Pinus mugo and P. uncinata, contrasting them with a reference lowland relative—P. sylvestris. We genotyped 438 samples at thousands of single nucleotide polymorphism (SNP) markers, tested their genetic differentiation and population structure followed by outlier detection and gene ontology annotations. Markers clearly differentiated the species and uncovered patterns of population structure in two of them. In P. uncinata three Pyrenean sites were grouped together, while two outlying populations constituted a separate cluster. In P. sylvestris, Spanish population appeared distinct from the remaining four European sites. Between mountain pines and the reference species, 35 candidate genes for altitude-dependent selection were identified, including such encoding proteins responsible for photosynthesis, photorespiration and cell redox homeostasis, regulation of transcription, and mRNA processing. In comparison between two mountain pines, 75 outlier SNPs were found in proteins involved mainly in the gene expression and metabolism.Mountain plants, challenged by vegetation time contractions and dynamic changes in environmental conditions, developed adaptations that help them to balance their growth, reproduction, survival, and regeneration. However, knowledge regarding the genetic basis of species adaptation to higher altitudes remain scarce for most plant species. Here, we attempted to identify such corresponding genomic regions of high evolutionary importance in two closely related European pines,  The sessile lifestyle of plants forces them to develop adaptations, enabling them to quickly, reversibly, and often enduringly cope with environmental changes or colonize new niches to avoid competition. Because photoperiod and temperature are important environmental factors for plants, long-lived trees must make trade-offs between survival, regeneration, development, and reproduction, fitting annual growth cycles in response to seasonal length variations . For alpPinus in the Pinaceae family of conifers has a widespread distribution, mostly in the Northern Hemisphere, with nearly 100 species being described [Pinus mugo complex are known: the dwarf mountain pine (Pinus mugo (Turra)) and the Pyrenean mountain pine (P. uncinata (Ramond)). The dwarf mountain pine is a shrubby species that creates dense carpets on the ground, occasionally reaching 3 m in height. This species inhabits stands above tree lines, up to about 2700 m [The genus escribed , includit 2700 m ,14. The t 2700 m ,16,17, et 2700 m ,18. The t 2700 m ,20.Although these two pines share a common history, have similar genomic backgrounds, and occupy comparable environments that demand the same specific adaptations, they are differentiated by a number of phenotypic and genetic characteristics. Biometric studies showed that in addition to their different growth forms, these two species differ in various cone and needle characteristics ,18,21. UAs the species overlap to a certain extent across altitude, temperature, and rainfall ranges, we might expect patterns of adaptive phenotypic variation to be similar for both. Generally, variation between species may be a consequence of adaptive changes, including selection for species-specific or high-frequency divergent alleles accumulated over the time of independent evolution, but this variation may partially result from mutation load, recombination, and demography. To date, attempts to identify potential drivers of the adaptation of these trees to mountain habits or to investigate their mutual dissimilarity have been notably limited and have focused on a small number of genetic regions. This small number of studies reflects the overall challenge in pine research related to their longevity and long generation time, which make experimental investigations impractical. Molecular studies focused on identifying potential loci under selection are also demanding, considering the large and complex genomes of pines, that hamper the acquisition of a reliable whole genome reference assembly . P. sylvestris L.). The Scots pine is a species with vast but mostly lowland distribution and is the closest living relative of both mountain pines from which they diverged approximately 5 million years ago [In the present study, we attempted to broaden our knowledge regarding the patterns of polymorphisms and divergence in two subalpine taxa to identify subjects of selection potentially responsible for their adaptations and speciation. We analyzed these two species because their evolutionary history has not been fully elucidated, and because they are both potentially threatened by ongoing habitat loss ,20,32. Wears ago ,34. We cears ago . This neears ago , some reAfter quality filtering of SNPs and individuals following our criteria of genomic origin and potential linkage of markers, frequency of alleles (MAF), percentage of individuals properly genotyped per marker, and percentage of SNPs genotyped per individual, the data set consisted of 6003 polymorphisms and 438 samples: 79 dwarf pines, 182 Pyrenean pines, and 177 Scots pines, derived from 14 populations spread across Europe .d), which in the case of Scots pine’s populations did not exceed 1000, ranged between 1193.4 (M14) and 1437.1 (U18) in the stands of other two species. The observed heterozygosity (Ho) was generally higher than the unbiased expected heterozygosity (uHe), resulting in multiple negative values of fixation indices (F) in populations. Two heterozygosity estimates did not differ notably in terms of mean values between species; however, in all cases, except for uHe between mountain pines, the differences were highly statistically significant (p < 0.001). In populations, Ho exhibited the lowest levels in Scots pine (from 0.160), while populations of the two mountain pines exhibited higher values ; however, in the latter two species, the statistics decreased in relation to Ho, while the Scots pine’s average increased (F) calculated on the whole dataset appeared to be positive (0.081), which was also observed in Scots pine (0.067) and its two populations; nevertheless, the majority of investigated stands exhibited greater diversity than was expected.The populations varied considerably in terms of the percentage of polymorphic loci. This index ranged from 61.1% to 91.3%, exhibiting a mean over the 14 populations that was equal to 80.4%, but higher averages within species reached above 90% . The majncreased . The fixTo validate the robustness of our marker set in terms of discrimination power among analyzed species and populations, and to utilize it for the reconstruction of relationships among them, we assessed our data using a series of distance, differentiation, and clustering methods.xyd = 1761.9) was observed between Scots and dwarf pines; the second largest gap, which was considerably smaller, was between Scots and Pyrenean pines with xyd = 1552.3, while the two mountain species were separated by 1523.5 nucleotides of differences on average. A similar pattern was also reflected in the results obtained from respective comparisons of population pairs  was higher than that observed between individuals of Scots (d = 1003.5) or dwarf mountain pine (d = 1308.7) and only slightly larger than observed among individuals of Pyrenean pine (d = 1426.8); however, it was markedly lower than the distances between taxa . The laron pairs , with exon pairs , which don pairs .p < 0.001). In the AMOVA with no imposed structure, 22.51% of the variation differentiated taxa and 77.49% segregated within them. The overall Fst fixation index values in these two versions of the test were equal to 0.2672 and 0.2251, respectively. More specific calculations of differentiation indices (Fst = 0.3612), and taxa from the P. mugo complex reached a considerably lower level of Fst = 0.1061 (or 0.1510 when population structure was included). Comparisons between individual populations, where Fst values ranged between 0.015 (M8 vs. M12) and 0.451 (M14 vs. S37), generally confirmed previous findings. One exception was found in the case of Pyrenean pine population U28, which exhibited a closer relationship with most Scots pine’s stands than with the Alpine dwarf pine provenance M14. Moreover, most of the populations in this species showed genetic similarity to dwarf pine population M8, often exhibiting higher similarity than to other populations in their own taxon. All the Fst values between taxa and among populations were significant (p < 0.001).Analysis of molecular variance (AMOVA) with populations hierarchically grouped within their respective species demonstrated that the majority of variance present in our data segregated inside populations (73.28%), and the variation between them was considerably lower (5.43%) than that among taxa (21.28%); all these results were statistically significant  was conducted, and principal component analysis (PCA) was subsequently employed to characterize variation within populations and to elucidate individual genotypes. In comparison between all 14 investigated populations, the three first axes of PCoA explained 58.8%, 12.6%, and 5.7% of the original variation, respectively, while in PCA, considering variation among individuals, these values decreased to 12.3%, 3.5%, and 2.0% , confirmTo verify the hypothesis of isolation by distance (IBD), i.e., to formally determine whether genetic differences are larger between populations when geographic gaps among them increase, we performed Mantel tests of correlation between genetic and geographic distances. This analysis was needed to ensure that STRUCTURE analyses would not be affected by bias caused by data with allele frequencies varying gradually, as the model underlying this clustering method is not well suited for such scenarios. These analyses were computed for the whole set of 14 populations, as well as in two-species comparisons and within taxa. Except for intraspecies tests in all other cases, these correlations were positive and significant . We consK values between 1 and 10, division into two groups  of their genomes. In the case of K = 3  method) for indication of best genetically explicit grouping from the examined range of o groups a was indo groups . Accordithe best b. Splittt K = 2, a validatof K = 3 , each spK values  were chaK values b, which K = 2 . We later performed a more in-depth examination of the loci that were found simultaneously in three analyses or were significant at more stringent level . In total, in all the comparisons conducted between species, 120 outlier SNPs were confirmed by at least two methods at the significance level of 0.05 , while only one such marker was detected between the last species and dwarf pine . BetweenEach of the 120 highly divergent outliers was subjected to Gene Ontology annotation. Sequences from the reference transcriptome (contigs) on which the SNPs were called and derived from were subjected to OmixBox, where they underwent phases of BLAST search, GO mapping, gene annotation, InterProScan annotation and final merging of the results from last two steps. From the initial input 5 contigs yielded no alignment in the xblast search  database with NCBI blastn to identify related nucleotide sequences that could substitute the original queries proved equally inefficient). Furthermore, 15 sequences failed at the BLAST quality filtering, mapping or annotation step, leaving 100 loci that successfully passed the whole annotation process, described by 239 different GO terms in total . The detThree comparisons among Scots and mountain pines  yielded only one marker that was supported by them all, and it was the singular marker that diverged between dwarf and Scots pines. This particular SNP was observed in a transcript (comp28590_c0_seq1) with very good xblast and annotation quality. The sequence was described as photosystem I P700 chlorophyll A apoprotein A2 (phyA), an integral component of the thylakoid membrane, which participates in electron transfer during photosynthesis. Except for that particular sequence, both alpine taxa were differentiated from Scots pine in 34 other loci, of which 29 were correctly annotated. Half of these markers (17) were also found at variance in Pyrenean pine and its lowland relative when they were analyzed independently along with 12 additional outlier loci not found in any other comparison .p/q value of 0.01 too.From genes with SNPs differentiating two focal pines, 241 terms were elucidated. More of the ontologies belonged to MF (45 different terms found for 50 out of 64 efficiently annotated transcripts) and BP domains (42 terms for 48 