APOL1 associated with end-stage kidney disease discovered by admixture mapping in admixed African Americans. To address confounding due to admixture, we estimated local ancestry at each marker and global ancestry. We performed regression analysis stratified by local ancestry and combined the resulting regression estimates across ancestry strata using an inverse variance-weighted fixed effects model. We found that 11 of the 24 loci were significantly associated with eGFR in our sample. The effect size estimates were not significantly different between the subgroups of individuals with two copies of African ancestry vs. two copies of European ancestry for any of the 11 loci. In contrast, allele frequencies were significantly different at 10 of the 11 loci. Collectively, the 11 loci, including four secondary signals revealed by conditional analyses, explained 14.2% of the phenotypic variance in eGFR, in contrast to the 1.4% explained by the 24 loci in individuals of European ancestry. Our findings provide insight into the genetic basis of variation in renal function among admixed African Americans.The incidence of chronic kidney disease varies by ethnic group in the USA, with African Americans displaying a two-fold higher rate than European Americans. One of the two defining variables underlying staging of chronic kidney disease is the glomerular filtration rate. Meta-analysis in individuals of European ancestry has identified 23 genetic loci associated with the estimated glomerular filtration rate (eGFR). We conducted a follow-up study of these 23 genetic loci using a population-based sample of 1,018 unrelated admixed African Americans. We included in our follow-up study two variants in  Chronic kidney disease (CKD) is a common health condition that increases the risk of kidney failure and cardiovascular disease. According to two National Health and Nutrition Examination Surveys, the prevalence of CKD in the USA increased from 10.0% in 1988–1994 to 13.1% in 1999–2004 UMOD, SHROOM3, and GATM-SPATA5L1 were associated with eGFR APOL1 has been identified as a risk gene for non-diabetic end-stage renal disease in African Americans There is strong evidence for genetic loci influencing eGFR. In the Framingham Heart Study, the heritability estimate for eGFR was 0.46 APOL1 influences eGFR. We used stratified regression to account for confounding of association by ancestry at the level of the individual as well as the marker We performed a follow-up study of these 24 loci for association with eGFR in admixed African Americans. Our main objectives were to assess transferability of reported genetic associations originally detected in individuals of European ancestry to our sample of admixed African Americans and to test if We assessed the transferability of association with eGFR for 23 index single nucleotide polymorphisms (SNPs) from European ancestry to admixed African Americans. Our sample of 1,018 unrelated individuals  providedGiven that the 8.8% of the phenotypic variance explained in our sample was considerably larger than the 1.4% explained among individuals of European ancestry APOL1 previously associated with end-stage renal disease We also tested two markers in vs. 2 chromosomes of African ancestry. The allele frequencies were statistically different at 10 of the 11 loci . Furthermore, we fine-mapped the associations at the 10 loci by leveraging the generally weaker levels of linkage disequilibrium in individuals of African ancestry compared to individuals of European ancestry, improving resolution by over an order of magnitude on average. We also found association with eGFR for a deletion in APOL1 originally associated with end-stage renal disease.Association analysis can be confounded by variation in ancestry. Similar confounding can result from population structure among discrete populations, APOL1Allele frequencies were significantly differentiated between African and European ancestries for 10 of the 11 loci. Given the amount of differentiation between the CEU and YRI samples at the genome-wide level, 10 of 11 loci showing significant allelic differentiation is not excessive. We found no evidence supporting the action of recent positive natural selection at the 10 loci discovered in individuals of European ancestry, suggesting that differentiation at the 10 loci reflects divergence due to random genetic drift following the ancestral split between Africans and Europeans. In contrast, evidence for balancing selection exists at We found that stratifying genotypes by local ancestry resulted in an additional 3.0% of phenotypic variance explained over genotypes uncorrected for local ancestry, indicating that local ancestry masked genotypic effects. Thus, accounting for local ancestry can increase the phenotypic variance explained by two distinct mechanisms: the direct effect of local ancestry, which is the basis of admixture mapping, and the indirect effect of masking genotypic effects, which is revealed by removing confounding. Previously, associations at 12/23 loci were reported to transfer to African Americans, but those results did not account for local ancestry and therefore are potentially subject to confounding SLC22A2, PHTF2, WDR72, and BCAS3/TBX2) and genes that affect renal function  There are three main limitations of our study. One limitation is that the HUFS sample of 1,018 unrelated individuals has less than 80% power in a follow-up study to detect effects explaining vs. two chromosomes of European ancestry but that allele frequencies differed substantially. Our fine-mapping approach identified SNPs more strongly associated with eGFR than the index SNPs originally discovered in individuals of European ancestry. In addition, we demonstrated that local ancestry can mask genotypic effects. Consequently, our approach explained an increased proportion of phenotypic variance. Taken together, 11 loci explained 14.2% of the variance in eGFR. The approach implemented in this study can explain some of the missing heritability by simultaneously identifying more strongly associated SNPs, controlling for confounding due to ancestry, and identifying secondary associations, thereby enhancing disease and trait locus mapping in admixed as well as ancestrally homogenous populations.In summary, we identified 11 genetic loci influencing eGFR in a population-based sample of African Americans. We used stratified regression to test for association conditional on local ancestry, thereby controlling for confounding due to variation in ancestry at the individual level as well as at the marker level. We showed that the effect size estimates were population-consistent across the subgroups of individuals with two chromosomes of African ancestry Ethics approval for the Howard University Family Study (HUFS) was obtained from the Howard University Institutional Review Board and written informed consent was obtained from each participant. All clinical investigation was conducted according to the principles expressed in the Declaration of Helsinki.http://hapmap.ncbi.nlm.nih.gov/downloads/frequencies/2010-08_phaseIIIII/). Genome-wide, the average proportion of African ancestry was 0.799 . Second, we estimated the covariance matrix for this set of SNPs using our sample genotypes. Third, this covariance matrix was spectrally decomposed and the effective degrees of freedom, effN, was estimated using the relationship kth eigenvalue of the K×K covariance matrix for the K SNPs in the set Recognizing that the originally discovered index SNP might not be the most strongly associated SNP in follow-up samples, we followed a previously described fine-mapping strategy 2) = 186×(serum creatinine)−1.154×age−0.203  (×1.210 if black). Due to non-normality, the distribution of eGFR was transformed using a Box-Cox transformation , the fixed effects model is more appropriate. We performed conditional analysis for associated loci by following the same stratified regression approach, with the addition of an additive covariate for the genotype of the most strongly associated SNP within the locus. Regression analysis was performed using R Serum creatinine levels were estimated on fasting samples using the modified Jaffé method. eGFR was calculated using the simplified Modification of Diet in Renal Disease Study equation p-value by recording how many times out of 10,000 independent replicates ≥10/11 SNPs showed allelic differentiation.To test whether 10/11 SNPs showing significant allelic differentiation was excessive, we randomly sampled without replacement11 SNPs from the 797,831 SNPs included in our study. For each SNP, we performed a test of proportions using the HapMap CEU and YRI allele counts. We estimated a Principal components analysis of the genome-wide data was performed to estimate how much genetic variance was explained by admixture De novo genotyping for rs73885319 and rs71785313 was performed using the iPLEX Gold assay on the MassArray platform . PCR and extension primers were designed using MassArray designer software and publicly available sequence data. Genotyping success rates were 98.1% and 97.6%, respectively. Quality control was assessed by testing for Hardy-Weinberg equilibrium.Figure S1Local genetic architectures for the 23 loci. For each locus, the set of SNPs was bounded by the two SNPs farthest from the query SNP for which P-values are shown based on physical position (NCBI build 36). The light blue curve depicts the recombination rate from the combined HapMap Phase II data. Linkage disequilibrium based on the HUFS sample is color-coded red for r2 to the top SNP between 0.8 and 1.0, orange for r2 between 0.5 and 0.8, blue for r2 between 0.2 and 0.5, and gray for r2 between 0 and 0.2. Green arrows indicate the direction of transcription.(PDF)Click here for additional data file.Figure S2Principal components analysis. Red represents CEU, blue represents YRI, and black represents the HUFS sample. Only the first principal component explained a significant amount of genetic variance.(PNG)Click here for additional data file.Figure S3Genome-wide Manhattan plots. (A) Unstratified by ancestry. (B) Stratified by ancestry.(PNG)Click here for additional data file.Figure S4Genome-wide distribution of admixture proportion.(PNG)Click here for additional data file.Figure S5Density plots. The phenotypic distribution of eGFR was Box-Cox transformed to reduce skew using the transformation 2.(PDF)Click here for additional data file.Table S1Percent variance explained among associated loci.(DOC)Click here for additional data file.Table S2Ancestry effects among the associated loci.(DOC)Click here for additional data file.Table S3Significant secondary associations.(DOC)Click here for additional data file.


