplementary information The online version contains supplementary material available at https:// doi. org/ 10. 1007/ s11032-022-01308-6. Vol:. (1234567890) In conventional breeding, germplasm collections are explored for desirable traits biologically, via controlled crosses in vivo. For some crops and some traits, it may be more efficient to explore germplasm collections informatically, to identify useful sequence variation in silico. In breeding programs where the trait of interest is well-defined genetically, meaning most genes impacting it are known, genome editing or transgenic approaches can be used to target and modify gene expression patterns to produce desired traits with little need for subsequent "clean up" via recurrent backcrossing (Wolter et al. 2019). In these cases, sequence data repositories, as opposed to living collections of germplasm, have the potential to facilitate target-gene-specific generation of genetic diversity (Rodríguez-Leal et al. 2017;Scheben and Edwards 2018;Belzile et al. 2020).
Currently there is momentum to commence systematic, whole-genome, whole-collection genotyping of gene bank holdings (McCouch et al. 2020). Progress has been made in barley, rapeseed, rice, sorghum, and Capsicum (Wang et al. 2018;Hu et al. 2019;Milner et al. 2019;Wu et al. 2019;Tripodi et al. 2021). Crop varietal production often involves winnowing phenotypic variation by progressive inbreeding, such that a new variety may be near isogenic, to satisfy the requirements that it be distinct, uniform, and stable, for intellectual property protections. Indeed, extensive varietal differentiation is a testament to a crop species' capacity to be recombined to create a wide array of genetically homogeneous and phenotypically predictable lines. Accordingly, gene bank accessions from domesticated crops tend towards genetic homogeneity. Whole-collection genomewide genotyping efforts focused on crop varieties and other homogeneous accessions appropriately sample only one or a few individuals per accession because that is all that is needed.
Wild species retain a vast reserve of genetic variation that was left unsampled as emerging crops passed through the domestication bottleneck (Hawkes 1977;Doebley et al. 2006). In contrast to crop varieties, accessions from wild populations are often genetically heterogeneous. In addition to ubiquitous single-nucleotide polymorphisms (SNPs), gene content also varies dramatically among individuals, with ~ 25% of genes belonging to the "dispensable" fraction of the species' pan-genome . Due to widespread structural variation, the non-coding dispensable fraction may be even higher (Hübner et al. 2019). In Beta vulgaris, for example, flow cytometric estimates of genome size varied from 633 to 875 MB, a 40% difference (Castro et al. 2013;McGrath et al. 2020). For heterogeneous accessions, genome-wide data from a single individual represents an incomplete accounting of sequence variation and is a poor predictor of what a user can expect to receive when the accession is requested for use in a breeding program.
Gene banks are increasingly involved in describing interesting, useful, and valuable genetic variants hidden in collections of wild germplasm (Tanksley and McCouch 1997;Gur and Zamir 2004;Hajjar and Hodgkin 2007;Mascher et al. 2019). A catalog of the wide range of sequence variants present in unimproved germplasm could support molecular breeding initiatives to generate diversity in elite cultivars using transgenic or genome editing approaches. Variants present alternative, naturally-occurring models for site-specific base editing in a crop, or target-sequence information for "de novo domestication" of unruly wild relatives with otherwise desirable stress tolerance, disease resistance, morphological, or nutritional properties (Zsögön et al. 2018;Li et al. 2018;Lemmon et al. 2018). Additionally, for conventional breeding projects, a catalog could support prediction of the frequency of particular traits or trait values in accessions. For traits that are wellunderstood genetically, population phenotypic variation can be predicted from variant frequencies at controlling genes. Prediction of phenotypic variation based on measurement of segregating genotypic variation could enable initial selection of accessions for integration into a conventional breeding program bioinformatically, instead of via extensive grow-outs and phenotyping or imprecise suggestions from passport data and surrogate predictors of genetic diversity (Reeves et al. 2020).
