Multi-trait genomic models in a Bayesian context can be used to estimate genomic (co)variances, either for a complete genome or for genomic regions (e.g. per chromosome) for the purpose of multi-trait genomic selection or to gain further insight into the genomic architecture of related traits such as mammary disease traits in dairy cattle.Data on progeny means of six traits related to mastitis resistance in dairy cattle  were analyzed using a bivariate Bayesian SNP-based genomic model with a common prior distribution for the marker allele substitution effects and estimation of the hyperparameters in this prior distribution from the progeny means data. From the Markov chain Monte Carlo samples of the allele substitution effects, genomic (co)variances were calculated on a whole-genome level, per chromosome, and in regions of 100 SNP on a chromosome.Genomic proportions of the total variance differed between traits. Genomic correlations were lower than pedigree-based genetic correlations and they were highest between general mastitis and pathogen-specific traits because of the part-whole relationship between these traits. The chromosome-wise genomic proportions of the total variance differed between traits, with some chromosomes explaining higher or lower values than expected in relation to chromosome size. Few chromosomes showed pleiotropic effects and only chromosome 19 had a clear effect on all traits, indicating the presence of QTL with a general effect on mastitis resistance. The region-wise patterns of genomic variances differed between traits. Peaks indicating QTL were identified but were not very distinctive because a common prior for the marker effects was used. There was a clear difference in the region-wise patterns of genomic correlation among combinations of traits, with distinctive peaks indicating the presence of pleiotropic QTL.The results show that it is possible to estimate, genome-wide and region-wise genomic (co)variances of mastitis resistance traits in dairy cattle using multivariate genomic models. Livestock provide a great source of data to investigate genome-wide effects on various phenotypic characteristics such as infectious diseases. There are several reasons for this, including: (1) vast amounts of phenotypic measures  are systematically recorded in modern livestock production and in Danish dairy cattle, for example, phenotypic information on a variety of traits, including clinical disease, is stored together with pedigrees in one central database; (2) important environmental factors, such as herd membership, affecting various phenotypes are recorded and animals within such groups receive rather homogeneous treatments; (3) low effective population sizes are frequent in livestock (e.g. compared with humans), which makes it easier to predict genetic merit and (4) recently, routine genotyping using dense SNP marker panels (e.g. >50 K) for thousands of animals has been initiated in several livestock species.Staphylococcus aureusEscherichia coli, coagulase-negative staphylococci (CNS), Streptococcus dysgalactiae, and Streptococcus uberis, ranged from 0.45 to 0.77, which implies that the mammary immune system, or the physical defense system, or both, act in a pathogen-specific manner. However, the existence of positive genetic correlations also implies the presence of pleiotropic effects or linked quantitative trait loci (QTL). Several studies have reported different heritability estimates for pathogen-specific mastitis traits [In the Nordic countries , treatment of udder infections (mastitis) in dairy cattle is systematically recorded by veterinarians or farmers. However, estimates of heritability of mastitis incidence are low  whole-genome effects for the purpose of, e.g., estimation of breeding values to select superior breeding animals or for prediction of future phenotypes such as disease risks, or (2) effects of single genes or markers, to guide the development of human or veterinary drugs through improved knowledge on the biological basis of traits. Approach (1) typically involves ‘whole genome’ models that model all SNP simultaneously, whereas approach (2) involves Genome-Wide Association Studies (GWAS), in which, typically, each SNP is tested individually using univariate association tests. Here, we suggest a compromise between these two approaches by employing whole-genome models in which variances and covariances are partitioned by chromosome segments. We hypothesize that this approach will capture a large portion of the genetic variance, while also providing further biological understanding of the traits in question. Investigating the effects of chromosome segments of variable size  and correlations among segment effects on different traits may provide interesting insights into the genetic and biological architecture of disease traits such as mastitis incidence.Statistical methods for genomic analyses typically employ fixed prior parameters, which make them less suited to estimate genomic (co)variances. Models that use a genomic relationship matrix, e.g. , could bThe objectives of this work were to (1) present a multivariate model for genome-wide and region-wise association studies, (2) perform simultaneous estimation of genomic effects  for mastitis resistance using more than one trait, and (3) estimate covariances between traits across the chromosomes and across regions of various sizes.The data comprised records of mastitis treatments and pathogen information  from Danish Holstein cows that calved for the first time between January 1998 and January 2009 (collection period). The data were extracted from the Danish National Cattle Database. Mastitis is a difficult trait to analyze due to its low heritability and a potential bias in the treatment of cows; thus, data were edited as described in . BrieflyStaph. aureus, CNS, E. coli, Strep. dysgalactiae, and Strep. uberis, were chosen to represent the pathogen-specific mastitis traits . The pathogen-specific traits were defined only for treatments with pathogen information. In contrast, the trait “general mastitis” contained all recorded (according to trait definition) treatments of mastitis, i.e. both treatments with and without pathogen information.General mastitis was defined as a binary trait for the period from15 days before to 300 days after first calving, i.e. a pheno type of “1” was assigned if a cow was treated for mastitis during this period and “0” otherwise. Only the first observed mastitis treatment for each cow was included. The five most common pathogens in Danish dairy herds, i.e. λ. The relationship between the observed binary variable, y, and the unobservable λ isFor computational reasons, it was necessary to summarize information per sire  due to the small number of sires and the large number of offspring per sire, and availability of SNP information on the sires only. Thus, PM of the mastitis traits were estimated as daughter yield deviations, as described by . Howeverτ is a fixed threshold and yi = 1 and 0 correspond to the presence or absence of mastitis for observation i, respectively. It was assumed that λ is normally distributed with a mean vector μ and covariance matrix τ and τ = 0 and where πi) that observation i is scored as “1” given the model parameter vector θ, isThe probability (where Φ(.) is the standard normal cumulative distribution.The following sire model was used to describe liability to mastitis:whereλijklm = liability to mastitis of daughter m of sire l calving in year-month class i at calving age class j and in herd-year-season class k;YMi = “fixed” effect of year-month of calving (123 classes);AGEj = “fixed” effect of calving age (17 classes);hysk = random effect of herd-year-season ;sirel = transmitting ability of sire l (8 547 levels);b1 = “fixed” regression coefficient of λ on the length of the period at risk;tijklm = period at risk for daughter m of sire l, defined as the number of days from 15 days before calving to the date of culling or to the end of the risk period; it was assumed that all cows with mastitis had a completed risk period;eijklm = residual ~ N and independent.In matrix notation, the model for the mastitis traits can be expressed as:λ is a n × 1 vector of the underlying liabilities of mastitis, n is the number of records for each trait, b is a vector of “fixed” effects as described previously, h is a vector of random herd-year-season effects, s is a vector of random sire effects, and e is a vector of random residual effects. Xb, Z are corresponding incidence matrices.where k is the trait of daughter k on the liability scale and adjusted for all effects other than additive genetic effects and residuals and n is the number of daughters of bull i. Independent improper uniform priors were assigned to each element of b. Herd and sire effects were assigned uninformative normal prior distributions I is an identity matrix, A is the additive relationship matrix, and th sample was saved for post-Gibbs analyses.A full Bayesian approach using Markov chain Monte Carlo (MCMC) methods  via GibbConvergence of the Gibbs chains for each model parameter was ensured using a standardized time series method of batch means ,18.Subsequently, genetic variances of the estimated PM were estimated using a standard linear animal model with pedigree information and REML. The PM were weighted based on the standard errors of prediction (SEP) of the posterior PM samples. From the estimated variances, heritabilities for each trait PM were computed for later comparisons with estimated genomic variances.2 and scaled to achieve an average weight of 1. The scale factor used in the present study was the average weight per trait of the 1 844 genotyped bulls. By scaling the weights to an average of 1, the computed residual variances will be directly comparable with the genomic (co)variances.Standard errors of prediction of the posterior PM samples were calculated to construct weights for each