The present study was to determine the nature of gene action and combining ability of six quantitative traits related to productivity of five varieties and ten hybrid combinations of durum wheat. Five modern durum wheat varieties were used in diallel crosses as parents. The study includes three F1 and two F2 generations. The experiments were done in a randomized block design in three replications during three years. Significant differences between the genotypes in both generations was found for all the traits. The general combining ability and specific combining ability showed reliability in both generations. Obtained results suggests that breeding schemes should include both types of genetic effects in order to improve productivity components. The ratio of variances showed that general combining ability has a greater influence on the inheritance of plant height, spike length and thousand kernels weight. For productivity tillering capacity, number of spikelets per spike and kernels weight per spike, specific combining ability has a great impact in inheritance. For thousand kernels weight a redetermination of the genetic formula was established in both generations. Durum wheat varieties Deni, Superdur and Progres were found to be the best general combinators for studied productivity elements. The most valuable cross combinations were Deni × Superdur, Superdur × Predel and Progres × Predel. Parental wheat varieties and progenies from these crosses can be used for improving productivity components and for increasing yields in durum wheat breeding programs. Breeding strategy of durum wheat is based on genetic informationon the inheritance of the main quantitative traits relatedto productivity. To obtain such information, it is necessary toapply a genetic model corresponding to the source materialto be used. In a regular breeding program, it is importantto identify the best parents for hybridization and crosses toselect valuable genotypes . Diallelcrosses have been used for a long time in genetic researchto determine the inheritance of a trait among a set of genotypesand to identify superior parents for hybrid or varietiesdevelopment.Information on additive gene effects i. e. general combiningability effects (GCA) is of great importance, because it successfullypredicts the genetic potential of parents who givedesired results in segregating generations. In determiningthe specific combining ability effects (SCA), a relationshipis established with the non-additive gene effects (dominanceand epistasis components). The identification of a good hybridcombination with high SCA on a given trait makes it possibleto expect a more probable transgressive form for the trait.Combining ability describes the breeding value of parentalvarieties to produce better hybrids as well as their crosses.The importance of combining ability is related to the evaluationof parental lines and their hybrids by their respectiveadditive and non-additive genetic effects in relation to a certaintrait. Diallel crosses give a more general view of combiningability, where general and specific combining ability are indicatorsfor nature of gene action . Assesmentof GCA effects show that it is not possible to choose agood general combiner for all traits of the productivity. Thisis due to the inability to combine in one genotype high GCAon all traits . However, some parents showdesired GCA effects for several traits. It is obvious that highyieldingvarieties included in crosses are mainly responsiblefor increasing productivity .A number of authors, using schemes of full and half diallelcrosses, have established the breeding value of a large numberof varieties and the gene action for traits related to productivity.In the publications cited below, the authors found that bothadditive and non-additive gene effects played a role in the inheritanceof tested traits. According to J. Yao et al. (2011) andM. Singht et al. (2018) plant height and spike length mainlycontrolled by additive gene effects. It was reported that inthe inheritance of thousand kernels weight the non-additivegene effects play an essential role , while A. Hannachi et al. (2017) and A. Hassanet al. (2018) establish inverse. Plant height, tillering capacityand number of spikelets per spike were mainly controlled bynon-additive gene effects , when A. Hannachi et al. (2017)reported that plant height and productivity tillering capacitywere additive. The inheritance of the spike length, number ofspikelets per spike, and kernel weight per spike are controlledby non-additive gene effects and they have a major role , also A. Pansuriya et al. (2014)for these traits and for spike length. Productivity tilleringcapacity and number of spikelets per spike are controled bynon-additive gene effects, on the other hand, for spike lengthand thousand kernel weight additive gene effects dominate ininheritance .It can be concluded from the published data that parentalvarieties have a great influence on both types of combiningability. On the other hand, they are carried out in differentgrowing conditions, which gives additional confirms to thisstatement of diverstityThe present investigation was undertaken to determine thenature and magnitude of gene action and general and specificcombining ability for five modern durum wheat varieties andfor six quantitative traits related to productivity in diallel crossof durum wheatParents and crosses. Five modern durum wheat varieties wereincluded in the study as the parental varieties in the half diallelcrosses. The varieties are selected among the new Bulgarianvarieties of durum wheats, including the old and the newvariety-standard and the Austrian variety Superdur, which hasrecently become widespread in Bulgaria. Victoria – Bulgaria,Deni – Bulgaria, Superdur – Austria, old variety-standard Progres– Bulgaria and new variety-standard Predel – Bulgaria.The choice of varieties is based on their previous observation.They are created in Field Crops Institute, Chirpan and are geneticallydistant. Progres and Deni are created by experimentalmutagenesis combined with hybridization and Victoria andPredel are created by hybridization. A diallel cross was performedin which all the described varieties were crossed witheach other without reciprocal combinations. The crosses wascarried out handmade at the beginning of heading time in fieldcondition. The following ten combinations were performed:Victoria × Deni, Victoria × Superdur, Victoria × Progres, Victoria× Predel, Deni × Superdur, Deni × Progres, Deni × Predel,Superdur × Progres, Superdur × Predel, Progres × Predel. Fromeach combination, 30 spikes were castrated and pollinated.From the harvested F1 plants, the seeds necessary for sowingof F2 generation were randomly selected.Management. The parents are sown in each replicationin two rows, the F1 hybrids in two rows, and the F2 hybridsin five rows. Genotypes are sown handmade in the field inbeds. Row length – two meters, row spacing – twenty cmand inside the row – five cm in a randomized block designwith three replications. After the full maturity phenophase,the necessary plants from each replication are harvested andcollected for biometric research. Twenty plants were selectedfrom the parents and F1 generation and thirty plants from F2generation at random. The diallel cross was performed in threeconsecutive years. Thus, generation F1 for three years and F2for two years are provided. The experiments was conductedin three harvest years 2014, 2015 and 2016. The experimentswas carried out in the breeding field of the Field Crops Institute– Chirpan according to the adopted technology forgrowing durum wheat. The predecessor is spring peas. Thesoil type is Chernozems compact Eutric Vertisols (by FAO).The three years meteorological condition are characterizedby higher temperatures compared to the multi-year period. The first year have 18.5 % and the second 58.2 %precipitation over the multi-year period during the growingseason, while in the third year precipitation are 17.5 % lessthan in the multi-year period .The following traits were observed. Plant height (cm) – itis measured from the ground surface to the end of the spikewithout the awns on the main stem in centimeters. Productivitytillering capacity (pcs.) – the fertile spikes of one plantare counted. Spike length (cm) – measured on the main stemfrom the base of the spike to the top of the uppermost spikelet.Number of spikelets per spike (pcs.) – the spikelets in the mainspike are counted. Number of kernels per spike (pcs.) – allkernels of the main spike are counted after handmade threshing.Thousand kernels weight (g) – five hundred kernels areweighed and multiplied by two. All traits are determined bymethodology by Y. Enchev et al. (1976).Statistical analysis. The data from the three years F1 andthe two years F2 are averaged and on them are conductedstatistical processing. In the processing of the experimentaldata, mathematical and statistical methods were used on theresults according to the set goal of the research. To performdiallel analysis was used combining ability analysis in diallelcrosses – by method II model I  with theprogram software of M. Burow and J. Coors (1994). Analysisof variance (ANOVA) by traits is derived through the sameprogram on M. Burow and J. Coors (1994).The results of analysis of variance showed statistically significantdifferences