In this study, we demonstrate one approach for cataloging DNA sequence variants from heterogeneous collections of individuals, to inform crop molecular breeding. Our motivation is to improve access to potentially valuable variation in crop wild relatives in the secondary and tertiary gene pools, where biological interrogation of variation using crosses is difficult due to reproductive barriers, as well as primary gene pool members where complex growth requirements or inbreeding depression prevents extensive development of inbred lines. We describe the pan-genome-like properties of data acquired by whole genome sequencing of pools of individuals ("pooled sequencing" or "pool-seq"). We develop a data structure that supports query of this "pool-seq pan-genome" by sequence homology or genome position. Through query, we calculate the proportion of genes expressed in sugar beet (Beta vulgaris) for which orthologous variation can be found in Patellifolia spp. (Thulin et al. 2010), a distant wild relative that diverged from Beta ~ 25 Mya (Romeiras et al. 2016). We likewise calculate the proportion of the entire sugar beet genome with orthologous sequence in Patellifolia-the fraction for which variant mining is uncomplicated by differences in gene content. We catalog whole-genome multi-allelic short haplotype (SH) variation (akin to "microhaplotype" sensu Kidd et al. 2014 andBaetscher et al. 2018) for six heterogeneous samples of Patellifolia spp. Using the catalog, we describe orthologous sequence variants for two sugar beet loci of agronomic importance found in the wild relative.

Materials and methods
Pooled DNA sequencing Leaf tissue from 17 to 25 individuals was collected from six wild populations of Patellifolia spp. in the Canary Islands and mainland Spain (Table 1; Frese et al. 2019). DNA was extracted using the DNeasy 96 Plant Kit (Qiagen GmbH, Hilden, Germany), concentration-normalized to 20 ng/µL, and pooled for DNA sequencing. Sequencing libraries were generated from DNA pools using the KAPA HyperPrep Kit (Roche, Basel, Switzerland) with a PCR-free workflow and average insert size of 300 bp then sequenced on a NovaSeq instrument (Illumina Inc., San Diego, USA) producing 1.8E8-3.4E8 150 bp paired end reads per pool (Table 2).

Data structure construction
Detailed bioinformatic procedures including all software settings are at https:// github. com/ NCGRP/ mb1su ppl. MASURCA 3.2.4 (Zimin et al. 2013) was used to produce a genome assembly for each pool (hereafter, "pool assembly"). Trimmed read pairs  (TRIMMOMATIC 0.33, Bolger et al. 2014) were mapped to the pool assembly using BWA-MEM 0.7.17 (Li 2013) to confirm proximity, filtered by quality using SAMTOOLS 1.8 ), and duplicates removed with SAMBAMBA 0.7.0 (Tarasov et al. 2015) before combining into "phased reads," sometimes called merged reads or "FLASHed reads" (Bushnell et al. 2017;Sundaram et al. 2020). We use the term phased read to refer to a single sequence derived from two or more sequences known to originate from the same physical DNA molecule. In the case of Illumina paired end sequencing, read phasing is a trivial operation of combining the two opposing reads of a read pair into a single sequence, since they derive from opposite ends of the same molecule. Reads from each Patellifolia population were filtered by alignment quality, proximity, and orientation, using the population's pool assembly as a reference genome. Reads were combined into a single sequence (creating a phased read) when both reads of a pair were mapped, properly oriented, within 1000 bp of one another, had a minimum mapping quality of 1, and belonged to the primary alignment, with no split reads allowed. If read pairs met these criteria but were non-overlapping then the intervening region was padded with a string of Ns of a length predicted from the pool assembly contigs to which they mapped. Read pairs that could not be combined into a single sequence by this procedure (unphased reads) were retained because they contain much additional information, albeit within shorter sequences. The reference-free procedure used by FLASH and BBMERGE (Magoč and Salzberg 2011;Bushnell et al. 2017), which considers sequence overlap alone, is also suitable for phasing read pairs (Baetscher et al. 2018).
For each Patellifolia population, a binary alignment map file (BAM file) specifying the map of processed read pairs (including phased and unphased reads, hereafter "reads") onto pool assembly contigs was produced. Mapped reads and their associated pool assembly contigs were processed into a single sorted multi-FASTA file. A BLAST nucleotide database was constructed for the multi-FASTA file and for the pool assembly alone using BLAST + 2.5.0. We define a data structure, hereafter referred to as a "pooled read archive" (PRA), that contains (1) an indexed reference genome, (2) a BAM map between pool-seq reads and the reference genome, (3) a sorted FASTA file containing pool-seq reads and contigs from the BAM map, and (4) a BLAST database for the FASTA file and reference genome. This amalgamated data structure allows the use of standard software to query and retrieve sequence variation from pooled sequence data by genome position (e.g., SAMTOOLS) or homology (BLAST).

