We present a hypothesis-driven study on the variation of melody phrases in a collection of Dutch folk songs. We investigate the variation of phrases within the folk songs through a pattern matching method which detects occurrences of these phrases within folk song variants, and ask the question: do the phrases which show less variation have different properties than those which do? We hypothesize that theories on melody recall may predict variation, and as such, investigate phrase length, the position and number of repetitions of a given phrase in the melody in which it occurs, as well as expectancy and motif repetivity. We show that all of these predictors account for the observed variation to a moderate degree, and that, as hypothesized, those phrases vary less which are rather short, contain highly expected melodic material, occur relatively early in the melody, and contain small pitch intervals. A large portion of the variance is left unexplained by the current model, however, which leads us to a discussion of future approaches to study memorability of melodies. Songs and instrumental pieces in a musical tradition are subject to change: as they are adopted by a new generation of listeners and musicians, they evolve into something new while retaining some of their original characteristics. The current article investigates to what extent this change of melodies may be explained by hypotheses on the memorability of melodies.stability Pearce and Wiggins  extendedimplicit memory for the music, through the mere exposure effect  from the Meertens Tune Collectionstune families, or groups of variants, by domain experts  a training corpus of 360 melodies for which annotations of phrase occurrences were available; (2) a test corpus of 1,695 melodies with tune families comprising at least five variants, but excluding tune families from the training corpus; (3) a background corpus of 1,000 melodies with tune families comprising very few variants. All melodies which could potentially be related to melodies from the test corpus—because they might be hitherto unrecognized variants of a tune family in the test corpus (tune family membership undefined), or because they were subtypes of a tune family in the test corpus—were excluded from the background corpus.The training corpus was used to train the computational method to find phrase occurrences; the background corpus was used to train information theoretical models; the test corpus was used to test the relationship between variation of the folk song phrases and their hypothesized memorability.To quantify the amount of variation, or stability of a given melodic phrase (the query phrase), we detect its occurrences in melodies belonging to the tune family from which it was taken (its source tune family): the more variants of the source tune family the query phrase occurs in, the higher the stability of the phrase.We detect occurrences through pattern matching, or the computational comparison of the query phrase to all melodies in its source tune family. The extent to which any segment in a given melody resembles the query phrase can be detected through various similarity measures. Earlier research on the above-mentioned training corpus with phrase occurrence annotations has shown that a combined measure of the similarity measures city-block distance  and irrelevant occurrences  for each of the three measures , part of the test corpus. This melody has ten phrases and shows how under the current formalizations, different hypotheses arrive at different predictions of stability for each phrase. Throughout this section, we refer to a query phrase as q, which is taken from its source melody, s. The source melody's notes are referred to as sj. The query phrase starts at index j = a and has a length of n notes.This section describes the formalization of hypotheses on memorability of melodiesphrase length as the number of notes n of which a given phrase is composed.We test whether the length of the phrases has influence on their stability by defining the SD(Len) = 2.23.In the example melody, the shortest phrases (phrase 2 and 4) have a length of seven notes, the longest phrase (phrase 9) has 16 notes. According to the prediction of the list length effect, we would expect the second and fourth phrases to be more stable than the ninth phrase. Over the whole dataset, phrase length takes values in the range  in the dataset, with a mean of phrase repetition, is measured by counting the occurrences of a phrase in its source melody. All phrases in a melody s are defined as sets of notes Pid. id refers to the sequential index of the phrase P in the melody. Each phrase's notes are represented by their onset from the start of the phrase and their pitch. The query phrase is a set of notes Q with the same representation. For every phrase Pid we determine its equality score to Q as follows:Rehearsal is modeled based on phrase repetitions: if a phrase is repeated multiple times within a melody, it is subject to more rehearsal, hence it may be expected to be more stable. The resulting predictor, Rep of the query phrase q by summing the equality scores of all f phrases Pid in the melody.Then we measure the number of phrase repetitions Rep = 2 for the first four phrases, Rep = 1 for the other six phrases. This would lead to the prediction that the first four phrases are more stable than the last six phrases. Phrase repetition takes values in the range of  in the dataset, with a mean of SD(Rep) = 0.39.In the example melody, the first and second phrase repeat exactly as the third and fourth phrase, respectively. The other phrases do not repeat anywhere in the melody. This means that phrase repetition is phrase position as a given phrase's sequential index, qid, from qid = 1 to qid = g for all g phrases in the source melody. For the example melody of Figure g = 10.We test the primacy effect based on the position of a phrase in its source melody. We formalize the Pos = 1, and the last phrase a value of Pos = 10. Phrase position takes values in the range of  in the dataset, with a mean of SD(Pos) = 2.06.In the example melody, the first phrase has a value of To quantify expectancy, we make use of two formalizations: one by Schellenberg , which ipitch(sj), or its height in the human hearing range, is represented by its MIDI note number. This entails that pitches are integers, in which a semitone difference between two pitches is indicated by a difference of one. The pitch interval between a note sj and its predecessor sj−1 is defined by pInt(sj) = pitch(sj) − pitch(sj−1), where a positive sign indicates that the preceding note is lower, and a negative sign that the preceding note is higher. Both models make predictions for single notes, rather than whole phrases. We derive predictions for whole phrases through averaging the note values over the length of the phrase.We base both models on pitch intervals between consecutive notes. The pitch of a given note pitch proximity, states that listeners expect small steps between melody tones. The further a given note is away from its predecessor, the more unexpected it is. The model does not make any predictions for pitch intervals equal to or larger than an octave.The first component of Schellenberg's model, In Figure sj belonging to a given phrase are averaged over the whole phrase, and the negative value of this average is used for easier interpretation, such that if a phrase has a high value of pitch proximity, its pitches are close to each other, while lower values indicate larger pitch intervals. Notes for which pitch proximity is not defined are discarded from the averaging procedure.To calculate the pitch proximity of a phrase, the pitch proximity values of the notes Prox = −13/9 = −1.44 and Prox = −20/7 = −2.85, respectively, which means that we would expect the seventh phrase to be more stable than the eighth phrase. Pitch proximity takes values in the range of  in the whole data set, with a mean of SD(Prox) = 0.69.We show the pitch proximity values for the seventh and eighth phrase of the example melody in Figure pitch reversal, which summarizes the long-standing observation from music theory that if leaps between melody notes do occur, they tend to be followed by stepwise motion in the opposite direction  = −1, or least expected, to PitchRev(sj) = 2.5, or most expected. As with pitch proximity, we calculate the average reversal of a phrase through calculating the arithmetic mean of its constituent notes. As pitch reversal makes predictions based on two pitch intervals, it is not defined for the first two notes of a melody. Notes for which pitch reversal is not defined are discarded from the averaging procedure.The other factor in Schellenberg's model is n Meyer, . See theRev = 3/9 = 0.33 and Rev = 1/7 = 0.14, respectively, which means that we would expect the seventh phrase to be more stable than the eighth phrase. Pitch reversal takes values in the range of  in the whole data set, with a mean of SD(Rev) = 0.24.We show the pitch reversal values for the seventh and eighth phrase of the example melody in Figure n-grams in a music collection, and based on these observed frequencies, assigns probabilities to notes in unseen melodies, given the notes preceding it. The preceding notes are also referred to as context. The length of the context can be set by the user. If the model cannot find a relevant n-gram of the context length specified by the user, it backtracks to shorter melodic contexts, and uses those frequencies to return the probability of a given note.The IDyOM (Information Dynamics of Music) model by Pearce analyzes the frequencies of n-gram length to the average phrase length of nine. We use IDyOM's long-term model, i.e., the model does not update itself while observing the query phrases, and we apply the interpolation weighting scheme C, which balances longer and shorter melodic contexts evenly. This was proven to be the best performing weighting scheme in experiments by Pearce  of a note to occur given the previous melodic context, based on the probabilities of the background corpus. We choose information content rather than probability, as the logarithmic representation makes it possible to compare the typically small probability values in a more meaningful way. Information content is often also referred to as Surprisal, as its values increases as events get less expected.We express the expectancy of a given melodic segment through its average information content. Information content is the natural logarithm of the inverse probability ℙ = 0.53.We show the information content for the seventh and eighth phrase of the example melody in Figure t for each phrase. FANTASTIC uses a music representation which codes the relative pitches and durations of consecutive notes, see the As Müllensiefen and Halpern  and Van n-grams of character sequences representing the pitch and duration relationships between notes. The lengths of motifs to be investigated can be determined by the user. For each investigated motif length l, the frequency of unique motifs vz,l is counted, and compared to the total number of motifs of that length Nt,l covering the phrase. The entropy Hl is then calculated from each unique motif's relative frequency fz,l, i.e., how often a given motif vz,l occurs in a phrase with relation to all motifs of that length in the phrase.We follow Müllensiefen  in theirNu,l) for normalization. A value of H = 1.0 then indicates maximal entropy, and minimal repetitiveness: there are