between the genotypes for all studied traitsin both generations. The values of the variances for GCA andSCA were significant in both generations (Table 1). Therefore,both additive and non-additive gene effects (dominance andepistasis) were of significant importance in the inheritanceof the traits. The studied traits related to durum wheat productivityshow that they are controlled by both additive andnon-additive gene effects.The ratio of GCA and SCA variances (σ 2g/σ 2s ) for F1 andF2 are presented in Table 1. For plant height, spike length,number of spikelets per spike and thousand kernel weight,the sum of squares indicates that additive gene effects have agreater influence in inheritance. For the other two traits, thesum of the squares indicates that non-additive gene effectshave a greater impact. This is proved by the ratio of the variancesof GCA and SCA, respectively. The preponderance ofadditive gene effects (σ 2g/σ 2s > 1) was found in the inheritanceof plant height, spike length and thousand kernel weight. Thespike length in F2 generation showed a significant increase,which indicates that the additivity increases. Domination ofadditive gene effects allow application of classical breedingmethods. For these traits selection can start in early segregatinggenerations (F2–F3).Domination of non-additive gene effects (σ 2g/σ 2s < 1) isobservedfor the productivity tillering capacity, number ofspikelets per spike and kernels weight per spike. Non-additivegene effects (dominance and epistasis) prevalence in theirexpressionThis analysis does not allow to determine or dominanceor epistasis are responsible for the inheritance of the traits. Itis well known that when inheritance is determined by nonadditive genetic effects, selection in early segregating generationswill be difficult. In this case effective selection must startin the later segregating generations F4–F5.Although the preponderance of additive genetic effectsfor the thousand kernel weight in the individual years andgenerations has been established, there is a change in thegenetic effects controlling the trait. This is due to the genotypeenvironmentinteraction and is explained by the phenomenonof redetermination of the genetic formula. In F1 in 2014 thenon-additive genetic effects preponderance, and in 2015 and2016 the additive ones. In F2 in 2015 the non-additive geneticeffects preponderance and in 2016 the additive ones (data notshown). In the individual years in both generations, all othertraits show a one-way ratio of variances that determine theinfluence of genetic effects.The analysis for GCA of parents and SCA of hybrids for thestudied traits in F1 and F2 is presented in the next two tables(Tables 2 and 3). From a breeding point of view, genotypeswith a negative value for plant height due to the connectionwith lodging are more valuable. For all other traits, positivevalues are preferable, as their increase will lead to an increasein productivity.Plant height. Table 2 presents the values for plant height.The varieties Victoria and Progres has a significant andpositive values for GCA in F1 and F2. They increase the plantheight in the hybrids in which he participated as parents.The varieties Superdur and Predel have negative significantvaluesof GCA in both generations. These varieties reducingthe plant height in the hybrids in which they participate.They can be used successfully in the breeding program forobtaining dwarf durum wheats. In terms of SCA, valuableare the hybrid combination Progres × Predel, with significantnegative values in both generations. The other crosses havedifferent values for SCA, and in different generations they aredifferently significant and change their signs according to thegeneration.Productivity tillering capacity. Table 2 presents the valuesfor GCA and SCA for the productivity tillering capacity.Significant values of GCA to increase the trait of productivitytillering capacity have Deni variety in both generations. Thevarieties Superdur and Predel have positive and significantvalues in F1 generation, while in F2 generation the valuesare significant but negative. Variety Victoria has a significantand negative GCA in F1 and a negative and nonsignificantin F2 and reduces the values of the trait. Of greater interestare hybrid combinations and their SCA values (see Table 2),as non-additive effects have been found to preponderance.The results show that one of the crosses Progres × Predel hassignificant and positive values in both generations for SCA.The other crosses occupy an intermediate position.Spike length. Table 2 presents the values for the generaland specific combining ability of parents and hybrids for spikelength. We define the varieties Deni, Superdur and Progresas good general combinators to increase spike length, as theyhave positive and significant values for GCA in both generations.Victoria variety has significant and negative values inboth generations and it decreases the spike length in the hybridsin which it participates. The SCА values of the hybridsshow that two crosses showed significant and positive valuesin F1 and F2 are Deni × Superdur and Progres × PredelNumber of spikelets per spike. The values for GCA andSCA for the trait number of spikelets per spike are presentedin Table 3. The Victoria and Deni varieties in both generationshave significant values to increasing number of spikelets perspike and they are good general combinators for this trait.Variety Progres has negative GCA and reducing the values ofthe trait. The other varieties have nonsignificant values, whichshows their insignificant role. The greate interest is in hybridcombinations, as non-additive gene effects have been shownto play a major role in inheritance. The hybrid combinationsVictoria × Deni and Victoria × Superdur show significant andpositive SCA effects in both generations. With the highestSCA value is the cross Victoria × Deni.Kernels weight per spike. Table 3 represents the valuesfor parental GCA and hybrid SCA. In F1 there are no varietieswith significant GCA effects. No good general combinatorshave been reported to increase kernels weight per spike inboth generations. In the F2 generation, the Progres and Predelvarieties increase the values of the kernels weight per spike,and the Superdur variety decreases it.These results are very contradictory and it is difficult todefine any of the varieties as a good general combiner on thistrait. We can consider that the varieties Progres and Predel aregood general combinators on the basis of showing significantand positive GCA effects in F2 generation. Greater attentionshould be paid to hybrid combinations, as SCA effectspreponderance. Four significant good hybrid combinationsare observed in terms of SCA effects. They are positive andsignificant in both generations. The most promising hybridcombinations are Deni × Superdur, Deni × Predel, Superdur× Progres and Superdur × Predel.Thousand kernels weight. The variety Progres (see Table 3)is good general combiners for increasing the values of thetrait thousand kernels weight. Variety Progres has positiveand significant values in both generations. On the other hand,general combiners that have been significant to reduce grainsize are the Predel and Superdur varieties in both generations.In Table 3 can be seen that the cross Superdur × Predel, whichin both generations shows positive and significant valuesfor the SCA effects, is interesting in terms of breeding. Theremaining crosses in most cases have a significant value inonly one of the generations. For all traits the values for GCAand SCA in most cases are in one-way direction and can berelied on their reliabilityFor the possibilities of heterosis in the breeding of durumwheat and obtaining transgressive forms, it is necessary toconsider the crosses with significant SCA effects on severaltraits. Of the studied hybrid combinations (see Tables 2 and 3)as the most promising with significant SCA effects are Progres× Predel for plant height; Progres × Predel for productivitytillering capacity; Deni × Superdur and Progres × Predel forspike length; Victoria × Deni and Victoria × Superdur for thenumber of spikelets per spike; Deni × Superdur, Deni × Predel,Superdur × Progres and Superdur × Predel for grains weightper spike; Superdur × Predel for the thousand kernels weight.Development of wheat varieties possessing improved yieldrelated characters had been the major objective of durumwheat breeders. Thus availability of genetically based variationfor traits like plant height, productivity tillering capacity,spike length, number of spikelets per spike, kernels weightper spike and thousand grain weight breeding populationis essential. Present genetic material used here to generateinformation on genetic nature of these traits. A number ofstudies by other investigations are in line with the resultsobtained by us for GCA and SCA. Many researchers havealso found significant GCA and SCA effects for the plantheight ;for productivity tillering ability ; for spike length ; for number of spikelets per spike; for kernels weight per spike ; for thousand kernels weight .The obtained results for the GCA and SCA give a very clearidea of the control in the inheritance of the traits elements ofthe yield. The impact of additive and non-additive gene actionin the inheritance of the structural elements of the yieldshows