Data structure evaluation
We evaluated PRA quality by calculating average read length and coverage of the pool assembly. We explored the utility of Patellifolia PRAs as a source of variants for sugar beet genes by determining the proportion of the sugar beet transcriptome with homologous sequence in Patellifolia pools. PRA BLAST databases were queried with all 24,255 primary transcripts in the sugar beet EL10_1.0 transcriptome (McGrath et al. 2020, https:// phyto zomenext. jgi. doe. gov/ info/ Bvulg aris_ EL10_1_0) with up to 100 K matches returned per query. BLASTN results were filtered to exclude gene models that matched < 40 and > 1000 reads. These cutoff values were determined empirically to capture the linear portion of the sigmoid curve relating cumulative query frequency and log BLAST hit count (Supplemental Fig. 1). Remaining matches were considered to represent the set of homologous genes, excluding highly repetitive (> 1000 hits), unmatched (0 hits), and poorly represented (1-39 hits) genes. We defined orthologous genes operationally, using BLASTN, as EL10_1.0 transcript queries from the homologous set that matched only one contig in the pool assembly from diploid P. procumbens or webbiana (i.e., they were present as single copy genes in the assembly), and two or fewer contigs from tetraploid P. patellaris.
We determined the proportion of the Patellifolia pan-genome represented in the pool-seq data that was homologous to the sugar beet genome. The nine chromosome scaffolds from sugar beet genome assembly EL10_1.0 (NCBI GCA_002917755.1) were fragmented into sequential 1 Kbp sequences, each of which was then used as a BLASTN query against the PRA for the purposes of determining orthology, 1 3 Vol.: (0123456789) as was done with the transcriptome except that up to 10 K matches were allowed to be returned with no subsequent filter on read depth per query applied, in order to retain information on repetitive sequences.

Variant mining
To demonstrate the capacity of pooled sequencing data to facilitate variant mining, we characterized variant frequencies within Patellifolia pools at agronomically-important cyst nematode resistance gene Hs4 (Kumar et al. 2021) and the Patellifolia ortholog of pseudo-response regulator BvBTC1, which determines annual versus biennial life cycle in sugar beet (Pin et al. 2012). Full length mRNA sequences were used to query PRA BLAST databases using BLASTN to identify Patellifolia contigs containing Hs4 and BvBTC1, along with the reads mapped to those contigs, as contained in the PRA BAM file. For detailed analysis and visualization, a gene region containing ~ 12 Kbp and ~ 3 Kbp was arbitrarily defined for BvBTC1 and Hs4, respectively, which encompassed complete coding sequence exons, introns, and some adjacent sequence. Short haplotype loci, defined here as short genomic regions containing one or more SNPs segregating as haplotypes (based on Baetscher et al. 2018), were identified, and major variant frequencies were estimated across each gene region along a tiling path that maximized locus variation, accuracy, and length, in order to simplify presentation of results (details in Supplementary Information).

Results
Pooled DNA sequencing and data structure evaluation Pool genome assemblies varied in size, averaging ~ 775 Mbp in diploids P. webbiana and procumbens, ~ 1.1 Gbp in tetraploid P. patellaris (Table 2). Estimated coverage per individual in the raw data pools varied from 1.9 to 5.2x. Pooled sequencing coverage > 1 × per individual produces allele frequency estimates that are equal to or more accurate than those computed from sequencing individuals (Schlötterer et al. 2014). Pool assemblies were fragmented, containing on average 271,575 contigs with mean N50 ~ 13 Kbp for diploid pools, 164,648 contigs with mean N50 ~ 18 Kbp for tetraploids (Table 2). After filtering during production of the PRA, coverage per individual remained above 1x (1.4-3.5x). Average processed read length ranged from 251 to 275 bp, a substantial increase from the initial 150 bp reads (Table 3). Complete PRA data structures occupied 222 ± 49 GB (± 1 SD) of disk space on average; compressed raw reads occupied 44 ± 16 GB. PRA data structures used in this study are available upon request from the authors.