no repeating motifs of length l at all in the phrase; a lower value indicates that there are some repeating motifs.The relative frequencies of all unique motifs are multiplied with their binary logarithm, summed, and divided by the binary logarithm of the number of all motifs of that length in the phrase  = 0.09.To illustrate the concept, refer again to Figure logit function, where ℙ stands for the probability that an event happens:Since our outcome variables are binary, i.e., a given query phrase occurs or does not occur in a given melody, we model the statistical relationship between the likelihood that a given query phrase occurs and its properties through logistic regression. In logistic regression, the odds that an event happens are predicted as a function of one or multiple independent variables. The logarithm of the odds is also known as the q has a match in a given melody s, based on the vector F of the independent variables hypothesized to contribute to long-term memorability of melodies.The goal of logistic regression is to find a curve that best separates the true events from the false events. In our case, this means that we want to predict the probability ℙ that a given query phrase In this equation, β represents the slope of the prediction function, ϵ represents the random effects of the model, i.e., the random error for each melodic segment, assumed to be normally distributed. If the prediction of the probability of occurrence  were perfect, this would lead to a curve separating the occurrences clearly from the non-occurrences.However, the tune family dependent error of the computational method detecting occurrences needs to be taken into account. This could be done by separate logistic regression models for each tune family; yet this would mean that we could not globally estimate how well a specific hypothesis accounts for probability of occurrence. We therefore choose another solution to model the relationship between phrase properties and occurrence: a generalized linear mixed model (GLMM) which can model the variation of all data at the same time.y axis. Hence, the decision function between occurrence vs. non-occurrence of the model is shifted, depending on the tune family.Generalized linear models are a framework in which relationships between independent variables and dependent variables of binomial, multinomial, ordinal and continuous distributions can be investigated. A special case of this framework are mixed models, in which not only a general random effect (ϵ), but also random effects for subgroups of the data can be taken into account. This way, we can model the tune family dependent error of the computational method. We assume that every tune family has a different intercept term in the model, i.e., the height at which the logistic regression curve crosses the F as the vector representing the independent variables of the query phrases, β as the slope of the prediction function, ϵ as the random error, but now also take into account the random effect μ, based on the individual error of each tune family, summarized in the vector tf. Then the model can be formalized as follows:We again assume tf as the between-tune-family variance, and the random effects, expressed by ϵ, as the within-tune-family variance. Using this model, we test our hypotheses on possible correlates of long-term melody recall.One could also think of the fixed effects, expressed by μ x of the predictor vector by subtracting the arithmetic mean SD(x) of a given variable.To be able to compare the independent variables derived from our hypotheses, we standardize all variables This leads to the overall model for all phrase occurrences, in which units can be compared against each other. We apply a Generalized Linear Mixed Model with fixed slopes and random intercepts for each tune family through the R package LME4AICc) , with one model parameter, to nine degrees of freedom (9 df), with seven model parameters, in Table s Cohen, . When thThe prediction coefficients show that phrase length and surprisal possess most predictive power: with increase of a given query phrase's length, its stability decreases. Higher expectancy leads to increased stability. Furthermore, the coefficients also indicate that earlier phrases tend to be more stable, as with an increase in the phrase index, the odds that a query phrase occurs in a given melody are decreased. Moreover, an increase in pitch proximity, or a decrease in the average size of the pitch intervals in a phrase, leads to a higher chance of an occurrence. More repetitions of a query phrase also result in the increased odds of occurrence. Pitch reversal and motif repetivity contribute least strongly to the model, but the signs of the parameters are as expected: if a phrase confirms expectations of pitch reversal, its odds of occurrence are increased, and likewise, if a phrase contains many repeating motifs, its odds of occurrence are increased.We also tested the model for multicollinearity, confirming that the approximate correlations of parameter estimates do not exceed 0.6, which justifies our treatment of the model parameters as independent predictors.To illustrate the predictions of the model, we show the predicted as well as the observed frequency of occurrence for the ten phrases of the example melody in Figure The current research shows that folk song collections are a valuable resource for studying the relationship between melody variation and memorability. All proposed hypotheses relating to recall in general and music recall in particular contribute to prediction of folk song variation, as model selection among all combinations of parameters leads to a model with all hypotheses as predictors.R2 = 0.05. This might mean that there are potentially more, and stronger predictors for melody variation that have not been tested in this study. It is also good to keep in mind that the phrase occurrences in folk songs do not represent “clean” experimental data in which all aspects but melody recall are controlled. The ecological validity comes at the cost of potential noise. Some aspects that might deteriorate the observed variation are (a) the computational method to detect occurrences; (b) the inherent ambiguity of phrase occurrences, i.e., humans do not agree on occurrences perfectly  and contain little surprising melodic material . Moreover, it is beneficial if a phrase occurs relatively early in a melody , and has mostly small pitch intervals . The repetition of a phrase in its source melody also contributes to its memorability , even though this effect is somewhat weaker in our analysis than other predictors. Average reversal, or the tendency for a melody to adhere to the gap fill principle, i.e., following a leap by stepwise motion in the opposite direction  and motif repetivity within the phrase (hypothesis 5) seem to account for long-term memorability to a more limited extent. All predictors related to expectancy indicate that more expected melodic material increases stability, leading us to reject hypothesis 4b.Alternatively, one could assume that a large proportion of melody variation is a result of drift, and therefore random  share the disadvantage that for the first few notes of a melody, no or little information on expectancy is available. This means that there is a potential imbalance between the initial and later phrases of a melody, as the predictor values of initial phrases are based on less information. The alternative, treating every phrase as isolated, so that no context from previous phrases is used for creating expectancy values, seemed unrealistic, however, as the recall of phrases is cued by previous melodic material  of the Netherlands Organization for Scientific Research (NWO).BJ is supported by the Computational Humanities Programme of the Royal Netherlands Academy of Arts and Sciences, under the auspices of the Tunes & Tales project. For further information, see We thank our colleagues from the Music Cognition Group for feedback at various stages of the research, Andrei Teodorescu and Esther Adi-Japha for their invaluable comments on the manuscript, the folk song experts at the Meertens Institute for their annotations and data curation, and Peter van Kranenburg for advice and feedback on the current research, as well as the publication of the Meertens Tune Collections.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Fusarium wilt, a soil-borne disease caused by the fungal pathogen Fusarium oxysporum f. sp. fragariae, threatens strawberry (Fragaria × ananassa) production worldwide. The spread of the pathogen, coupled with disruptive changes in soil fumigation practices, have greatly increased disease pressure and the importance of developing resistant cultivars. While resistant and susceptible cultivars have been reported, a limited number of germplasm accessions have been analyzed, and contradictory conclusions have been reached in earlier studies to elucidate the underlying genetic basis of resistance. Here, we report the discovery of Fw1, a dominant gene conferring resistance to Fusarium wilt in strawberry. The Fw1 locus was uncovered in a genome-wide association study of 565 historically and commercially important strawberry accessions genotyped with 14,408 SNP markers. Fourteen SNPs in linkage disequilibrium with Fw1 physically mapped to a 2.3 Mb segment on chromosome 2 in a diploid F. vesca reference genome. Fw1 and 11 tightly linked GWAS-significant SNPs mapped to linkage group 2C in octoploid segregating populations. The most significant SNP explained 85% of the phenotypic variability and predicted resistance in 97% of the accessions tested—broad-sense heritability was 0.96. Several disease resistance and defense-related gene homologs, including a small cluster of genes encoding nucleotide-binding leucine-rich-repeat proteins, were identified in the 0.7 Mb genomic segment predicted to harbor Fw1. DNA variants and candidate genes identified in the present study should facilitate the development of high-throughput genotyping assays for accurately predicting Fusarium wilt phenotypes and applying marker-assisted selection. Fragaria × ananassa Duchesne ex Rozier) plant health and yield are adversely impacted by several soil-borne diseases , an ozone-layer depleting chemical compound banned by a global treaty enacted to protect Earth’s atmosphere . The effFusarium wilt was first discovered in strawberry in California in 2006  and other economically important plants (R) genes have been discovered, cloned, functionally characterized, and deployed in tomato (R) genes belong to super-families with highly conserved nucleotide binding (NB) and C-terminal leucine-rich repeat (LRR) domains . To explore these questions and develop insights into the genetics of resistance to Fusarium wilt in strawberry, we analyzed 565 germplasm accessions in the University of California, Davis (UCD) germplasm collection. Using genome-wide association and genetic mapping approaches, we identified and genetically and physically mapped a dominant gene (Fw1) that confers resistance to Fusarium wilt in strawberry. Our study was enabled by the availability of a high-density single-nucleotide polymorphism (SNP) genotyping array (F. vesca (A. Heller) Staudt), a diploid (2n = 2x = 14) ancestor of F. × ananassa . These included 50 UCD cultivars released since the inception of the breeding program in 1927, and numerous previously undocumented and uncharacterized germplasm accessions representing genetic diversity