trait included in the genomic model to adjust for heterogeneous variances of the sire records. The weights were computed as 1/SEPThe bulls selected for this study were genotyped using the Illumina Bovine SNP50 BeadChip . The raw marker data were edited using the following criteria: (1) a locus was removed from the analyses if the minor allele frequency was less than 5%, if the proportion of animals genotyped for this locus was less than 95%, if the average GenCall score at the locus was less than 60%, and if the proportion of missing marker genotypes was larger than 10%; (2) an individual was deleted if the call rate  had a score below 0.85. After editing, 1 844 bulls had daughters with mastitis and pathogen data, and 37 862 SNP were available and used in the analyses.Genomic parameters were estimated using a Bayesian model in which SNP effects, within a trait, were assumed to originate from the same normal distribution. This represents the gBLUP method  implemen1 and PM2 are vectors with PM for the two traits on a common list of individuals, μ1 and μ2 are the PM means of each trait, xi are vectors of coded genotypes of the individual for i = 1, …, M SNPs, bik is the random regression coefficient modeling the effect for SNP i on trait kW is a diagonal matrix with 1/SEP2 as diagonal elements, l is a vector of latent effects that models the correlated part of the residuals (note the use of the same vector l for both traits), ν1 and ν2 are scale factors for the effect of the latent vector l on each trait, which can be interpreted as the elements of the first eigenvector of the residual variance-covariance matrix (see below), and e1 and e2 are the uncorrelated parts of the model residuals.where PMxi was done as 2p-2, 2p-1, and 2p for homozygotes for the first allele, heterozygotes, and homozygotes for the second allele. This is similar to [p is the frequency of the first allele. Such coding standardizes the means of the genotype covariates to zero, assuming Hardy-Weinberg equilibrium of genotype frequencies, and the regression of such a genotype coding on the PM represents the allele substitution effect for substituting the first coded with the second coded allele. Covariances between the SNP effects were also modeled using a latent variable, but this was specified as a hierarchy in the Bayesian model. In this multi-trait model, the effects of a SNP on the two traits were correlated; therefore the variance of marker and residual effects were var(b1b2) were assumed the same across the genome.The genotype coding in milar to , except The distributional assumptions of the model parameters were:ν| = 1, where ν = , |u| = 1, where u = , and where N denotes a normal distribution with mean and variance parameter, U denotes a uniform distribution on the given interval.with the constraint that |The modeled residual variance-covariance structure can be shown to be:R, such that it can be shown that ν =  is the first eigenvector of R, R, and b, are correlated through the use of common latent vectors, s, and the variance-covariance structure for SNP effects can be shown to have a covariance of u1,u2) can be interpreted as the first eigenvector of the variance-covariance matrix, where the first part corresponds to a special form of the spectral decomposition of the variance-covariance matrix μ1, μ2, bi1, bi2, because these parameters have conditional normal distributions that are independent between traits and therefore can be updated in a “single trait manner”. Also ν1 and ν2 have conditional normal distributions and were updated as a regression on the vector l. They were scaled to unity norm after sampling to apply the constraint on |ν|. The same inverse scaling was applied to the latent vector l, because ν and l are multiplicative in the model. Applying the same scaling to both ν and l is arbitrary but forces the model to uniquely explain all the variance through l and makes parameters identifiable. The vector of latent residual effects, l, works across traits but its conditional distribution is also normal and derived by unifying the two trait equations into a single equation:The MCMC estimation for this model was straightforward for where Model fit was assessed by visual inspection of model residuals plotted against the reliability of the estimated breeding values (EBV) for the six traits and significance of the slope of regression line from zero was tested using a t-test. Reliability of EBV was calculated as:c were constructed. From the MCMC samples of individual DGV, MCMC samples of genomic variances and covariances were subsequently constructed by computing , which was done for the whole-genome DGV and for the interval-wise DGV. Furthermore, MCMC samples of genomic correlations, Posterior statistics for any function of the model parameters can be easily obtained when such a function is computed on the primary MCMC samples of the model parameters. This was applied to compute direct genomic breeding values (DGV) of individuals and genomic and residual (co)variances per chromosome and parameters derived thereof. For all these estimates, posterior means and posterior standard deviations were obtained. The genomic parameters were based on the constructed DGV of individuals which automatically take into account the covariance generated between SNP due to linkage disequilibrium (LD). Markov chain Monte Carlo samples of individual genomic values for trait 1 . Figure The number of daughters with data from individual bulls and the low heritabilities of the traits both affected the reliability of the EBV and the posterior standard deviations of the PM. For example, 80% of the bulls had between 5 and 50 daughters with phenotypic information. This resulted in average reliabilities of EBV of 0.30, 0.36, 0.32, 0.30, and 0.38 for mastitis caused by Staph. aureus. The slope of the regression line was significantly different from zero  for all traits except Staph. aureus mastitis. For Staph. aureus mastitis, the estimation errors of the DGV clearly increased when reliabilities of the EBV reached values below 0.5. This trend was observed for all the pathogen-specific mastitis traits. For general mastitis, which had higher heritability and EBV reliabilities estimation errors of the DGV increased when EBV reliabilities were below 0.7.Model fit was assessed by plotting model residuals (observed PM-DGV) against different variables. In Figure Strep. uberis, E. coli, Staph. aureus, and Strep. dysgalactiae. Analysis of a trait in different pair-wise trait combinations, resulted in similar GPV for the trait. As expected, the GPV of general mastitis was higher than that of pathogen-specific mastitis traits, except when compared to mastitis caused by CNS. Table The average of the posterior means of GPV from the pair-wise analyses of the mastitis traits differed among traits Table . Among tGenomic correlations Table  among thBos Taurus 4.0; [All chromosomes explained significant amounts of genetic variance for each trait, except chromosome X BTA30), which explained substantially less variance than would be expected based on its size. For example, the variance explained by chromosome X was 93% lower than expected for general mastitis. For the other chromosomes, the trend is that chromosome-wise GPV , i.e. lStaph. aureus mastitis; BTA1, 11, 14, 17, 19, and 20 for CNS; BTA6, 11, 13, 14, 16, 19, and 21 for E. coli; BTA3, 14, 17, 19, 20 and 25 for Strep. dysgalactiae; and BTA6, 13, 14, 18, 19, 25 and 27 for Strep. uberis. Additional chromosomes with less pronounced effects, but still above their expected value, were observed for most of the pathogen-specific traits. Chromosomes showing a large variance for general mastitis were BTA3, 5, 6, 14, and 19. Only BTA19 had higher GPV than expected according to size for all traits.Some chromosomes deviated from the general trend and explained more variance than would be expected according to their relative size, i.e. they may contain relatively more QTL or QTL with larger effects on the trait and such chromosomes differed across traits; chromosomes with relatively large GPV were BTA6, 13, 14, 16, 19, and 26 for l. For all trait pairs, there was a high proportion of chromosomes with larger covariances than expected, which may indicate the presence of pleiotropic QTL. In addition, in several cases a limited number of chromosomes accounted for a major part of the total covariance, e.g. BTA3, 6, 10, 11, 13, 14, 16, 19, 21 and 29 for the covariance between Staph. aureus and E. coli , resulting in overall positive genomic correlations between the traits, given the default prior assumptions for the latent vector, Staph. aureus. Differences between chromosomes were still noticeable but were far less pronounced compared with the chromosome-wise genomic covariances. Similar to the chromosome-wise GPV, some chromosomes had larger genomic correlations than expected based on the genome-wide genomic correlation. This could indicate the presence of pleiotropic QTL, e.g. BTA16 and 19 for the combination of Staph. aureus and Strep. uberis. In contrast to the genomic covariances, the genomic correlations did not depend on chromosome size but were similar across chromosomes.In Figure BTA19 was further investigated as this chromosome showed a clear effect on all traits. Profiles of genomic variances across this chromosome were created by computing posterior variances in half-overlapping blocks of 100 SNP for each trait. This means that one computation was done for blocks with SNP 1–100, 101–200 etc., and a second computation was done for blocks with SNP 1–50, 51–150 etc. and then the values of overlapping blocks were averaged to smooth out blocks of 50 SNP.E. coli. This peak was most pronounced for CNS and Strep. uberis. Also, a peak was observed around 10 Mb for E. coli and Strep. dysgalactiae. No clear peaks were observed for general mastitis, possibly because of the composition of this trait.In general, the genomic