transcripts) than were affiliated with CC (23 terms found for 38 sequences). Molecular functions were most commonly represented by the binding of organic cyclic compounds, heterocyclic compounds, or ions and by transferase, transcription regulator, and catalytic activities . Among bIn this study, we analyzed genetic relationships between a pair of closely related coniferous taxa—dwarf mountain pine and Pyrenean mountain pine. Studies of the adaptive variation of these species are especially important due to environmental changes and ongoing habitat loss in mountainous areas. Although these taxa face rather similar environmental pressures and share a common genetic background ,31, theyP. mugo genotyping in this study, probably an outcome of imbalanced mixing of species samples during array development. To keep as many individuals of this focal species as possible, we made a trade off on the number of markers, excluding those that performed the worst in P. mugo.The number of finally used markers (6003 SNPs) appeared low compared to the number of those primary arranged on the array . This drop was a result of a combination of factors, first of all of a medium-low conversion rate on the test set of samples . The seP. mugo complex exhibited more common variants and their allele frequencies were more evenly distributed, as observed in distance and differentiation indices, than between any of these samples and the five Scots pine populations.Patterns of genome-wide polymorphism at a set of nuclear SNPs in the analyzed pines showed that most variation  was distributed within populations. This result is in line with patterns previously found in the case of pollen transmitted chloroplast markers ,30,39 anFor the majority of statistical analyses, a closer relationship between Pyrenean pine and Scots pine was observed, rather than between the latter and dwarf pine, and the pattern was mostly affected by two Pyrenean pine populations. A close genetic relation between these taxa, which could have preserved more of the ancestral polymorphisms, was also observed in earlier comparative analyses of transcriptomes, phenology, and certain phenotypic traits . P. mugo complex [Fst = 0.151); moreover, a larger proportion of variation was found among species (9.14%) than among populations (5.95%). Similar to previous resequencing studies of nuclear loci [Our study provides a new example ,41,42 of complex ,38. The ear loci ,31, no fFst estimates—on average, half the size of that observed in the two other species. Only the Abruzzian site M16 emerged as an individual cluster in Bayesian clustering under K = 7. Earlier studies showed that trees from that population exhibit many phenotypic [Fst estimates. This population also did not show signs of closer affinity to Pyrenean pine such that more than that one specimen from this stand was grouped with samples of the sister species in PCoA analysis  appeared particularly similar to each other, as they grouped together on PCA and PCoA plots, the phylogenetic dendrograms, and equally clearly in STRUCTURE analysis. These stands also exhibited the greatest diversities of individual genotypes, well expressed in measures of heterozygosity and on PCA plots. Moreover, the two populations were characterized by considerably higher similarity to Scots pine, and on the UPGMA tree with all three taxa included, they were even located at the branch specific to Scots pine. Distinctness of the two stands and their striking genetic similarity, especially in the context of significant mutual geographical distance, was observed earlier based on mitochondrial and chloroplast markers ,30,39 anxyd) showed little variation among Scots pine populations compared to the other taxa, whilst conclusions based on allele frequency differentiations (Fst) indicated that this species is the least consistent of all. Although Scots pine appeared very consistent not only on the UPGMA tree but also on the plots obtained with multivariate analyses, STRUCTURE showed divergence of the Iberian Peninsula population (S37) that also exhibited the highest Fst in pairwise tests in relation to provenances of its own and of other species, which can be interpreted as a signal of its stronger spatial isolation from other species’ sites [Although Scots pine was not the focal species in our study, some observations regarding its genetic variation may be noted based on the conducted analyses. Distinct patterns of differentiation of populations within species were obtained using our two approaches. Estimates based on numbers of nucleotide differences  has been demonstrated [Loci, from which the 35 outlier SNPs differentiating two mountain species from the reference taxon were derived may serve as potential targets of selection that have shaped today’s diversity of these pines. Transcripts for which gene ontology annotation was possible primarily represent proteins taking part in photosynthesis, cell redox homeostasis, photorespiration or oxidant detoxification, regulation of transcription and mRNA processing. Some of these genes encoded diverse protein-related agents , molecules participating in transport or in cortical microtubule organization. The set of identified genes corresponds to previous studies in alpine conifers and other plants, in which the existence of various adaptive strategies for reducing photodamage  and serine/threonine-protein kinase VPS15-like (isoform X1). The first molecule is an element of the adaptor protein (AP) complex and most likely functions as a vesicle coat component involved in targeting proteins from the trans-Golgi network (TGN) to the endosomal-lysosomal system ,57, therpinaster  and Abieies alba ,61. Thisssoniana . Althougssoniana . The molssoniana , this prssoniana , to whicssoniana . This messoniana , and altssoniana ,69,70,71ssoniana . Folatesssoniana ,74. Distssoniana ,76.Arabidopsis [Pinus pumilla in Asia, that their mean stem height was approximately four-fold lower at the upper distribution limit (49 cm) than at the lower limit (187 cm), and the ratio of stem height to length was also lower at the upper distribution boundary [Considering that these species exhibit substantial distinctions in growth forms, some anatomical and morphological traits and phenology, certain genes may be responsible for the observed diversity. Good candidates could potentially be among factors regulating the development and receptivity of individuals to periodic life cycle events, such as different kinds of phytohormones. Among the uncovered outliers, only three annotated sequences matched the prediction directly; one was annotated as the ethylene-responsive transcription factor ERF112, and the other two were transcription factors acting in response to gibberellins (two isoforms of scarecrow-like protein 3 (scl3)). Although the role of the first protein is less clear, the involvement of gibberellin signaling pathways is notable. Gibberellins (GA) constitute a group of plant hormones important for the regulation of various developmental processes, such as flowering, germination, senescence of fruits and leaves, dormancy or stem elongation; therefore, genes affected by GA appear to be likely candidates for controllers behind the observed shifts in phenology and phenotypes of pines. Mutants in GA biosynthesis and downstream responses have been observed in a variety of taxa, often causing dwarfism or semi-dwarfism of plants, including alpine plants ,78. The bidopsis . Alpine boundary . Moreoveboundary ,82, amonboundary , suggestIn the future, information regarding the patterns of expression of genes important in speciation history, including those demonstrated here, and of epigenetic marks could help to elucidate the evolutionary trajectories of these plants. As these differences cannot be fully explained by nucleotide variation alone, these factors are usually important drivers of phenotypic and phenological variation in long-lived, sessile organisms. A better ecological description of habitats occupied by mountain species is needed because more detailed eco-physiological findings may help to elucidate the mechanistic connection between the identified diverged sequences and the selection pressures acting on the trees. Moreover, correlation studies conducted on a larger set of populations to check if the environmental factors and genetic diversity of investigated pines vary dependently would be required, with special focus on the revealed outlier sequences. Another, well-suited test for altitude-related adaptations could incorporate association studies performed on repeated pairs of genetically homogenous populations, coming from lower versus higher altitude locations.The nuclear loci investigated in this study showed largely homogeneous patterns of variation between the taxa; nevertheless, using a novel set of SNPs, we managed to delineate the three species. Differentiation within species appeared moderate; however, some of the patterns of population structure appeared consistent between analyses, especially the differentiation found in the Pyrenean pine population. The outlier loci possibly targeted by selection and variable between two mountain species and the reference, represented two main groups of biological functions—were involved either in oxidation-reduction processes or regulation of transcription, including transcripts engaged in the gibberellin signaling pathway, known of its important function in plant development and of its connection with dwarf phenotypes, which are important adaptations observed in high-mountain species.Considering the longevity of pines, their predominantly outcrossing mating system with considerable pollen transport abilities and effective population sizes, our results indicate that the SNP array, providing genotyping data directly comparable between different experiments, may serve as a new diagnostic tool enhancing the discrimination power of previously limited biometric and genetic features of the species that may be useful in a variety of applications in population genetics.Pinus mugo Turra), Pyrenean pine (P. uncinata Ramond), and Scots pine (P. sylvestris L.) were investigated. Initially, cones from five mother trees, distanced from each other by a minimum of 50 m, were collected from 14 natural populations of the taxa—four or five stands per species. The formal biometric identification of the mother trees was conducted by Prof. Krystyna Boratyńska from the Institute of Dendrology, Polish Academy of Sciences, who generously shared the material . Seedlings obtained from the open-pollinated seeds were grown under unified conditions of a common garden experiment at a glasshouse facility of the Centre for Ecology and Hydrology, Edinburgh, UK . From tDNA was extracted from needles using a DNeasy 96 Plant Kit . Needles were dried on silica gel prior to extraction and DNA was quantified using a Qubit spectrophotometer  to ensure a minimum standardized concentration of 35 ng/µL. We genotyped 49,829 SNPs that were used for the development of the Axiom_PineGAP SNP array . Details about the array design and initial quality assessments performed on the called SNPs are described in Perry et al.  and candhttp://pngu.mgh.harvard.edu/purcell/plink/, accessed on 29 August 2019; [http://www.cmpg.unibe.ch/software/PGDSpider/, accessed on 30 June 2017; [https://cran.r-project.org/bin/windows/base/old/3.6.1/, accessed on 22 July 2019; [From the initial set of 49,829 SNP markers designed on the array and 20,795 loci that passed basic quality tests (details available in ), the nust 2019; ), PGDSpine 2017; ), and R ly 2019; ,90).%P), (2) number of private polymorphisms (Sp), (3) mean within group distance (d), (4) observed heterozygosity (Ho), (5) unbiased expected heterozygosity (uHe) taking into account sample sizes, and (6) fixation index (F). Calculations of %P, Sp, Ho, uHe and F were conducted in GenAlEx v.6.503  percentage of polymorphic sites , and ofch 2017; ).xyd) in MEGA, both for three species and for the two mountain pines only. Differentiation of populations was investigated by the hierarchical analysis of molecular variance (AMOVA) using Arlequin v.3.5.2.2  method [K values—DeltaK [http://taylor0.biology.ucla.edu/structureHarvester/, accessed 26 June 2020; [http://omicsspeaks.com/strplot2/, accessed 11 July 2020; [Pinus mugo complex only to more specifically investigate the discrimination power of the array within this aggregate. In this case, K values between 1 and 9 were inspected, with each employing four runs with the same parameters as above.To reconstruct the genetic structure of the analyzed group of populations, and thereby to assess the robustness of our SNPs set in terms of discrimination power for studied populations and species and to delineate more subtle genetic relationships among them, we employed a number of clustering methods. In these tests, we checked the distribution of genetic variation among different levels of the population hierarchy, i.e., among (1) the three species (herein MUS), (2) two mountain pines vs. Scots pine (MU vs. S), (3) two focal species (M vs. U), (4) dwarf vs. Scots pine (M vs. S), (5) Pyrenean vs. Scots pine (U vs. S), and (6) populations within each taxon separately afterwards . To investigate whether populations tend to group by species identities or other patterns, the unweighted pair group method with arithmetic mean (UPGMA) phylogenetic tree was calculated based on the mean between population distances . Firer 2020;  to deterer 2020; ) and geoer 2020; ) were user 2020; ,101,102.) method  and the s—DeltaK . Both wene 2020; ), while ly 2020; ). An anaFst statistics, namely, FDist, BayeScan, and FLK  MU vs. S, (2) M vs. S, (3) U vs. S, and (4) M vs. U. For the analysis, we used three methodological approaches, all based on ease see ). Tests ch 2020; ), and inch 2020; ), we emphttps://www.biobam.com/omicsbox/, accessed on 11 June 2020; [Respective contigs containing outlier SNPs revealed in those comparisons were imported into OmicsBox v.1.2  and anane 2020; ,111. Altne 2020; , we deci