that in order to maximize the productivity of durumwheat, a system should be used that includes both variancesin simultaneouslyPlant height and spike length are used for an individualselection by the classical methods. In both generations theyare controlled by additive gene effects. In most cases thousandkernels weight is also controlled by additive genetic effects.This shows that it is possible for breeders to obtain betterresults in improving these traits. It should be noted that inthe case of plant height, spike length and in most cases forthousand kernels weight, the selection may start in the earliersegregating generations F2–F3. Because they are controlledby additive genetic effects. It should be noted that the mainstructural elements of yield – spike length and in most casesthousand kernels weight are controlled by additive gene effects.Preponderance of additive gene effects in inheritance ofplant height has been reported by a number of other researchers; for spike length; for thousandkernels weight .For other three traits preponderance non-additive gene effectin this investigation was observed. Therefore, selectionin early segregating generations will be difficult. In this case,it is recommended that an effective selection must start in thelater segregating generations F4–F5 when the influence of thenon-additive effects (dominance) decreases and the additivityincreases. The results from this study for productivity tilleringcapacity are in line with those obtained by other authors; for number of spikeletsper spike ; for kernels weight per spike .For thousand kernel weight, a redermination of the geneticformula of the trait was found. This is due to the genotype-environmentinteraction. Redetermination of the genetic formulais especially evident in the case of quantitative traits that arecontrolled by a large number of small polygens significantlyinfluenced by environmental conditions . The presence of this phenomenon makes itdifficult to lead an effective selection on the thousand kernelweight in different years and generations and the selectionmust be conducted longer . When the phenomenon of redeterminationof the genetic formula is observed in the individualyears, different forms are selected, controlling the trait in thebreeding process. This means that in different years valuableforms are selected in which the trait is controlled by both additiveand non-additive genetic effects.The deepening of the research allows to specify the methodsof the applied breeding strategy and to optimize and increasethe efficiency of the selection. The possibility of evaluatinggenotypes and their breeding value as a starting material forincreasing productivity is also important. With the conductedresearch it is possible to get information about two of themost important moments in a successful breeding program –choosing parents for hybridization and leading a purposefulselection. The selection on a separate trait can increase theyield, but a more significant increase would be obtained bysimultaneously comprehensively improving its elements.Varieties that have significant GCA effects for more thanone trait are of grait interest for breeding. The results for therespective traits are presented in Tables 2 and 3. Tables showwhich varieties are good combiners on the studied traits. VarietyVictoria is a good general combiner on the trait numberof spikelets per spike and a bad combiner for the traits plantheight and spike length. The Deni variety is a good generalcombiner in terms of productivity tillering capacity, spikelength and number of spikelets per spike. The Superdur varietyis defined as a good combiner for plant height and spikelength and a bad combiner for thousand kernels weight. VarietyProgres shows significant and positive values for GCA for thetraits spike length and thousand kernels weight, and is a badcombiner for number of spikelets per spike and plant height.Variety Predel is a good combiner for the trait plant height anda bad combiner for thousand kernels weight. A good generalcombiner at the same time on three traits is the Deni variety.Good general combinators on two traits at the same time arethe varieties Superdur and Progres. Good general combinatorson one trait are the varieties Victoria and Predel. VarietiesVictoria and Progres are bad combiners on two traits. VarietiesSuperdur and Predel are bad combiners on one trait. The onlyexception is the Deni variety, which has no traits like a badcombiner. The varieties Deni, Superdur and Progres emerge asthe best general combinators for the elements of the productivityon several traits at the same time. To increase the yield, itis necessary to simultaneously improve several valuable traits.The certain general combining abilities are a prerequisite forthe correct selection of parental forms and their crossing forthe purposes of the durum wheat breeding program.As can be seen, the varieties bearing high GCA most oftenenter the crosses with high SCA. According to the varioustraits, there are good crosses, such as combined parents withhigh X high GCA and those who have combined parentswith low X low GCA. Some with high SCA values are also a combinations of high X low GCA. As the most valuablehybrid combination with significant SCA effects on severaltraits its define Deni × Superdur, Superdur × Predel and Progres×Predel.Determining the combining ability shows that it is not possibleto have one variety can good combinator for all traits.Not all crosses with high SCA effects were obtained fromthe crosses of a good X good GCA parent . Rather, crosses with high SCA effects are obtainedfrom crosses between bad X bad and bad X good combiner.They argue that such manifestations are due to the involvementof dominant or epistatis gene effects. Crosses withhigh SCA may be more likely to be sources of transgression. Transgressive lineson a certain traits can be a source for creating highly efficientdurum wheat varieties. Evaluations of gene action explain thegenetic potential of breeding materials and contribute to thetargeted management of breeding progress in durum wheatproductivity.The study found that both additive and non-additive geneeffects are of significant importance in the nature of gene actionof the productivity traits. This implies a breeding systemthat includes both gene effects for improving the elementsof productivity. Inheritance of plant height, spike length andthousand kernels weight is mainly controlled by additive geneeffects and it is possible to start selection of genotypes in theearly segregating generations F2–F3. Inheritance of productivitytillering capacity, number of spikelets per spike andkernels weight per spike is controlled by non-additive geneeffects. Therefore, the selection on these traits should start inthe later segregating generations F4–F5. There is obtained achange in the genetic effects affecting the expression of thetrait thousand kernels weight, which indicates the presenceof the redetermination of the genetic formula.The authors declare no conflict of interest.Adel M., Ali E. Gene action and combining ability in a six parent diallelcross of wheat. Asian J. Crop Sci. 2013;5(1):14-23. DOI 10.3923/ajcs.2013.14.23Ahmad E., Akhtar M., Badoni S., Jaiswal J. Combining ability studiesfor seed yield related attributes and quality parameters in breadwheat (Triticum aestivum L.). J. 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Genetic analysisin F1 generation of diallel crosses for yield and yield componentsin hexaploid wheat (Triticum aestivum L.). Agriways. 2018;6(2):17-26.Talha M., Swati, Negi A., Harsha. Identification of bread wheat lineswith superior combining ability for yield contributing traits andyellow rust resistance suitable for NWPZ of India. Electron. J.Plant Breed. 2018;8(2):695-703. DOI 10.5958/0975-928X.2017.00105.3.Tiwari R., Marker S., Meghawal D. Combining ability estimates forspike characters in F1 hybrids developed through diallel crossesamong macaroni wheat (Triticum durum Desf.) genotypes. J. Pharmacogn.Phytochem. 2017;6(2):237-241.Tiwari R., Marker S., Ramteke P. Gene action and combining abilityanalysis for quality traits macaroni wheat (Triticum durum Desf.).Vegetos: Int. J. Plant Res. 2015;28(1):130-133. DOI 10.5958/2229-4473.2015.00017.8.Topal A., Aydin C., Akgun N., Babaoglu M. 