Identifying recombination events and the chromosomal segments that constitute a gamete is useful for a number of applications in genomic analyses. In livestock, genotypic data are commonly available for half-sib families. We propose a straightforward but computationally efficient method to use single nucleotide polymorphism marker genotypes on half-sibs to reconstruct the recombination and segregation events that occurred during meiosis in a sire to form the haplotypes observed in its offspring. These meiosis events determine a block structure in paternal haplotypes of the progeny and this can be used to phase the genotypes of individuals in single half-sib families, to impute haplotypes of the sire if they are not genotyped or to impute the paternal strand of the offspring’s sequence based on sequence data of the sire.2) and performance of this approach were evaluated by using simulated and real datasets. Phasing results for the half-sibs were benchmarked to other commonly used phasing programs – AlphaPhase, BEAGLE and PedPhase 3.The hsphase algorithm exploits information from opposing homozygotes among half-sibs to identify recombination events, and the chromosomal regions from the paternal and maternal strands of the sire (blocks) that were inherited by its progeny. This information is then used to impute the sire’s genotype, which, in turn, is used to phase the half-sib family. Accuracy . Single nucleotide polymorphisms (SNPs) are the most common form of genetic variation. With the advent of new molecular technologies and the sequencing of many important species, a considerable amount of these markers can now be genotyped cheaply and precisely on a routine basis, not only for humans but also for livestock. In animal breeding, these markers are now used to estimate breeding values for commercially important traits.blocks) have been identified, they can be used to determine which progeny carry segments that are identical by descent (IBD), to phase the genotypes of the progeny or to impute sire or progeny genotypes, depending on whether the parent or the progeny has sparser marker data.Human genotypic data is usually sampled from a population of unrelated individuals or from trios, since the number of individuals in each family is small. However, in livestock populations, genotypes are often available from half-sib families. This data structure lends itself well to study the combinatorics that occurred during meiosis and allows identification of the recombination and segregation events that gave rise to the paternal haplotypes that are observed in the half-sib progeny. Once chromosomal segments  that implements the method is freely available as an R package. The following sections describe the method, results with simulated and real datasets and compare its phasing accuracy to several other methods that are frequently used for phasing.The aim of this study was to propose and evaluate a fast algorithm designed to identify recombination events in the sire of a half-sib family using SNP marker genotypes. This information can be used to identify recombination events. Here, we assume that genotypes are available on a group of paternal half-sibs, and the genotype of the sire is not required. The algorithm identifies which chromosomal segments each half-sib inherited from the paternal and maternal strands of the sire. This information is then used to impute the sire’s genotype, which can be useful in case the sire is not genotyped or if it is genotyped at a lower marker density, and to phase the genotypes of the half-sib progeny. Alternatively, if haplotyped sequence data is available for the sire, this method can be used to impute the paternal sequence in the haplotype that each offspring inherited, provided that the offspring is genotyped. Although restricted to half-sib data structures, this approach allows phasing of very small datasets  and can also be used to identify the location of recombination events or as a diagnostic tool to evaluate the accuracy of other haplotyping methods. A program . First, all markers that have opposing homozygotes within a half-sib family are identified. At these markers, the paternal alleles are unambiguously identified and used to sort individuals into groups according to the paternal allele they received. The grouping of offspring at consecutive markers provides information about the most likely phase in the sire. We can then identify blocks of consecutive markers that were inherited together from the sire. This allows detection of likely recombination points, which can be visualized as a seed groups based on the strand they inherited from the sire to provide an anchor from which to extend the blocks. For this purpose, we arbitrarily assign a “P” to progeny receiving the 0 allele and individuals that received the 1 allele are coded “M”. This loosely refers to paternal and maternal strands but note that the assignment is entirely arbitrary and P/M are simply used to distinguish between the two paternal strands; i.e. the strands of grand-parental origin inherited from the sire. Half-sib progeny that are heterozygous for this locus are recoded to unknown by entering the dash symbol (-).The following algorithm was used to partition the genome of each half-sib progeny into blocks according to the haplotype it inherited from the sire. First, the markers for which the sire can be determined as heterozygous based on the offspring genotypes are identified Figure A. SecondP/M) for this locus . These vectors represent the two possible configurations of the grand-parental origin of the paternal allele. These vectors are compared to the FMV and the number of switches (recombinations) between each vector and the FMV is computed. The vector that needs fewer recombination events to explain the observed data is kept for the next step  and replaces the relevant values in the FMV, while the other genotypes (heterozygous sites) carry over as they were previously in the FMV. The values in the main matrix for the last locus are then updated accordingly  is then created with the same number of rows as the number of half-sibs to temporarily store the grandparental origin codes  that are created from the next opposing homozygous locus is greater than zero. However, switches can also result from genotyping errors, which occur at a frequency of around 1% [Recombination occurs when the minimum number of switches between FMV and the vectors  from the sire. These averages are recoded as s Figure .P and M) is then replaced by the paternal allele codes (0 or 1) pertaining to these origin codes. If the paternal origin code was uncertain, the origin was determined from the adjacent loci. The maternal haplotypes of the half-sibs are then obtained by simply subtracting the haplotype of a half-sib progeny from the sire from the individual’s genotype .Three simulated datasets  were generated to evaluate, benchmark and compare the algorithm with other commonly used phasing methods. Accuracy of phasing was evaluated as the RAn R script was used to generate phased genotypes on a single chromosome for 500 000 SNP markers for a single sire and 400 half-sib offspring in order to evaluate runtimes of the algorithm on genotypes from high-density arrays. There were no genotyping errors. Allele frequencies were sampled from a uniform distribution U, and recombination rates were distributed as U.true haplotypes for sires and offspring. To evaluate the robustness of the algorithms to genotyping errors, the 1% of the genotypes from these datasets was randomly selected using the sample function of R and randomly changed.This dataset was generated with the software QMsim that simulates data based on the population structure of commercial livestock animals . We simuTo compare the phasing component of our algorithm with other methods, QMsim was used to generate one population with the following structure: 10 generations, 1 chromosome of 500 cM and 10 000 markers, and 10 males and 200 females per generation. Only the genotypes from the last two generations were used and the genotypes of the sires from generation 8 were used to estimate the accuracy of imputation of the sires’ genotypes.Data generated by the SheepGenomics and the CRC for Sheep Industry Innovation on 4884 sheep genotyped with the 50K Illumina Ovine SNP chip and distributed across 110 half-sib groups were used. For expediency, after standard quality control filters, only data from chromosome 1 were used since it is the longest and has the largest number of markers (~5500). Data were from multiple breeds, the main breeds being Merino, White Suffolk, Border Leicester and Poll Dorset. Samples for genotyping were collected under approval number AEC12-049 of the University of New England Animal Ethics Committee.BEAGLE 3.3.2  and Alph2 between the phased and true haplotypes in the offspring for dataset C. We match both of the arbitrarily assigned paternal/maternal haplotypes with the correct simulated haplotypes, and selected the ones that gave the highest R2 per chromosome. Then, for all predicted haplotypes, the squared product moment correlation between them and the true haplotypes was calculated. Marker loci that could not be phased by any of the programs were omitted before calculating the R2 values.To compare phasing accuracies between programs, the R programming language was used to calculate the RAccuracy of phasing was also evaluated by calculating switch error rates (SWR). This was a function of the number of times an incorrect change of phase occurred in the inferred haplotype, divided by all possible switches. The mean of this number for each population was recorded and was calculated as:http://www-personal.une.edu.au/~cgondro2/hsphase.htm. R is the de facto standard language for statistical programming and is widely used in genetic analyses. To achieve high performance, the algorithm was written in C++. The R package includes several functions to run the analyses and to visualise and evaluate results.For ease of use an R package was created which is freely available from the Comprehensive R Archive Network (CRAN) or from We initially tested our algorithm for speed using dataset A that consisted of a half-sib family with 500 000 markers and 400 individuals. For this example, the time needed for strand identification and phasing was ∼126 and ∼249 seconds respectively . Runtimes scaled nearly linearly in the number of animals and the number of markers. The algorithm is very fast and simple to parallelize which makes it suitable for analyses of very dense marker panels and even for sequence data. Using dataset C , we compared hsphase with other software programs. Population-based phasing took 42 minutes for AlphaPhase with pedigree, 157 minutes without pedigree and 46 minutes for BEAGLE. PedPhase 3 was used to phase half-sib groups one at a time with 20 half-sibs per family , which required ~0.5 seconds per family (~30 seconds for the