Popcorn to estimate the shared heritability, i.e. genetic correlation, using only summary statistics. Here, we evaluate Popcorn under several parameters and circumstances: sample size, number of SNPs, sample size of external reference panel, various population pairs, inappropriate external reference panel, and admixed population involved. Our results determined the minimum sample size of the external reference panel, summary statistics, and number of SNPs required to accurately estimate both the genetic correlation and heritability. Moreover, the number of individuals and SNPs required to produce accurate and stable estimates was directly proportional with heritability in Popcorn. Misrepresentation of the reference panel overestimated the genetic correlation by 20% and heritability by 60%. Lastly, applying Popcorn to homogeneous (EUR) and admixed (ASW) populations underestimated the genetic correlation by 15%. Although statistical approaches estimating the shared heritability between ancestral populations will provide novel etiologic insight, caution is required ensuring results are based on the appropriate sample size, number of SNPs, and the generalizability of the reference panel to the discovery populations.While novel statistical methods quantifying the shared heritability of traits and diseases between ancestral distinct populations have been recently proposed, a thorough evaluation of these approaches under differing circumstances remain elusive. Brown et al.The online version contains supplementary material available at 10.1007/s00438-021-01817-7. Popcorn to estimate genetic correlation using summary statistics. Although Popcorn produces unbiased estimators of genetic correlation and heritability, it requires large sample sizes, large number of SNPs and matched external reference panels, and is limited to the utility of homogenous populations. We evaluated Popcorn under several parameters and circumstances: sample size, number of SNPs, sample size of external reference panel, various population pairs, inappropriate external reference panel and admixed population involved. It provides plenty of valuable reference information for researchers using the method to obtain more accurate and stable estimates for both genetic correlation and heritability.As the number of genome-wide association studies conducted in both single- and multi-ancestral populations increase, the significance of estimating genetic correlation for complex traits has become more enormous. Brown et al. Although the causes of many complex diseases are not yet fully understood, genetic variation clearly impacts the susceptibility of diseases such as prostate Schaid , breast shared heritability, the measure of the common genetic contribution for two traits or a common trait between two ancestral populations, can provide important information for the transferability of epidemiological results. For example, the known genetic architecture of a trait in population A will transfer to population B if the shared heritability of the trait is substantial between populations A and B. On the contrary, we will not expect the same results on B if the shared heritability is close to 0. Estimating shared heritability could facilitate mapping the causative loci for diseases in multiple ethnic population with information from GWAS studies  for each SNP analyzed and sometimes include the allele frequency. Popcorn considers both allele effect sizes and allelic impact to define trans-ancestral genetic-effect correlation as correlation coefficient of the per-allele SNP effect sizes  a large sample size and number of SNPs is required to achieve a sufficient SE for accurate estimation, (2) limited to relatively common SNPs with allele frequency greater than 0.05, and 3) relies on LD similarity between the external reference panels and the target populations.Popcorn to estimate genetic correlation across differing ancestral populations is powerful, potential limitations include a thorough evaluation of Popcorn. First, it is important to define a ‘large’ sample size and the number of SNPs to better interpret results when applied to summary statistics. Different sample sizes are available for different traits and include a wide range. For example, summary statistics of 184,035 individuals are available for coronary artery disease  other than European and East Asian should also be evaluated. All of the previous simulations were performed on Europeans and East Asians and the only two real data applications focused on RA and T2D are also on these two populations and obtained relatively underestimated results due to, as explained in the paper, the correction of genomic control in summary association data  involved when the test parameters  change. Lastly, it is instructive to check how Popcorn will perform if we use an inappropriate reference panel. External reference panels are the only resource to provide the information of LD matrix while we do not have individual-level data of target populations. The similarity of LD structure between reference panel and target population determines the accuracy of following estimation. It is very important to choose an appropriate external reference panel during the analysis process in Popcorn while sometimes the structure of the target population is unclear.Although the application of Popcorn utilizes summary association statistics from differing ancestral populations as input and LD based on external reference panels similar to the populations. It first estimates the LD matrix products then maximizes an approximate weighted likelihood function to find heritability and genetic correlations, respectively  and ‘stable’ (SE is less than 0.1) estimates.Popcorn are robust to violation of infinitesimal assumption  using hapgen2 . Results from other tests which are about number of individuals in reference panel, sample size and number of SNPs are shown in Figures S2–S6 and S8–S12 and listed in Table Popcorn requires 400–500 for EUR and 700 individuals for EAS and YRI. Second, accurate genetic correlation estimates with low SE requires sample size of 10,000 for Pair 2 and 15,000 for Pair 3 and the number doesn’t change for different true genetic correlation values while at least 15,000 individuals are needed for accurate estimation of heritability with low SE and higher true heritability requires larger sample size to be accurately estimated. As for number of SNPs, more SNPs are needed for estimates of larger true genetic correlation and heritability. The required minimum number of SNPs does not have large discrepancy in either of the two population pairs. Only if we have large enough sample size, around 20,000 SNPs could be able to provide accurate estimates for heritability of 0.1 and only 90,000 are needed even for heritability of 0.9. However, genetic correlation estimates require more SNPs, ranging from 110,000 to 168,000, according to different true genetic correlation. We did similar tests across differing ancestral population pairs, such as EUR vs. YRI Pair 2) and EAS vs. YRI Pair 3). The simulation steps are as same as those outlined above in reproduction part, and the detailed numbers of individuals and SNPs finally left in the two tests are shown in Table  and EAS . The simFor the summary statistics in pair 1, we chose 500 individuals randomly from YRI to serve as external reference panel for EAS. The correct reference panel was used for EUR. As shown in Fig. Popcorn cannot be applied to admixed population since it fails to account for long-range LD induced by admixed populations and take covariate effects into consideration.After filtering out SNPs with minor allele frequency below 1% and related individuals, we had 26,119 EUR individuals, 32,421 ASW individuals and 238,164 SNPs in the analysis. The results are shown in Fig. Popcorn performed with AFR serving as the external reference panel for ASW. As we could see in Fig. Popcorn method. We also tested how Popcorn under several input parameters and circumstances. We confirmed that 300–500 individuals in the external reference panel are able to provide adequate information for LD structure estimates. When the sample size reaches 5000–7000 and the number of SNPs 80,000–180,000, Popcorn is capable to generate accurate and stable estimates for both genetic correlation and heritability. We obtained similar conclusions from other ancestral population pairs though there was slightly different minimum number of sample size, number of SNPs and number of individuals in external reference panel. Moreover, we confirmed that misrepresentation of the reference panel overestimated the genetic correlation by 20% and heritability by 60%. Lastly, we found that the method overestimates the genetic correlation by 7–9% and underestimate the heritability by 25% with 39% more of SE when admixed population involved. The conclusions above are drawn according to the definition of ‘ideal estimates’ and should be modified if there is stricter or looser standardization. It provides plenty of valuable reference information for researchers using the method to obtain more accurate and stable estimates for both genetic correlation and heritability.In this work, we evaluated We used simulated data to do the evaluation both because we lacked real data results and simulation has multiple advantages: (1) we could change conditions and parameters as we want and expect the results; (2) we could use a small dataset to speed up the process to save time; and (3) we could produce large datasets, which is rare in real life, to do the test. However, the results and conclusion could be biased for real data since all tests are performed on simulated data with ideal conditions which are not possible to completely represent real life. We would like to extend our evaluation applied to more real data sets and related results in the future.Popcorn on the simulation of EUR and ASW. Popcorn fails to account for long-range LD induced by admixed populations and take covariate effects into consideration. Determining the genetic correlation of complex traits among admixed populations from summary statistics is challenging. However, African Americans have a higher incidence and mortality than other ancestral populations for several traits including several cancer types. Many results of various cancers for homogenous populations (Europeans and Asians) from GWAS have been reported in previous publications but limited sample size and results for African Americans and other admixed populations. If the genetic correlation of prostate cancer between those non-admixed populations and African Americans can be estimated, the transferability of the results from former to African Americans can be instrumental for avoiding additional tests and research. We expect to extend Popcorn to estimate genetic correlation for admixed populations. A possible direction is to capture the complex LD and long-range correlations which was neglected before though adjusting principle components of SNPs as covariates into the calculation of LD scores Below is the link to the electronic supplementary material.