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We use UK Biobank and a unique IVF family dataset (including genotyped embryos) to investigate sibling variation in both phenotype and genotype. We compare phenotype  and genotype  distributions among siblings to those in the general population. As expected, the between-siblings standard deviation in polygenic scores is  Consequently there is less variation  among siblings from the same family than in a group of randomly selected, unrelated individuals. In this paper we explore these observations from the perspective of genetic similarity and DNA inheritance—see Fig. The sibling distribution of (additive) polygenic scores (PGS) for such traits is centered at the parental midpoint39.The sibling genetic variance is roughly half that found in the general population . The probability distribution of sibling polygenic scores has standard deviation Whether observed phenotypes also exhibit these properties depends further on the nature of environmental influences, and interactions between genotype and environment40. If environmental influences are themselves roughly additive, and mostly independent of genotype , we expect that sibling phenotypes are also normally distributed, roughly about the parental midpoint, with reduced variance compared to that found in the general population. The degree of reduction in variance depends on the heritability of the trait in question.Full siblings are identical at approximately half of all DNA loci, and each receives approximately half of their DNA from each parent. This has the following implications for complex traits that are roughly additive in genetic architecture: We examine the properties discussed above from an empirical (or descriptive) perspective, using sibling and family data from UK Biobank (UKB) and from in-vitro fertilization (IVF) clinics. In the latter case routine embryo biopsies taken for genetic screening purposes have been genotyped by the company Genomic Prediction (GP), using an Affymetrix array similar to the one used by UKB. Specifically, we examine variance in and correlation between sibling genotypes and phenotypes across a number of complex traits, developing evidence for observations 1. and 2. above.42. For example, in42 the authors write“It is also important to note that all embryos produced by a couple are genetically related and share on average 50% of SNPs [single nucleotide polymorphism]. One must conclude that owing to inherent limitations of the PRS-ES [polygenic risk score for embryo screening] models and limited variation in the genetic makeup of embryos produced by a couple, the clinical utility of PRS-ES is almost certainly diminutively small”.As we illustrate below, the genetic variation among embryos (siblings) is quite substantial: it is common to find, within a specific family, embryos that are both high and normal risk for a specific condition, or even in overall Genetic Health Index score, a composite predictor of multiple disease risks with the purpose of capturing general health43. That PGS have strong performance among siblings  has already been demonstrated and repeatedly verified in previous work44. In “A surprising objection to the use of PGS in the context of IVF is that the variation within families  is negligible and therefore it has little utility as a screening mechanism5. However, because there is less data available in the tail of the distribution, for some conditions there is some possibility that undetected nonlinear effects play a role that is not anticipated from the analysis of the bulk of the training population. Note that efficacy of all the predictors described here, and of the health index, has been tested among siblings in44.Embryo ranking is influenced by outlier status . The predictive models used are additive, and have been shown to accurately predict odds ratios for outliers ; see Figures 9–12 in reference46 that training on unrelated individuals can lead to inflation of some effect sizes, due to house-hold effects, genetic nurture, etc. Efficacy of all the predictors described here, and of the health index, has been tested among siblings in44, resulting in performance estimates that correct, at least to some degree, for these issues.It has been revealed through the study of siblingssibling-pair method for detecting recombination events by comparing the genotypes of two siblings. Large biobanks such as UKB have tens of thousands of sibling pairs, which allow high-statistics mapping of recombination rates in sexual reproduction.Family data can be further used to explore the specific genotype differences between siblings. These arise through the randomness of the recombination process that produces the sperm and egg genotypes in reproduction. We develop a new The sibling-pair method makes use of the following observation , nevertheless the recombination events themselves, which take place in the meiosis that produces a specific sperm or egg cell, are obviously independent of each other . Hence the location of each boundary of these special regions is an unbiased and independent draw from the probability distribution which characterizes recombination. Cataloging the location of these boundaries therefore allows us to estimate this probability distribution—i.e., the recombination rate (in Morgans) as a function of position on each chromosome. Because this method of recombination mapping only requires the genotypes of two siblings, it can be applied to very large existing datasets.As a check on the method, we test it using datasets in which we have access to parental as well as sibling genotypes. IVF family data is especially useful here because the number of embryos is typically larger than the number of siblings in a family, and the number of pairwise analyses one can use for testing is large. By specifically looking at SNPs where the mother and father are homozygous and heterozygous (or vice versa), we can easily track recombination events which switch the chromatid region that is passed on to the child. We have used smaller datasets with both parent and sibling data to test and calibrate the sibling-only method described above. See “We have developed the sibling-pair method for detecting recombination breaks using imputed SNP genotypes. This limits the spatial resolution of the results relative to what can be obtained using whole genomes, however it is sufficient to map out the probability distribution and to locate recombination hotspots . In this paper we apply the method to imputed SNP data from UKB and from an IVF family dataset.The sibling-pair method can also be applied to whole genome data, which would result in more precise spatial resolution. We anticipate that large datasets of recombination events can be analyzed using machine learning techniques to identify the specific DNA features  which are associated with higher probability of recombination in a given region.44, on siblings and unrelated populations. See the 43, including details of its construction and properties. Additional information about biobanks can be found in “In this paper we use a number of different phenotypes and PGS, based on previous publications42 concerning within family variation of PGS/phenotype compared to the general population.Modern developments such as large-scale genetic biobanks and PGS allow us to explore a number of quantities that arise in classical population genetics. We present such results in this section. In addition, we correct some misconceptions found in the literatureSome basic explanation of the notation is required before presenting the results. The methods themselves, including details about recombination, are described in “We repeatedly compare the PGS differences among unrelated individuals and siblings. V according toWe extract the assortativity 43. Expressed in terms of the average lifespan reduction Lastly, we also present results for a Genetic Health Index, which is a linear combination of absolute risks estimated from PGSThe results discussed here provide an empirical exploration of the theoretical predictions given in “We identify the set of sibling pairs of self-reported European  ancestry within the UKB. We construct a set of randomly paired individuals: each individual is assigned to a pair with the partner chosen at random from the aggregate sibling group. We then calculate the phenotype difference between sibling pairs and random pairs with the expectation that the sibling pairs will display less variation that that of the random pairs. In Fig. S) and unrelated (U) distributions to test whether the former are smaller by In Table m, and test the S) and unrelated (U) standard deviation in PGS. The interpretation of m here  is unclear to us and deserves further investigation.For case–control phenotypes, we can still observe the PGS difference and correlation between siblings in PGS and also demonstrate that the variance in scores between siblings is quite substantial. In Fig. pairs of (full) siblings—however, in the UK Biobank, larger family structures are present. We identify larger families by collecting all sets such that if A-B and B-C are full sibling pairs, the superset A-B-C must be a family (we filter against parent-child relationships). The number and size of families found this way is described in the These calculations summarize how the collection of sibling pairs compares to the collection of unrelated pairings. We now explicitly show that individual families display a level of variance comparable to what is claimed. In the prior plots and tables, we focused solely on Figures The distribution of PGS for all embryos (including different families) is similar to the PGS distribution to the UKB general population. Within a specific IVF family, the embryo PGS distribution is centered around the midparent PGS. In Fig. As before, the variation in the cohort has an inter- and intra-family component. However, for this cohort we have access to the PGS of the parents for each embryo. We next demonstrate that distribution of embryo PGS is distributed around the midparent value which leads to the inter-family variation. In Fig. 43) distributions in the UK Biobank compared to GP parental  and embryo samples. Figures Figure Among the families displayed in these figures, at position number 15 from the left, we encounter an interesting case of sibling polygenic distribution relative to the parents. In the family all siblings have significantly higher Health Index score than the parents. This arises in an interesting manner: the mother is a high-risk outlier for condition X and the father is a high-risk outlier for condition Y.  