entire dataset). The program hsphase had a similar speed and took 19.5 seconds for the entire dataset. Based on these results, hsphase was orders of magnitude faster than AlphaPhase or BEAGLE and slightly faster than PedPhase 3. It should be noted that this comparison excludes the time needed for reading the genotypes into R, which adds an additional 3.2 seconds to hsphase, but this can vary significantly depending on the original format of the data.Figure 2 between true and detected strands was calculated to evaluate the accuracy of paternal strand detection. The value of R2 was very sensitive to errors related to phasing and identification of recombination events, but high values were achieved for most half-sib groups which indicate that the error rate was very low. Genotype errors, low-density markers and small half-sib groups had an adverse effect on the algorithm’s ability to correctly allocate grand-parental origin to the paternal chromosomal segments, and larger half-sib groups were required to give acceptable accuracy (R2 > 0.90) and get a clear blocking structure, i.e. a structure with a realistic number of recombinations and few segments where the correct paternal segments could not be identified. As expected, R2 increased and its standard deviation decreased as the number of half-sibs increased  per family. Since sire genotype imputation made use of information from multiple half-sib blocks, the accuracy was higher than the accuracy of strand allocation but was still directly related to correct block detection. As shown in Table With genotyping errors of 1%, changes to accuracies and percentage of markers imputed were negligible  was more sensitive to the marker density. In the worst scenario , 92% of heterozygous sites were correctly phased with an SWR of 7.5%. With high-density markers , the SWR was 3.5% and with a family size of 40 it was 1.7% but the RDataset C was used to compare the hsphase algorithm with other methods in terms of phasing accuracy. The hsphase approach used information from only one half-sib family at a time, whereas AlphaPhase and BEAGLE used the information of all 1200 individuals across families because these methods rely on population parameters and therefore require larger datasets for satisfactory performance. PedPhase also used data from one family at a time but the program will not allow families with more than 23 individuals and also requires genotypes of the sire. Figure 2 obtained by randomly phasing dataset C was ~0.28 (based on the mean of 10 000 repeats), which sets the baseline for comparison of the different methods. The R2 of AlphaPhase with use of pedigree and hsphase were nearly the same. The R2 of AlphaPhase without use of pedigree was less than 0.5  in the middle of a strand can affect the phasing of the rest of the strand. The same effect was observed with BEAGLE  was low for all methods, ranging from 0.01 to 0.05%, except for PedPhase, which had an SWR of ~0.5%. This suggests that these population-based methods as well as hsphase are all good at phasing over smaller chromosome segments and this can be useful for the purpose of QTL (Quantitative Trait Loci) mapping or in case–control studies.As mentioned above, it is also possible to use the phased half-sib data to create a block structure, which is useful to evaluate the algorithms based on their power to infer these blocks, both visually and by counting the number and distance between recombination events in each individual. Based on length of the chromosome, a certain number of recombination events are expected. An unrealistic number of recombinations in the blocking structure provide evidence of either a pedigree error or algorithmic problems. Overall, we observed an improvement in accuracy with hsphase compared to other methods, particularly with 1% genotyping errors Figure B. With tFigure 2 between observed and imputed sire genotypes had a mean of 0.95 and a median of 0.98 (Figure The accuracy of imputation of sire genotypes with hsphase was evaluated using all 110 half-sib families and compared to the true genotypes of the sire. The Rblocking structure can be used for phasing and imputation of sire genotypes. An R package hsphase that implements the method has been made available. The computational speed of the algorithm allows it to be used on large datasets. The accuracy of blocking and sire imputation of the algorithm was high when eight or more half-sibs were available. Imputation of sire genotypes was accurate and might eliminate the need to genotype the sire. For phasing, even a single family of four individuals had an R2 above 0.95 but the percentage of markers phased was ~70%. In addition, it was shown that the blocking structure derived from the paternal strand of origin is a valuable diagnostic tool to quantify and detect phasing and pedigree errors irrespective of the phasing method employed. Lastly, we suggest that if sequence or high-density marker data is available for the sire, the blocking structures lend themselves to imputation of the paternal strand in half-sib family groups.In this work, we proposed a simple method that relies on linkage disequilibrium within families and uses loci with opposing homozygotes within a half-sib family to identify paternal chromosomal segments and recombination events. The resulting paternal The authors declare that they have no competing interests.MF and CG designed the algorithm and experiments to test it. JHJW and BPK advised on the design of the experiments to test the algorithm. All authors read and approved the final manuscript.


Critically endangered breeds and populations are often crossed with more common breeds or subspecies. This results in genetic admixture that can be undesirable when it challenges the genetic integrity of wild and domestic populations, causing a loss in special characteristics or unique genetic material and ultimately extinction. Here, we present two genomic selection strategies, using genome-wide DNA markers, to recover the genomic content of the original endangered population from admixtures. Each strategy relies on the estimation of the proportion of nonintrogressed genome in individuals based on a different method: either genomic prediction or identification of breed-specific haplotypes. Then, breeding programs that remove introgressed genomic information can be designed. To test these strategies, we used empirical 50K SNP array data from two pure sheep breeds, Merino (used as target breed), Poll Dorset and an existing admixed population of both breeds. Sheep populations with varying degrees of introgression and admixture were simulated starting from these real genotypes. Both strategies were capable of identifying segment origin, and both removed up to the 100% of the Poll Dorset segments. While the selection process led to substantial inbreeding, we controlled it by imposing a minimum number of individuals contributing to the next generation. Cross-breeding is a strategy commonly used in livestock and occurs naturally in many wild populations. The increase in fitness that a new genetic input can infuse has been widely studied, and mixing breeds have been used in livestock to increase genetic variability and the performance for productive traits . However, the data set is useful for evaluating the performance of our strategies.The data used was obtained from the Australian Cooperative Research Centre for Sheep Industry Innovation (Sheep CRC) Rowe . IndividP-value cut-off of 10–15), had no genome location or their LD with another SNP on the chip were greater than 0.99. After the quality control, 48 599 SNP were used. Data for genotyped animals were removed if their genotype call rate was <0.9 or their mean heterozygosity was greater than 0.5, which would indicate sample contamination. Sporadic-missing SNP were imputed using Beagle  included in the OvineSNP50 BeadChip . The quality control measures applied were the following: SNP were removed if they had a call rate of less than 95%, a minor allele frequency of less than 0.01, a GenCall score of less than 0.6. The SNP were also removed if they were out of Hardy–Weinberg equilibrium (a Two methods were implemented to predict breed proportion of Merino and Poll Dorset.i being of Merino origin (bMi) for each of the up to 210 possible haplotypes for a specific segment as:This method, described by Bolormaa et al. , relies pMi is the frequency of the ith haplotype in the pure Merino animals and pPDi is the frequency of the ith haplotype in the pure Poll Dorset animals. All haplotypes were classified as either Merino or Poll Dorset in origin based on their b values. Haplotypes with a b value lower than 0.4 were classified as Poll Dorset and those with a b value higher than 0.6 were classified as Merino. The remaining haplotypes were left unassigned because their breed origin was ambiguous. The overall proportion of an animal's genome that is of Merino origin was calculated as the number of Merino assigned haplotypes divided by the total number of haplotypes.where Merino proportion of the admixed individuals. In other words, the phenotype was the Merino proportion of each animal, as determined by pedigree records. The pure Merino and pure Poll Dorset animals were used as the reference population with phenotypes coded 1 and 0, respectively. Then, the Merino proportion was predicted in individuals with only genotypes of the three populations . The GBLUP approach was adapted from VanRaden et al. , μ is the intercept, 1 is a vector of ones, Z is a incidence matrix relating additive genetic effects to phenotypes, g is a vector of additive genetic effects, and e is the vector of residuals. The following distributions were assumed: g ~ N  and e ~ N . G was a genomic relationship matrix, calculated as done in Yang et al.  were used to simulate several introgression scenarios from which the Merino genetic background was intended to be recovered . A populm, and to create gametes, a Poisson distributed (λ = 1) number of crossingovers (one crossover is expected on average per Morgan) with no interference were generated in random positions over the chromosome.The sheep genome is made up of 26 autosomes. Each chromosome was considered to be 1Sex was randomly assigned to the genotypes used to create the individuals . The mixed population mated randomly during one, three or five generations to produce different levels of admixture of the Poll Dorset genetic information into the Merino background. Five generations of management were then simulated using two different approaches to remove the Poll Dorset genetics. The real origin of the alleles was known in all generations and was used to evaluate the efficiency of recovery. The pedigree was also known and used for calculating coancestries and inbreeding. Twenty replicates per scenario were simulated.Once the mixed populations comprising 100 individuals were created, we selected the purest Merino individuals in order to recover the largest number of Merino alleles over several generations. For that purpose, a group of pure individuals from the original Merino and Poll Dorset populations was used as reference for the following approaches:b values were computed for all available individuals using eqn (1), and a mean b value per individual was calculated. Those individuals with largest mean b values were assumed to be the purest Merinos.A random sample of 188 pure Merinos and all 188 pure Poll Dorset genotypes were used for training the haplotype approach at the beginning of each replicate. In the following generations, haplotype A random sample of 188 pure Merinos (the same subset as the haplotype approach each replicate) and the 188 pure Poll Dorset genotypes were included with known breed (i.e. phenotypes), together with the genotypes for the selection of candidates in each generation. Breed proportions were then predicted using model (2). The predictions were used to identify the purest Merino animals in each generation of management.