Principal Component Analysis (PCA) projects high-dimensional genotype data into a few components that discern populations. Ancestry Informative Markers (AIMs) are a small subset of SNPs capable of distinguishing populations. We integrate these two approaches by proposing an algorithm to identify necessary informative loci whose removal from the data deteriorates the PCA structure. Unlike classical AIMs, necessary informative loci densely cover the genome, hence can illuminate the evolution and mixing history of populations. We conduct a comprehensive analysis to the genotype data of the 1000 Genomes Project using necessary informative loci. Projections along the top seven principal components demarcate populations at distinct geographic levels. Millions of necessary informative loci along each PC are identified. Population identities along each PC are approximately determined by weighted sums of minor (or major) alleles over the informative loci. Variations of allele frequencies are aligned with the history and direction of population evolution. The population distribution of projections along the top three PCs is recapitulated by a simple demographic model based on several waves of founder population separation and mixing. Informative loci possess locational concentration in the genome and functional enrichment. Genes at two hot spots encompassing dense PC 7 informative loci exhibit differential expressions among European populations. The mosaic of local ancestry in the genome of a mixed descendant from multiple populations can be inferred from partial PCA projections of informative loci. Finally, informative loci derived from the 1000 Genomes data well predict the projections of an independent genotype data of South Asians. These results demonstrate the utility and relevance of informative loci to investigate human evolution. It projects the high-dimensional genotype data of individuals onto the low-dimensional space spanned by leading eigenvectors of the covariance matrix. A large number of population genetics studies indicate variations along the top principal components are strongly aligned with the differences in ethnicity, geographic locations, or environmental conditions of the subjects . PCA projections have therefore become a standard tool to analyze the genotype data collected from multiple populations.Principal Component Analysis (PCA) is a simple yet powerful method to unravel the population structure from DNA sequences in humans or other species10). In contrast to PCA where population differences in their projections are distributed in millions of SNPs, AIM studies typically identify a small number of SNPs sufficient to delineate these populations with high accuracy. This apparent paradox is due to strong correlations of many SNPs undergoing linkage disequilibrium (LD). SNPs in the same or proximal LD blocks share identical or very similar allele frequency distributions hence can be pruned without deteriorating their power to discern populations. Some prior studies reconcile this paradox by identifying AIMs based on PCA, such as sparse PCA11 and PCAIMs12. The former imposes sparsity constraints on the contributions of SNPs to each principal component and obtains approximated PCs spanned by a few AIMs. The latter calculates the weights of SNPs to principal components in terms of their loadings (coefficients) in the corresponding Singular Value Decomposition (SVD), and randomly samples a few AIMs with probabilities proportional to the weights. Although these approaches successfully incorporate PCA information to identify AIMs, they are still aimed to find a few markers sufficient to approximate the PCA structure of the complete genotype data.Despite its utility, the primary limitation of PCA is the difficult interpretation in terms of individual Single Nucleotide Polymorphisms (SNPs). PCA is derived from the genotype data of all SNPs. It is not straightforward to pinpoint a subset of SNPs responsible for the variations along the principal components. Diametric to PCA, a rich volume of literature can be found in identifying the ancestry informative markers (AIMs) that distinguish specified populations  but also at sub-continental levels within East Asia, Africa, and Europe. Consequently, we identify the informative loci along PCs 1–7. We then approximate projections along each PC by weighted sums of genotype values over the informative loci. Furthermore, the informative loci allude various aspects about human evolution. The distributions of homozygote major/minor alleles of the informative loci along each PC reveal the directions of genotype changes during population evolution. Simulations from a simple demographic model based on several waves of founder population separation and mixing recapitulate the population distribution of projections along the top three PCs. Informative loci are distributed over the whole genome but excessively concentrate on selected hot spots, and their genes are significantly enriched in a number of functional categories. Genes located at two hot spots along PC 7 exhibit differential expressions among European populations. We also develop an algorithm to infer the local ancestry identities of tracts in the phased genotype data of a mixed subject according to the partial projections of subsets of consecutive informative loci on the genome. The tract inference outcomes of our algorithm on five mixed American populations better match the known colonization history of America and prior genotype studies than those derived from RFMix, a standard tool for local ancestry inference. Finally, we project the concatenation of the 1000 Genomes data and an external data of 168 South Asian subjects by using both PCA of the joint data and the coefficients derived from the 1000 Genomes data alone. These two approaches yield highly correlated projections, which affirms the transferability of informative markers in determining projections.Based on the notion of necessary informative loci, we develop algorithms to capture several aspects of evolution and mixing of human populations and conduct a comprehensive analysis of the 1000 Genomes data16, RFMix17, and Yang et al.18. Some of these algorithms incorporate information from PCA or SVD analogous to our method . Nevertheless, our work has two major contributions. First, we introduce the notion of necessary informative loci and indicate their importance in understanding the evolution and mixing history of human populations. Second, we demonstrate the utility of necessary informative loci by implementing a comprehensive analysis at a wide scope including all the populations in the 1000 Genomes data and eight aspects of their evolutionary and mixing history.Each component in this work has been covered by similar algorithms or theoretical analysis in prior studies. PCA projections are a standard tool in population genetics. Abundant methods have been proposed to identify ancestry informative markers from genotype data, and some of them find AIMs using the information of PCA projections (see the aforementioned overview). The notion that population identities are quantitative traits which are additively determined by the sequences on many informative loci can be seen directly from the non-sparse distribution of the corresponding SVD loadings. The evolution and mixing histories of most populations covered in the 1000 Genomes Project are well characterized by decades of research utilizing rich evidence from contemporary and ancient DNAs, linguistics and archaeology. Numerous local ancestry inference algorithms are available, such as ADMIXTUREWe download the variant calling files (VCF) from the phase 3 data of the 1000 Genomes Project. The data comprises 2504 subjects from 26 populations across four continents. Table We collapse the phased data by counting the number of minor alleles for each entry and construct the genotype matrix 21. PC 3 separates native Americans, Europeans and East Asians, and South Asians. PC 4 separates native Americans and all other populations. PCs 5–7 demarcate populations within East Asia, Africa and Europe respectively. PC 5 separates two ethnic groups in/near Indochina (KHV and CDX), Han Chinese (CHB and CHS), and Japanese (JPT). PC 6 separates an East African population (LWK), two Nigerian populations (YRI and ESN), and two Far West African populations (GWD and MSL). PC 7 separates Finnish (FIN), two Northern/Western European populations (GBR and CEU), and two Southern European populations (IBS and TSI). Furthermore, on PCs 1–3 subjects of mixed populations stretch along the lines connecting their ancestral populations . In contrast, PCs 8–10 carry no extra information about population demarcation. Projections along PC 8 separate African populations similar to PC 6. Projections along PCs 9–10 do not separate any population.We visually examine the projections of 1000 Genomes subjects along the top ten principal components and find the top seven PCs account for separation of populations at distinct geographic levels. Figure 22  and compute their first seven PC projections :Derivation of Eq.  is repornecessary and sufficient informative loci respectively. Necessary informative loci are far more abundant than sufficient informative loci because the former include all SNPs that carry non-negligible information about population differences, while the latter can be formed by a small number of positions with sufficiently strong information to delineate populations. As mentioned in “The 30 million loci have unequal contributions to the principal components. In each PC, the majority of loci possess small coefficients near 0  alleles over the informative loci. To verify this hypothesis, we construct proxy projections as weighted sums of minor/major alleles over the informative loci and compare the proxy projections of all subjects with the projections based on SVD Eq. . The weiFigure The 1000 Genomes data provide not only a snapshot of contemporary populations but also evidence about their evolution. Here we present two analyses of the 1000 Genomes data pertaining to human population evolution. First, we examine the dominant patterns of genotype changes between populations and reconstruct their phylogenetic relations. Second, we visualize the fractions of homozygote major and minor alleles among the informative loci of subjects from selected populations and impute the directions of genotype changes along each PC during population evolution.An alternative analysis without incurring PCA is to directly compare the population allele frequencies of all loci and detect the dominant patterns of genotype changes accordingly. For each locus, we quantize the allele frequencies of each population into a three-component binary vector. For instance, 24. Within Eurasia, two leading patterns (PEA and IEU) group East Asians (EAS) and native Americans (AMR), as well as Europeans (EUR) and South Asians (SAS) together. It is commonly accepted that ancestors of native Americans crossed the Bering land bridge from Northeast Asia during the last Ice Age24. Rich evidence from philology and archeology agrees that Indo-European ancestors moved from Central Asia east to the Indian subcontinent and west to Europe24. Within Europe, Finnish (FIN) is more distant from other Europeans, which is also supported by a smaller-scale study in Northern Europeans25. Northern Europeans (NEU) and Southern Europeans (SEU) are distinct partly due to the gene flow from North Africa to Southern Europe26. Within East Asia, Japanese (JPT) is more distinct