variance on BTA19 Figure  was spreStaph. aureus and the other traits. The magnitude of the genomic correlations differed between trait combinations, with the largest genomic correlations obtained between Staph. aureus and general mastitis because of their part-whole relationship. The genomic correlation between pathogen-specific traits was highest for Staph. aureus and CNS, likely because both are staphylococci. The genomic correlation between Staph. aureus and Strep. dysgalactiae was also high, while that between Staph. aureus and Strep. uberis was the lowest, followed by the correlation between Staph. aureus and E. coli. The positions and widths of the pleiotropic regions differed between trait combinations. For example, a very narrow region around 35 Mb was observed for the genomic correlation between Staph. aureus and Strep. uberis, while it was much wider around 30 Mb for the genomic correlation between Staph. aureus and E. coli.Establishing the profiles of genomic correlations for BTA19 as described above, revealed the pleiotropic regions along the chromosome. Figure The estimated values for GPV express the proportion of the total variance  of the PM that is explained by the markers and can therefore be related to the heritabilities of the PM. However, because the PM are mean phenotypes, the explained variance in PM is increased relative to heritabilities of individual phenotypes. The GPV estimates were 80% to 87% of the pedigree based estimates of heritability but almost perfectly lined up with each other. Variances explained by markers can be expected to be lower than pedigree-based variances because the markers used may not be in complete LD with the causal polymorphisms .Staph. aureus, followed by Strep. dysgalactiaeE. coli, CNS, Strep. uberis and general mastitis. In our study, the rankings of Staph. aureus and Strep. dysgalactiae and CNS and Strep. uberis were shifted around. Heritability of general mastitis was up to three times higher than that of pathogen-specific mastitis in [The ranking of the GPV across traits was slightly different from the ranking of heritabilities reported in , in whictitis in  while inThe posterior means of the genome-wise genomic correlations were all lower than the traditionally estimated genetic correlations based on pedigree ,11,24. AGenomic proportions of the total variance were also estimated per chromosome for all traits. Generally, the magnitude of the GPV was increased with size of the chromosomes. However, some chromosomes had slightly higher GPV than average compared to their size and for other chromosomes, the GPV was a little lower than expected based on size. The dependency on chromosome size can partly be explained by the number of markers on each chromosome. The model assumes a priori the same variances for all SNP, which is in line with the standard assumption in gBLUP . Thus, lBased on the results presented here, higher than expected (based on size) chromosome-wise GPV may indicate the presence of QTL on the chromosome. Chromosomes that explained most variance may also harbor the most important QTL (major genes) affecting the trait. Clear differences in the GPV profiles were observed between the six traits. However, working at the chromosome level is likely not detailed enough to detect clear pathogen-specific regions since no clear distinctions between traits were detected regarding chromosomes which explain more variance than expected, except for BTA19, which had a relatively high GPV for all traits, including general mastitis. This may indicate that this chromosome harbors QTL with a general effect on mastitis resistance.Information about QTL in the present study could be better compared to traditional QTL methods. In contrast to multi-trait implementations of traditional QTL mapping based on linkage e.g. -28, we uIn general, the genomic model used here was rather basic, as both a common variance and covariance for SNP effects were applied. It is possible to extend the model to take in account different (co)variances per chromosome or of other defined genomic regions. This would be necessary to more accurately predict effects of QTL affecting one or more traits. Also, there are different ways of defining genomic regions, which is an area that needs further investigation. Below, we discuss how for example this could be done in a rather simple way.The most interesting feature of our multi-trait genomic model is the ability to estimate covariances between defined genomic regions for each trait, which would be more difficult with other approaches. For example, with traditional BLUP estimation, it would be necessary to build 30 genomic relationship matrices and to simultaneously estimate 90 covariance components. Dividing each chromosome into several segments would further increase these numbers and the memory requirements for computation. For the present SNP-based model, the model is run once and relevant parameters are inferred from the MCMC samples. As with the genomic variances, the traditional gBLUP model [Interesting chromosomes are indicated by covariances above the average covariance of the genome or chromosome. Chromosomes showing large effects were in some cases much clearer based on covariances than based on GPV. Similar to the chromosome GPV, a clear relationship with chromosome size was also observed for the chromosome covariances.All chromosome covariances among the pathogen-specific mastitis traits were positive. This indicates that genes that control mammary response towards one pathogen (e.g. release of immune factors a.o.) to a certain degree also control response towards other pathogens. However, it is difficult to interpret the absolute differences between the chromosome covariances because our model pulls these estimates towards a common average. In reality, the chromosome covariances will be more different than shown here, but it would be difficult to estimate variances and covariances for 30 chromosomes in a fully unconstrained way.Staph. aureus and E. coli differed much more (higher covariance than expected on more chromosomes) from their expected values (based on chromosome size) than the covariances between Strep. uberis and Strep. dysgalactiae or covariances between general mastitis and the pathogen-specific mastitis traits. Also, the use of a common prior resulted in lower genome-wide genomic correlations, which quantify the relatedness between two traits.Information about chromosome-wise covariances can be useful when a QTL has been found and knowledge about potential effects on other traits is required. One could argue that chromosome covariances between traits vary more when the pathogens are more distantly related or show different infection patterns. For example, the chromosome covariances between Staph. aureus/E. coli combination suggest that BTA16 and 19 are the only chromosomes that harbor QTL affecting mastitis caused by each of these pathogens. However, BTA16 and 19 also seem to be clear candidates for harboring pleiotropic QTL affecting both Staph. aureus and Strep. uberis. Finally, at least five chromosomes  are likely to harbor QTL that affect resistance towards Staph. aureus and general mastitis.It is not clear whether our method can be used to identify chromosomes that harbor pleiotropic QTL using the current settings. According to Figure A QTL that affects specific mastitis must also affect general mastitis, but it may not be detected, e.g. the specific mastitis may only contribute little to general mastitis. More likely, the QTL detected for general mastitis are QTL affecting the more prevalent and multiple mastitis cases.One way to overcome the problem of averaging out QTL for the purpose of QTL mapping may be by splitting the chromosomes up into smaller regions, for example based on neighboring SNP that are in LD with each other. Then, the defined region consists of SNP that are more likely to cluster around potential QTL and the effect is not distorted by many SNP with very small or zero effects. In the present study, this was done in a simple way by computing genomic (co)variances in half-overlapping intervals of 100 SNP on BTA19 because this chromosome was the only chromosome with a clear effect on all traits. This method revealed different variance profiles between the traits. No clear peaks were detected because of the use of a common prior which, as explained above, equals out the variance across the defined regions. The peaks were more pronounced. The use of a mixed prior distribution for the SNP effect may be more appropriate to detect QTL regions. However, to date this method only works well for single-trait analyses and must be further investigated.The LD between SNP is accounted for when genomic (co)variances are calculated. This means that the total genomic variance may differ from the sum of region-wise or chromosome-wise variance, because the latter would ignore covariance between the parts. In our analysis, these sums of chromosome and region variances were smaller than the total genome-wide variance, indicating presence of negative covariances between the parts.The results from the present study show that it is possible to study, genome- and region-wise genomic (co)variances of mastitis resistance traits in dairy cattle using a multivariate genomic model. It was found that larger chromosomes explained more genomic variance than smaller chromosomes due the larger chromosomes having more SNP. Some chromosomes explained more variance than expected according to chromosome size. This could indicate that these chromosomes harbor QTL affecting the traits. Clear differences in variance profiles among the investigated traits were observed, indicating that the mammary response to infections differs between pathogens. All chromosomes explained positive covariances between the traits as a result of the model assumptions. As with the genomic variance, some chromosomes explained more covariance than expected according to their size. This could indicate the presence of pleiotropic QTL. With this methodology and PM as phenotypes, the estimated genomic correlations between the traits were found to be lower than genetic correlations estimated by traditional methods based on pedigree, which indicates that these values are not necessarily comparable. In our model, a rather simple approach was applied to model SNP effects, i.e. a common variance and covariance for the SNP effects. However, the results provide an opportunity to develop this model with different model assumptions, e.g. mixture priors for the SNP effect, which could allow the model to more accurately accommodate differences in (co)variances across the genome.The authors declare that they have no competing interests.LPS performed the statistical analyses and drafted the manuscript. LJ developed the software for the analyses and gave valuable inputs to the description of methods. LJ, PM, TM and MSL provided valuable suggestions for analyses, interpretation of results and the discussion. All authors were involved in proof reading the manuscript and have approved the final manuscript.