in the collection (File S2). To develop populations for quantitative trait locus (QTL) mapping, S1 progeny were developed by self-pollinating greenhouse-grown plants of the cultivars Fronteras and Portola. These cultivars were identified as highly resistant in the GWAS. Both were self-pollinated prior to knowing if they were heterozygous or homozygous for the Fusarium wilt resistance gene described herein. Genotypes of the parents and grandparents (Fronteras = 04C018P004/05C165P001 and Portola = 97C093P007/97C209P001) were subsequently inferred from the haplotypes of SNPs in linkage disequilibrium with the Fusarium wilt resistance gene. Fruit originating from self-pollination were harvested and macerated in a pectinase solution (0.6 g/L) to separate achenes (seeds) from receptacles. S1 seeds were scarified with a concentrated sulfuric acid solution  for 14 min, rinsed in water, dried on blotter paper, and germinated at room temperature (approximately 22-24°) in June 2016. S1 seedlings were grown in kiln-dried artificial media  in a shade house in Winters, CA from June to October 2016.The UC-Davis Strawberry Germplasm Collection was the source of the plant material investigated in our studies. We selected 565 1 populations were phenotyped in the fall-planted experiment. Neither field had ever been planted with strawberries. The soil type was a Yolo loam based on information provided by the Web Soil Survey (WSS), USDA Natural Resources Conservation Service (https://websoilsurvey.sc.egov.usda.gov/). The spring-planted field was not fumigated, whereas the fall-planted field was flat-fumigated in July 2016 with a chloropicrin-based fumigant  at 500 lbs/acre. The fumigated field was sealed with a totally impermeable film (TIF) tarp for one week.Germplasm accessions were phenotyped in experiments planted in the spring of 2016 and fall of 2016 in separate fields at the UC-Davis Plant Pathology Farm, Davis, CA. SEntries in both experiments were arranged in balanced square lattice experiment designs with four single-plant replications per entry. The configuration was 24 × 24 (= 576 entries) in the spring-planted experiment and 31 × 31 (= 960 entries) in the fall-planted experiment. The number of entries and lattice configuration were greater in the fall-planted experiment because additional germplasm accessions were tested for a study to be reported elsewhere. The incomplete block assignments and randomizations were generated in the R-package ‘agricolae’ . Bare-ro1 populations phenotyped in the fall-planted 2016-2017 experiment, seeds were germinated in June 2016, transplanted to peat pellets, and grown in a shade house in Winters, CA before being pathogen-inoculated and transplanted to the field in October 2016.The spring-planted GWAS experiment was phenotyped in the spring and summer of 2016, whereas the fall-planted GWAS experiment was phenotyped in the spring and summer of 2017. For the spring-planted 2016 field experiment, clonal propagules were produced from stolons of mother plants grown in a low-elevation (41m) nursery in Winters, CA, harvested in January 2016, and stored at -3°. The plants were removed from the freezer and stored at 3.5° for one week prior to planting in the field in April 2016. For the fall-planted 2016-2017 field experiment, clonal propagules of germplasm accessions were produced from stolons of mother plants grown in a high-elevation  nursery in Dorris, CA. The mother plants were harvested from a low-elevation field nursery in January 2016, stored at -3°, and planted in April 2016 at the high-elevation nursery. Clonal propagules were harvested in October 2016 and stored at 3.5° for two weeks before pathogen-inoculation and planting. For S1 seedlings and clonal propagules of the germplasm accessions were inoculated with a virulent isolate of F. oxysporum f. sp. fragariae (AMP132) immediately before planting. To produce spores (inoculum), the pathogen was grown on potato dextrose agar (PDA) under continuous fluorescent lighting at room temperature for 30 days, as described by 6 spores/ml. Spore inoculum was prepared one day prior to planting and stored at 4° overnight. The suspension was shaken to re-suspend spores before inoculation. Seedlings and bare-root plants were dipped in the spore suspension and immediately planted.Seventeen-week-old SFor each study, phenotyping was initiated as soon as symptoms appeared and continued on a weekly basis in the spring of 2016 (4-9 weeks post-inoculation) and bi-weekly basis in the spring of 2017 (26-36 weeks post-inoculation). We utilized the progression of disease symptoms as a guide for both initiating and terminating phentoyping. Symptoms had fully progressed and were most extreme among resistant and susceptible checks in the final time point in each year (9-weeks post-inoculation in 2016 and 36-weeks post-inoculation in 2017). We used a previously described 1-5 rating scale to phenotype disease symptoms, where symptomless plants were scored as 1, stunted plants were scored as 2, chlorotic plants were scored as 3, wilting plants were scored as 4, and plants killed by the pathogen were scored as 5 , and ground using stainless steel beads in a Mini 1600 . Genomic DNA (gDNA) was extracted from powdered leaf samples using the E-Z 96 Plant DNA Kit  according to the manufacturer’s instructions. To enhance the quality of the DNA and reduce polysaccharide carry-through, the protocol was modified with a Proteinase K treatment, a separate RNase treatment, an additional spin, and heated incubation steps during elution. DNA quantification was performed using Quantiflor dye  on a Synergy HTX .For DNA isolation, newly emerging leaves were harvested from field grown plants of the germplasm accessions and shade house-grown seedlings of SSNP genotyping with the Affymetrix IStraw35 Axiom Array  was performed using a mixed linear model for the lattice experiment design with incomplete and complete blocks as random effects and entries as fixed effects. Statistical analyses were performed using the R-packages ‘lme4’ and ‘car’  and werehttp://bioconductor.org/packages/release/bioc/vignettes/GENESIS/inst/doc/pcair.html; p-value inflation factors (λ), ignoring population structure, were 3.09 for the 2016 and 3.69 for the 2017 GWAS experiments . SNP probe sequences from the Affymetrix IStraw35 Axiom Array  with ‘GENESIS’ , heterozygous loci were expected to segregate 1 AA: 2 AB: 1 BB in the Fronteras and Portola S1 populations, where A is the allele inherited from one grandparent and B is the allele inherited from the other grandparent. S1 individuals were genotyped with the Affymetrix IStraw35 Axiom Array  threshold of 8.0 and ordered using the multi-point ML algorithm in JoinMap 4.1 with default parameters and three rounds of locus ordering  and dominance (d) effects, degree of dominance (d/a), and the proportion of the phenotypic variance associated with the additive and dominance effects of the SNP locus .Linkage groups were scanned for quantitative trait loci (QTL) using the interval mapping function in MapQTL 6 . SeveralNP locus . SNPs wehttps://doi.org/10.25387/g3.6007715.All data required to replicate the analyses are available as supplements cited in-text or in Supplemental Data Files 1-4. Supplemental Data Files 1 and 2 contain the raw genotypic data for the germplasm accessions and mapping populations, respectively. Supplemental Data File 3 provides additional information regarding SNP nomenclature, alleles, and genomic locations. Supplemental Data File 4 provides the raw phenotypic (disease symptom) scores for every time point in 2016 and 2017 studies. Supplemental material available at Figshare: F. oxysporum f. sp. fragariae were symptomless and classified as resistant , the phenotypic correlation between years was positive and highly significant , and the classification of accessions as resistant or susceptible was highly consistent over years  entoypes ; File S2periment ; File S2periment ; File S2periment ; File S2Fusarium wilt on a chromosome 2 homeolog in the octoploid genome. To investigate this, genetic and QTL mapping studies were conducted in S1 populations developed by self-pollinating cultivars (Fronteras and Portola) inferred to be heterozygous for the hypothesized resistance gene (File S2). The phenotypic distributions for both S1 populations were bi-modal with fairly distinct separation between resistance and susceptible classes (R_), whereas progeny with phenotypic scores ≥ 2.5 were classified as homozygous susceptible (rr). Using these classifications, the observed phenotypic ratios were not significantly different from 3 R_: 1 rr, the phenotypic ratio expected for the segregation of a dominant gene. We observed 68 R_: 24 rr among Fronteras S1 progeny  and 64 R_: 28 rr among Portola S1 progeny . Shifting the threshold upward to 3 or downward to 2 did not change the statistical inference.From the strength of the GWAS signal and short physical distance spanned by significant SNPs on chromosome 2 in the diploid reference genome -4, we hy classes . For hyp1 population, whereas 7,345 co-dominant SNPs were genotyped and mapped in the Portola S1 population . Because SNP marker densities were low in several genomic regions, the number of linkage groups (40 in the Fronteras S1 and 50 in the Portola S1 population) exceeded the haploid chromosome number (28). Nevertheless, by cross-referencing SNPs previously mapped by F. × ananassa linkage groups numbered using the nomenclature of 1 populations  and nearly identical across the linkage group 2C haploblock within each population (File S3). The additive and dominance effects for the AX-166521396 SNP locus were -0.85 and -0.86 in the Fronteras S1 population and -1.12 and -0.94 in the Portola S1 population (File S3). The AX-166521396 SNP explained 85% of the phenotypic variation for resistance to Fusarium wilt in both S1 populations (1 population (File S3). We concluded that the QTL was caused by the segregation of a dominant gene conferring resistance to Fusarium wilt, hereafter identified as Fw1. One recombinant individual was observed between the upper and lower SNP haploblocks among 186 S1 individuals. The recombinant individual (16S408P105) was susceptible to Fusarium wilt, homozygous for the susceptible haplotype in the upper haploblock, and heterozygous for the resistant haplotype in the lower haploblock; hence, Fw1 appears to be located upstream of the lower haploblock within or near the upper haploblock harboring the AX-166521396 SNP locus . The haplotype associated with the resistant Fw1 allele was observed in 161 accessions (28.4%), whereas the haplotype associated with the susceptible Fw1 allele was observed in 368 accessions (65.0%). Within the upper haploblock, which harbors AX-166521396, the resistant haplotype was observed in 189 accessions (33.4%), whereas the susceptible haplotype was observed in 370 accessions (65.4%). To retrace the breeding history of Fw1, we assembled and analyzed pedigree records for F. × ananassa germplasm accessions originating between 1814 and 2014  and Shasta (PI 551663)—both of which were heterozygous (Fw1 homozygotes were rare in the germplasm studied (<3% of the accessions). Soquel (PI 666602) was the only homozygous resistant cultivar out of 50 tested  or heterozygous (A/G) in 190 accessions  included the cultivars Guardian (PI 551407), Wiltguard (52C016P007), Earliglow (PI 551394), and Tufts (63C120P001) and UCD germplasm accessions 39C082P019, 61S016P006, and 97C085P006 , we suspect that they