from Han Chinese populations (CHI) and populations in/near Indochina (DKM). The closeness of Chinese ethnic minority (CDX) and Vietnamese (KHV) with Han Chinese is likely due to their frequent mixing during historical time27. In contrast, Japanese continuously exchanged goods and culture with mainland Asia but remained genetically isolated. Within Africa, an east African population (LWK) is distinct from other west African populations (WAF), which is also supported by a recent survey of African population genomes28.Supplementary Table Separation of populations along certain principal components can emerge from multiple possible evolutionary trajectories. For instance, the distributions of Eurasian subject projections on PC 2 . Demarcation of those populations is manifested on PCs 1–3, yet simple models based on genetic drifts of founding populations seem unable to explain the outcomes along all three principal components. While EUR and EAS are at extreme ends and SAS and AMR are in the middle along PC 2, their proximity relations are inverted along PC 3. We suspect that the founding populations of SAS and AMR come from mixtures from ancestors of EUR and EAS respectively. A demographic model of five populations is constructed accordingly . The p-value of informative loci density in each window is calculated according to the background HMM. The detailed procedures of assessing locational concentration of informative loci are reported in “A 19.Supplementary Figure entclass1pt{minima30 provides the gene expression data of four European populations  and one African population (YRI). We treat gene expressions as molecular phenotypes and examine the phenotypic variations of three aggregate European populations  at two hot spots pertaining to PC 7—chr6 32–34 Mb and chr17 43–45 Mb. Supplementary Table It is of interest to know whether genetic variations of the informative loci at the hot spots affect phenotypic variations between populations. Physiological and clinical phenotypes across populations are poorly documented. Alternatively, the Geuvadis ProjectBesides locational preferences, we also check whether the genes encompassing the informative loci on each PC are enriched in specific functional classes. We perform functional enrichment analysis of the genes harboring the informative loci. For each PC we identify the functional classes which are enriched with the genes possessing high SVD loadings. Supplementary Table The informative loci and their constituting genotypes provide the signatures of delineating populations at different levels in the 1000 Genomes data. To demonstrate the validity of those signatures beyond the data examined, we perform two analyses by generalizing the information of those markers to independent data. First, we develop an algorithm to infer the local ancestral identities in the phased genotype data of subjects from five mixed American populations according to the partial projections of the informative loci derived from twenty one reference populations. We infer the tracts of mixed American subjects in the 1000 Genomes data and find that the tract labels are compatible with both their known migration/mixing history and the results using a well-known tract inference tool RFMix. Second, we project the concatenated data of the 1000 Genomes data and an external dataset of 168 South Asian subjects by using both PCA and the coefficients derived from the 1000 Genomes data alone. These two approaches yield highly correlated projections, which affirms the transferability of informative markers in determining projections.As previously shown, the capacity of delineating populations is distributed among the informative loci over the entire genome. In principle, the partial projection on a chromosomal segment should also demarcate the constituting populations if it covers a sufficient number of informative loci. We exploit this property and develop an algorithm to infer the tracts of distinct ancestral identities in a mixed subject. In brief, the algorithm constitutes training, test and aggregation phases. The training data contains subjects from reference populations such as Africans and Europeans, while the test data covers subjects from mixed populations such as African Americans and Latin Americans. In the training phase, it subdivides each chromosome into minimal tracts that distinguish the reference populations in the training data. In the test phase, it calculates the partial projections on tracts of the test data and reports the most likely population labels accordingly. In the aggregation phase, it combines the tracts inferred from multiple PCs. The output constitutes locations and population labels of tracts for each mixed subject. The algorithm is described in the Materials and Methods and Supplementary Text We apply the algorithm to partition informative loci and build classifiers with the training data of 21 reference populations in the 1000 Genomes data and the test data of 5 mixed populations: PUR, MXL, CLM, ACB and ASW. To simplify analysis, we assume the ancestors of the test subjects are all from America, Africa or Europe, and ignore contributions from East and South Asia. We further subdivide African and European reference populations into subcontinental populations of GSI (GWD and MSL), NGI (YRI and ESN) and LWK for Africans, and FIN, NEU (GBR and CEU) and SEU (IBS and TSI) for Europeans respectively.We infer tracts and assign their population labels in a hierarchical fashion. Tracts inferred from PC 1 possess African or non-African labels. Non-African tracts are subdivided into native American and European tracts according to PCs 2–4 informative loci. The tract labels inferred from PCs 2–4 may not be consistent. We resolve contradictions with two alternative criteria. Criterion 1 (relaxed criterion) assigns the labels with the strongest scores, and criterion 2 (stringent criterion) reports only the tracts with consistent population labels across PCs 2–4 and leaves all the other tracts unassigned. African and European tracts are further subdivided into subpopulation tracts according to PC 6 and PC 7 informative loci respectively.16 and RFMix17 has been performed in a prior study31. Yet only summary information of the inference results is reported. To directly compare the performance of the two methods, we apply RFMix to the 1000 Genomes data and examine the inference results of the two methods.Admixture analysis of the 1000 Genomes data using standard methods of ADMIXTURE31. To rectify this problem, we down-sample each continental-level reference population to 85 subjects and re-run RFMix to the 1000 Genomes data. The new RFMix inference results are closer to those of our algorithm and the summary information in prior studies.We infer the tracts of 22 pairs of autosomes and their population labels of 419 mixed subjects and summarize the inference results in Fig. Several salient properties arise from the inferred local ancestry tracts using partial PC projections. First, relaxed criterion (top left panel) yields much less unassigned tract proportions (black bars) than stringent criterion (top right panel). Second, the five mixed populations exhibit varying levels of African, European and American lineages. The two African descent populations (ASW and ACB) both have low mixture levels of Europeans. Among the three Latin American populations, MXL, CLM and PUR possess increasing mixture levels of Europeans and decreasing mixture levels of native Americans. The American lineage is negligible among ACB and ASW, while the African lineage is considerably higher among PUR than the other two Latin American populations. Third, among the two African descent populations (ACB and ASW) the Nigerian lineage (NGI) dominates the other two African subpopulations, while among the three Latin American populations the Southern European lineage dominates the other two European subpopulations. In contrast, among the African descent populations Northern and Southern European lineages have roughly equal contributions. These properties are compatible with prior studies of the 1000 Genomes data and knowledge about the population migration and mixing history in Americas.The inferred local ancestry tracts using RFMix have considerably different distributions from those inferred from PC projections and to some extent deviant from prior knowledge about population mixing. When including all subjects in the reference populations, PUR subjects possess far more American lineage than MXL and CLM subjects. But the SEU lineage dominates the NEU and FIN lineages in the three Latin American populations. In contrast, when equalizing the reference populations, MXL, CLM and PUR possess decreasing levels of the American lineage as the inference results using PC projections. Yet the NEU lineage constitutes a similar mixed level as the SEU lineage rather than being dominated by the SEU lineage. Hence only the inference results using PC projections are fully compatible with the prior knowledge about population mixing.32. The external data are far less dense than the 1000 Genomes data: 11,700,630 loci appear in the original data and 8,233,400 of them appear in both datasets. We concatenate the 1000 Genomes and the external South Asian data on the intersected loci and compute the projection of each subject with two methods. First, we apply PCA to the joint data and calculate the full projections using all intersected loci. Second, we derive the SVD loadings of informative loci from the 1000 Genomes data alone, and calculate projections of the joint data using these coefficients. Detailed procedures of evaluating these two projections are reported in Materials and Methods.We concatenate the 1000 Genomes data and an independent South Asian dataset and demonstrate that the SVD loadings derived from the 1000 Genomes data informative loci provide a close approximation to the PCA projection of the concatenated data. We download and process the SNP data of 168 subjects of South Asian descentSupplementary Figure To quantify generalization along each PC, we calculate the correlation coefficients between the two types of projections of the 1000 Genomes subjects and the external South Asian subjects respectively, and report them in Table In this study, we introduce a new concept of necessary informative loci based on PCA projections of genotype data across populations. Necessary informative loci complement the classical ancestry informative markers (AIMs) in their construction and functions. PCA projections of the data restricted to AIMs (or sufficient informative loci by our definition) approximate those of the complete data. In contrast, PCA projections of the data removing necessary informative loci are substantially less correlated with those of the complete data. Based on the notion of necessary informative loci, we conduct a comprehensive analysis to the 1000 Genomes data and capture several aspects of evolution and mixing of human populations. Projections along the top seven principal components demarcate populations at super-continental, continental, and sub-continental levels. Necessary informative loci along each principal component comprise millions of SNPs. Projection values along each PC are approximated by weighted sums of genotype values over the informative loci, where the weights are determined by allele frequency differences between the demarcated populations. Furthermore, the informative loci elucidate various aspects of split and mixing of human populations. Allele frequency distributions of informative