ΔF) of 0.0125 (assuming random mating).Exogenous information was eliminated in each generation of management by choosing the 10 purest Merino animals per sex  to equally contribute to the next generation (10 offspring each). Individuals were mated randomly. The above procedure implies a theoretical rate of inbreeding per generation (Merino proportion)  and (ii) inbreeding coefficient (F). The F values were calculated considering the real coancestries between the original individuals  and the genealogy of the admixture and management periods. From these, values of ΔF were calculated as:In every generation, two variables were calculated to evaluate the efficiency of the strategies: (i) percentage of Merino (t is the number of the current generation (one to five) . The number of individuals actually contributing was increased to 40  in scenarios with five and 20 generations of admixture, to assess the rate of removal of Poll Dorset genetic material that was accomplished.The previous scenarios constitute the upper bound of efficiency as de-introgression is tested in the same loci used for the management. We also investigated the recovery of ungenotyped loci by only using half of the markers for de-introgression and evaluated the efficiency using the other half in the scenario with 20 generations of admixture . The number of markers in a haplotype was 10, as in the other scenarios, and alternate SNP were masked.The distribution of the haplotypes in chromosome 1 of 25 randomly sampled pure Merinos, 25 randomly sampled pure Poll Dorset and 25 randomly sampled crossed individuals is shown in b value >0.6) and most of the segments in the Poll Dorset group are recognized as Poll Dorset . The results in the crossed animals showed a mixed pattern with 58% of the segments considered Poll Dorset and 37% of the segments considered Merino. The higher number of Poll Dorset segments in the crosses could suggest that the Poll Dorset individuals are not as pure as expected. Thus, some Merino segments, present in Poll Dorset individuals are recognized as Poll Dorset. The distribution of the b values of the 10 SNP segments in the three groups of individuals (across the entire genome) is shown in Fig. S2.As stated before, most of the segments in the Merino group were recognized as Merino .The classification of individuals from the GBLUP genomic prediction of Results for the percentage of Merino recovered for the haplotype approach and GBLUP approach were very similar in all scenarios; consequently, only the results for the haplotype approach are presented.Merino proportion obtained after one or five generations of management in the different introgression scenarios are shown in The values of ΔF obtained were close to the expectation (ΔF1 = 0.01) in the first generation of management, but they became higher than the expectations in the subsequent generations . This is because ΔF was calculated assuming random selection and mating in the parents. Selecting the purest individuals resulted in individuals that were more related than if they were selected at random after the second generation of management.The results of inbreeding reached after managing one or five generations with the haplotype approach are shown in ΔF after five generations of management is lower when using GBLUP . The differences in ΔF appeared in the final generations, once the maximum Merino proportion was achieved, but the de-introgression method was still being applied. If estimated proportions are similar for all available individuals, the selected breeding animals are chosen at random not involving a higher level of relationship between them, and thus, ΔF is closer to expectations. In contrast, the haplotype-based method still detected differences between candidates related to common origin leading to higher ΔF.The results of inbreeding were slightly different when using the GBLUP approach . The accumulated Results obtained when doubling the number of contributing individuals to 40 (haplotype approach) for five generations of admixture are shown in ΔF in the first generation of breeding is close to the expectation, but it is higher in the following generations of breeding.A more extreme situation was tested in which exogenous material was admixed for a longer period of 20 generations. In this scenario, the number of breeding individuals during de−introgression was also 40. The results , right dThe results obtained when using different SNP for de-introgression and evaluation are shown in Many populations are close to extinction due to genetic introgression. Our results demonstrate that some of this introgression could be reversed by detecting and breeding those individuals containing chromosome segments of the original population.b values (from the haplotype method) was 0.99 in the whole population, but just 0.54 when calculated for the crossed individuals. Despite this medium correlation, there was a clear tendency of higher b values implying higher GBLUP solutions . This was confirmed when evaluating their performance in the de-introgression process. The degree of Merino recovered was the same for both methods, suggesting that they identify almost the same individuals as the purest Merinos.In the present study, we used a real sheep data set to demonstrate the ability of two methods to find out the origin of genetic information in an admixed population from two different breeds, even after several generations of introgression. Results showed that both methods were able to detect the proportion of Merino and Poll Dorset with high accuracy. The correlation between the prediction of the Merino content using GBLUP and With respect of the number of generations effectively removing the Poll Dorset haplotypes, the performance was very similar to what was observed in previous studies . We tested the performance of Merino prediction through GBLUP using 188 pure Poll Dorset and 20 crossed individuals from the original data set as the reference population. The efficiency of the method did not decrease, obtaining similar results as in the whole reference data set (Table S1).The current methods heavily rely on a group of genotyped pure individuals to train Merino proportion of individuals and mate the purest for de-introgression. We obtained very similar results when using Structure (Table S2), but the software took much longer to evaluate the Merino proportion in the individuals .We also compared the results with those obtained in equivalent scenarios using the program Structure . In that case, molecular markers could help identify those traits and focus the restoration effort in keep them and maintain the rest of the genome. Also, phenotypes can be used directly for this purpose as in the study by Fernández et al. , to achiThe time elapsed between the admixture events and the start of breeding for recovery is also an important factor to take into account for the possibilities of recovery. The degree of Merino recovered after a longer period of admixture was noticeably smaller as shown in When the admixture is not recent, more haplotypes will remain unassigned when using the same number of SNP and haplotype length, because the length of the introgressed haplotypes will decrease due to recombination in each generation. This will lead to individuals that cannot be identified as Merino or Poll Dorset for both strategies, and successful de-introgression will require a denser marker map. This highlights the importance of acting quickly to control introgression events. We observed that after 20 generations of admixture, some recovery can be achieved, but if the unmanaged period is too long, this recovery will be less effective.The methods here described are designed for populations on which a SNP chip has been developed. The availability of SNP chip data in domestic species is increasing, especially due to genomic selection studies  and are developed using only a subset of the total diversity of different breeds. This bias could affect the results of a de-introgression process, especially if one of the breeds was not involved in the development of the SNP array, because markers will be more informative for one breed than for the other. It could also affect de-introgression efficiency of ungenotyped low-frequency alleles, because their LD with the higher frequency SNP on the array would be limited. In our case, the purest Merino individuals were still recognized despite potential SNP chip biases, evidenced by the efficient de-introgression. However, it is important to consider how the choice of markers may affect the estimation of breed proportion.ΔF and still allows for the removing of exogenous information. Increasing the number of individuals selected to contribute, or setting an explicit restriction on ΔF could lead to an acceptable recovery without losing too much genetic diversity, but it has to be assessed in each particular situation and decide if this increase in inbreeding is acceptable to obtain a certain recovery of the native genetic alleles.The increase in inbreeding every generation of management is a side effect of the methods due to the reduction in the number of individuals contributing to the next generation. Both GBLUP and the haplotypes approach implied a similar increase in inbreeding due to the de-introgression process. It cannot be avoided, but it can be controlled. As shown, increasing the number of individuals contributing decreases We have demonstrated that de-introgression of exogenous genome segments is feasible. The parameters simulated cover a wide range of situations and altering parameters will influence outcomes. For example, selecting 10 contributing individuals may not be feasible in a very small population. The expected effect on inbreeding levels must be evaluated with regard to speed (i.e. number of generations) and numbers of contributors to decide whether it is desirable to de-introgress.