harbor novel Fusarium wilt resistance genes. These germplasm accessions, with one exception (97C085P006), originated between 1939 and 1975, upstream of apparent bottlenecks in the UCD breeding program  receptor-like proteins” and “nucleotide binding LRR proteins” (Fw1 are Toll/interleukin-1 receptor (TIR) NB-LRR encoding genes  found in a small cluster located between 577,691 and 606,648 bp on chromosome 2 in the F. vesca genome  in octoploid strawberry that confers resistance to a virulent isolate of F. oxysporum f. sp. fragariae found in California . While Fw1 locus was sufficient to explain phenotypic variability for resistance to Fusarium wilt in our study (F. oxysporum f. sp. fragariae (N13581 and N15309). The effectiveness of Fw1 against these isolates and other isolates of the pathogen is unknown. Moreover, several factors, including the absence of characterized resistance genes, has precluded the assignment of isolates to races through the study of differential host-pathogens interactions. The present study opens the way to exploring the race structure of F. oxysporum f. sp. fragariae isolates by testing host differentials  carry a single R-gene (Fw1)—the other 70% were susceptible to Fusarium wilt. With the emergence of the pathogen in California over the last decade  have been described in tomato (I gene (discovered in 1939) was less durable than the I-2 gene (discovered in 1954); however, both were eventually defeated by the emergence of new F. oxysporum f. sp. lycopersici races (R-genes operate by different mechanisms that appear to affect durability and collectively provide greater safety against pathogen evolution than the individual R-genes (Fusarium wilt R-genes in the arms race with the pathogen (The potential for new races of pathogen , which ml emerge ,b. As out decade , we experawberry . Several R-genes . Consequpathogen .Fusarium wilt resistant cultivars in strawberry will be critically important as the pathogen spreads and increases in importance in California and other parts of the world (Fusarium wilt phenotypes and accelerate breeding efforts. Because the Fw1 R-allele was present in 97% of the resistant germplasm accessions tested, including several cultivars spanning the breeding history of strawberry in California (Fusarium wilt resistance genes exist in strawberry (Fusarium wilt is unknown, and the genes encoding Fw1 and the other R-genes predicted by our study remain to be identified, cloned, and characterized. The identification and characterization of effector genes in F. oxysporum f. sp. fragariae will be critical for understanding the interaction between the strawberry and F. oxysporum f. sp. fragariae and the co-evolution of resistance and avirulence genes (The development and deployment of lifornia ; File S2lifornia , our stuce genes .


Increasing evidence suggests that a single individual is insufficient to capture the genetic diversity within a species due to gene presence absence variation. In order to understand the extent to which genomic variation occurs in a species, the construction of its pangenome is necessary. The pangenome represents the complete set of genes of a species; it is composed of core genes, which are present in all individuals, and variable genes, which are present only in some individuals. Aside from variations at the gene level, single nucleotide polymorphisms (SNPs) are also an important form of genetic variation. The advent of next-generation sequencing (NGS) coupled with the heritability of SNPs make them ideal markers for genetic analysis of human, animal, and microbial data. SNPs have also been extensively used in crop genetics for association mapping, quantitative trait loci (QTL) analysis, analysis of genetic diversity, and phylogenetic analysis. This review focuses on the use of pangenomes for SNP discovery. It highlights the advantages of using a pangenome rather than a single reference for this purpose. This review also demonstrates how extra information not captured in a single reference alone can be used to provide additional support for linking genotypic data to phenotypic data. It has become clear now that a single reference genome is not sufficient to fully represent the entire genetic diversity of a given species. This is due to the presence of structural variation in the form of copy number variants (CNVs) and presence/absence variants (PAVs), which alter the total amount of genetic information that is present within the individuals of the species . CNVs arStreptococcus agalactiae. This has led to a series of similar studies in other micro-organisms [The concept of the pangenome was introduced in 2005 by Tettelin et al. , who prorganisms ,5,6,7 asrganisms ,9, soyberganisms ,11, ricerganisms ,13, and rganisms ,15. The rganisms . The panThere are a number of factors that can determine how successful a pangenome study will be; these include the quality of the reference assembly, its annotation, and the selection of appropriate individuals . The quade novo genome assemblies, k-mer based approaches, and iterative mapping and assembly approaches. These are illustrated in Several methods have been employed for assembling pangenomes; these include whole k-mer-based approach, each sequence is broken down into shorter segments of length k. The relationship between these segments or k-mers can be represented as edges of the graph where each k-mer is a node, and overlapping nodes are connected by an edge. The graph can include many edges, which connect to the same nodes, thereby forming loops. A genome can be reconstructed from k-mers following relationships between the nodes. When more than one genome is present, additional information about the origin of the node has to be taken into consideration. This is achieved by colouring the nodes, with nodes originating from a given sample being assigned to a particular colour so that they can easily be traced. In this way, an entire pangenome can be represented as a coloured de Bruijn graph, allowing for the identification of sequences, which are common or unique among the genomes that constitute the pangenome [The whole de novo genome assembly approach is used when individuals have been sequenced to a high enough coverage that would allow them to be assembled individually . In thisangenome ,23. In tBrassica rapa [Brassica oleracea [Glycine soja and comparative genomics analysis of these accessions with cultivated soybean (G. max), it was found that 80% of the pangenome was present in all accessions while the remainder was variable and displayed higher sequence variation compared to the core genome [Brassica rapa genomes , it was revealed that a significant amount of divergence had already occurred between B. rapa genotypes prior to domestication [B. oleracea pangenome, it was found that almost 20% of the genes were affected by presence/absence variation [In the last five years or so, pangenomic studies in plants have become popular. A number of examples are available in a range of species such as maize ,9, soybeica rapa , Brassicoleracea , and ricoleracea ,13. Irreoleracea . During e genome . In anote genome . During tication . In a moariation . In a paariation . Yet anoSingle nucleotide polymorphisms (SNPs) are single base pair positions in genomic DNA at which alternative alleles occur ,25. SNPshttp://broadinstitute.github.io/picard) marks duplicate reads without removing them. It performs additional tasks such as estimating the percentage of optical duplicates, which are sequences that arise from one flow cell cluster, but are incorrectly identified as being part of multiple adjacent clusters. These are different from PCR duplicates, which occur as a result of the same DNA molecule being present in two different flow cell clusters after PCR amplification. Post-alignment processing may also involve removal of reads that fall below a given mapping quality threshold or reads that do not map in concordant pairs. Post-alignment processing is followed by variant calling. The latter process can be carried out using heuristic-based or probability-based algorithms. SNP callers using a heuristic approach rely on the abundance and quality of data. Two such SNP callers are VarScan2 [Before the advent of next-generation sequencing, methods for SNP detection were relatively low-throughput and did not require prior sequence knowledge. SNPs were detected using DNA conformational changes or recognition of restriction enzyme site differences . HoweverVarScan2  and SGSaVarScan2 . VarScanVarScan2 . ProbabiVarScan2 ,35,36, aVarScan2 . Single VarScan2 , SOAPsnpVarScan2 , and UniVarScan2 ,35,36.SNPs can be identified at the genome-wide level. Genomic SNPs tend to be evolutionarily neutral, meaning they are not subject to selective pressures; their abundance in a population depends on random genetic drift, allowing for a more complete estimate of diversity levels . SNPs caThe majority of studies to date have relied on a single reference genome to call SNPs between multiple individuals. However, using a pangenome, which represents the complete gene content of any given species, would increase the efficiency of SNP calling in several ways. Irrespective of the algorithm used, or the approach (reference-based or reference-free) employed to identify SNPs, using the pangenome as the reference for read mapping would take into account regions displaying PAVs. In this way, it will be possible to know the number and types of SNPs contributed by each individual in the pangenome. This would also increase the overall number of SNPs that would be identified if the reference had otherwise been based on a single individual alone. In addition, using the pangenome as a basis for SNP discovery would cut down the time and effort required to map reads to several individuals one at a time. This also means that SNP results coming from different references would not have to be consolidated into a single SNP set after analysis. Another major advantage of using the pangenome for SNP discovery is that it allows for the discrimination of SNPs, which occur in core and variable regions of the pangenome. Identification of SNPs in the variable genome for instance can be helpful in characterizing novel metabolic pathways  and findVarious applications of SNP markers exist. SNPs have been used extensively in plants for the purpose of crop improvement. Some of the applications include studying genetic diversity, constructing high-resolution genetic maps, LD-based association mapping, and phylogenetic analysis . InformaGlycine soja, which is the wild relative of the soybean Glycine max, the majority of genes affected by SNPs or indels causing stop codon gain or loss and frameshift were rare events, usually found in only one of the seven G. soja accessions [Glyma02g25230, which is one of the two homologs of Spiral2, a key microtubule gene for directional cell elongation that is associated with the right-handed helical growth in Arabidopsis [G. soja accessions, but not in G. max. These indels were responsible for amino acid changes in one of the Huntingtin, elongation factor 3 (EF3), protein phosphatase 2A (PP2A), and the yeast kinase TOR1 (HEAT)-repeat motifs, suggesting the potential association with the twining growth habit exhibited by G. soja compared to the erect growth found in G. max. This study also highlighted the potential of using newly identified genetic variation contained within genomic regions that have been fixed in G. max. This information may be used to design crosses