TMEM154 gene with validation data from over 2,800 sheep representing nine cohorts. While no single genotype has been shown to have complete resistance to OvLV, consistent association in thousands of sheep from multiple breeds and management conditions highlight a new strategy for intervention by selective breeding. This genetic marker-assisted selection (MAS) has the potential to be a useful addition to existing viral control measures. Further, the discovery of multiple additional genomic regions associated with susceptibility to or control of OvLV suggests that additional genetic marker tests may be developed to extend the reach of MAS in the future. This review will cover the strengths and limitations of existing data from host genetics as an intervention and outline additional questions for future genetic research in sheep, goats, small ruminant lentiviruses, and their host-pathogen interactions. Small ruminant lentiviruses include members that infect sheep  and goats . Breed differences in seroprevalence and proviral concentration of OvLV had suggested a strong genetic component in susceptibility to infection by OvLV in sheep. A genetic marker test for susceptibility to OvLV has been developed recently based on the  Historically, small ruminant lentiviruses (SRLV) were defined by infection and disease in host species, specifically sheep and goats. The history of ovine lentivirus (OvLV), also known as maedi-visna or ovine progressive pneumonia virus, have been covered in detail ,2,3 and Small ruminant lentiviruses are common and inflict economic losses in livestock production. Ovine lentivirus infection is highly prevalent in most sheep-producing countries, including the USA, Canada, most European countries, India, China, Japan, and multiple countries across both South America and Africa ,9,10,11.Similarly, CaLV occurs in many countries around the world ,3,4. TheMany advances have been made in developing intervention strategies against SRLV. One effective strategy is diagnostic testing followed by culling SRLV positive individuals ,40. AnotAnother intervention strategy with some effectiveness for OvLV has been extensive rearing ,46,47. POther intervention strategies that have been or could be tried for SRLV include vaccines and drug treatments. Multiple vaccines have been tried for SRLV, but all have had limited efficacy and some led to increased viremia and disease ,12,13. UUsing the range of available intervention strategies for SRLV, eradication programs have been established in many countries, and these programs have met with some success ,50. HoweHistorically, selective animal breeding has been based on choosing those individuals with desirable phenotypic traits for breeding, in the hope of producing a next generation of animals with a higher frequency of desirable phenotypic traits. That process is dependent on the ability to measure phenotypic traits in the parental generation. For traits like milk yield, body weight, and hair color, those measurements are readily available. However, some other high value traits are more difficult to measure directly on each individual, so a highly correlated proxy for the phenotype may be desirable for these traits. Examples would include carcass traits like steak tenderness potential  and susceptibility to infectious disease (that cannot be measured apart from exposure to infectious agents). In cases like these, the use of genetic markers with consistent trait association to determine which animals are used for breeding may dramatically improve the average rate of trait improvement per generation ,53. Such a marker-assisted selection (MAS) strategy for infectious disease susceptibility traits has multiple advantages over direct phenotypic measurement. As discussed above, ease of measurement can be a substantial advantage, particularly when healthy animals do not have to be exposed to pathogenic agents. Another potential advantage relates to population health. A small fraction of individuals are responsible for a disproportionate fraction of total population transmission events for a wide variety of pathogens. In general, the 20/80 rule suggests roughly 20% of individuals are responsible for approximately 80% of transmission for many infectious pathogens ,55. ExpeAdditional advantages of MAS include the avoidance of drug use and scalability with flock size. First, MAS does not involve drug use of any kind. This can be appealing on its own, and it avoids the issue of pathogens developing resistance to drugs that might be used in other species, such as humans. Further, genetic marker use scales well with flock size so that even large flocks can undergo MAS. As with any intervention, there is more labor input with larger numbers of animals, but the effort required is manageable for many operations. In some cases, the cost can be reduced greatly to improve the cost-benefit by sire-only genotyping and selection. The population genetic gain is slower with sire-only selection, but there is a large reduction in numbers of samples and cost required. The genetic gain relative to selection of both sires and dams is related to the mode of inheritance for the desirable allele(s). There is still relatively rapid genetic gain with sire-only selection for dominant markers, but additive markers achieve slower gain and recessive ones achieve greatly reduced gains per generation with sire-only selection. Nonetheless, sire-only selection may have a place in many large producer operations.Of course, genetic marker tests do not have to be used in isolation from other intervention approaches but can complement existing strategies. Genetic markers for probability of infection have application in a broad range of settings. Test and cull procedures do reduce prevalence if the rate of new positives is lower than the rate of culling . By reduA critical issue in development and use of genetic markers for MAS is the definition of relevant phenotypes. In the case of small ruminant lentiviruses, the probability of becoming infected, and an animal’s control of virus once infected are the two most important general classes of phenotypic traits for potential application in MAS. The simplest way to record probability of becoming infected under field conditions is to use direct measures of the presence or absence of the virus in individuals averaged over a population ,70,71,72An animal’s control of small ruminant lentiviral replication has been measured in two related ways. The first is by direct measurement of proviral concentration ,80,81,82The use of genetic markers for control of viral replication would provide advantages in multiple scenarios. Many producers might find reduced viral replication and reduced average lesion severity among infected sheep to be useful adjuncts to reducing prevalence, particularly if they could be achieved inexpensively. Some producers with markets in their own countries have concluded the costs of OvLV eradication too high to implement. However, the worst pathology can impede commercial production ,18,19,20Many other phenotypic measures are related to SRLV infection and disease progression, and these include important production traits like cumulative lifetime offspring weaning weights, milk yield, culling ages, offspring growth, and clinical signs of SRLV disease, among others. It is critical that such traits be included in selection criteria whenever available to enhance overall genetic gain. Indeed, many producers already use many of these traits in phenotypic selection either directly by incorporation into a formal selection index, or more generally by removing individuals with the most severe clinical disease. Such traits are also important measures for development of markers for marker-assisted selection, and joint consideration of these traits will be important as the field progresses. Given defined phenotypes, development of genetic markers begins with evidence those specific phenotypes have a genetic basis in the species of interest. In order to use marker-assisted selection, there not only need to be genes involved in a trait, but the population needs to possess multiple functional genetic variants affecting those genes. That is, there need to be multiple genetic versions, known as alleles, to select one or more over others in making breeding decisions. For both sheep and goats, multiple reports support breed differences in seroprevalence of small ruminant lentiviruses as evidence for a genetic basis for probability of infection ,32,33,34Once a genetic basis is established in the species of interest, genetic marker development proceeds through multiple evidence-based stages . For traMany methods to achieve initial discovery of a genetic association have been used, and such methods continue