In the studies of mental and behavioral disorders, comorbidity is an important issue since multiple correlated disorders are usually recorded to understand the etiology of substance dependence, which is imperative to the development of effective treatment and prevention strategies. Many studies have been reported the comorbidity between substance abuse disorders and psychiatric disorders such as anxiety and major depression. In order to investigate the association between the comorbidity of complex diseases and genetic locus, it is critical to develop a computationally efficient and powerful multiple traits association test. Recently, taking the advantage of high throughput genomic data, lots of genetic variants have been identified for individual drug addiction based on genome-wide association studies (GWAS). Despite many successes, the current GWAS may be insufficient to detect genetic variants with moderate-to-small effect since a stringent significance threshold is used to control the false discovery rate, which is a key factor to the missing heritability problem.To detect novel genetic variants, joint analyzing correlated traits are promising solutions. First, joint analyzing correlated traits may increase the power in detecting genetic variants with moderate effects across multiple traits by exploiting the correlation between traits. Second, joint analysis can alleviate multiple comparison problems which incurred in analyzing individual trait separately. Comprehensive studies have been used to demonstrate that jointly testing correlated traits is more powerful than testing a single trait at a time. Therefore, it is important to consider the comorbidity of correlated traits in order to detect novel genetic loci in GWAS. We introduce a multiple traits association test based on least square. The proposed method only needs to specify the marginal distribution of multiple traits. We systematically investigate the strengths and weaknesses of the multiple traits association test through simulation and comprehensive real data analysis. We demonstrated the advantage of multiple traits association test when multiple traits share common genetic variation. However, when multiple traits share no or weak common genetic variation, the multiple traits association test has no advantage.


The goals of our analysis were to map functional loci, which contribute to the case-control status of a trait of interest, using large pedigrees. We used logistic regression fitted with the generalized estimation equation to test associations between a dichotomous phenotype and all genotyped common and rare single-nucleotide polymorphisms. In addition to the association study, we also developed and applied a simple and fast identical-by-descent-based test to identify loci that were shared among affected individuals more often than expected by chance. Among the top significant loci, we assessed the statistical power and the false discovery rate of both methods. We also demonstrated that family-based studies, compared with the standard population-based association studies, have great values and advantages for the discovery of multiple rare causal variants. Population-based genome-wide association studies (GWAS) using unrelated individuals are becoming increasingly popular in genetic research. Recent large GWAS have shown that common genetic variants are involved in common diseases, but most of the variants found in this way account for only a small portion of the trait variance. On the other hand, accumulating evidence from candidate-gene-based resequencing suggests that many rare genetic variants contribute to the trait variance of common diseases. Pedigree resources are conventionally believed to be powerful for identifying rare variants and are considered appropriate for the application of linkage strategies. However, linkage analysis often requires nuclear families characterized by multiple informative offspring and is more applicable for quantitative traits ,2. OtherThe family data from Genetic Analysis Workshop 17 (GAW17) provide us with a great opportunity to investigate appropriate approaches for the family-based association tests. The approaches we consider in this work include fitting a logistic regression model with adjustments of covariates and a novel approach using identical-by-descent (IBD) measures.We used the family data sets provided by GAW17. This data set had 697 subjects  from 8 extended families and fully informative markers for 3,205 genes. Assuming that recombination was not allowed within genes, IBD scores were also provided at each gene location  ,5 with fSingle-nucleotide polymorphisms (SNPs) with minor allele frequency (MAF) less than 1% were considered rare in our work. In the first stage, we excluded rare SNPs before the association analysis and considered only common causal variants. A rare variant, as part of a group of rare variants in the same gene, is also more likely to contribute to the susceptibility of a disease. However, if we apply logistic regressions directly on the rare variants, the GEE will fail because of the singularity in the correlation matrix. The association methods developed for common variants will have limited efficiency for mapping rare variants unless enormous sample sizes exist. Grouping and collapsing rare variants into meaningful groups  has been shown to be a feasible option to improve efficiency in studying rare variants . TherefoAfter assigning a collapsed genotype to grouped rare variants, we evaluate the association between collapsed genotypes and disease outcomes using the logistic model specified in Eq. (1).Phenotypes of relatives are similar because relatives share similar environment and similar genetic variants (genotypes or haplotypes). Genotypes are similar because these relatives share genes that are identical by descent. Intuitively, the disease-associated loci are more likely to be similar in case samples than in control samples. Comparing the distributions of IBD scores between arbitrary pairs of case subjects and pairs of control subjects appears to be a promising approach to identify loci associated with a trait. Based on this general idea, we formulated a new test using a 2 × 3 contingency table that can identify loci shared among affected individuals more often than expected by chance. Our algorithm considers all relationships simultaneously and can be used to test association in pedigrees of arbitrary size.K extended families with multiple affected offspring are randomly collected from a natural human population. Consider a SNP marker with two alleles, A and B, that is genotyped for all individuals in these K extended families. For an arbitrary pair of samples i and j within a family k, the IBD score between them at a SNP marker is defined as 0, 0.5, or 1 if 0, 1, or 2 of their shared alleles, respectively, arose from the same allele in an earlier generation. Between any two individuals, there are 14 combinations of their IBD scores and genotypes. We list all 14 states in Table S1, S2, …, S14. Assuming that allele B is the disease allele, a pair of individuals shares exactly two copies of inherited B alleles only in S1, exactly one copy in S2, S4, and S7, and one copy with probability 0.5 in S8.Suppose that B alleles IBD. On the other hand, under the alternative hypothesis of association, we expect to observe that pairs of affected individuals share at least one copy of the B allele with greater chance. This also means, under the alternative hypothesis, that we expect that affected individuals involved in forming pairs will share at least one copy of the inherited B allele with a greater chance than unaffected individuals.Under the null hypothesis of no association, the frequencies of the 14 states are the same in affected and unaffected samples. Consequently, the pairs of affected and pairs of unaffected individuals have equal frequencies of sharing zero, one, or two copies of Based on this general idea, we tabulate affected individuals and unaffected individuals by a 2 × 3 contingency table in the following way. The affected individuals can be separated into three groups: Group 1 contains those individuals who form pairs IBD at both alleles; group 2 contains individuals who form pairs IBD at exact one allele and who are not in group 1; and group 3 contains the rest of the individuals. Similarly, unaffected individuals can be assigned to the three groups in the same manner. The cells of Table nBB1 of cell  is 2. Individuals who form pairs IBD at exact one allele include individuals 1, 6, 7, and 12. Because individuals 6 and 7 have already been assigned to group 1, only individuals 1 and 12 are assigned to group 2. Note that, individuals 10 and 13 form a pair  at S8  is 2 + 0.5(2) = 3, and the cell count n0 of cell  is 0.5(2) = 1. Similarly, among the unaffected individuals, none of them form pairs with two IBD alleles; individuals 2 and 8 form a pair , which has one IBD allele; and the rest of the unaffected individuals, individuals 3, 4, 5, 9 and 11, form pairs with zero IBD alleles. Hence the cell counts nBB0, nB0, and n0 of cell , cell , and cell  are 0, 2, and 5, respectively.Next, we demonstrate this tabulating procedure using a toy. In our example, 13 individuals form two three-generation pedigrees  is small, we may observe extremely low cell counts for nBB1 and nBB0. Under such circumstances, p-values by shuffling the affected statuses of samples within each family. And as a by-product, possible biases caused by different family sizes or family structures will also be corrected. In our toy example, the chi-square test p-value  in terms of detection power and false discovery rate using the 200 simulated extended family data sets in GAW17. We then carried out standard stratified association analyses with the population-based data sets so that we could further investigate the application and the value of using family-based approaches. In particular, we were keen to find out whether family-based approaches have certain advantages in discovering rare causal variants.p-value to present the gene-level p-values. In this way, we were able to make fair comparisons across genes with different sizes. We calculated the correlations of these FDR-corrected [p-values for all possible pairs out of 200 rounds of simulations, and the average correlation of these across all 200 rounds of simulations was 0.965, which suggested that the results given by the association analyses were fairly stable. We noticed that the association tests were still inflated with some false positives, as shown in the Q-Q plots  and combining rare SNPs. Within each gene, we first made corrections for the false discovery rate (FDR) ; then weorrected  gene-levs Figure . The estp-values with an arbitrary cutoff value α. Genes with p-values less than 0.05 were considered