loci of each PC implicate the heterogeneous directions of genotype changes during the evolution of human populations. Projections and genotype distributions of five populations  along PCs 1–3 are recapitulated by simulations from a simple demographic model based on several waves of founder population separation and mixing. The informative loci are significantly concentrated in certain hot spots of the genome (such as chr6 32–34 Mb harboring HLA genes for PCs 5–7) and enriched in certain functional classes . Genotypic variations of informative loci on hot spots may also affect phenotypic variations, as genes located on two hot spots (chr6 32–34 Mb and chr17 43–45 Mb) exhibit differential expressions among three European populations. Furthermore, we develop an algorithm to deconvolve the genome of a mixed descendant from multiple populations into the tracts of distinct ancestral origins using partial projections of necessary informative loci. Finally, we validate the transferability of informative loci by demonstrating that their SVD loadings suffice to recapitulate the PC projections of an external genotype dataset of South Asian populations.33 and PCA projections34. In addition, genetic drifts and geographic or ecological isolation are viewed as the fundamental processes of speciation35. We verify these propositions in a large genotype data of human populations (1000 Genomes data) and identify the SNPs putatively responsible for population splits during their evolution.Our study of informative loci confirms an intuitive interpretation of PCA on genotype data and a common view about the origin and evolution of human populations. Population identities are an aggregate outcome derived from a large number of informative loci distributed in the entire genome. Except for populations arising from early splits of human evolution (such as Africans versus non-Africans), individual markers are unable to perfectly segregate the target populations , including ones that also use SVD loadings or PCA20. Our algorithm resembles PCAdmix19 as both methods utilize partial projections of subsets of consecutive loci to discern local ancestry. Yet there are also several fundamental differences between the two methods. PCAdmix assumes a one-to-one mapping between each principal component and each ancestral population . Our method does not hold this strong assumption and thus allows more flexible relations between populations and PCs, such as the presence of multiple populations along the gradient of one PC . The ancestral populations are multiple independent entities for PCAdmix but are organized as a hierarchy with varying levels of details for our method. Hence our analysis reports tracts of non African-European-Southern European separately. PCAdmix uses windows of a fixed size (number of SNPs), but our algorithm chooses windows with varying sizes where partial projections in each window maintain minimal separation of the ancestral populations. Despite these differences , we do not claim superiority of informative loci to the state-of-the-art methods. Rather, we intend to demonstrate that the partial information contained in the informative loci can impute missing attributes such as local ancestry of mixed subjects or PCA projections of external subjects. Nevertheless, for local ancestry inference, partial projections based on informative loci have one advantage over likelihood based methods such as RFMix, since SVD loadings and partial projections are not highly sensitive to the reference population sizes, but likelihood scores are.The distributive nature of informative loci renders them amenable to dissect the genome of a mixed descendant from multiple populations into the tracts of distinct local ancestries. Abundant local ancestry inference algorithms have been proposed  they are located on autosomes, (2) they are biallelic among the subjects, (3) they have valid entries in more than 90% of the subjects. 30,761,503 loci meet those conditions. The resulting data is a We download the variant calling files (VCF) from the phase 3 data of the 1000 Genomes ProjectWe first express covariance matrix This is the diagonalization form of entclass1pt{minimaThe projection vector of the 36 to the genotype matrix and directly evaluating the covariance matrix PCA is computed by both invoking PLINKFor each PC, a locus is selected as an informative locus if it satisfies one of the following conditions. First, it is among the top and bottom ranking loci such that the correlation coefficient between the full and partial projections by truncating the top/bottom ranking loci mentclass2pt{minimWe approximate projections along a PC as weighted sums of genotypes over the informative loci. On the Intuitively, locus mentclass2pt{minimWe develop an algorithm to detect the dominant patterns of genotype changes from the 1000 Genomes data. The inputs are the genotype data and population labels of all subjects. The outputs are a sorted list of dominant patterns of genotype changes and their occurrence counts. The detailed procedures of the algorithm are described in Supplementary Text Along each PC, we count the fractions of homozygote major and minor alleles among the top or bottom 100,000 informative loci for each subject. The homozygote allele fractions of the subjects from selected populations are displayed on two-dimensional planes and colored according to their population labels.To find the evolutionary processes that possibly explain the genotype characteristics of the 1000 Genomes data, we build simple evolutionary models of three and five populations and demonstrate that their simulation outcomes recapitulate the PCA projections and homozygote allele fraction distributions of the observed data. The primary assumptions of the models are (1) recombination is the dominant evolutionary mechanism, and sequence mutation plays a negligible role, (2) a new population is originated from a few founding members who are either drawn from one parent population or mixed from two parent populations, (3) mixing takes place only during the founding population formation, while inbreeding within populations occurs in the remaining time. The detailed descriptions of the model and simulation procedures are reported in Supplementary Text To detect the hot spots in the genome with excessive densities of informative loci, we first construct an HMM describing the location-varying background density of all SNPs. We subdivide each chromosome into windows of 1 Mb and count the number of SNPs within each window. The background model assumes that the SNP count within each window follows a Poisson distribution, and consecutive windows tend to possess similar Poisson rates. The p-value is the probability that the loci count within a window exceeds the count of informative loci given the background model. We define hotspots as windows with p-values 30 and deposited at ArrayExpress database37, http://www.ebi.ac.uk/arrayexpress/, accession number E-GEUV-1). The transcript level read count data (https://www.ebi.ac.uk/arrayexpress/files/E-GEUV-1/GD660.TrQuantCount.txt.gz) is processed and p-values of three pairwise population comparisons  of differential gene expressions are calculated using DESeq238. Two hot spots—chr6 32–34 Mb and chr17 43–45 Mb—contain informative loci along PC 7 separating European populations. At each hot spot we count the fraction of differentially expressed genes  are generated from the Geuvadis ProjectStandard functional enrichment analysis such as hypergeometric tests or GSEA operate at gene level: the basic elements are genes. The genotype data, instead, are locus based: the basic elements are loci, and one gene may possess multiple loci. There is a freedom to adopt gene based or locus based functional enrichment analysis. The former aggregates the scores of multiple loci in the same gene into one score. The latter treats all loci of the genes in the same functional class as its unique members. We adopt a gene based approach since it dilutes the inflated importance of genes harboring multiple informative loci.39. Both the test statistics  and the Kolmogorov–Smirnov (KS) p-values of enriched gene sets (p-values We first assess functional enrichment for informative loci along each PC. All genes harboring the informative loci are selected. Here we define the score of a gene as the maximum over the absolute values of the SVD loadings in the constituting loci. Standard GSEA is applied to the informative loci on each PC and each gene set from the MSigDB databaseWe then identify the genes that harbor informative loci along all seven PCs and assess functional enrichment of those all-informative genes. The score of a gene along a PC is previously defined. We sort genes by their scores along each PC and define a gene as all-informative if its score along each PC is in the top 25% of the sorted gene list. 283 all-informative genes are identified accordingly. We perform Fisher’s exact test on those 283 genes and report the top-ranking gene sets in terms of their hyper-geometric p-values in Supplementary Table The capacity of delineating populations is distributed among the informative loci over the entire genome. In principle, the partial projection on a chromosomal segment should also demarcate the constituting populations if it covers a sufficient number of informative loci. We exploit this property and develop an algorithm to infer the tracts of distinct ancestral identities in a mixed subject. In brief, the algorithm constitutes training, test and aggregation phases. The training data contains subjects from reference populations such as Africans and Europeans, while the test data covers subjects from mixed populations such as African Americans and Latin Americans. In the training phase, it subdivides each chromosome into minimal tracts that distinguish the reference populations in the training data. In the test phase, it calculates the partial projections on tracts of the test data and reports the most likely population labels accordingly. In the aggregation phase, it combines the tracts inferred from multiple PCs. The output constitutes locations and population labels of tracts for each mixed subject. Detailed procedures of the algorithm are reported in Supplementary Text To verify the utility of the informative loci beyond the 1000 Genomes data, we concatenate the 1000 Genomes data and an independent South Asian dataset and demonstrate that the SVD loadings derived from the 1000 Genomes data informative loci provide a close approximation to the PCA projection of the concatenated data.32. The VCF file of 11,700,630 loci is provided in the website https://www.ebi.ac.uk/ena/data/view/PRJEB57368. We consider the intersection of the loci in the VCF files of the 1000 Genomes and the external South Asian data and filter out the loci which have different definitions of major and minor allele sequences between the two VCF files. 8,233,400 loci are selected and the joint data of 2504 1000 Genomes subjects and 168 external South Asian subjects are generated accordingly.We download an independent genotype dataset of 168 South Asian subjects reported in Chambers et al.We compute the PCA projections of the joint data using two methods. Method 1 employ eigen decomposition to the covariance matrix of the normalized concatenated data Eq. . Method data Eq. , and \doThe source codes of four data analysis programs and example data of running those programs are deposited under synapse.org/#!Synapse:syn25946110/files/Yeang_1000G_programs.zip.Supplementary Information.