Their lower overall Health Index scores result from high risk of conditions X (mother) and Y (father). However, the embryos, each resulting from unique recombination of parental genotypes, are normal risk for both X and Y and each embryo has much higher Health Index score than the parents. This can be discerned from detailed examination of individual genomes and associated polygenic scores.It is worth noting that the Health Index sums absolute risk (probability of getting the condition) per condition times lifespan impact. Absolute risk is a nonlinear function of polygenic score, whereas all polygenic scores used in this paper  are linear in the genotype. In this case the absolute risks of the parents for X (mother) and Y (father) are very high. Embryo genomes, due to the diploid nature of human sexual reproduction, are a blend of maternal and paternal genotypes. In this case all of the polygenic scores of the embryos cluster around the parental midpoint values for both X and Y. Due to nonlinearity, the absolute risks for X and Y of the embryos are all much lower than for the parents, and the embryos have higher Health Index scores than the parents.47 for chromosomes 1 and 22. Figure 47 (regions with very high recombination activity) are readily visible. These are average results from 21 k self-identified European sibling pairs. Similar results for the remaining autosomal chromosomes are presented in the Results are obtained using the method described in “Agreement between sibling-pair method and deCODE results is very strong. In particular, the features in plots of cumulative breaks per chromosome are clearly similar in both sets of results. In the Because our method uses flanking windows for statistical comparisons, breaks which are very close to the ends of chromosomes  will be under counted. This observation also affects methods which track the state of parental hetero- and homozygous sites in offspring. It is difficult to know which methods more severely over or under count breaks in the endpoint regions.It is important to note that even slightly inaccurate maps of recombination breaks are still useful for machine learning methods which attempt to predict local recombination rate based on DNA motifs in the region. From the machine learning perspective, the impact of modest inaccuracies is simply a small decrease in statistical signal. The over-representation of certain motifs or specific mutations in hotspot regions should still be detectable by automated learning methods. The primary benefit from the sibling-pair method is a very large expansion in the size (and ancestry group coverage) of available maps  of recombination events across the genome.In Table Although the UKB cohort is predominantly self-reported European, there are a non-trivial number of sibling pairs with other self-reported ancestry. The question of variation in recombination rate by self-reported ancestry group can be investigated, at least at a preliminary level, using the non-European siblings found in UKB. Application of the new method to UKB sibling pairs yields the following whole genome recombination lengths for the three largest (self-reported) ancestry groups: Europeans  3338 cM, South Asian (292 pairs) 3073 cM, African (174 pairs) 3453 cM. If we adopt the European distribution as the null hypothesis—mean 33.38 breaks per individual in a pair, SD = 4.8—we obtain the following results: (1) the South Asian deviation in average is 2.65 fewer breaks (with N = 292). In null model SD units this is We plan to investigate this topic in the future with more non-European sibling data as it becomes available. It is possible that the differences in total recombination rates found above are the result of some kind of systematic error. For example, the sibling-pair method might exhibit higher or lower recombination detection rates due to differences in how genome imputation works across different ancestry groups.Roughly half of the genetic variation in a population is within-family, and the other half between families. This implies that the standard deviation of sibling polygenic score distributions is roughly 44. It was also shown that expected gains from selection on PGS or Health Index score are substantial43. For the latter result to hold there must be significant variance among siblings on the relevant PGS. In this paper we exhibited this variation using many traits.In earlier work it was shown that PGS perform almost as well in differentiating siblings by disease status or quantitative trait value as in pairs of unrelated individualsWe have also developed a new technique that directly probes DNA recombination—the molecular mechanism responsible for sibling genetic differences. This new sibling-pair method can be applied to large datasets with many thousands of sibling pairs. In this project we created a map of roughly 1.44 million recombination events using UKB genomes. Similar maps can now be created using other biobank data, including in non-European ancestry groups that have not yet received sufficient attention. The landmark deCODE results were obtained under special circumstances: the researchers had access to data resulting from a nationwide project utilizing genealogical records  and widespread sequencing. Using the sibling-pair method results of comparable accuracy can be obtained from existing datasets around the world—e.g., national biobanks in countries such as the USA, Estonia, China, Taiwan, Japan, etc.It seems possible that deep learning approaches using this training data could identify new DNA motifs that are associated with increased or decreased local recombination probability. This may advance our molecular understanding of meiosis, a fundamental biological process. Regarding applications, we note that many chromosomal abnormalities are the result of errors introduced through recombination. Improvements in computational analysis of embryo genotypes may result in better accuracy in embryo screening against aneuploidy.The two datasets used in this work are the 2018 release of the UKB and a cohort of parent and embryo genotypes from families undergoing preimplatation genetic testing for polygenic (PGT-P) screening at GP.48. We restrict all samples to those with European ancestry with a total of 32 individual parent-embryo groups. Pre-implantation genetic testing for aneuploidy was carried out on all embryos and only euploid embryos were considered for analysis in this work. GP data was collected along internal GP guidelines, conforming with local legislation and institutional requirements. The patients/participants provided their written informed consent to participate in this study. Written informed consent was obtained from the individual(s) for the use of any potentially identifiable data included in this article, although no identifiable information was used, nor made available to researchers.The GP samples are processed on the same (Affymetrix) SNP array platform which is used by the UKB. The details of the genotyping procedure and quality control are described at length inhttps://www.ukbiobank.ac.uk/privacy-policy). All data handled by researchers in this work was de-identified.UKB data was collected under policies conforming with national and requirements and subject to privacy rights  ancestry unless otherwise stated. The details of the genotyping and quality control steps are found in the supplements.27, while case–control predictors are described in44. Several predictors are trained using PRS-CS and publicly available GWAS which have a much higher case-count than available in the UK Biobank. Details of the training are described in the Supplement of43 and we provide a brief summary in the Polygenic predictors are obtained through training on either the UK Biobank or a wholly separate GWAS. The testing set we use is the set of  21 k sibling pairs in the UK Biobank :not IBD will be half that found for the difference between unrelated individuals Since on average half the SNPs are IBD and that variance is additive, the variance in the difference between siblings 50. Similar results can be found in Eq. (2) of a more comprehensive review in51 and empirically for Crohn’s Disease, Schizophrenia and Autism in references53.Again, we have neglected assortation. Slight deviations from this result are observed for some traits for which assortation is significant. Consequently the standard deviation in the distribution of sibling differences will be differences in sibling scores, because parental midpoint is not required.Note in Figs. x is the PGS, The discussion until this point has assumed quantitative phenotypes. For case–control phenotypes, several approaches exist in the literature. For the context of this work, the mixed-distribution model of polygenic scores is adopted where both cases/controls follow normal distributions but are shifted from one-another. This is written asi given by43.With this model of risk, we can construct a quantity which describes expected lifespan gain for an individual N flanking this locus . We can then define an indicator function Here we describe a novel