detected in each simulation. Averaging over 200 replicates, the chance of wrongly declaring noncausal genes  was 0.096 and 0.033 at an α level of 0.05 and 0.01, respectively.We also evaluated false-positive rates. We declared the significance of the gene-level α level of 0.05 and 0.01, respectively. Among all 3,205 genes, the family-based association study successfully identified gene VEGFA as the most significant gene with a power as high as 81% at α = 0.05. Four other causal genes with the highest discovery rates were LPL, VNN1, SHC1, and SIRT1. Compared to the other 31 causal genes, these 5 genes have both strong effects and relatively high frequencies of carrying risk variants.We further evaluated the power of detecting true functional genes at an p-values of all SNPs were the empirical p-values based on 10,000 permutations. Within each gene, the FDR-corrected minimum p-values were used to present the gene-level significance. As shown in Figure p-values across all 200 rounds of simulations was 0.461. As shown in the Q-Q plot in Figure α = 0.05 and α = 0.01 were 0.112 and 0.039, respectively. The five causal genes with the highest discovery rates were VEGFC, SHC1, VEGFA, HIF3A, and SIRT1. At a significance level of 0.05, our IBD test successfully picked up genes VEGFC and SHC1 with a power of 82% and 67%, respectively, which ranked them first and fifteenth out of all 3,205 genotyped genes.The proposed IBD test was performed on all common and rare SNPs. Raw FLT1, which has three common variants and large genetic effects, is the only gene with a detection power greater than 50%. For most other causal genes with rare variants, family-based studies had better power of detection than population-based studies. The Q-Q plot in Figure α = 0.05 and α = 0.01 were 0.089 and 0.029, respectively. Although all three types of analyses have comparable false-positive rates, the receiver operating characteristic (ROC) curves (Figure As a comparison to the family-based analyses, we also performed a standard stratified analysis on the 200 simulated population case-control data sets. We assessed the power of population-based studies for all causal genes based on the outputs from the PLINK computer program. SIRT1, which is enriched with rare causal variants. We also showed that the linkage of disease alleles can be tested based on IBD scores in extended pedigrees. By incorporating information from not only parents and siblings but also other ancestors, we developed a chi-square test based on a 2 × 3 contingency table. Our IBD test provides an attractive alternative to the conventional tests because it is computationally fast and does not require one to specify an inheritance model explicitly.In this work, our analyses provide new insights into the genetic studies of family data with large extended pedigrees for dichotomous traits. We tested the utility of two types of family-based approaches: a logistic regression fitted using GEE and our proposed IBD test. The logistic regression with GEE was used to test the associations in large pedigrees while simultaneously controlling for environmental covariates. To properly handle the rare variants, we provide an operable and straightforward scheme to collapse the rare variants within a gene. This simple collapsing strategy was shown to be useful. As an example, we had a reasonable power for identifying causal gene VEGFC and HIF3A using the IBD tests was significantly higher than the power obtained using the logistic regressions. In other instances, family-based association analyses had better power to detect genes that have relatively high frequencies of risk alleles and relatively large genetic effects. In the worst scenario, if the risk allele was extremely rare, not present in early founders, and of small genetic effect, both methods failed. Because the two family-based approaches have their own advantages for dealing with rare variants, these two approaches can potentially compensate each other. Combining these two types of analysis may be a more powerful solution in the search for causal variants.We compared the performance of family-based studies using these two approaches with the performance of the population-based studies using the standard stratified analysis. Population-based studies seemed to have better power for detecting common variants, and the family-based studies seemed to have better power for detecting rare variants. If a risk allele is present in early founders and the effects of risk alleles are relatively large, the IBD analyses clearly outperformed the family-based association analyses. We noticed that, even for rare variants that have extremely low frequencies or that are found in only a few families, the IBD analysis has a good chance of picking up them. For example, in this work, the power of detecting risk genes Although hunting for rare causal variants using family data sets seems promising, many practical issues need to be addressed before the effectiveness of family-based analyses can be fully recognized. For example, the IBD test can produce unstable results, and it is not very straightforward to obtain the gene-level IBD scores in the first place. Also, we noticed that all analyses were inflated with some false positives. We suspect that the inflated false positives may be caused by those nonfunctional variants whose genotypes are highly correlated with the functional variants. Luedtke et al.  offers aThe authors declare that there are no competing interests.TL and TA conceived the project. TL performed the statistical analysis. Both the authors read and approved the final manuscript.


Associations between specific host genes and susceptibility to Mycobacterial infections such as tuberculosis have been reported in several species. Bovine tuberculosis (bTB) impacts greatly the UK cattle industry, yet genetic predispositions have yet to be identified. We therefore used a candidate gene approach to study 384 cattle of which 160 had reacted positively to an antigenic skin test (‘reactors’). Our approach was unusual in that it used microsatellite markers, embraced high breed diversity and focused particularly on detecting genes showing heterozygote advantage, a mode of action often overlooked in SNP-based studies. A panel of neutral markers was used to control for population substructure and using a general linear model-based approach we were also able to control for age. We found that substructure was surprisingly weak and identified two genomic regions that were strongly associated with reactor status, identified by markers INRA111 and BMS2753. In general the strength of association detected tended to vary depending on whether age was included in the model. At INRA111 a single genotype appears strongly protective with an overall odds ratio of 2.2, the effect being consistent across nine diverse breeds. Our results suggest that breeding strategies could be devised that would appreciably increase genetic resistance of cattle to bTB  with implications for the current debate concerning badger-culling. Mycobacterium bovis and has been rising in incidence steadily in the UK herd over the last 20 years, costing taxpayers approximately 80 million pounds in 2007/08 Bovine tuberculosis (bTB) is caused by Received wisdom appears to be that genotype-phenotype associations are best found in cattle by genome-wide scans In view of the above we chose an alternative, candidate gene based approach, exploiting improved knowledge about genes most likely involved in combating mycobacterial infection (see Methods), and opportunistically sampling small numbers of cattle from each of many farms from a large catchment area. We also used tests of association that were either very general, or aimed specifically at detecting heterozygote advantage. Our approach therefore largely bypasses issues relating to false positives, untested modes of inheritance and, though the high farm diversity, genetic and environmental non-independence. The downside of our approach is increased genetic and environmental heterogeneity. Nonetheless, we are able to show strong associations to two genomic locations, including one where a genotype consistently gives 2–3 fold protection in each of nine different breeds.M. bovis antigenic protein M. bovis and slaughtered. ‘Control’ samples comprise cattle from the same abattoir that were not reactors, though this may have been because they were untested. Skin samples were collected post mortem from the distal edge of the ear using a stainless steel ear notcher and stored in 96% ethanol. Ear tag numbers were checked against abattoir records to confirm bTB reactor status, breed designation and age at slaughter. Data on farms where cattle were resident just prior to slaughter were extracted from the VetNet RADAR database.Tissue samples were collected opportunistically from a single abattoir in the west of England between July 2008 and December 2008. ‘Case’ samples are from cattle that reacted positively to the single intradermal comparative cervical tuberculin (SICCT) test which measures the immunological response to tuberculin, an www.geneontology.org) and a literature review we identified a panel of eight polymorphic microsatellites lying close to genes linked to M. tuberculosis, M. bovis or other bacterial infections, summarized as MARKER : BMS495 , BMS499 , BMC9006 , BMS468 , BMS2753 , BMS2847 , BMS2213  and BOVILS84 . Toll-like receptors (TLRs) and nucleotide-binding oligomerization domains (NODs) are recognize and bind to elements of a pathogen www.ncbi.nlm.nih.gov/mapview/) and version 4.0 of the Bos taurus genome.Using Gene Ontology  and all individuals were screened at each accessory locus.For independent control of population substructure (see below), we also screened 10 further microsatellite markers chosen specifically to lie distant from known immune related genes MARKER : BMS1787 , BMS2573 , BM4509 , BMS2513 , BMS1720 , BL1043 , BMS1172 , TGLA75 , MB065  and BMS529 . Finally, following identification of three putative associations in the first round screen, nine further confirmatory markers were developed in regions flanking INRA111 , BMS2753  and BMS495 [INRA072 ], using either MARC or by developing new markers from microsatellites found in the flanking sequences (1at and 85a). Primers for new markers were designed using Primer3Plus  and scoring by two observers (EED and JIH) following Hoffman and Amos Genomic DNA was prepared using phenol-chloroform extraction following Proteinase-K digestion. Microsatellites were amplified using a standard PCR protocol K distinct genetic groups exist in a dataset. We specified 105 and 106 iterations for the burn-in and experimental period respectively and conducted five independent runs for each value of K = 1–20, specifying the correlated allele frequencies model and assuming admixture. The most