Of the 24,255 primary transcripts in the EL10_1.0 transcriptome, 1422 were determined to be highly repetitive (chloroplast, rDNA, and mitochondrial genes, plus gene models with repeated amino acid motifs), 3793 unmatched, and 2130 poorly represented in Patellifolia pools (Supplemental Fig. 1). Thus, 70% of the sugar beet transcriptome had homologous sequence regions in Patellifolia. Twentyfive to thirty percent was single copy, here considered orthologous, and therefore a straightforward target for variant mining. Similarly, homologous sequence for 72-80% of the sugar beet genome was found in the Patellifolia pools, 15-21% of it as single copy regions (Table 3). Thus, approximately one fifth of the sugar beet genome is accessible for improvement using sequence diversity mined from Patellifolia, without the complicating issue of paralogy (Fig. 1). Put differently, no homologous counterpart for about 25% of sugar beet genome EL10_1.0 was found in the Patellifolia pan-genome using our procedure.  Table 4.

Discussion
Biological exploration of germplasm through careful breeding and artificial selection has been used to improve crops since the dawn of agriculture. Digitization of germplasm collections so that they may also be explored using information is a longstanding objective of the gene banking enterprise (Volk et al. 2021). Increasingly standardized and interoperable data bases have facilitated query of collections' basic descriptive, or "passport," data (Weise et al. 2020). Enhancing our ability to interrogate collections informatically, at the level of DNA sequence variation in addition to passport and phenotypic data, will accelerate agricultural progress (McCouch et al. 2020).
The pool-seq pan-genome Pooled sequencing, the process of sequencing DNA from multiple individuals simultaneously, induces a pan-genome-like data structure in its output, with sequence variation captured as independent reads derived from different individuals in the  Fig. 3). A single locus with three major variants (red and green found in one pool each, blue in four pools) in intron 4 of BvBTC1 is marked using arrows to show how SH loci appear as bars of the same width, stacked vertically among the pools. Within a pool, the horizontal assemblage of bars shows which variant is the major one, and its probability of being sampled, by virtue of shading, relative to the other pools with the same major variant. A portion of Hs4 was missing from the Tenerife P. patellaris pool assembly pool. Reads may vary in length and configuration depending on sequencing technology, but, assuming PCR-free library construction, should represent actual sequence variants at the approximate frequency they occur in the pool of individuals (Lynch et al. 2014;Schlötterer et al. 2014). This form of pan-genome representation differs from the common one (separately assembled genomes from multiple individuals) and lacks the power to evaluate properties such as adjacency and synteny or core versus disposable fractions ). However, it in principle can reveal the totality of sequence complexity in a pan-genome, albeit as short physical fragments instead of analytically derived contigs, scaffolds, or chromosome length pseudomolecules. For cataloging sequence variation, the "poolseq pan-genome" is a cost-effective and appropriate alternative to sequencing many individuals separately. In outcrossed wild populations, all individuals are expected to have distinct genome sequences due to recombination of standing variation during sexual reproduction history. Individual multi-locus genotypes and long DNA sequence Most major variants at SH loci within exon 5 are identical among pools. Four SH loci where the major variant differed between the six pools were found, labeled sh1-4 with positions marked using a bullet at bottom of panel. In the top panel, variant sequences are shown to the right of the colored bars for sh1, sh2, and sh4, and to the left for sh3. To aid visualization, in the bottom panel, colored bars for sh1-4 have been widened to the right of the locus start point, until they contact the next SH locus with a major variant difference between pools, as in Fig. 2. Major variant frequency is indicated. The three Hs4 exon 5 major variant haplotypes (a, b, c) and their minimum probability of being drawn from the pool is shown at right, calculated as the joint probability of drawing the four contributing SH locus major variants simultaneously. Hs4 exon 5 haplotypes can be recovered most efficiently by sampling the pools marked with an asterisk. The joint probability of drawing haplotype b is low, recommending increased sampling intensity of the procumbens-Tenerife population in a variant mining experiment intent on recovering major variant haplotypes of Hs4 exon 5 1 3 Vol.: (0123456789) haplotypes (those beyond typical linkage disequilibrium decay distances) may not be easily recovered from the population more than once because they are broken up by recombination. A catalog of SH loci across the genome can represent what variants are present, and at what frequency they will be encountered, when sampling a population. A similar catalog of SH loci could be constructed by sequencing individuals separately, but only with added effort and expense relative to pooled sequencing.