to determine if the fixed regions are associated with phenotypes of agricultural value, thereby providing additional candidate genes for the development of new, improved varieties.The abundance of SNPs, coupled with high-throughput discovery and detection methods make them ideal candidates for use in genetic studies involving linkage mapping, map-based positional cloning, and quantitative trait loci (QTL) mapping . In the cessions . As an ebidopsis , was fouSNPs, if associated with a target trait, can be used for marker-assisted selection (MAS) to identify individuals containing a combination of alleles of interest from large segregating populations . SNPs caPhylogenetic studies in plants have traditionally relied on sequence diversity in genes of interest. SNPs in nuclear and chloroplast genes represent a rich source of phylogenetic information that has been used to elucidate the evolutionary relationships in a wide variety of crop species. The analysis of SNP diversity and conservation between the sequences of different individuals can help better understand patterns of inheritance. By considering rates of mutation, a molecular clock may also be applied to estimate the timing of species divergence. Molecular phylogenetics has been applied to a number of plant genomes . One exaB. oleracea pangenome allowed for the visualization of not only the number of uniquely present and absent genes for each accession, but also the number of genes present and absent in different combinations of accessions. In addition, the length of each branch in the tree was proportional to the number of nucleotide substitutions per site. The evolutionary patterns observed in the tree can then be linked to agronomic traits associated with each accession.The advantage of using pangenomes for phylogenetic analysis is that with the additional information provided by SNPs identified in regions showing PAV, it will be possible to infer more accurate relationships between accessions. Furthermore, the variable genes can be used to identify which genes are uniquely present and absent in each accession, and these numbers can be placed on the phylogenetic tree. In the recent publication by Golicz et al. , the plaST statistic, which uses differences in allele frequency between populations to determine the presence of selective pressure in one population compared to another [G. max with seven wild accessions of G. soja identified 682 genes in G. max involved in abiotic stress regulation, which were found to have undergone positive selection [G. soja accessions had fewer genes (ten positively-selected genes shared by at least three wild accessions) that were under positive selection, implying that adaptation to different environments may have been the driving force behind this phenomenon. This study also showed that the variable genome of the soybean pangenome had undergone weaker purifying selection and/or greater positive selection compared to core genes, suggesting that lineage-specific genes evolve faster than shared genes.Advances in NGS and bioinformatics software have allowed SNPs to be readily available, and in large numbers. This has in turn allowed the identification of genomic regions that show evidence of selective pressure, thereby helping us understand how populations and species evolve ,53. In t another . Another another . Yet ano another . Under n another . Since selection . On the Oryza sativa (rice) accessions, LD was used to determine the chromosome positions of each newly assembled contig relative to the Nipponbare reference genome. Reads from all accessions were aligned to the variable genome and SNPs were called between the accessions. The LD between a specific SNP identified against the new contigs and all the SNPs previously identified against the core genome, i.e., the Nipponbare reference, was calculated. The chromosome location of the SNP in the core genome having the highest LD with the SNP on a specific contig of the variable genome was deemed to be the approximate location of that contig. In this way, the genes found in the novel contigs were assigned to their correct genomic positions relative to the Nipponbare reference [SNPs identified in the pangenome can also be used to place newly assembled contigs in the pangenome reference. This method is particularly useful when using the iterative mapping and assembly approach, which can result in a large number of contigs. Since the starting point of the assembly is a single reference, and new contigs are generated at each step of the iterative assembly process, it is very useful to know the positions and orientations of the contigs relative to the pangenome reference, especially if they harbour genic sequences. In studies involving association mapping or QTL analysis, candidate genes are mapped to a narrow genomic region in which the causal genes are selected based on the gene annotation of the reference genome . In the eference .The use of pangenomes for SNP discovery can pose some challenges. Similar to single linear reference genomes, the quality of pangenome assemblies in terms of completeness and annotation is of utmost importance. Mis-assembled genomes can impede the accurate alignments of reads, which can in turn affect downstream analyses such as the identification of large or small variants such as SNPs. Large, complex genomes such as many plant genomes are prone to mis-assemblies due to their repetitive nature . IncorreExisting pangenome analysis tools have been designed with small microbial genomes in mind. However, with the increasing interest in pangenomic analyses of higher, more complex organisms such as plant genomes, there is a need to develop tools, which will be able to handle the deluge of information that will be produced. Tens of thousands of genes will have to be analysed. An even more considerable number of SNPs will be identified both in genic and non-genic regions. Therefore, there is a need for tools that will be able to assist with a number of tasks such as the detection of orthologous genes, pangenome modelling, functional annotation of SNPs and phylogenetic analyses, in both an accurate and timely manner. In addition, the results derived from the pangenomic analyses will have to be stored and maintained in large repositories, as well as allow fast access to users. The integration of genomic, gene expression data and SNP data will also be necessary to link the core genome and the variable genome with expression levels and variants such as SNPs and indels. Such functional information should be able to provide a link between the pangenome and the trait observed, and be made readily accessible to plant breeders.It is becoming clear that the analysis of a pangenome rather than a single linear reference genome will ensure that the entire genetic diversity within any given species is fully represented. The use of long read sequencing technologies coupled with the reduced cost associated with NGS will make high quality genome assemblies more readily available to the research community, and this will fuel more pangenome studies in the future. The additional information captured within the pangenome in the form of variation at both the gene level and the nucleotide level will provide a valuable link between genotypic data and phenotypic data, especially in the case of crop genomics. With the onset of climate change, crops, which are able to adapt to a wide range of changing environments, are being highly sought after. Therefore, the evolution of variable genes and their associated SNPs can greatly help with the improvement of crop varieties in the light of an increasing global population and an ever-changing climate.


Plasmodium falciparum exhibits fragmented population structure or local adaptation at the northern limit of its African distribution where the dry Sahel zone meets the Sahara, samples were collected from diverse locations within Mauritania over a range of ~1000 km. Microsatellite genotypes were obtained for 203 clinical infection samples from eight locations, and Illumina paired‐end sequences were obtained to yield high coverage genomewide single nucleotide polymorphism (SNP) data for 65 clinical infection samples from four locations. Most infections contained single parasite genotypes, reflecting low rates of transmission and superinfection locally, in contrast to the situation seen in population samples from countries further south. A minority of infections shared related or identical genotypes locally, indicating some repeated transmission of parasite clones without recombination. This caused some multilocus linkage disequilibrium and local divergence, but aside from the effect of repeated genotypes there was minimal differentiation between locations. Several chromosomal regions had elevated integrated haplotype scores (|iHS|) indicating recent selection, including those containing drug resistance genes. A genomewide FST scan comparison with previous sequence data from an area in West Africa with higher infection endemicity indicates that regional gene flow prevents genetic isolation, but revealed allele frequency differentiation at three drug resistance loci and an erythrocyte invasion ligand gene. Contrast of extended haplotype signatures revealed none to be unique to Mauritania. Discrete foci of infection on the edge of the Sahara are genetically highly connected to the wider continental parasite population, and local elimination would be difficult to achieve without very substantial reduction in malaria throughout the region.To determine whether the major human malaria parasite  Plasmodium falciparum causes more human deaths and disease than all other eukaryotic pathogens combined, but recent progress in malaria control has led advocacy for elimination from some endemic areas  and significance values between populations with at least 10 isolates were calculated using fstat version 2.9.3.2, updated from  was calculated in genalex 6.501  . Genotype calls were made for each infection sample at all SNPs covered by a minimum of 10 reads. The data set was filtered iteratively by alternatively excluding isolates and SNPs in a stepwise manner. During the first iteration, isolates with >90% missing data were excluded prior exclusion of SNPs with >90% missing data. The percentage of missing data was recalculated following each removal of isolates or SNPs. The level of missing data allowed was decreased in steps of 5%, with multiple steps per iteration if all isolates or SNPs were below the threshold. The process was repeated until all isolates and all SNPs had less than 5% missing data, with 65 of the initial 86 isolates passing this filtering process and being used for subsequent analysis.Parasite DNA prepared from the clinical infections sampled in 2014 were processed for whole‐genome paired‐end short read sequencing on an Illumina HiSeq following the pipeline for quality control and sample preparation at the Wellcome Trust Sanger Institute. Reads were aligned to the FWS fixation index, estimating on a scale from 0 to 1 the fixation of alleles within each infection sample relative to the diversity observed in the total population sample  were taken to indicate loci most likely to be under local selection.Tajima's Plasmodium falciparum‐positive malaria cases which had been sampled from eight diverse sites in Mauritania during the 2012 and 2013 transmission seasons  per locus ranged from 0.39 to 0.89 . Overall, the mean number of genotypes detected per infection was 1.56 