Naemorhedus caudatus) is an endangered species found in the mountains of eastern and northern Asia. Its populations have declined for various reasons, and this species has been designated as legally protected in South Korea. Although various ecological studies have been conducted on long-tailed gorals, none have investigated the gut microbiome until now. In the present study, we compared the diversity and composition of the gut microbiome of seven populations of Korean long-tailed gorals. By analyzing the gut microbiome composition for each regional population, it was found that four phyla—Firmicutes, Actinobacteriota, Bacteroidota, and Proteobacteria—were the most dominant in all regions on average. The alpha diversity of the gut microbiome of the goral population in the northern regions was high, while that in the southern regions was low. Through the analysis of beta diversity, the seven long-tailed goral populations have been divided into three groups: the Seoraksan population, the Samcheock population, and the Wangpicheon population. It was possible to confirm the regional migration of the animals using the gut microbiome based on the site-relational network analysis. It was found that the most stable population of long-tailed gorals in Korea was the Seoraksan population, and the closely related groups were the Samcheok and Wangpicheon populations, respectively. Wangpicheon appeared to be a major point of dispersal in the migration route of Korean long-tailed gorals.The long-tailed goral ( Naemorhedus caudatus) is a vulnerable species distributed in the eastern and northern Asian mountains, including Russia, China, and Korea [The long-tailed goral  following the manufacturer’s protocol. The extracted metagenomic DNA was used as template for gene amplification of the V4–V5 region of the 16S ribosomal ribonucleic acid (rRNA). The bacterial 16S ribosomal RNA gene sequence-biased primers 515F (5′-GTGCCAGCMGCCGCGG-3′) and 907R (5′-CCGTCAATTCMTTTRAGTTT-3′) were used to amplify polymerase chain reaction fragments that were 420 base pairs in length . Each seThe analysis of the composition and biodiversity of the gut microbiome for each regional population of long-tailed gorals in South Korea revealed that, at the phylum level, the population of Seoraksan National Park presented the most various biodiversity, with 17 phyla, followed by the population of Samcheok Area with 14 phyla, and that of Wangpicheon Conservation Area, with nine phyla. Eight phyla were detected in the Odaesan National Park, Taebaeksan National Park, and Woraksan National Park populations. . SurprisAs for the analysis of the composition and biodiversity of the gut microbiome for each regional population of long-tailed gorals in South Korea on the genus level, the numbers of genus of each population was a very different among the regions. The population of Seoraksan National Park presented the most various biodiversity, with 262 genera, and the population of the Samcheok Area had 136 genera, while the Wangpicheon Conservation Area had 45 genera. Forty-three genera were detected in Odaesan National Park, followed by the population of Taebaeksan National Park, which had 31 genera, and that of Woraksan National Park, with 30 genera. . SurprisAlpha diversity indicators, based on sampling sites, showed comparable values for Observed OTU index, Chao1 index, ACE index, the Shannon index, and Simpson’s index. The diversity indices of the gut microbiome in the Seoraksan National Park population were the highest, while those in the Woraksan National Park and Juwangsan National Park populations were the lowest. The analysis of all five indices showed no difference in microbiome diversity among the Juwangsan National Park, Wangpicheon Conservation Area, and Woraksan National Park . The SamBy the beta diversity analysis using Principal Coordinate Analysis with Bray-Curtis distances, all OTUs were in the 5% range, showing three core groups: Seoraksan National Park and Samcheock Area groups, Wangpicheon Conservation Area group, and other group . SeoraksThe total sample was divided into the following three groups in the beta-diversity analysis using PLS-DA with maximum distance: Seoraksan National Park, Samcheok Area, and Wangpicheon Conservation Area . The betThis is the first research study investigating the regional relationships between long-tailed goral populations and gut microbiome biodiversity. The populations in each region showed different diversity by presenting different percentages of microbiota phyla and genera . In the In previous studies, the genetic diversity of Korean long-tailed goral populations, based on the analysis of partial mitochondrial DNA, was divided into two—north and south—geographical groups . HoweverCervus elaphus), 45% of the population migrated, and young males migrated up to 65 km [Cervus nippon) migrated between their summer and winter habitats and traveled up to 31.9 km [Capreolus capreolus), 40% of the population migrated from the summer highlands to the winter lowlands over a distance of 12.0 ± 6.2 km [Wild animals have three moving behaviors related to their habitat: staying within a certain range of an area (home range), scattering out of the herd due to competition , or moving out of their home range (migration) . Severalto 65 km . Sika de 31.9 km . In the ± 6.2 km , and malIn the present study, we used site-relational networks with social network analysis and Animal Social Network Repositories, which are valuable tools to understand the patterns, evolution, and consequences of sociality . We usedThe results of this network analysis showed that active migrations of goral populations occur between regions , even thAlthough a large number of ecological studies exist on the long-tailed goral, the relationships or differences between populations in South Korea—and especially the possibility of migration—remained unclear. In this study we have used a gut microbiome metadata for network analysis. The alpha diversity, beta-diversity, and network analyses of the microbiome produced three different results. First, it was revealed that the Seoraksan population is the most stable and is a major migrating population. Second, there are three separate populations . Third, based on the network analysis, it appears that active migration occurs between populations, along a north-to-south migration route, and, occasionally, a few individual gorals move from south to north. Although Samcheok was not a designated as a protected area, this population was closely related to the Seoraksan population, and represented an independent group with sustainable individual gorals.Overall, the present metadata analysis of the gut microbiome of long-tailed gorals could adequately explain the variation in the diversity of populations and geographical migration between populations.


Pimelea spicata and Eucalyptus sp. Cattai. For both species, we genotyped plants from a ‘condemned’ population and designed ex situ collections, characterizing how the size and composition of the collection affected the genetic diversity preserved. Consistent with previous observations, populations where genetic diversity was optimized captured more alleles than populations of equal size chosen at random. This benefit of optimization was larger when the propagation population was small. That is, small numbers of individuals (e.g. 20) needed to be selected carefully to capture a comparable proportion of alleles to optimized populations, but larger random populations (e.g. >48) captured almost as many alleles as optimized populations. We then examined strategies for generating translocation populations based on the horticultural constraints presented by each species. In P. spicata, which is readily grown from cuttings, we designed translocation populations of different sizes, using different numbers of ramets from each member of propagation populations. We then performed simulations to predict the loss of alleles from these populations over 10 generations. Large translocation populations were predicted to maintain a greater proportion of source population alleles than smaller translocation populations, but this effect was saturated beyond 200 individuals. In E. sp. Cattai, we examined strategies to promote the diversity of progeny from a conservation planting scenario with 36 individuals. This included the optimization of the spatial arrangement of the planting and supplementing the diversity of the condemned population with individuals from additional sites. In sum, we studied approaches for designing genetically diverse translocations of condemned populations for two species that require contrasting methods of propagation, illustrating the application of approaches that were useful in different circumstances.We consider approaches for conserving genetic diversity from plant populations whose destruction is imminent. We do this using SNP genotype data from two endangered species,  The driIn some landscapes, particularly near urban areas, habitat disturbance is both extensive and ongoing. This means species that have experienced contractions in the extent of their habitat will be subject to further reductions, in addition to changes in other evolutionary processes , and many of these have small populations. If we want to maximize the number of populations and species that can be preserved in ex situ collections and translocations, we need to understand how to undertake these actions as efficiently as possible in terms of time, space and materials. This emphasis on efficiency leads to a variety of trade‐offs in the design of translocation populations. For example, it is typically possible to conserve more genetic variation  by maintaining a greater number of individuals in a collection but at the cost of using more resources or nursery space  from the source population and then propagating it, for example in a nursery. This is similar to the maintenance of a germplasm core set for a crop, and the process can similarly be approached with the goal of maximizing the diversity and representativeness of the collection  and the design of a spatially optimized ex situ planting (E. sp. Cattai).Here we examine strategies for designing translocation populations that aim to conserve genetic diversity from a condemned source population, using the framework of a broadly applicable workflow Figure . The wor22.1P. spicata and Eucalyptus sp. Cattai  is an endangered shrub, listed on both state  and federal (EPBC Act) legislation. It is perennial and can resprout from tap roots following disturbance. It is likely capable of self‐pollination, and although it grows prostrate branches, it is considered unlikely to be capable of vegetative reproduction in the wild. The range of P. spicata spans approximately 100 km (north to south) on the east coast of Australia  Airport – in the suburb of Badgery's Creek, Sydney . As part of the Biodiversity Offset Delivery Plan (BODP) for the airport site, and in accordance with the EPBC Act Offsets Policy, we set out to design a translocation population based on cuttings of P. spicata from the airport site, to compensate for the impacts of construction. The translocation was planned to occur in two phases. The first was the propagation of individuals from the condemned population  and federal (EPBC Act) legislation. It often has a mallee growth habit. Little is known about the reproductive biology of the species, however eucalypts tend to hybridize inter‐specifically, and it is therefore plausible that E. sp. Cattai would hybridize with other Eucalyptus species in the region. Eucalyptus sp. Cattai has a severely restricted and fragmented distribution, occurring