Recombinatorial introgression of desirable variants via crossing is often not an option when working with secondary or tertiary gene pools. But in cases where introgressive breeding is possible, the pool-seq pan-genome expresses what is delivered when a heterogeneous gene bank accession is requested: the capacity to recombine into a target line some proportion of the sequence variation segregating in the accession. In other words, the data are an approximate representation of the gamete pool. Thus, a pool-seq pan-genome data structure encapsulates the constraints of reproductive biology inherent to the breeding process, as well as relating logically to most phenotypic characterization and evaluation data held in gene bank data bases, which is usually assessed at the level of populations not individuals .
Production of a PRA to enable query of a poolseq pan-genome involves three main steps: read phasing, mapping of reads to a reference assembly, and production of BLAST data bases. Read phasing is useful for short read data because it increases the complexity of sequences exposed to homology query by increasing their length. The mapping step uses a reference genome assembly as a scaffold upon which to filter reads based on proximity, orientation, and alignment quality. The map enables query by position in the reference as opposed to query by homology. In general, direct homology query of reads is preferred because they represent physical molecules present in the pool that come from a single individual, with no reference to bioinformatically imputed contig sequences. Nevertheless, query by reference position can be useful in certain situations, such as for polyploids or when duplicated genes or common sequence motifs would cause homology query to return excessive numbers of reads.
Pooled sequencing data as a gene bank breeding resource

Application: variant mining
As proof of concept, we considered in detail two genes of agronomic importance in sugar beet. Haplotypic variation in the "bolting gene," BvBTC1, produces differences in bolting time, most coarsely at the level of assuming a biennial vs an annual life cycle, but with some additional variation within categories attributable to rare haplotypes and probably mediated by other genes in the flowering pathway (Pin et al. 2012;Höft et al. 2018;Kuroda et al. 2019). Sequence variants "mined" from BvBTC1 might be useful for improving early-bolting resistance, affecting decisions regarding planting time.
The Patellifolia ortholog of BvBTC1 was found by querying the PRA pool assembly. Examination of mapped reads revealed many differences in SH locus major variants between pools across the genic region (Fig. 2). Because major variant frequencies were generally high (Table 4), one could recover variants of interest with high probability by re-sampling the biological material from which the pooled sequencing data were drawn. Moreover, for most major variants in this set of six pools, only two alleles were found (visualized in Fig. 2 using red and green) which could be recovered with relative ease, by accessing only two populations.
The cyst nematode resistance gene Hs4 has been transferred to some sugar beet germplasm via the translocation of large genomic segments from Patellifolia (Kumar et al. 2021). Via query of pool assemblies, we found that Hs4 is single copy in P. procumbens and P. webbiana. The homeolog from tetraploid P. patellaris diverges less from the P. procumbens/webbiana ortholog than the analogous situation in BvBTC1, but orthologs are still identifiable by the presence of shared indels. Thus, in the Patellifolia/Beta vulgaris tertiary gene pool relationship, ploidy variation seems to be a surmountable problem. This may not hold for all extended gene pools-depending on initial polyploidy events ("allo" vs "autopolyploidy") and evolutionary processes affecting homeologous regions since then, it may not always be possible to distinguish homeologs.
Polyploids are an underutilized resource for mining sequence variants due to technical difficulties encountered in polymorphism assessment. Since phasing beyond the limits of a single read pair is not possible, within the pooled sequencing context a tetraploid individual is no different from two diploids-regardless of parental genome, sequence reads can be recovered from the PRA. But, accurately mapping reads to the correct parental genome will not be possible unless homeologs can be distinguished, making variant frequency estimation impossible in some cases.