and the proportion of all locus scores that had more than one allele was 0.13. As predicted from the low infection endemicity locally, the sites sampled in Mauritania had lower proportions of mixed genotype infections than seen elsewhere in West Africa  identified low but significant differences (P < 0.05) in eight of 21 pairwise comparisons, with FST values ranging up to 0.048. Two particular sites (Selibaby and Aioun) were involved in each of the comparisons that showed significant differences  of the multilocus genotypes of each isolate did not show any separate clustering of samples from the different sites, or from the two different years   than seen previously in comparable sequence data from highly endemic African population samples . The majority of the genomewide SNP profiles from different infections were unrelated, but there was a small number of infections that had closely related genotypes  and were not significantly different from zero. Consistent with the results from the microsatellite analyses of samples from the previous years, this is consistent with high levels of gene flow within the region, so the isolates were considered as a single population for subsequent analysis. The overall allele frequency distribution for the Mauritanian population was negatively skewed, with a mean Tajima's D value of −1.67, averaged over 2965 genes that each had at least 3 SNPs , and towards the end of chromosome 6. Additional windows of elevated |iHS| values were observed in regions of chromosomes 4 and 5 that, respectively, included the antimalarial drug resistance genes dhfr (encoding the antifolate drug target dihydrofolate reductase) and mdr1 (encoding the multidrug resistance 1 transporter). The antimalarial resistance gene dhps (encoding the antifolate drug target dihydropteroate synthase) is situated between the two closely adjacent windows of elevated |iHS| values on chromosome 8.To scan for evidence of loci under recent directional selection, the standardized integrated haplotype score (|iHS|) was calculated for all SNPs with minor allele frequencies >5% in the overall Mauritanian population sample. This test identifies chromosomal regions which are likely to have been subject to recent positive selection, by identifying alleles associated with extended haplotypes relative to the alternate allele at that position. The short generation time and high recombination rate in malaria parasites quickly breaks down these haplotypes, so signatures of elevated |iHS| are generally indicative of recent selection upon the parasite population. The results identified six regions where elevated |iHS| values were associated with three or more SNPs . The genomewide mean FST between the samples from these different countries was only 0.004, but there were four genomic loci at which SNPs had FST values above 0.2  also showed these loci to be highly differentiated . The overall summary of the genomewide allele frequency spectrum as indicated by the negative Tajima's D index in Mauritania was similar to that previously seen in a more highly endemic population elsewhere in the West African region, but it is notable that a few particular genomic loci showed marked differences in allele frequency. Most of the SNPs with highly divergent frequencies mapped within or adjacent to the antimalarial drug resistance genes crt, mdr1, and dhps, known to have spatial and temporal allele frequency variation elsewhere in West Africa due to historical drug selection  gene locus to have the most highly divergent SNP allele frequencies  of variation among 10‐locus microsatellite genotypes of P. falciparum clinical isolates sampled from eight different locations in Mauritania in 2012–2013.Fig. S2 Principal components analysis (PCA) of variation among genome‐wide SNP profiles of P. falciparum clinical isolates sampled from four different locations in Mauritania in 2014.Fig. S3 Principal components analysis (PCA) of variation among genome‐wide SNP profiles of P. falciparum clinical isolates sampled from Mauritania (current study) and a previous population sample from the Republic of Guinea .Fig. S4 Genome‐wide scan of Jost's Dest index of SNP frequency differentiation between P. falciparum from Mauritania (current study) and a previous population sample from the Republic of Guinea .Table S1 Microsatellite genotypes for 203 P. falciparum clinical infections sampled from eight different locations in Mauritania.Table S2 Allelic diversity  of P. falciparum at 10 microsatellite loci at eight endemic locations in Mauritania (sample sizes are given in the paper).Table S3 Estimates of effective P. falciparum population size (Ne) based on the observed local microsatellite allele diversity (He) assuming a standard mutation rate under either a stepwise mutation model (SMM) or an infinite alleles model (IAM), at each of the Mauritanian sites with sample sizes of at least 10 infections and at other sites in four previously studied West African countries.Table S4 Pairwise values estimating differentiation between local populations in Mauritania summarising data for 10 microsatellite loci as measured with a) FST and b) Jost's Dest.Table S5 Sequence accession numbers, intra‐infection SNP frequency fixation indices (FWS) and pairwise differences among individual P. falciparum clinical infection samples from Mauritania.Table S6 Overall population Tajima's D values for genes with at least 3 SNPs, based on allele frequency distributions of the majority allele called in each of 65 P. falciparum clinical infection samples from Mauritania.Table S7 Windows of the P. falciparum genome containing elevated standardised integrated haplotype scores in the overall analysis of genomewide SNP diversity in Mauritania.Table S8. Genomic positions of P. falciparum SNPs with FST values >0.2 comparing the overall Mauritanian population sample with a previously published population sample from a more highly endemic area in the Republic of Guinea .Table S9 Windows across the P. falciparum genome for which extended haplotypes were observed in Guinea relative to Mauritania as detected by Rsb analysis. No windows of extended haplotype in Mauritania relative to Guinea were detected from this scan.Click here for additional data file. Click here for additional data file. Click here for additional data file. Click here for additional data file.


Exploring linkage disequilibrium (LD) patterns among the single nucleotide polymorphism (SNP) sites can improve the accuracy and cost-effectiveness of genomic association studies, whereby representative (tag) SNPs are identified to sufficiently represent the genomic diversity in populations. There has been considerable amount of effort in developing efficient algorithms to select tag SNPs from the growing large-scale data sets. Methods using the classical pairwise-LD and multi-locus LD measures have been proposed that aim to reduce the computational complexity and to increase the accuracy, respectively. The present work solves the tag SNP selection problem by efficiently balancing the computational complexity and accuracy, and improves the coverage in genomic diversity in a cost-effective manner. The employed algorithm makes use of mutual information to explore the multi-locus association between SNPs and can handle different data types and conditions. Experiments with benchmark HapMap data sets show comparable or better performance against the state-of-the-art algorithms. In particular, as a novel application, the genome-wide SNP tagging is performed in the 1000 Genomes Project data sets, and produced a well-annotated database of tagging variants that capture the common genotype diversity in 2,504 samples from 26 human populations. Compared to conventional methods, the algorithm requires as input only the genotype (or haplotype) sequences, can scale up to genome-wide analyses, and produces accurate solutions with more information-rich output, providing an improved platform for researchers towards the subsequent association studies. Each cluster is characterized by the similarity (redundancy) between its observation vectors si and a centroid vector (tag SNP) will be the “representative” of that cluster ) in order to capture most of the haplotype diversity in a given block , i.e., Without any prior information, the problem of finding tag SNPs in a given genomic region can be cast as finding a number of distinct metaSNPs which can represent all common variations in layers (blocks) in the respective region. Given k-th SNP is used as seed, the corresponding metaSNP is initialized by using a set of  weights specific to that seed, i.e., a length-N vector of zeros except for the k-th element which is 1. This choice initializes the metaSNP sk. In the next step, the pair-wise associations between each SNP vector si and the metaSNP is calculated by the similarity metricI ∈  is a normalized estimation of the mutual information [x and y, and α is a nonnegative power exponent that shapes the similarity metric in a nonlinear manner pushing smaller values of the normalized mutual information closer to zero. We use α = 5, as in [When the ormation  between 5, as in . This meAlgorithm 1 Attractor metaSNPk-th SNP as seed.1. Start with the k-th SNP and all other SNPs, i.e., w(i) = J, i = 1, …, N.2. Calculate the pairwise associations (weights) between the 3. Estimate the metaSNP by taking the weighted average of all SNP vectors, i.e., i = 1, …, N.4. Calculate the (multi-locus) associations between the metaSNP 5. Repeat the steps 3-4 until the two consecutive weight vectors obtained at the 4th step are very similar, i.e., w, and the metaSNP 6. Return the attractor N seeds. In that case, we will find a limited number of attractor metaSNPs, each of which has multiple “attractee” seeds  [N} such that it will consist of only one attractee seed  to efficiently result in the same set of attractor metaSNPs. To overcome such complexities, we developed a sliding-window based heuristic using the two objectives described below, which we observed that do not compromise performance.We can do an exhaustive search by applying the attractor algorithm for all tractor) . It woulFirst, for a given seed SNP, we will constrain the weighted average (metaSNP) and the association calculations to the seed’s “genomic neighborhood” with X local SNPs , i.e., use  Project  providesk ∈ 1, …, N) in the data, we quickly estimate a “short-attractor” (consisting of 101-SNPs) by using the Algorithm 1 with w is larger than 0.5; otherwise, discard the seed.Second, to estimate all attractor metaSNPs in the data efficiently, we will reduce the number of possible seeds by evaluating their potential to be an attractee seed. For every SNP  mutual information between the n-th top SNP and the attractor metaSNP”. By default, we set n to 10 as it leads to good performance in most data sets.Since the weights used for the attractor metaSNPs are equal to their associations with the individual SNPs, it is straightforward to select the tagging SNP as the one with the largest weight. In case of multiple (co-)top-ranked SNPs with identical (largest) weights, we choose the one that is located closest to the median of their genomic positions. After identifying all tag SNPs, one can order them to assist the selection of informative tag SNP subsets for various genotyping needs  captured by a given choice of tag SNPs. The coverage rate (R) can be defined as “the ratio between the maximum number of genomic sequences covered (Gi) and the total number of