at approximately twelve sites in north‐western Sydney  has been cleared for development. A conservation project was developed under the Saving Our Species initiative by the Department of Planning, Industry and Environment , which identified translocation as a priority conservation action. Unlike P. spicata, E. sp. Cattai cannot be easily propagated from cuttings for translocation purposes, so we examined the design of ex situ populations using seedlings grown from seeds that were collected prior to clearing  that includes it. This work supports the species status of E. sp. Cattai, which will be described in a future publication, and identified putative interspecific hybrids that were excluded from ex situ collection designs.y Figure . One of g Figure . Our exa2.3P. spicata individuals from 16 sites across the range  or very close relatives. We set out to collect as much of the available diversity as possible, so when it was unclear if two stems were genetically identical (e.g. connected underground), we tended to sample both. However, we wanted to identify and remove the highly similar individuals prior to commencing the design of translocation populations. This is because genetically very similar individuals are likely to contribute few or no novel alleles, relative to each other. We used individual pairwise kinship, estimated using the PLINK method  from the condemned population , and its composition (the specific selected plants) influenced the diversity that could be captured in it. We considered a range of propagation population sizes  that reflected the scope of planned conservation activities and the desire to limit resource requirements. We then designed populations of these sizes in two ways. First, populations of each size (NP) were optimized for gene diversity. To do this, we used the simulated annealing optimization algorithm  at random from the genotyped individuals. This was repeated 100 times for each value of NP, and outcomes were averaged to inform the level of diversity that could be expected if individuals for the propagation population were selected at random. For each candidate population design, we began with the SNPs that were ‘common’ in the condemned population  and calculated the proportion of these SNPs that were polymorphic in the candidate propagation population. We used this measure of the proportion of common alleles that were captured to compare candidate propagation populations of different sizes  and that were designed in different ways (optimized vs. random). For these analyses, we removed all loci with missing data. We did this to avoid making corrections for missing data when counting alleles in candidate propagation populations. Here we used a minor allele frequency of >2% as the threshold delimiting common SNPs. This represented a trade‐off between keeping data for as many SNPs as possible, while removing SNPs that might be especially subject to variation due to genotyping error .For n Figure . We want2.5P. spicata population was to design a translocation population using individuals derived from the propagation population. Here, we had the opportunity to use multiple cuttings (ramets) from each individual (genet) in the propagation population and to thus amplify the size of the translocation population  were derived from optimized propagation populations of different sizes . For this analysis, whose goal was to explore the consequences of propagation and translocation population sizes on the conservation of alleles in the medium term, we used simple designs in which translocation populations had an equal number of ramets from each individual (genet) in the propagation population. In reality, different numbers of ramets of each individual could be used, either to further optimize genetic diversity or to allow for different levels of propagation success among individuals. In this exercise, for example, to construct a translocation population with NT = 256 individuals from a propagation population of NP = 32 individuals, we used eight ramets of each individual in the propagation population. Following a forward simulation of 10 generations, the number of SNP loci that remained polymorphic was calculated and expressed as a proportion of the total number of loci where the minor allele was common (>2%) in the condemned population.The next step towards conserving the genetic diversity from the condemned n Figure . We next2.6E. sp. Cattai, the conservation plan was to use a propagation population composed of seedlings that were harvested from the original site as seed and propagated ex situ  using the seedlings that had been collected from the saltwater site (excluding four putative interspecific hybrids). We then asked what proportion of common SNPs in the adult population  were polymorphic in the candidate propagation populations that we designed. Similar to P. spicata , which can result from a single genotyping error.For u Figure . We theru Figure . To addru Figure  to desig Section , we comp2.7E. sp. Cattai, where there is little prospect for using cuttings to amplify the material in propagation collections, we expect it will be particularly important to promote genetic diversity in progeny from an ex situ planting. Therefore, we examined additional approaches for bolstering this diversity, including the incorporation of a small number of seedlings from additional populations into the collection  using a combination of the seedlings from saltwater, supplemented with seedlings from other sites . We recognized that there might be a perceived trade‐off between the aims of designing a population that was as diverse as possible, and the possible impact of ‘swamping’ the diversity of the condemned population that we were trying to preserve. Therefore, we used multiobjective optimization to characterize any trade‐off that existed between maximizing gene diversity, and maximizing the representation of individuals from saltwater in the population. Details for the implementation of the multiobjective optimization are provided in Appendix In n Figure . Specifi2.8f, describing the propensity for genetically similar plants to be near each other. The function, f, was follows:Finally, we examined an approach for optimizing the spatial arrangement of a propagation population, using the 36 seedlings chosen from Saltwater Figure . The aimi and j represent a pair of plants, iS,j is the spatial distance between individuals i and j, iG,j is a measure of the genetic similarity between individuals i and j, and npairs is the number of pairs of plants. In other words, if a given pair of plants, i, j, are genetically similar , it will add a large value to f if they are close together , and a small value if they are far apart . This means f will be large if many genetically similar plants are close together, and smaller if genetically similar plants are far apart. We minimized f using a simulated annealing algorithm  in terms of the spatial distances between plants exceeding selected thresholds of genetic similarity. Next, we recognized that one random arrangement might be unrepresentative. We therefore generated a set of 1000 random arrangements, and for each of these, calculated the number of pairs of genetically similar plants that were close together.After optimizing the arrangement of the population, we wanted to evaluate that we were satisfied with the outcome. This is because the function 33.1P. spicata and Eucalyptus sp. Cattai each consisted of tens of thousands of markers, of which 6076 and 2509 (respectively) had complete data and were polymorphic in the condemned populations that were examined in detail. General features of these data sets are summarized in Table The raw SNP data sets for P. spicata, we set the threshold for identifying highly genetically similar individuals to kinship = 0.4 . We used a threshold of kinship = 0.45 to identify highly similar individuals of E. sp. Cattai and remove them from the data set  to small positive values (maximum = 0.25). The condemned Saltwater site had the greatest observed levels of allelic richness, with 1.69 for adult trees, and 1.68 for seedlings.In 3.2P. spicata and Eucalyptus sp. Cattai. We examined the proportion of common SNPs in the condemned population that were polymorphic in the propagation populations . For both species, the proportion of SNPs that were captured increased as a function of the size of the propagation population  random population was 95.2% of the number of SNPs captured in an optimized population of equal size , and the proportion of individuals from the local (condemned) population  were close together , whereas the  random solution had nine such cases. Also, the optimized solution had 38 cases where genetically similar plants were spaced far apart (distance >50 m) while the  random arrangement had 16  that were observed in the condemned population. In contrast, in E. sp. Cattai, there was an upper limit on the proportion of alleles from the population of adult trees that was captured in a propagation population derived from seedlings. Fortunately, this upper limit was relatively large (around 95.1% of SNPs), but this serves as a useful reminder that the quantity and type (seeds vs. cuttings) of material that is collected initially places constraints on the preservation of genetic diversity of condemned populations  that were optimized and random. It seems likely that properties of different condemned populations, and the ways in which they must be sampled, will affect the diversity that can be gained by optimizing small collections. For instance, if the individuals that are available from a condemned population are clustered in family groups of highly unequal sizes, it might be especially useful to ‘balance’ the available diversity using genotype information. Similar observations have been made in relation to the benefit of balancing the representation of individuals from different groups ranging from different families at the local scale, to different ancestral population groups at the landscape scale  of simulated evolution, larger populations maintained a greater proportion of the diversity from the condemned population. This effect was largely saturated in translocation populations with more than 200 individuals. The size of the propagation population (number of genets in the collection) that was used to assemble the translocation population also had a substantial effect, essentially imposing an upper limit on the amount of diversity that was maintained. This meant the propagation population size was limiting to the diversity represented in large translocation populations. In sum, we concluded that if there was a premium on the efficient use of propagation resources, a reasonable strategy for P. spicata was to maintain an optimized propagation population of 32 plants and to use these in establishing a translocation population of 256 plants, or 8 ramets of each of the 32 selected genets. We predicted this strategy would preserve polymorphism at 95.8% of genetic loci identified in the source population. However, we note there is substantial uncertainty associated with this quantitative prediction, owing to the possibility of greater attrition of polymorphism during propagation  over an appropriate time frame. We also described strategies for designing a planting of Eucalyptus sp. Cattai to promote the production of genetically diverse seed for translocation. These workflows are united by a common framework , provided these plants were carefully chosen. We found that 256 vegetative cuttings of k Figure , which cThe authors declare there are no conflicts of interest.Appendix S1Click here for additional data file.