algorithm for detecting recombination events using sibling pairs. This sibling-pair method does not require parental genotypes. Let cus Fig. . : Partially identical (type 2): No IBD segments (type 3): From these observations, roughly one quarter of a sibling’s genome will match identically with the other. A recombination event can then be detected by scanning along the chromosome for regions in which both siblings agree completely (modulo rare genotyping errors) in For a given window, there are 3 distinct types of region for a sibling pair. Let the father’s chromosome strands (chromatids) be Almost all breaks will be transitions from region type 1 to type 2 or region type 2 to type 3 because a jump from type 1 to type 3 would require a coincidence in meiosis between both the sperm and egg, which is highly unlikely. The sibling-pair method is designed to detect breaks from type 1 to 2  regions, but will not record changes from type 2 to 3. Therefore the sibling-pair method will detect 1/2 the total number of breaks.Z which signals discontinuities in statistical properties of flanking windows:a is a positive number much less than N, which keeps the denominator from ever becoming zero. This function has useful properties: The numerator is large in magnitude when the N, which tends to occur in type 1 regions.The denominator is small when at least one of the flanking windows has close to maximal similarity Z reaches a local maximum near a recombination break point, with We define an indicator function N, a are tuned, and performance evaluated, using family data (both IVF and from UKB) in which parental genotypes are available. The parameters are chosen so that Z is robust against genotyping errors or mutations (which reduce similarity of IBD regions from 1), and clusters of low MAF SNPs (which can cause non-IBD regions to appear IBD). With parental genotypes we can make use of hetero- and homozygous loci to directly track which segments of chromatid have been passed to each sibling.The parameters Z has been properly adjusted. Many biobanks, including UKB, have large numbers of siblings in their cohort, whereas trios containing mother, father, and child are comparatively rare. Thus, this new technique will add significantly to the amount of data available for study of recombination. In this work, we create a dataset of  1.44 million recombination events found in 21 k UKB sibling pairs. We anticipate that datasets like ours will be useful in machine learning to discover the molecular mechanisms which control the local rate of recombination in the genome. For example, deep learning could be used to detect specific DNA motifs which are associated with recombination hotspots or regions where recombination is rare.What is novel here is that recombination breaks can be detected using sibling pair data alone, once the indicator function Note we assume that each recombination event can be considered as a draw from a probability distribution. Effects such as crossover interference (which are consequences of the underlying molecular mechanisms) cause breaks to be less likely to occur in close proximity to each other, violating the assumption that each individual break is an independent event. However, this is a small correction as with only  70 breaks across 22 chromosomes it is unlikely that two breaks occur close together. Since crossover interference does not inhibit a sib1 break conditional on a nearby sib2 break, the results from the sib-pair method detects very slightly more breaks in close proximity than occur in a single meiosis. However, as mentioned this is a very small effect as nearby breaks are rare.Supplementary Information.


Functional annotations have the potential to increase power of genome-wide association studies (GWAS) by prioritizing variants according to their biological function, but this potential has not been well studied. We comprehensively evaluated all 1132 traits in the UK Biobank whose SNP-heritability estimates were given “medium” or “high” labels by Neale’s lab. For each trait, we integrated GWAS summary statistics of close to 8 million common variants (minor allele frequency  However, despite their increasingly large sample sizes  have enabled the discovery and identification of thousands of genetic loci across a wide range of phenotypes3. To increase the power of GWAS, earlier work have leveraged linkage results5 or summary statistics from independent GWAS of the same or related traits9. To integrate information across sources, meta-analysis10 and Fisher’s method11 are two standard and powerful approaches. For example, meta-analysis of summary statistics has been shown to be as powerful as mega-analysis of individual-level data, when there is no heterogeneity between the studies13. On the other hand, Fisher’s method is more robust to differential directions of effect by combining p values from different studies.The standard GWAS approaches are designed for discovering common variants with relatively large effects (i.e. low polygenicity), and so they are not optimized for analyzing the large number of small effects in highly polygenic traits18. To overcome limitations such as incomparable metrics of measurement and differential ascertainment biases across different annotations, several authors have proposed methods to integrate multiple annotations into one single measure: a meta-score23. For instance, Kircher, M. et al.22 combined more than 60 genomic features into one combined annotation dependent depletion (CADD) meta-score to provide a measure of the relative deleteriousness for each variant, while Ionita-laza, I. et al.23 developed Eigen, a functional meta-score of similar nature using an unsupervised spectral approach.Recently, it has been shown that variant functional annotations can prioritize according to their biological relevance26, their potential for improving power of GWAS has not been well studied or understood. To integrate GWAS summary statistics with meta-scores, in addition to meta-analysis and Fisher’s method, we also consider the weighted p value approach27 and the stratified false discovery rate (sFDR) control method28, which extended the traditional FDR control methodology29. Both weighted p value and sFDR have been used to leverage linkage evidence30, gene-expression data32 and pleiotropy33 to increase power of GWAS. Here we use these data-integration methods to integrate CADD or Eigen functional meta-scores with GWAS summary statistics of 1132 phenotypes from the UK Biobank data34.Despite the popularity of using these meta-scores for genomic studies35 proposed a modified weighted p value-based method called FINDOR to leverage polygenic functional enrichment to improve power of GWAS. To achieve this, FINDOR uses a stratified linkage disequilibrium (LD) score regression method36 to compute the expected 37. FINDOR then stratifies the GWAS SNPs into 100 equally-sized bins based on their expected GWAS p values. An application of FINDOR by Kichaev, G. et al.35 to 27 traits, selected from the UK Biobank data34, showed that the method was able to improve power of GWAS by identifying additional associated variants. Based on FINDOR35, these 27 traits were constructed from “a set of 27 (roughly) independent and heritable traits, retaining only traits that exhibited a phenotypic correlation Integrating functional annotation scores with GWAS summary statistics has been previously studied. Recently, Kichaev, G. et al.35 in several ways. First, unlike FINDOR, we use methods that prioritize GWAS findings based on external information alone to minimize concern of over-fitting. That is, the weighting factor and stratification are determined based on the annotations alone, independent of the observed GWAS summary statistics. Second, we utilize existing meta-scores that are already calibrated and easier to implement in practice, instead of using many individual functional scores. Third, we focus on evaluating methods’ robustness to the possibility of uninformative or even misleading functional annotations, because our understanding of the functionality of a genetic variant is incomplete and evolving. Finally, we comprehensively examine all 1132 UK Biobank traits for which the confidence for their SNP-heritability estimates were considered medium to high by Benjamin Neale’s lab from the Broad Institute . For each trait, we integrated GWAS summary statistics of close to 8 million common variants with their functional scores using three different data-integration methods: FINDOR with 75 individual functional scores, and weighted p value and stratified false discovery control methods with CADD (or Eigen) meta-scores.To answer the question of whether prioritizing variants according to their biological function could improve power of GWAS, our study here is different from the FINDOR evaluation of Kichaev, G. et al.In addition to the large-scale UK Biobank application, we also conducted a large-scale simulation study using different study designs, from leveraging the observed genomic data combined with simulated genetic data or vice versa to using only simulated data. We also considered different and complementary performance measures, from the traditional family-wise error rate (FWER) to false discovery rate (FDR), power, recall, precision, and relative efficiency. Finally, we sought to evaluate the