Application: germplasm selection
The pool-seq pan-genome can be utilized to select germplasm from large gene bank collections. As with BvBTC1, major allele frequencies across the Hs4 genic region were high and the number of variants tended towards two (Table 4). As an example, let us suppose one was especially interested in Hs4 exon 5. We show that there are three major haplotypic variants covering that ~ 182 bp region, composed of four SH loci, among the six pools examined (Fig. 3). To retrieve these three haplotypes with greatest efficiency, one should use populations represented by the P. webbiana, procumbens-Tenerife, and patellaris-Spain A pools, because these have the highest major variant frequencies at the four SH loci.
The principle illustrated in Fig. 3 can be extended. Because the frequency of all SH locus variants, minor or major, in the pool-seq pangenome can be estimated, the probability of recovering sets of unlinked variants scattered across the genome can be approximated as their joint probability, equal to the product of the individual variant frequencies under the assumption of independent assortment. The minimum probability of recovering long DNA sequence haplotypes from a population can be similarly calculated (it is a minimum probability because physically adjacent variants will usually violate independent assortment). This allows one to select germplasm accessions with the highest probability of delivering haplotypes of interest, and to set the scale of the experiment, in terms of the number of individuals needed to recover desired variants at any position, or set of positions, in the genome.
Whole genome data sets are large and complex. They are often used collectively to describe population structure among accessions or classify germplasm by genetic distance, which, in turn, is used to select accessions from a gene bank (Muñoz-Amatriaín et al. 2014;Milner et al. 2019). For heterogeneous accessions, whole genome data may also be profitably employed using the principle of query, to select accessions based on sequence variation at loci of interest. The nature of species is such that most variation is shared among populations, with the level of allelic diversity primarily dependent on mutation rate and population size (Kimura and Crow 1964). The distribution of allelic variation at loci under selection (e.g., agronomic loci) can deviate substantially from the predominantly neutral loci used for population structure analyses (Reed and Frankham 2001;Reeves et al. 2012). Pool-seq pan-genome data structures enable query and selection of accessions without explicit regard to population structure, accession provenance, or passport information, which may not be meaningful predictors of the occurrence of desirable sequence variation (Reeves and Richards 2018;Reeves et al. 2020).

Future opportunities
Summary and visualization of whole genome data requires a reduction in complexity, and thus a reduction in accuracy when variation at specific sets of loci is desired. Major variant frequency variation displayed in Fig. 2 is one such reduction; there are many other SH locus variants that are not shown. However, a crop genome in its entirety can be mapped to orthologous sequence variants from its broader gene pool (Fig. 1). All loci so mapped are accessible for improvement using sequence information from, in this case, a set of populations from the tertiary gene pool. To express this idea visually, for every bar in Fig. 1, a Fig. 2 can be constructed (see https:// github. com/ NCGRP/ mb1su ppl for visualization). The resulting pre-processed data could be integrated into gene bank data bases to enable rapid query by homology or genome position for variant frequencies, opening up the possibility of selecting accessions based not only on passport data and population structure, but also by targeted query of sequence variation, at any locus.
As crop improvement increasingly supplements conventional field breeding practices with in vitro techniques like transgenics and genome editing, the importance of accurate, comprehensive, sequencebased characterization of gene bank accessions grows. Knowledge of the full complement of sequences is important to ensure genome editing targets are present and to avoid off-target effects (Danilevicz et al. 2020). Pool-seq pan-genomes allow collections to be characterized progressively, one accession at a time; no reanalysis of existing data is required to add data for new accessions. This contrasts with population structure-based characterization, which requires reapplication of the variant calling pipeline and reanalysis with each new sample. Pooled sequencing data is therefore extensible at the level of accessions, but also at the level of the haplotype within accessions, because there is no conceptual barrier to adding single-molecule long read data to existing short reads. This could extend the length of SH loci recovered.

Conclusion
We have proposed one option for a query-ready data structure that captures whole genome sequence variation for heterogeneous populations, where representation by a single individual is inadequate. A data structure based on relatively unprocessed DNA sequence, closely representing the physical molecules from which it was constructed, is likely to be more "futureproof" than derived analytical products, and will provide novel opportunities for crop improvement as new analytical methods are developed.