to evolve ,88. One p-value) in the discovery animal set, but testing in multiple scenarios across the world suggests some will be spurious by chance even using traditional p-value thresholds.Regardless of methodology used, the initial discovery of a genetic association is often the first published report, but the genetic marker(s) in this stage are not ready for broad use. The initial associated marker could be from one of three major types, only two of which are likely to have broad utility. First, the marker could be a functional genetic variant, such as an amino acid substitution at a functional position, a promoter variant with differential transcription factor binding and differential transcription, a variant that creates or destroys a microRNA target site, or other regulatory variants ,89,90. AFor use as a predictive genetic marker, the next important question is whether the marker will be associated with the trait(s) of interest in the target population, such as a producer’s own flocks. Stage 2A consists of confirmation by replicating the association in separate validation animal sets and is intended to address this question. This stage tends to eliminate spurious associations and markers in only weak linkage disequilibrium with functional genetic variants. Functional variants and markers in strong linkage disequilibrium across populations tend to show replication of association, and therefore pass this stage ,90,92. IIt is important to note that genetic markers need not show association in all conditions to be useful. One common cause of failed association is low allele frequency in one or more animal sets. This can result in low statistical power to detect a true association, even if present. However, if sufficient power exists and there is still a lack of association, it is important to refine the conditions under which genetic markers are potentially useful. Ideally, the validation sets would include animals from different breed backgrounds, locations, management conditions, and possibly differing viral subtypes. These criteria permit the formation of informed conditions for genetic marker use that take into account conditions of any failed association studies. A third evidence-based stage (2B) of genetic marker development involves potential trade-offs in other traits besides the ones identified in the discovery and replication of association stages. For instance, if genetic gain in reduced susceptibility to small ruminant lentiviruses came at the price of dramatic losses in production efficiency, that could restrict the conditions under which the genetic marker might be usefully employed. Further, there are many scenarios under which reductions in susceptibility to one pathogen could create conditions for an increase in susceptibility to another pathogen . For exaPRNP . At. AtTMEM1plotypes . The thrTMEM154 genetic marker test. First, the effect size for odds of OvLV infection under field conditions is quite large, but does not represent complete resistance. This may seem strange to some who have been accustomed to the strong resistance to classical scrapie provided by the ARR haplotype, but complex traits (multiple genes involved) are likely to be the norm for most traits of commercial interest, including susceptibility to infectious disease. Within the realm of complex trait genetics, the effect size of 2.85-fold relative risk is not only a very useful difference for producers, it is also quite large for a single gene. This implies a 185% excess risk of OvLV for animals with at least one copy of haplotype 2 or 3. A relatively well-characterized complex trait is human type 2 diabetes, for which at least 40 validated loci have been found [versus genotypic), those estimates are still considerably smaller than that of TMEM154 with OvLV. The TMEM154 genetic marker test consistently provides a very useful, large difference in odds of OvLV infection. The currently available data on effect size, allele frequencies, and apparent mode of inheritance have many positive implications for the use of this en found . Among ten found ,167,168.The use of genetic marker tests depends on allele frequency because it affects the speed and ease at which genetic gain can be made in a population. The favorable haplotype 1 was observed at relatively high frequency but was still the minor allele in most populations studied . This suTMEM154 test, the favorable haplotype 1 appeared recessive to the less desirable haplotypes 2 and 3 [TMEM154 genetic marker test, and the recessive mode of inheritance for the favorable haplotype 1 creates a tradeoff for producers between rapid genetic gain at higher cost, or somewhat slower gain at lower cost.Mode of inheritance is another factor with implications for the rate of genetic gain possible using a genetic marker test for MAS. In the case of the current  2 and 3 , though The exciting developments to date not only provide a meaningful intervention for OvLV, they also raise many other important questions. Some of these questions relate to the further development of genetic marker tests as interventions for small ruminant lentiviruses. Other questions are broader and regard the nature of functional roles of both host and viral components in host-pathogen interactions. Below, we review some important research needs and opportunities in these areas.TMEM154, and more can be done to develop this test. While the test has been validated in many sheep of diverse breeds and management locations, further testing may continue to expand the range of conditions under which use of the test is supported by data. Alternatively, there may be situations in which the test is less helpful. The extent of current data suggest those situations may be very limited, but if they are identified it will be important to address potential reasons. Those could include differing breeds, locations, management conditions, and possible viral adaptations to compensate for host defenses, among others.The existing genetic marker test in sheep is based on the three most common haplotypes at TMEM154 haplotypes 1–3 regards potential correlated responses to selection using this test. A critical need will be studies to assess potential correlated responses to selection involving production traits. There is little evidence of loci associated with production traits located on sheep chromosome 17 near the TMEM154 gene in the current SheepQTL database [A second important issue in the continuing development of the current genetic marker test based on database ,172, so TMEM154 genetic marker test has a relationship with control of OvLV, in addition to odds of infection. Further, it is possible that genetic improvement in susceptibility to one agent may improve or decrease susceptibility to other agents or other traits related to the same agent, and clear examples have been documented, including with the CCR5 delta-32 mutation and HIV versus West Nile Virus [TMEM154 genetic marker test has a relationship with highly prevalent and economically important helminth parasites of small ruminants, but there are many other infectious agents that will also be of interest. These are early days in assessing the potential relationship of current intervention tools based on host genetics to other traits in sheep.Also, as with any genetic marker test for susceptibility to infectious disease, another area of interest for potential correlated responses to selection is other infectious disease traits. A simple example would be association with other SRLV traits, and the literature so far has not addressed whether the current le Virus ,176,177.TMEM154 in sheep concern the additional haplotypes identified by Heaton et al. that were not observed at sufficient allele frequencies to perform meaningful tests of potential resistance  than one would predict from the sum of the individual components . Once muWe note that particular caution should be used in interpreting and applying MHC gene associations with infectious disease traits. Such associations are very useful for study of host-pathogen interaction and antigen presentation. However, there are additional concerns related to correlated responses to selection when using MHC-based genetic marker tests for marker-assisted selection. First, since the classical MHC genes are used to present antigens from a diverse variety of sources, it is possible that selection toward homozygosity for one allele might diminish the immune system’s ability to respond to other pathogens. Further, the MHC region is characterized by long linkage disequilibrium that spans many immune system-related genes ,211. Thuversus free viral particles [One of the potential benefits of MAS applied to infectious disease traits is the possibility of eliminating the highest transmission individuals prior to infection. However, it is still not known how to identify predominant forms of infectious virions for OvLV. There are open questions about transmission through cell-associated virus articles ,213,214.articles , there iSome argue that selection to dramatically improve the control of viral replication is selection for tolerance to the virus and could increase the difficulty of detecting the lowest proviral concentration positives as infected. In theory, if such low concentration individuals were important sources of transmission, this could slow eradication efforts. However, the relationship between proviral concentration and transmission is unknown. It is possible that higher proviral concentration could indicate not only more provirus within an individual, but also more infectious virus shed from an individual. If so, the superspreaders of OvLV might be individuals with high proviral concentration. As such, there could be disproportionate benefit to selective elimination of these individuals. However, development of tools to measure transmission will be necessary to answer this question.TMEM154 in goats, but both other