samples (P)” for the given choice of tag SNPs [t is the number of genomic patterns observed on the given selection of tag SNPs. In genotype data, those patterns are the distinct sequences of genotypes, each consisting of the three-level genotype values of an individual in the selected tag SNPs, i.e., 0 encodes for the reference homozygous genotype, 1 encodes for the heterozygous genotype, and 2 encodes for the alternate homozygous genotype. For example, assume that 5 samples (I-V) are genotyped on four SNP loci and the corresponding sequences are “2111”, “2200”,“2201”,“2110”, and “2200”. If the first two SNPs are tagged, there will be only two genotype patterns “21” and “22” observed on the samples I,IV and II,III,V respectively. The pattern “21” can represent the genotype sequences “2111” (I) and “2110” (IV), each belonging to exactly 1 individual, so that the maximum coverage of this pattern is G1 = 1. The second pattern “22” represents the genotype sequences “2200”  and “2201” (III), where the sequence “2200” covers 2 individuals (samples II and V) and the maximum coverage is G2 = 2. Using R is calculated as (G1+G2)/P = (1+2)/5 = 0.6. Intuitively, an optimal tagging approach should find a subset of SNPs possessing larger number of genomic patterns with perhaps a broader coverage obtained by each pattern, e.g., the last two SNP loci in this example will result in 4 distinct patterns covering 100% of the individuals (R = 1). R is a versatile metric that can be readily used in the haplotype data to represent the “haplotype diversity” captured by a set of tagged SNPs [As the performance metric we used “tag SNPs , i.e.,Rged SNPs .In genotype data sets, we compared our results with the state-of-the-art algorithm Tagger  which isR) obtained by the top-c tag SNPs of a solution, whereby different values of c are used to illustrate the tradeoff between the coverage rate (R) and the genotyping cost (c), which is the number of SNPs that are tagged  in the given genomic region.We run the metaSNP method versus Tagger and ER on four ENCODE regions and Chromosome 22 in HapMap, and obtained the ranked estimates of tag SNPs solved by each algorithm. For the 1KGP data, we compared our predictions with those of the Tagger obtained for several short  segments of the Chromosome 22, due to limitations pertaining the Tagger algorithm. In all simulations we used the recommended default settings of algorithms unless otherwise noted. We demonstrated the coverage rate  obtained from a rich multi-population sample set . Combined with genotype imputation this results in many variants with (ignorably) low frequencies in the overall population, e.g., the variants carrying only the reference homozygous genotype for all samples in the populations. In terms of tagging costs, as one can expect, compared to HapMap relatively more tag SNPs are required to reach the same coverage rate in the larger population .First, we evaluated our method in the Chromosome 22 genotypes to provide a baseline tagging results against the metaSNP’s HapMap predictions. Then we used the Chromosome 21 genotypes, the shortest autosome, to further scrutinize our predictions. It is seen in We observed similar performance in other chromosomes as well. As a performance comparison, we tested Tagger algorithm in the same 1KGP data sets. Since Tagger is based on the (offline) pair-wise analysis of all SNPs, the limitations occur due to memory use. To overcome this and to set out a fair comparison, we divided the data into several chromosomal segments  then processed the individual segments. We note that the performance of our algorithm improves with the increased data size, i.e., given more variants residing in the neighboring genomic distances. This can be observed from In addition to the coverage rate, we assessed the tagging performance of the proposed method by comparing the genotype-phenotype association of the tag SNP and the SNPs that were correlated with the tag SNP.χ2 test. The analysis indicates that the meta SNP method identified one of the designated SNP as the tag SNP and assigned the 2nd and 3rd highest weights to the other two designated SNPs. The association of these three SNPs and the phenotype are significant  in the ENm014 genotypes data. In this figure, we see that the tag SNP was accurately predicted in the first iteration (w1) and lasted to the last iteration (w7) given the threshold ϵ = 1E − 7, which presents that the algorithm can efficiently converge within the few iterations.The computational complexity of algorithms is evaluated in terms of running times in the benchmark HapMap data. We carried out all experiments on a hardware with Core(TM) i7 CPU @2.6GHz, 16GB memory, and Mac OSX 10.10.5. The pairwise LD-based Tagger is the fastest approach in this study as it can process each ENCODE data set in a minute . On the step 1 and step 2 in Algorithm 2) is run with the cluster support:The genome-wide application of the metaSNP algorithm  and 256GB RAM using R.In rCluster  and R. [rCluster . Each instep 1 and step 2 are 134.37 hours and 153.3 hours, respectively.For the whole genome, the total running times for α could be chosen for optimizing different objectives of attractor searching: in Algorithm 1 we used α = 2 in step 1 for obtaining all valuable short-attractors even with low degrees of LD at the expense of getting highly-correlated  ones; then in step 2, as opposed to that, we used α = 5 to focus on only the sharpest (distinctive) attractors. Further, the algorithm can be started with a user-defined SNP set as the “primary seeds” to be force-included in the final results. In this case, the α parameter can be accordingly adjusted  for those seed SNPs to ensure the discovery of “sharp” attractors that mutually exclude each other’s seed SNP.This study addresses the problem of efficient SNP tagging in very large genomic distances by exploiting the underlying multi-locus LD patterns. We emphasize that our SNP tagging approach is block-free and undemanding in the sense that it is not based on any prior information derived from the empirical data such as haplotype block structures, recombination hotspots, or LD maps. In contrast, although the other methods that used the distance measures that are closely related to the mutual information , 17, theSince the objective is based on a general measure of correlation between the variables  the employed algorithm can handle phased haplotype sequences as well as the genotype data. This is a great advantage over existing algorithms since the procedures that apply statistical inference on data management  is prone to error and often introduce dependencies and arbitrary patterns to the end results, whereby algorithms capable of handling different data types can avoid such limitations. This allows the flexibility for analyzing multiple data sets in a study, which re-phasing all the data sets using the same method may be infeasible as well as scrutinizing the pipeline of analysis.As a measure of multi-locus correlation we used the mutual information that can be efficiently estimated between a continuous valued metaSNP variable and an individual SNP variant. For this, we employed the numerical method in  which isIn addition to the ranked tag SNPs, the proposed method reports their metaSNPs and the attractors representing the association landscapes, providing an information-rich output for subsequent analyses. An example output corresponding to ENr113 genotypes results is given in The main contributions of the proposed algorithm are the definitions of “attractor” and “metaSNP” for the simplified representations of “multi-locus LD” and “variation” in the haplotype blocks, respectively, which may provide valuable information in both dimensions of the SNP data. Furthermore, these quantities can be iteratively estimated up to a certain precision, allowing efficient heuristic designs which can be applied to very large data set. In particular, our sliding-window heuristic can employ the vast amount of information in several layers, i.e., using the first layer of data (sliding a 101-SNPs window) we find all potential attractee seeds that may form a typical attractor, then using the second layer of data  we find the desired long attractors to capture any long-range multi-locus LD pattern. Since the SNP variability is not uniform across a chromosome , the disr2 < 0.05) is observed within the 100 kb distance in all populations [J) to be able to capture the multi-locus associations that might be (jointly) present in larger distances. Because the density of SNP varies across the genome and metaSNP algorithm automatically determines the size of a haplotype, we used a sliding window of 10000 SNPs to recruit a consistently large number of SNPs within a genomic region for the algorithm to identify the haplotype within a reasonable time. This also provides an opportunity for analyzing the structure of the associations of variants and reveal the properties of the “long-range” correlations of variants as the correlation of DNA sequences, which will be an interesting topic in the future study [In this study, we defined the genomic neighborhood of a tag SNP as the set of X = 10,001 nearby variant that will exhibit a substantial LD decay in the corresponding genomic distance . Although in 1KGP data sets a large drop in pair-wise LD  samples, which is a more cost-effective solution compared to Tagger’s estimates on the same data sets. In default settings, the metaSNP approach yields a proper tradeoff between the amount of required genotyping and coverage rate, offers useful parameters to fulfill requirements in different applications, is versatile to perform on different data types, and produces rich output for subsequent association studies.S1 FigDetails are given in (PDF)Click here for additional data file.S1 TableThe performances of the two tagging methods in Tables (XLS)Click here for additional data file.S2 TableThe exclusive and intersecting sets of tag SNPs that are found by the two algorithms, metaSNP and Tagger.(XLS)Click here for additional data file.S2 FigMulti-locus mutual similarity (LD) estimates are displayed in the estimated attractors that correspond to the discovered tag SNPs, top-10.(PDF)Click here for additional data file.S3 FigMulti-locus mutual similarity (LD) estimates are displayed in the estimated attractors that correspond to the discovered tag SNPs, top 11-20.(PDF)Click here for additional data file.S4 FigMulti-locus mutual similarity (LD) estimates are displayed in the estimated attractors that correspond to the discovered tag SNPs, top 20-27.(PDF)Click here for additional data file.S3 TableTagging performance of the proposed method through the comparison of genotype-phenotype association of the tagged SNP and the SNPs that were correlated with the tagged SNP.(XLS)Click here for additional data file.S4 TableEach of the 27 sheets correspond to an estimated attractor, given in the same order as supplementary figures. For convenience, only the data for the 100 top-ranking SNPs are displayed, corresponding to the SNP information, the estimated mutual information weights, and the trilevel genotype values.(XLS)Click here for additional data file.S5 TableDetailed information of the tag SNPs selected by each algorithm from the analyzed data bases, corresponding to Figs (XLS)Click here for additional data file.S1 FileDetailed description of the mutual information model used for the attractor metaSNP algorithm.(PDF)Click here for additional data file.