likely K was assessed both from the average maximum likelihood across replicates.Population sub-structure can readily generate spurious genotype-phenotype associations when subsets of a population differ both in exposure to disease and genetically 2 statistic Use of PCA is a relatively novel approach to correct for substructure Beyond the PCA-based approach described above, we used two further tests for genotype-phenotype associations. First, we tested for heterozygote advantage by fitting a binomial General Linear Model (GLM) with disease status  as the response and single locus heterozygosity (scored as 0 or 1) plus ‘group’ and the heterozygosity-group interaction terms as predictor variables. Fitting ‘group’ ( = either breed or STRUCTURE group) controls for variation in genotype frequencies between subsets of the total sample. Significance of a term was determined through an ANOVA test comparing two models, one with and one without that term fitted. All models were fitted using R 2.10.1 a priori defined groups. An Excel macro for conducting these tests, GEPHAST, is available at (http://www.zoo.cam.ac.uk/zoostaff/meg/amos.htm).Since the correlation in heterozygosity between a gene and a nearby microsatellite is inevitably imperfect, statistical power may be increased by testing for a general association between any genotype and disease status The GEPHAST method was developed for use on categorical data, particularly where binary classifications are possible. However, the cow data we have include age, a variable that we would ideally like to control due to the issue of dairy cattle living longer and therefore having a higher chance of being exposed than equivalent beef cattle. GEPHAST also lacks the capacity to fit interaction terms that might be important, for example, if a particular genotype correlates with reactor status in some breeds but not others. As an alternative approach and for comparison we therefore recoded the GEPHAST algorithm into R, replacing the chi-squared tests with AIC values from a GLM as our test statistic. Genotypes were fitted as factors and, given the number of potential levels, we again did not interpret the model fits directly but instead used genotype randomisation within breed/STRUCTURE group. P-values are then expressed as the proportion of randomisations that yielded AIC values equal to or lower than the original value. A maximum of 100,000 randomizations were used in any one test and missing data were excluded such that sample size remained constant across randomisations.A total of 547 skin samples were collected during 12 visits to the abattoir, representing 44 breeds or breed crosses ( = ‘breeds’) collected from at least 109 farms (in four cases VetNet failed to return data on farm origin). For most breeds the sample set tended to be dominated by either reactors or non-reactors, but with four breeds  we obtained at least 14 reactors and at least 26 non-reactors. For study, we selected these animals along with other less numerous breeds containing at least five reactors and five non-reactors . However, in one breed, homozygote non-reactors are in excess, driving a strong interaction term in GLMs where group = breed but reducing significance when the breed with the converse trend is mixed with other breeds to form a STRUCTURE group. Markers flanking BMS2753 and BMS495 add little if any support for an association with heterozygosity.To explore three of these putative associations further, we added further flanking markers to INRA111, BMS2753 and BMS495, the latter included because it yielded borderline significance in most of the tests applied to it. For heterozygosity alone, an association with INRA111 is given further support from loci 1at and INRA131. Of these, associations with locus 1at vary greatly depending on what factors are fitted to control for substructure. The reason lies with the small number Since cow age may be a confounding factor influencing the relationship between reactor status and genotype, we next repeated the GEPHAST analysis using a program written in R that allows use of general linear models as a test of association. Since this also provides an interesting independent  comparison with the GEPHAST program, we fitted four models  each for both group = breed and group = STRUCTURE group. Results are summarised in Here we present an analysis of the relationship between genotype and a positive reaction to the SICCT test for tuberculosis in the British cattle herd. Using a candidate gene approach, six of the ten markers we used gave evidence of an association between reactor status and either genotype or heterozygosity. Adding further markers to three putative associations yielded no, medium and strong confirmatory evidence of an association.M. bovis, proximity to badgers and other risk factors. Despite this concern, substructure among Eurasian cattle seems surprisingly slight, with one study based on 19 highly informative microsatellite markers finding only six groups among 48 very diverse breeds Bos indicus in Columbia A primary concern of association studies is the possibility that population sub-structure causes spurious associations 2[1] = 13.86, P = 0.0002) yet is the exact converse of the pattern expected of an artefact, where close relatives from a single farm and controls from diverse farms should carry few and many different genotypes respectively.The extent to which population sub-structure appears not to be too big an issue in our study is illustrated by our most consistent association, INRA111. Here, by inspection, the 2-2 homozygote is ‘protective’, in the sense of being consistently over-represented in our non-reactor controls. Calculating effect size across all ten breeds reveals a consistent pattern with all but the least numerous breed showing an excess of 2-2 genotypes in non-reactors, with an average odds ratio of 2.18 . Such a Age is likely to be a confounding factor in studies of bTB susceptibility, either due simply to the fact that older cattle have had more opportunity for exposure or through a correlation between age and breed (and thence genetics), with dairy cattle generally being slaughtered at an older age than beef cattle. Another possibility is genuine association between the disease, genetics and age. This might be manifest either as older cattle being a biased subset of survivors, lacking some genetically susceptible individuals that had died earlier from bTB (or become reactors and been slaughtered) or other disease, or perhaps through a direct correlation between genotype and age of maximum susceptibility. We therefore investigated the impact of age by fitting GLMs where age was fitted as a covariate, with or without interaction terms with group and genotype. In many cases, adding in age caused an appreciable change in P-value, but not always in the same direction; in some cases the existing association appeared stronger and in others weaker. This seems to confirm the importance of considering age when studying the epidemiology of bTB but also shows that the relationship is by no means simple. Where significance is reduced, this presumably indicates a potentially spurious association driven, for example, by age providing a surrogate measure for breed or group. However, when significance is actually increased, this suggests that the genetic association is genuine, with age reducing the error variance and helping to expose a link to reactor status. These results together emphasize the importance of considering both genetics and the environment, and the dangers of considering either on their own.P-values  are likely to be genuine associations between genotype and reactor status, particularly for the two strongest and most consistent associations, INRA111 and BMS2753.Beyond the issue of genetic substructure and confounding factors such as age, the second persistent problem of association mapping is that of false positives 2[1] = 23.7, P = 1.1×10−6). Since 2-2 s are numerous, this pattern is also significant in the heterozygosity test.Despite considerable concordance between the different tests, there is also appreciable heterogeneity. Thus, BOVILS84 reveals an association with PCA alone, while BM2753 reveals strong associations with the GEPHAST but not heterozygosity. This is to be expected. The PCA approach assumes an ordering of effect where one homozygote is most susceptible and the other is least, a pattern that is not compatible with heterozygote advantage. GEPHAST tests for any genotype association and should show overlap with both PCA and heterozygosity, though might be less powerful when the assumptions of the other two tests are met well. In this respect, INRA111 is interesting because it yields significant associations with all three methods, but spectacularly so for GEPHAST in group 2. By inspection, despite this group being defined by an independent set of markers and containing all breeds sampled, the protective 2-2 genotype comprises only 28% (n = 50) reactors but 72% (n = 81) non-reactors, a large excess  associations with the same nearest features of ASB3  box protein 3). SOCS-3 can act to inhibit cytokine signaling to immune pathways and has been identified as playing a role in combating mycobacterial infections, making it a plausible candidate gene Our two strongest associations are BMS2753 and INRA111. BMS2753 was chosen for its proximity to IFNGR1 and lies in a region containing several immune-related genes, including interleukin (IL) 20RA, IL22RA2, and TNF alpha-induced protein 3. Further work is needed to identify exactly which gene(s) is involved. In contrast, INRA111 was included because of a tentative association with ovine footrot and lies in a poorly defined region of the current version of the cow genome that was elsewhere shown to be associated with mastitis In conclusion, we have successfully applied an unusual approach to the task of finding genetic factors that influence susceptibility of cattle to bTB, as indicated by the SICCT test, focusing on heterozygote advantage in microsatellites near candidate genes screened in a sample of cattle from diverse breeds and farms. We show that population substructure is not as big a problem as many believe. Instead, strong associations extend across breed groups and in one case a single genotype consistently exhibits approximately twofold protection. Assuming the SICCT test reflects genuine susceptibility, this implies considerable promise for increased resistance through selective breeding. Our study illustrates the benefits of marrying ‘small science’ and ‘big science’ and may impact on the heated debate concerning the role of badgers in transmission, because the greater the proportion of variation in reactor status that can be ascribed to the host genetics, the less there is left to explain by other factors such as badger proximity.