candidate genes and genome-wide approaches may provide insights into additional gene regions and variants associated with CAEV traits in goats. Any genes identified in connection with OvLV may also be of interest in goats with respect to CAEV, especially given the close relationships among SRLV, ability to infect multiple species, and recombination between SRLV. Further, the recent development of large-scale genome-wide genotyping reagents for domestic goats [The discussion of future opportunities has thus far focused mainly on sheep, but there are many opportunities to address SRLV in goats using genetic methods. Many studies have noted breed differences among goats in susceptibility to CAEV ,31,32,33ic goats  suggestsGenomic selection refers to a separate, but related, technology compared to the marker-assisted selection described thus far. While marker-assisted selection generally involves smaller numbers  of markers placed very close to or consisting of functional mutations, genomic selection uses very large numbers (many thousands or more) of markers throughout the genome to assist in making selection decisions . This isBovine dairy applications of genomic selection have been among the most successful in livestock species to date ,219. SucIn addition to the difficulties in short linkage disequilibrium contexts, the development of genomic selection for infectious disease traits in small ruminants faces several technical hurdles in the near term. The necessity for large reference populations with consistent phenotypic data has been a major limitation for infectious disease traits . While rHowever, in the long-term genomic selection is a very promising tool for advancing livestock breeding and multiple opportunities exist to integrate infectious disease and health traits into genomic selection for small ruminants. First, the addition of markers validated for marker-assisted selection into genomic selection breeding schemes is feasible. Also, a major current limitation is the density of genotyping arrays. However, a high density array for sheep will be released in the near future that may mitigate this concern. Further, and genotyping by sequencing may soon be economically feasible. Once it is, density of markers will no longer be a constraint and short linkage disequilibrium will be an advantage rather than a disadvantage . In thisIntervention strategies for SRLV based on host genetics and genomics have great promise that is only beginning to be fulfilled. There is evidence to suggest more genetic marker tests will follow, and combining tests use may have long-term benefits against rapidly evolving SRLV. However, it is important to understand evidence-based stages of genetic marker test development so producers and other users of these tests are aware of both the strengths and weaknesses of existing evidence and potential types of research developments that may be expected going forward. Finally, increased understanding from host genetics may play an important role in understanding virus-host interactions for SRLV, and potentially for other lentiviruses.


FKBP5 sequenced in 91 lymphoblastoid cell lines derived from white non-Hispanic individuals. The application of the sliding-window test procedure detected an association in a sub-region spanning an exon and two introns, when rare and common variants were analyzed together.Aggregating information across multiple variants in a gene or region can improve power for rare variant association testing. Power is maximized when the aggregation region contains many causal variants and few neutral variants. In this paper, we present a method for the localization of the association signal in a region using a sliding-window based approach to rare variant association testing in a region. We first introduce a novel method for analysis of rare variants, the Difference in Minor Allele Frequency test (DMAF), which allows combined analysis of common and rare variants, and makes no assumptions about the direction of effects. In whole-region analyses of simulated data with risk and protective variants, DMAF and other methods which pool data across individuals were found to outperform methods which pool data across variants. We then implement a sliding-window version of DMAF, using a step-down permutation approach to control type I error with the testing of multiple windows. In simulations, the sliding-window DMAF improved power to detect a causal sub-region, compared to applying DMAF to the whole region. Sliding-window DMAF was also effective in localizing the causal sub-region. We also applied the DMAF sliding-window approach to test for an association between response to the drug gemcitabine and variants in the gene  Traditional genome-wide association analysis approaches, which analyze a single variant at a time, are underpowered to detect associations with rare variants . DMAF allows combined analysis of common and rare variants, and can be extended to the analysis of pooled sequencing data, for which many collapsing methods are not applicable. Our method allows weighting of markers based on minor allele frequency 2, was also compared; these approaches are distinguished as DMAFabs and DMAFsq. By using a positive function of the difference in MAF, our method places equal importance on risk variants (which are expected to have jX > jY) as on protective variants (which are expected to have jX < jY). The test statistic is then computed as the weighted sum over the variants of interest, jw is the weight for variant j and A is the set of variants of interest. A may include all variants in a window or only rare variants. We used a threshold of MAF ≤ 0.05 to classify variants as rare. When using DMAFsq with equal numbers of cases and controls, the test statistic V is equivalent to Q, the test statistic of SKAT .For each single nucleotide variant (SNV) jw, such as weights based on functional information  for variant j and jq is the overall MAF for the variant. This model places greater emphasis on rare alleles, which are a priori believed to be more likely to have larger effect sizes  of p was compared to M. The multiple-test corrected p-value for the window corresponding to the element p1 is the proportion of elements of Mmin that are smaller than p1. The first row of M was then removed and p2 was compared to the column minimums of the smaller M to achieve the step-down correction, which is less conservative than a Bonferroni correction. To preserve monotonicity of p-values, the multiple-test corrected p-value for pj, j > 1 was calculated as For sliding-windows of a given size (number of variants), multiple-test correction was performed using a step-down permutation-based approach  = Πj cjORij, where ijOR is the odds ratio of the variants carried by individual i for variant j and jc is a constant of proportionality. For each region and genetic model, jc was chosen to produce a population prevalence of 10%. To test the sensitivity of DMAF and other methods of rare variant analysis, we sampled 100 sets of 200 cases and 200 controls from each simulated data set to mimic a small but realistic sample size for sequencing studies , denoted as C-alphaall or C-alpharare. All other methods, except Variable Threshold (VT), were applied to variants with MAF ≤ 0.05. KBAC was applied using software obtained from the authors; VT was applied using software obtainedWe compared DMAF to eight other rare variant association testing methods Table . Both DM2, and CMC also pool information across subjects. In contrast, the other methods examined pool information across variants.The nine rare variant association testing approaches differed in the dimension across which information is pooled. For example, DMAF computes the frequency difference for each variant; thus information from all subjects is pooled into a single piece of information for the variant. In addition to DMAF, the methods C-alpha, Hotelling’s TUsing the sequence data from simulation study I, we simulated two sets of phenotypes with causal variants clustered in a sub-region of regions 1, 2, and 3. In both models, the set of rare variants (MAF ≤ 0.05) was subdivided into thirds based on position. The first and last third of rare variants and all common variants were neutral. The middle third of rare variants were all risk variants (model G) or half risk, half protective (model H). The effect sizes for risk variants were OR = 1.7 for variants with MAF > 0.01, OR = 2.0 for 0.001 ≤ MAF ≤ 0.01, and OR = 2.2 for MAF < 0.001. We analyzed 1000 simulated data sets based on models G and H for regions 1, 2, and 3 using window sizes ranging from 10 SNVs to the entire region, in increments of 10 SNVs. For the longest window sizes, fewer than 1000 simulations were analyzed since not all simulations included more than 110 polymorphic variants. Window sizes that were analyzed for 700 or more simulations were included in the power calculations.abs was used for the analysis since it outperformed DMAFsq for a majority of the scenarios in simulation study I when rare and common variants were analyzed together. The window position was shifted in increments of 5 SNVs or 10% of the window length, whichever was greater. In addition to the analysis of models G and H, we analyzed 1000 simulations based on a null model for each region and window size to check that type I error was controlled.While models G and H included effects at rare variants only, both rare and common variants were analyzed together to reflect realistic circumstances under which the MAF threshold for causal “rare” variants is unknown. DMAFp-value for any window was less than 0.05. In addition to assessing power, we were interested in the effectiveness of sliding windows for localizing the causal sub-region. For each simulation and window size, we determined whether the window (or set of windows) with the most significant p-value overlapped the causal sub-region by at least half the