Bos taurus. In turn, characterization of population structure among diverse bull  genomes enables detailed assessment of genetic resources and origins. By analyzing 432 unrelated bull genomes from 13 breeds and 16 countries, we demonstrate genetic diversity and structural complexity among the European/Western cattle population. Importantly, we relaxed a strong assumption of discrete or admixed population, by adapting latent variable models for individual-specific allele frequencies that directly capture a wide range of complex structure from genome-wide genotypes. As measured by magnitude of differentiation, selection pressure on SNPs within genes is substantially greater than that on intergenic regions. Additionally, broad regions of chromosome 6 harboring largest genetic differentiation suggest positive selection underlying population structure. We carried out gene set analysis using SNP annotations to identify enriched functional categories such as energy-related processes and multiple development stages. Our population structure analysis of bull genomes can support genetic management strategies that capture structural complexity and promote sustainable genetic breadth.Since domestication, population bottlenecks, breed formation, and selective breeding have radically shaped the genealogy and genetics of  Bos taurus (cattle) has long experienced selection for high quality milk and meat production. To maintain and encourage genetic diversity, it is important to characterize the population structure of cattle. Inferring population structure and genetic differentiation play an increasingly important role in conservation efforts, genealogy, and selection programs. In this study, we have analyzed a large number of whole genome sequences of Bos taurus males (bulls) from 13 breeds, representing 16 countries, to characterize population structure and genetic diversity.Recognizing the importance of cattle genome diversity in genome-wide association studies, genomic predictions, and optimal breeding, there have been substantial efforts to obtain genome-wide genotypes of multiple breeds in diverse geographical locations1245678Moreover, most studies assumed discrete structure among representatives of a studied population, as defined by self-identified breeds. Recent studies using unsupervised classification, admixture models, and other techniques demonstrate greater structural complexity12Bos taurus genomes from 13 breeds and 16 countries, as part of the 1000 Bull Genomes ProjectApplying latent variable probabilistic models, we analyzed 432 unrelated n = 432 unrelated Bos taurus samples with average sequencing coverage >5  with no missing values and minor allele frequencies >0.05 .The dimension of the population structure in logistic factor analysis (LFA) was set at envalues . The estenvalues . At the envalues . We enabR2 (hereafter referred to as R2) are 0.070 and 0.087, respectively  out of 426 SNPs with R2 > 0.6, as well as all 29 (100%) SNPs with R2 > 0.7. On the other hand, the X chromosome shows the least variation with respect to logistic factors, containing zero SNP with R2 > 0.5. The top 1000 genomic features that are associated with differentiated SNPs are shown in We discovered diverse and pervasive genetic differentiation with respect to the population structure of bulls. We found that the median and mean values of McFadden’s pseudo ectively . Chromosk = 6 PCs, communality statisticsk PCs are used to detect local adaptation. Absolute correlation statistics between the top 6 LFs and the top 6 PCs were very high: 0.999, 0.894, 0.890, 0.994, 0.994, and 0.992 for each comparison between ith LF and ith PC for i = 1, …, 6. High concordance between the two methods can also be seen in a scatterplot of the top two PCs, compared to that of LFs  positioned between 71101370 and 71600122 and 15 SNPs (11 within 50 kbp of known genomic features) positioned between 38482423 and 39140537. 83% of those most differentiated SNPs (20 out of 24 SNPs with known genomic features) are within or close to genes related to the selection sweep according to ref. R2 > 0.174) is available as Among SNPs with the highest R2 measures than intergenic SNPs without annotations . On the other hand, among intergenic SNPs, we found no significant correlation  between SNP-feature distances and R2 measures . Start/stop codons and 3′/5′ UTR do not exhibit statistically significant difference from other genic SNPs. Lastly, we used 338 genes that are closest to SNPs with R2 > 0.5 in the To better understand evolutionary and biological processes, we conducted gene set analyses using genomic annotations of SNPs. Firstly, we found that SNPs located within known genomic features have about 1.8% higher measures . SecondlBos taurus has played a crucial role in ancient and modern societies alike by providing agricultural support and essential nutrients. Accurate characterization of its population structure helps conservation of genetic resources and optimal selection programs, ensuring a healthy and sustainable cattle population. In this process, we can better infer the genetic and functional variation that underlies the population structure. Using 432 samples from the 1000 Bull Genome Project, we provide a comprehensive sequencing-based assessment of population structure among cattle of European and Western ancestry.k ancestral populations. This critical choice of k depends on analytical solutions, such as log probability of data58Assumptions underlying population structure and its estimation methods have evolved to address growing genomics data in terms of complexity and scales101718k ancestral populations. Particularly, we utilize latent variable probabilistic models that can estimate a broad range of arbitrarily complex structure including admixture, continuous, and discrete populationWe circumvent this challenge by using complementary methods that do not need to select When modeling SNPs with logistic factors in generalized linear models, we found widespread genetic differentiation due to population structure. Despite making no assumption about structure, the majority of the most differentiated SNPs in our study have been identified as under selection sweep by previous studies. Chromosome 6, which harbors a large proportion of the highly differentiated SNPs, has been previously suggested to have been subjected to one or more selective sweeps22Our genome-wide study of differentiation suggests stronger evolutionary pressure on genic regions. Prolonged changes in environment, driven by domestication and development of cattle breeds, have likely caused genetic differentiation that focuses on functional regions of genomesThis study paves a way to further our understanding of population structure among modern European and Western cattle breeds. Identification of genetic differentiation with respect to population structure may inform conservation efforts to preserve heritage breeds and maintain genetic diversity. Methodologically, our sequencing-based analysis of population structure represents non-parametric approaches that can identify genetic differentiation and complexity without strong assumption on structure in population genomics.Bos taurusThe 1000 Bull Genomes Project has collaborated to gather whole-genome sequences of breeds from Australia, Austria, Canada, Denmark, Finland, France, Germany, Italy, Netherlands, New Zealand, Norway, Spain, Sweden, Switzerland, and United Kingdom. Its initial efforts have vastly expanded known single nucleotide polymorphisms (SNPs) and copy number variations (CNVs) in To initially explore the genome-wide SNP data, we employ hierarchical clustering which enables straightforward visualization of relationships among samples. In particular, similarities/dissimilarities among 10% of 4.0 million SNPs are represented by Manhattan distances,To hierarchically cluster samples, UPGMA (Unweighted Pair Group Method with Arithmetic Mean) is applied to Manhattan distancesTo infer population structure directly from a genome-wide genotype matrix, we consider a probabilistic model of individual allele frequencies. In particular, by using logistic factor analysisY with m SNPs and n bulls. For each yij, an individual-specific allele frequency for ith SNP and jth bull is fij ∈ . This collection of parameters (a m × nF matrix) is transformed into real numbers via the logit function, which allows computation of the underlying latent structure. Overall, the statistical model considered isConsider a genotype matrix d logistic factors (LFs) H which can be estimated by applying principal component analysis (PCA) to F). Note that A is a matrix of coefficients in a logistic regression. The dimensions of logistic factors are estimated by comparing the observed correlation matrix to a series of hypothesized structures derived from selected variables of large loadingsd = 1, …, 100, while applying principal component analysis on the mean-centered genotypes . For robustness analysis to confirm genetic differentiation, we alternatively used cross-validation approximations to choose dThen, the population structure is captured by R2 that is appropriate for a logistic regressionith SNP,To approximate how much of the variation in genotypes is explained by the population structure, we calculate McFadden’s pseudo R2 in logistic regressions, we will henceforth refer to it as R2 when clear in context. Significance analysis with respect to logistic factors  are done with a resampling-based jackstraw methodwhere k principal components (PCs), with appropriate normalization specific to each measure. Selection is detected when SNPs (or other genetic markers) are substantially explained by the first k PCs13R2 measures using LFs.Additionally, we performed genome-wide scan for selection in the panel of SNP data using Bos taurus reference genome from the Center for Bioinformatics and Computational Biology, University of Maryland .For genome annotation, we used the latest R2 measures are significantly different according to feature types, we used the Mann-Whitney-Wilcoxon (MWW) testR2 than those in intergenic regions. Among SNPs with known feature assignments, MWW tests were used to infer if a particular feature type is associated with significantly higher R2 measures. Bonferroni correction is applied on a set of four MWW tests to adjust for multiple hypotheses testing36When testing whether the distribution of McFadden’s pseudo R2 > 0.5, we apply Lastly, because some of SNPs are in intergenic regions with no known annotations, we utilized the closest features function from How to cite this article: Chung, N. C. et al. Population Structure Analysis of Bull Genomes of European and Western Ancestry. Sci. Rep.7, 40688; doi: 10.1038/srep40688 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.