functional annotation similarity between variants in linkage disequilibrium (LD), which has not been previously studied but an important consideration when integrating functional scores with GWAS.10, Fisher’s method11, weighted p value27, sFDR28, and FINDOR35. The meta-analysis and Fisher’s method were only included in some of the simulation studies to demonstrate that, although commonly used in many other scientific settings, they are not suitable for integrating GWAS with genomic functional scores.Focusing on integrating functional scores with GWAS summary statistics to improve power of GWAS, we considered five data-integration methods, namely meta-analysisPrior to the large-scale UK Biobank application using methods for which we understand their performance properties, we conducted a large-scale simulation study using three complementary study designs: (i) leveraging the observed functional annotations and integrating them with simulated GWAS, (ii) simulating functional annotations and combining them with observed GWAS, and (iii) using only simulated data. For an unbiased method evaluation, we also considered different performance measures, ranging from the traditional FWER to false discover control, and from the traditional power to recall, precision and relative efficiency.p value, and sFDR) because it was unclear if FINDOR remained valid when the LD structure between SNPs was not preserved. Based on the results from simulation study designs II and III, we found that meta-analysis and Fisher’s method had severe robustness issues to partially informative, uninformative or misleading additional information. Thus, we decided to exclude them from real data application. Finally, in the UK Biobank data application, we compared the recently proposed FINDOR method with weighted p value and sFDR, the two robust methods found through the earlier simulation studies. Figure In simulation study design I, we evaluated the type I error rate of all five methods. Overall, all methods showed reasonable type I error control in this setting. In simulation study designs II and III, we only evaluated four methods  meta-scores. We were unable to evaluate FINDOR in this setting, because FINDOR implements LD score regression (LDSC)38 and the validity of using LDSC for permuted annotation is unclear. The performance measures used here are t, and Here, real UK Biobank GWAS summary statistics of the 1132 traits were integrated with Recall results shown in Fig. Recall rates are  for meta-analysis and  for Fisher’s method after integrating permuted CADD scores. In contrast, these values are  for the weight p value method and  for the sFDR control. The Precision results in Fig. Recall.The entclass1pt{minimap value approach, which was demonstrated by Yoo, Y.J. et al.5 when integrating linkage results with GWAS. Results stratified by the four types of traits analyzed, nonsig, nominal, z4, and z7 , where RE was defined as one minus (the average ranks of the truly associated SNP after data-integration) divided by .Here, both the GWAS summary statistics and the additional information available for data-integration were simulated, with varying degree of informativeness, including uninformative or possibly misleading annotation scores. The performance measures here are power and relative efficiency  meta-scores as described earlier. The total number of independent, significant loci detected at the Recall and New Discoveries were calculated.The UK Biobank GWAS summary statistics from Nealelab  were integrated with variant’s functional annotation scores using three data-integration methods, where FINDOR used 75 individual annotation scores, and weighted p value and sFDR data-integration methods, stratified by the four types of traits analyzed .Figure Overall, integrating the existing functional annotations with the UK Biobank GWAS association statistics did not lead to striking improvements, irrespective of the data-integration method. Results of using Eigen Figure  or countp value and sFDR; the counts stratified by the four trait categories are also provided in Table The overall limited improvement is also evident from Table and the baseline GWAS alone. Additionally, Figure Further, the intersection of significant loci between methods displayed in Figure New Discoveries for traits in the nonsig category may be considered as false positives, as their SNP-heritablity testing p values were Although the ground-truth is unknown in application studies, the New Discoveries after data-integration using, respectively, FINDOR, and weighted p value and sFDR when using CADD  and 30010 (red blood cell (RBC) count) have phenotypic correlation of − 0.51 and genetic correlation of − 0.66, using Nealab co-heritability browser (see Web Resources).The number of ses Fig. b, and thry Table . This isNew Discoveries after data-integration using, respectively, FINDOR, and weighted p value and sFDR when using CADD . It is also clear that, Recall increases as a trait SNP-heritability estimate increases  meta-scores.There has been much discussion about the value of integrating functional annotations into genetic association studiesNew Discoveries and higher Recall) for traits with higher estimates of SNP-heritability  to provide a set of meta-scores that are independent of the GWAS summary statistics of the UK Biobank data. Although this approach is valid for examining type I error control, we were intrigued by the question of whether meta-scores of SNPs in strong LD are similar. To answer this question, we defined  Figures  and S5.  Figures .p value approach and k values, however, has an effect on method performance. Figure p value approach, the default Recall rate. For the sFDR method, Recall rates. Thus, unlike the previous linkage and GWAS integration setting, the default value of Throughout this paper, we have used the default tuning parameter values, 42. In practice, given two families of multiple tests, the underlying compositions of the null and alternative hypotheses may differ, unless the two studies used the same study design including phenotype definition, genotyping platform, environmental exposure, and study population43. When the truly associated SNPs do not completely overlap between the different studies, using random-effect  does not guarantee improved power, because it violates the assumption that the effect sizes come from the same distribution.Among the five data-integration methods, despite meta-analysis and Fisher’s method being applicable in many scientific settings, their applications to genetic association studies are typically restricted to combining evidence from multiple GWAS of the same phenotype and from the same population. This is because the statistical power of meta-analysis (and Fisher’s method) relies on the assumption of homogeneity beyond direction of effectThe use of meta-analysis and Fisher’s method is also questionable when p value and sFDR are more natural choices when only integrating one piece of additional information , while FINDOR is more suitable when integrating a set of functional annotations. All of these integration methods only require summary statistics, and once functional annotations are prepared in appropriate format, all methods can compute millions of SNPs within a few minutes. Possible limitations of weighted p value include the difficulty of handling categorical additional information. This is also true for FINDOR, but can be easily handled using sFDR. The performances of all methods, however, are likely to be affected by different, subjective choices of groups and weighting schemes, and gold standard stratification and weight do not yet exist in this setting. Overall, FINDOR and weighted p value were similar to each other, and they led to more new discoveries for traits considered heritable as compared with sFDR  obtaining GWAS summary statistics for previously understudied variants e.g. in coding sequence, which tend to have higher functional effects than the variants currently studied as they came from the exome sequencing data of the UK Biobank45.Potential future work include (1) leveraging cell-type-specific annotations as complex traits often exhibit cell-type-specific functional enrichmentsp value for SNP i, N, the standard normal distribution, under the null hypothesis of no association between the SNP and the GWAS trait under the study.Let independent of 22 or Eigen23 functional meta-score available for SNP i, which will be the focus of this study.Let 46 to integrate and assuming the functional meta-score is uninformative, N distributed.For the meta-analysis approach, we first assume the best-case scenario where p values instead of the test statistics, Fisher’s method combines 42. In practice, given two families of multiple tests, the underlying compositions of the null and alternative hypotheses may differ, unless the two studies used the same study design including phenotype definition, genotyping platform, environmental exposure, and study population43. When the truly associated SNPs do not completely overlap between the different studies, using random-effect  does not guarantee improved power, because it violates the assumption that the effect sizes come from the same distribution. However, for completeness we include the two classical data-integration methods in our initial method evaluation.Although