With the advent of next-generation sequencing technology, rare variant association analysis is increasingly being conducted to identify genetic variants associated with complex traits. In recent years, significant effort has been devoted to develop powerful statistical methods to test such associations for population-based designs. However, there has been relatively little development for family-based designs although family data have been shown to be more powerful to detect rare variants. This study introduces a blocking approach that extends two popular family-based common variant association tests to rare variants association studies. Several options are considered to partition a genomic region (gene) into “independent” blocks by which information from SNVs is aggregated within a block and an overall test statistic for the entire genomic region is calculated by combining information across these blocks. The proposed methodology allows different variants to have different directions (risk or protective) and specification of minor allele frequency threshold is not needed. We carried out a simulation to verify the validity of the method by showing that type I error is well under control when the underlying null hypothesis and the assumption of independence across blocks are satisfied. Further, data from the Genetic Analysis Workshop  Genome-wide association studies (GWAS) have been extremely successful in identifying a bounty of common genetic variants linked to complex diseases and traits in the human population. While the identification of many novel variants associated with many traits has been a great accomplishment of GWAS, these genetic variants usually have small effect sizes and only account for a small proportion of the phenotypic variation. For example, height has been a well-known heritable quantitative trait with an estimated Although assessing the role of rare variants in complex diseases is becoming increasingly feasible, detecting associations with rare variants still remains a challenging problem since rare variants are hard to pick up due to their low frequencies. Standard GWAS methods such as single-marker association tests are not appropriate strategies for detecting these low-frequency variants due to the fact that power diminishes with decreasing allele frequencies. As a result, a bevy of creative algorithms targeting rare variants have emerged. Such tests “collapse” information from rSNVs within a gene, a genomic region, a pathway, or some other defined properties. Without loss of generality and for ease of reference, we use genomic region when discussing such tests. Burden tests constitute a big portion of the existing literature FBAT) to test for variants jointly over a region of interest Investigators often use either population-based or family-based sampling designs to study the genetic basis of complex diseases. A population-based design samples affected and unaffected individuals who are unrelated, such as case-control samples. Almost all the methods proposed in the literature for detecting rare variant associations, including those discussed above, are for case-control studies. On the other hand, a family-based design treats a family as a sampling unit, which can be as simple as trios or as complex as large extended pedigrees with potentially multiple affected individuals per pedigree. For family studies, half of the offspring are expected to inherit a copy of the minor allele from a parent who has a copy of it. Therefore, variants that are rare in the general population could be quite common in certain families and are potentially more informative. Aggregation-based rare variant tests for analyzing family-data, however, are very limited and in fact only a handful have been proposed to date. Zhu et al. (2010) PDT and FBAT. We evaluated the proposed methods based on simulation and application to the Genetic Analysis Workshop FBAT extensions to rare variants by De et al. Due to low allele frequencies, it is hypothesized that rare variants do not exhibit strong linkage disequilibrium (LD) with either rare or common SNVs PDT, FBATFBATrbPDT and rbFBAT) will be presented in the next subsection.In this subsection, we first briefly describe two popular family-based tests, Pedigree Disequilibrium Test PDT,  and FamiLet FBAT uses the covariance between the traits and the genotypes as a measure of association. Specifically,The general test statistic for PDT considers trios and discordant sibpairs in each pedigree. For a given SNV with two alleles The PDT test statistic isFBAT statistic to test for rare variants by collapsing variants within a genomic region. More specifically, if there are FBAT statistic for SNV FBAT statistic for rare variants is defined as the sum of these As in population-based approaches, single-SNV statistics may lack power to detect associations with rare variants. De et al fbatv0 and fbatv1 denote the fixed threshold (using only rSNVs) and the allele frequency weighted  approaches, respectively.De et al. PDT and FBAT. The idea is to balance the two extreme assumptions  that existing methods rely on by hypothesizing that distant SNVs are independent while dependency exists among nearby SNVs. In this approach, a genomic region is divided into blocks and SNVs within each block are aggregated to arrive at a statistic. Further aggregation is then performed across blocks but the block statistics are now assumed to be independent in the second layer of aggregation. The approach analyzes rare and common SNVs jointly and does not require a particular MAF threshold selection.We propose a novel collapsing idea that can be incorporated into standard family-based tests FBAT or the PDT) for the Suppose there are B blocks spanning the genomic region within which aggregate effect of the SNVs will be assessed. Details of the how to construct these blocks will be provided in the following subsection. Now consider block PDT statistic  size is determined by either the number of base-pairs  or by the number of SNVs (a novel concept). Determination of a good window size in either definition is an important but difficult problem as its choice can be influenced by factors such as LD patterns and MAF of the causal SNVs. Since it is not feasible to investigate the relationship between optimal window size and these factors analytically, we consider several reasonable options and evaluate how blocking schemes may affect the performance of Although multiple genes (in the thousands) are being considered in this study, for simplicity, each blocking scheme with multiple window sizes are applied to all genes to gain an understanding of the overall performance so that general recommendation can be made. For example, if the window size is set to be Option 1: Each gene is divided into blocks of equal length in bp  randomly selected causal variants. This process is repeated fbatv1 using allele frequency weights, fbatv0 with three different MAF thresholds . When the assumption of independence between blocks is violated (as in Options 1–3), there can be some inflation of type I error . However compared to the one-block approach, the type I error is better under controlled. On the other hand, The fbatv0 with all MAF thresholds and fbatv1 are a bit conservative. As expected, power increases with effect sizes in all methods. When SNVs have opposite effect directions, substantial power loss is observed for fbatv0 and fbatv1, while the power based on blocking approaches remains comparable with the power of the same direction effect sizes.The results indicate that type I error is maintained with a nominal In the first analysis, different blocking options with various specifications are compared utilizing the disease status from the first replicate. Specifically, two fixed window size and two fixed number of blocks are used with varying window size and number of blocks: Option 1 , Option 2 , Option 3  and Option 4 .rbPDT for the different options with different size or number of blocks selections. The rbFBAT are illustrated by ROC curves in rbPDT, rbFBAT results are more stable for Option rbPDT and rbFBAT are very comparable as shown by the figures. Overall, rbPDT and rbFBAT are at par and blocking scheme selection might have an effect on the results especially depending on the distribution of gene lengths and number of SNVs within the genes.The results are provided in INSIG1, LPL, PIK3C2B) containing small, moderate and large number of SNVs  with small, moderate and large lengths  and PRKCB1 gene (a larger one) are plotted. For the RRAS gene, although there are two visible clusters, as can be seen in PRKCB1 are very sparse. Obviously, very large number of blocks (see Option PRKCB1) is not a good approach due to its large degrees of freedom. Very small number of blocks may not be the right choice either. For instance, the smallest p-value of To further investigate the effect of blocking, we select rbPDT and rbFBAT with two recently proposed methods, fbatv0 and fbatv1fbatv0 and fbatv1 since they are also extensions of FBAT and software implementations are available (beta version of FBAT v2.0.4). We set the MAF threshold for fbatv0 as rbPDT and rbFBAT, only one representative from each option  are based on splitting a given genomic region (e.g. gene) into blocks under the assumption that SNVs between different blocks are independent while dependency among SNVs within a block is being taken into consideration. A statistic for each block is calculated using the SNVs located within the block and statistics across these blocks are combined to arrive at an overall test statistic for the genomic region of interest. An inherent assumption for our test statistic to be valid is that the statistics across blocks that summarize information from multiple SNVs are independent. However, dependency among SNVs within a block is allowed and accounted for. As such, the proposed methodology may be viewed as a compromise between methods that assume independence of all rare SNVs and those that depict dependency of all variants within a region. This compromise can lead to increase in power by “creating independent data” while holding the type I error rate at base since it still accounts for dependency in a proper fashion. As an further advantage, our methods do not require an MAF threshold and can analyze rare and common variants jointly. We show that, based on ROC (AUC) evaluations, rbPDT and rbFBAT perform similarly and reasonably well compared to two recently proposed family-based methods, fbatv0 and fbatv1, for detecting rare variants. For a fixed significance level  is to use a hierarchical clustering method based on data to partition the genomic region into blocks if the sample size is large and LD within block is strong. We illustrated this by considering a data set with Blocking option and blocking parameter (size or number of blocks) unquestionably play an important role in the implementations of rbPDT and rbFBAT outperform fbatv0 and fbatv1, both of which are susceptible to different directional effects.Another important feature of the proposed methodology is its suitability for detecting association when a mixture of protective and risk variants are involved. The proposed methodology squares the SNV scores before adding them up to prevent cancelation of opposite effects within a block. The advantage of this feature is clearly seen in our simulation results displayed in rbPDT and rbFBAT provide much needed and viable alternatives. Such methods are important in the hunt for rare variant association given the potential enrichment of rare variants in family data and their insensitivity to population stratification.There are still many challenges in understanding the involvement of rare variants in complex disease etiology. Given the limited availability and underdevelopment of statistical methods for analyzing family data for detecting rare variant association, we believe that