length of the window or set (measured by the number of markers).An analysis for a given simulation and window size was considered to have detected an association if the multiple-test corrected FKBP5 as a candidate gene for association with gemcitabine resistance  between FKBP5 and gemcitabine sensitivity . The methods aSum, KBAC, RVT1, and WSS were unable to detect a significant association even when common variants were included in the analysis.When rare variants alone were analyzed, no method found a significant association , gives our method flexibility to adapt to a wide range of traits. DMAF demonstrates improved power compared to many widely used methods in the presence of both risk and protective variants. Its sliding-window implementation can increase power to detect an association due to a causal sub-region relative to whole-region analysis, and can localize associations within a gene or region. Both implementations of DMAF are available as an R package2, C-alpha) had the greatest power. We also found that aSum, a method designed to accommodate protective variants but which pools information from variants, had weaker power on simulations with protective variants. Taken together, these results suggest that pooling data from individuals improves power for analysis of risk and protective rare variants. This indicates that sequencing pooled DNA could be used as a cost-saving measure in association studies without loss of power due to a combination of risk and protective variants.On simulations with both risk and protective variants, rare variant analysis methods which pooled data from individuals  between the causal sub-region and the rest of the region. This reduced correlation results in a lower signal-to-noise ratio (compared to region 1) when non-causal variants are included in the analysis. The fact that a wide range of window sizes in the sliding-window analysis performed better than the whole-region analysis demonstrates that the sliding-window approach is a robust, powerful alternative for region-based rare variant analysis.FKBP5 for gemcitabine response, the strongest association was p = 0.019, which was more significant than the whole-gene association (p = 0.049); however, multiple tests (window sizes) were required to achieve this. Due to the robustness of results to the window size that was demonstrated in our simulations and real data analysis, in the future it would be possible to perform a sliding-window analysis using a single window size. This could result in increased power, without the need for additional multiple-test correction. Sliding-window analyses also allow localization of region-based association signals, which will be valuable for understanding the functional regions responsible for identified associations.In the sliding-window analysis of de novo mutations, then a region-based analysis method such as DMAF would be necessary to detect the variants’ combined effect on a trait influenced by the protein. In candidate pathway studies, multiple genes are grouped to detect their combined effect on a trait. If each gene in the pathway contributes a few rare variants of moderate effect, then the combined whole-region analysis would include dozens or hundreds of causal variants, as simulated here.To highlight the usefulness of region-based association methods such as DMAF, our simulation studies involved large numbers of causal variants which explain a modest proportion of the trait variance. This is a realistic model for sequencing studies of candidate genes or pathways. In a candidate gene study, many non-synonymous changes to the gene could affect the shape of the protein encoded by the gene, and many synonymous variants could each have a small impact on the protein’s translation rate. However, if these variants are rare SNVs, or even The results of our simulation studies Table  indicateThe dichotomization of gemcitabine response based on upper and lower 50% of IC50 values is somewhat artificial, as it results in assigning distinct phenotypes to individuals with similar intermediate responses. DMAF, like many methods for rare variant analysis, is currently applicable only to binary traits. In the future, it would be beneficial to extend DMAF to quantitative traits. It would also be worthwhile to explore the possibility of determining window size based on number of base pairs or extent of LD, rather than number of SNVs. Finally, it would be valuable to explore other variant-weighting schemes, such as a positional weighting scheme within each sliding window.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Complex disorders are a class of diseases whose phenotypic variance is caused by the interplay of multiple genetic and environmental factors. Analyzing the complexity underlying the genetic architecture of such traits may help develop more efficient diagnostic tests and therapeutic protocols. Despite the continuous advances in revealing the genetic basis of many of complex diseases using genome-wide association studies (GWAS), a major proportion of their genetic variance has remained unexplained, in part because GWAS are unable to reliably detect small individual risk contributions and to capture the underlying genetic heterogeneity. In this paper we describe a hypothesis-based method to analyze the association between multiple genetic factors and a complex phenotype. Starting from sets of markers selected based on preexisting biomedical knowledge, our method generates multi-marker models relevant to the biological process underlying a complex trait for which genotype data is available. We tested the applicability of our method using the WTCCC case-control dataset. Analyzing a number of biological pathways, the method was able to identify several immune system related multi-SNP models significantly associated with Rheumatoid Arthritis (RA) and Crohn’s disease (CD). RA-associated multi-SNP models were also replicated in an independent case-control dataset. The method we present provides a framework for capturing joint contributions of genetic factors to complex traits. In contrast to hypothesis-free approaches, its results can be given a direct biological interpretation. The replicated multi-SNP models generated by our analysis may serve as a predictor to estimate the risk of RA development in individuals of Caucasian ancestry. The study of genotype-phenotype relationship in complex disorders represents a great challenge in the field of translational genetics, due to their importance from a public health perspective and to the difficulties involved in their analysis at the genetic level Genome-Wide Association Studies (GWAS), a powerful method for the large scale analysis of genotype-phenotype relationships To start, most of the susceptibility loci so far discovered by GWAS are of small predisposing risk p-value for a gene by combining the p-values obtained from the association tests on all the individual SNPs belonging to that gene. Gene-level p-values, in turn, were employed to define a pathway-level p-value to investigate pathway-trait associations. However, despite the fact that the limitations of classical GWAS in the context of complex diseases are increasingly being recognized and that pathway-based association studies are receiving growing attention, there is still no optimal approach able to overcome the above described challenges and provide a comprehensive interpretation of genome-scale data.A further weakness of current analytical methods is that they analyze genome-scale datasets without necessarily taking the existing biological knowledge about the trait of interest into account. It has been suggested that using prior knowledge can help reduce the dimensionality of large scale datasets, and may guide the process of extracting biologically meaningful results in a more effective manner hypothesis-based analysis method that combines a non-deterministic computational approach to the analysis of large-scale genotype datasets with pre-existing biological and biomedical knowledge in order to increase our understanding of the genetic basis of complex disorders. In the following sections we provide a detailed description of our method, called KBAS (Knowledge-Based Association Study), and we present its application to large-scale genotyping datasets for Rheumatoid Arthritis (RA) and Crohn's disease (CD). We will use these examples to show how our method can be used to compare alternative hypotheses about the disease of interest which in turn can lead to new insights into the genetic structure of the complex disease under consideration. We also present the results of a replication study, in which we validated the results obtained on RA through a different independent dataset.The work presented here focuses on developing an innovative Since complex disorders are widespread and important from the public health perspective, dissecting their genetic architecture and reconstructing the integrated networks of factors underlying their pathogenesis may help develop more specific and sensitive screening and diagnostic tests and more efficient therapeutic targets hypothesis-based approach that performs a holistic analysis of genome-wide association data. models, consisting of sets of markers corresponding to the hypothesis under consideration. The models are then tested and refined on the basis of their ability to accurately classifying subjects as affected or not affected on the basis of their genotypes.We propose a encoding scheme that converts the genotypes of the markers under consideration to numerical values. Each marker is then given a weight that quantifies its contribution to the overall genotype-phenotype association. The combination of a set of markers and their corresponding weights represents a model. The genotype values corresponding to each marker in the model, along with their respective weights, are combined according to an appropriate mathematical