meta-analysis and Fisher’s method are applicable in many scientific settings, their applications to genetic association studies are typically restricted to combining evidence from multiple GWAS of the same phenotype and from the same population. This is because the statistical power of meta-analysis (and Fisher’s method) relies on the assumption of homogeneity beyond direction of effectFor a practical implementation of meta-analysis when p value approach27 treats p value approach is an attractive method for this study setting, where the primary data are GWAS summary statistics, and the additional information available are genomic functional scores derived independently from the GWAS of interest.Unlike meta-analysis and Fisher’s method, which assume p value implementation, the 27. To transform 30, studied two possible weighting schemes: exponential, 30. This is because the exponential weighting scheme is highly sensitive to large values of 22.For a valid weighted p value approach that up- or down-weights each SNP according to its external information 28. When 5. In addition, sFDR is robust to the situation when Unlike the weighted irrespective of p value approach above.) As a result, there are two groups of GWAS SNPs, where group 1 contains 5% of the GWAS SNPs with the highest functional meta-scores and group 2 contains the remaining SNPs. It is worth emphasizing that group 1 is only presumed to be the high-priority group, as the stratification is based on genomic To implement sFDR in our setting where p values, but using the same pre-specified FDR 28, for each group of SNPs we first transform their GWAS p values, 47, and we then reject the SNPs with 5.We then apply FDR control, separately, to the two groups of GWAS k, and let 47, p values, and the procedure starts from 48, Let p values among the rejected SNPs for group k, the group-specific weight is,p values,After rejecting SNPs with p value approach27, and they have been shown to be a robust version of the SNP-specific 5. If the additional information is truly informative, p value approach. In that case, the weighted p value approach is more powerful than sFDR. On the other hand, if the information is just random noise, p value method still up- or down-weights the GWAS p values according to the SNP-specific The sFDR group-specific weights, 38 to estimate the SNP-heritability, which ranges from 0 to 48%.We obtained the UK Biobank GWAS round 2 summary statistics from Nealelab (Web Resources). Nealelab performed association studies for 4236 complex traits using regression model with additively coded genotype, as well as age, sex and the first 20 principal components as covariates. For each of these traits, Nealelab also applied the LD-score regression methodp value In addition to testing if the SNP-heritability is 0%, Nealelab also provided a confidence level  to the heritability inference for each trait. Thus, we restricted our analysis to the 1132 traits denoted with “medium” or “high” confidence labels, which were primarily based on the effective sample sizes 49. Lastly, we excluded SNPs with minor allele frequency (MAF) less than 1%, as joint analysis of multiple rare variants simultaneously50 is beyond the scope of our study.The UK Biobank GWAS results of Nealelab were derived from 51, and the Eigen meta-scores (v1.0), using the ANNOVAR tool52, for all the 7,895,174 common, bi-allelic autosomal SNPs.We obtained the CADD meta-scores (v1.6), using the CADD toolIn addition to the raw CADD meta-scores, the CADD tool also made available rank-based scores called phred scores,For consistency between CADD and Eigen, we similarly obtained phred-scaled Eigen scores. Figure Because Eigen scores were calculated using an unsupervised learning approach, in contrast to CADD scores inferred using labeled data, we also compared these two scores genome-wide Figure  and acroHere we used the real CADD and Eigen functional meta-scores, combined with simulated GWAS summary statistics, to evaluate type I error control of the data-integration methods examined.53. Independent of the observed genotype data, we simulated trait values, from N, for 1756 individuals from the 1000 Genomes Project who are unrelated to each other54. We examined 422,923 autosomal, bi-allelic and common  have CADD and Eigen meta-scores available, and (c) have the 75 annotations used by FINDOR.To simulate GWAS summary statistics that contain realistic LD patterns, we utilized the publicly available genotype data of the 1000 Genomes ProjectN distributed and We then obtained GWAS summary statistics for the 422,923 SNPs by regressing the trait values of the 1,756 individuals on their additively coded genotypes. Because the trait values were randomly generated, independent of the genotypes and populations, the resulting GWAS p value, and sFDR control as described above. Although Kichaev, G. et al.35 showed that FINDOR calibrates well when a GWAS consists of a mixture of null and associated SNPs, we also examined the performance of FINDOR in this setting when all GWAS SNPs are under the null hypothesis of no association. We applied the FINDOR tool using the same set of LDscores and the 75 annotations37 that were used by Kichaev, G et al.35 for their study; see Web Resources.Finally, we integrated the GWAS summary statistics with their corresponding CADD (or Eigen) meta-scores using the four methods, meta-analysis, Fisher’s method, weighted For each simulation replicate , we obtained the number of false positives using the conservative Bonferroni corrected significance level, permuted CADD (or Eigen) scores to evaluate robustness of a method to random annotation scores. Prior to the permutation, we examined the similarity of functional annotations between SNPs in linkage disequilibrium.Here we combined the observed UK Biobank GWAS summary statistics with Permutation does not preserve the potential correlation between functional scores of nearby SNPs. However, for the purpose of evaluating type I error control, it provides a valid set of annotation scores that are independent of the GWAS summary statistics. Nevertheless, we examined if SNPs in strong LD have similar annotation scores, as this has not been previously studied.i and j, respectively. We first defined a pair-wise similarity measure as Using CADD as an example, let p value, and sFDR control. We were not able to evaluate FINDOR here, because FINDOR implements the LD SCoring (LDSC) tool38 and the validity of using LDSC for permuted annotation is not clear.After we permuted the functional scores of the 7,895,174 common, bi-allelic autosomal SNPs, for each of the 1132 traits of the UK Biobank data, we integrated the GWAS summary statistics with the permuted annotation scores, using meta-analysis, Fisher’s method, weighted 55 to identify genome-wide significance findings, t, t. In addition to counting the number of significant SNPs per GWAS, we also counted the number of independent, significant loci. We first defined independent loci using the LDclumping algorithm of PLINK (v1.07)56, with a sliding window of 1 Mb and a LD Before data integration, we first used permuted functional scores for each trait t, we used the same t.After integrating the UK Biobank GWAS summary statistics with Recall is conceptually the same as Power, defined later for our simulation studies where the ground truth is known and before data-integration  for the remaining null SNPs. The top left plot in Figure Without loss of generality, we assumed the total number of SNPs N for the remaining SNPs. Importantly, the locations of the We then assumed Category I is completely informative (homogeneity): (1) Category II is partially informative: (2) Category III is  misleading: (5) Category IV is uninformative: (8) For each of the eight scenarios, we simulated 1000 data replicates, independently of each other. For each replicate, we applied the four data-integration methods that are suitable for this simulation study, namely meta-analysis, Fisher’s method, weighted p value, and sFDR control. Finally, we evaluated the methods using various performance measures, which we describe below.Using n Figure , which fp value We first used the Bonferroni corrected threshold to declare significance, k SNPs (e.g. As the Bonferroni approach can be conservative, we explored two alternative decision rules: fixed-region and fixed-FDR rejections. The fixed-region rule rejected the top Finally, we considered ranked-based relative efficiency as a performance measure. To this end, we first ranked all the truly associated p value and sFDR methods. We excluded meta-analysis and Fisher’s method from the analysis here, because severe robustness issues (to partially informative, uninformative, or misleading We studied all 1132 UK Biobank traits for which the confidence for their heritability inference was considered “medium” or “high” by Nealelab. For each trait, we analyzed the 7,895,174 autosomal SNPs that are bi-allelic and common (MAF Recall, the proportion of the initial GWAS findings that were retained after data-integration, as previously defined for the simulation studies. Finally, we used New Discoveries to represent the number of new genome-wide significant findings at the To summarize the application results, we first counted the numbers of independent, significant loci (at the Supplementary Tables.Supplementary Figures.