formula, producing a score variable for each subject, and the distributions of scores for the subjects in the case and control groups are then compared to evaluate the model’s classification ability. The idea at the base of our method is that, if the set of markers included in the model is relevant to the phenotype, their joint signal, obtained by combining their individual association signals into an overall variable, will be able to accurately classify cases and controls. The optimal combination of SNPs and their corresponding weights leading to a model with maximized classification ability is determined through an iterative adjustment procedure based on Genetic Algorithms (GA) which generates, tests and refines different models relevant to the hypothesis under investigation. A detailed explanation of the steps employed by KBAS method is provided in the following sections.To start, we define an The KBAS method we propose is aimed at verifying or disproving a hypothesis put forth by the user. In this context, the hypothesis is the statement that a particular set of genes contributes to the trait under investigation. The set of genes to be included in a hypothesis will in general be determined by the investigator on the basis of existing biological knowledge. Biochemical and regulatory pathways, gene ontology classes, gene expression databases, protein-protein interactions databases, and biomedical literature are some examples of sources of information that can be used to generate relevant hypotheses Once our hypothesis is formulated, the method tests whether a subset of genetic markers related to the specified set of genes is able to precisely separate cases from controls, when converted into a single variable through an appropriate mathematical combination of their genotype values. In the following sections we will assume that the markers under consideration are SNPs, and therefore only exhibit two alleles, but the method can be applied to any kind of polymorphic marker, given a way of encoding its genotypes into numerical values. In a typical scenario, an investigator may wish to determine which of the two different sets of genes is more likely to be involved in a disease of interest. This question can be answered by creating two competing hypotheses, each producing a set of SNPs belonging to the two gene sets, and evaluating them on the basis of their power to discriminate cases from controls.fitness function over the potential solutions of the problem under consideration KBAS uses a Genetic Algorithm to adjust the weights of the SNPs composing a model, in order to maximize the model’s ability to accurately classify subjects into the case and control groups on the basis of the scores they receive. A Genetic Algorithm is a heuristic search algorithm able to efficiently explore very large and complex parameter spaces, in order to maximize a organisms) to the problem under consideration; each of which contains an encoded representation  of the set of parameters describing the solution. Solutions are then evaluated according to the specified fitness function, and are optimized through a simulated process of evolution using operators borrowed from evolutionary biology such as mutation, crossover and selection A GA receives a number of randomly generated potential solutions , according to the following formula inspired by the definition of Bayes factor i is the score for individual i, Gi is the genotype of individual i for the set of SNPs included in the model, and State1 and State2 are the two phenotype states being compared to each other, i.e. case vs. control.The definition of the fitness function is a critical aspect in the use of a GA. In our application the fitness of a model is a measure of the model’s ability to discriminate cases and controls, which in turn is calculated on the basis of the set of scores assigned by the corresponding model to the subjects in the case and in the control groups. The score corresponding to a particular model is defined, for each subject, as the logarithm of ratio of the conditional probabilities of the subject’s genotype under the two phenotype states of interest  with causal variants in neighboring regions.If the successful model shows a fitness p-value of its permutation test is also significant, it is considered replicated.Like in any association study, the significant findings should be further validated in an independent case-control dataset to prove their replicability. In the replication step, a score variable is generated and tested in the replication dataset using the same model that was generated and tested in the discovery dataset. If a model successfully discriminates cases from controls in the replication dataset and the vs. healthy) as the response variable. In addition, to investigate potential interactions among the successful models under consideration, all their pairwise interaction terms are included as predictor variables as well, and a stepwise selection procedure was applied to only retain the statistically significant variables.To evaluate how the disease-associated successful models produced by the GA affect the risk of developing the disease under consideration, a multiple logistic regression model is fitted using the scores produced by these models as the independent variables, and the disease state . In addition, we tested the applicability of the KBAS method to other diseases like Crohn’s disease (CD) and type I diabetes (T1D). In particular, the results related to CD will be described in this manuscript. The tests were performed using genotype data provided by the Wellcome Trust Case-Control Consortium (WTCCC) vs. NBS) can be tested in two more comparisons, one between the case group and the other control group (e.g RA vs. 58C), and the other one between the two control groups (58C vs. NBS). This increases the robustness of the inferred associations and reduces the risk of overfitting, because the successful model should be able to separate the case group from the second control group, and should not be able to separate the two control groups from each other. This in turn shows that results are reproducible and provides evidence that the GA is not simply learning to classify different groups of subjects or finding models consisting of chance aggregations of SNPs due to small differences between the groups unrelated to the disease , but produces results that are directly related to the disease of interest.Using two control groups provides the advantage that the successful model produced by the comparison of the case group against one of the controls  Due to the suggested auto immune nature of the rheumatoid arthritis and Crohn’s disease, we focused on fourteen pathways related to different aspects of the human immune system as test-set pathways. Moreover, we selected ten other pathways involved in processes unrelated to the immune system, and therefore are likely to be irrelevant to the pathogenesis of RA and CD, to serve as negative controls in our analysis. For each pathway, we selected all validated SNPs found within the transcripts encoded by the genes belonging to it, extending up to 3,000 bp upstream and downstream. We then filtered this set of SNPs to retain only those that were genotyped in the WTCCC study. To further reduce the number of selected SNPs, the investigator has the option to choose a subset of “representative” SNPs from each transcript (e.g. only one SNP), on the basis of a prioritizing rule that preferentially selects non-synonymous coding SNPs, followed by promoter SNPs, exon-intron junction SNPs, synonymous coding SNPs, other exonic SNPs, and intronic SNPs. Finally, to test if the association detected for RA-associated pathways can be generalized to other cohorts, we tested the significance of the corresponding successful models in an independent case-control dataset of white Americans (NARAC) http://genome.ufl.edu/rivalab/KBAS/as a 64bit GNU/Linux command-line executable. The program allows users to specify the input genotype datasets (case and control groups), and the GA parameters such as number of organisms, number of generations, weights encoding scheme, etc. It also provides users with an interface to the Genephony system p-value on the output file. All results described in the remainder of this paper were generated using the KBAS software.The KBAS method described here was implemented in a freely available software package, that can be downloaded at For each of the twenty four initial sets of SNPs derived from the pathways listed in p-values associated with the fitness of each successful model on the basis of the pairwise comparisons between the case group and the two control groups (i.e. RA vs. 58C and RA vs. NBS). Note that the significance level was adjusted to 6.944×10−9 according to Bonferroni’s correction, given the number of artificial chromosomes (n = 200), simulated generations (n = 500), investigated pathways (n = 24) and pair-wise population comparisons (n = 3). To validate the significance of theses fitness values, we assessed the goodness-of-fit of each model using permutation testing performed over 100,000 rounds. Given the total number of pair-wise comparisons (n = 48), we used a corrected significance threshold of 0.00104 according to Bonferroni’s correction. A randomization test p-value between 0.05 and 0.00104 was considered borderline. A model was considered significant if in both RA vs. 58C and RA vs. NBS comparisons had significant p-values, and was considered non-significant if resulted in non-significant p-values in at least one of the two comparisons. In all other situations, it was considered borderline. The p-values obtained from permutation tests are also shown in p-values.sons n = . To valiFc epsilon RI signaling, Fc gamma R-mediated phagocytosis, regulation of autophagy and T-cell receptor signaling pathways, KBAS was able to identify a model that classifies cases and controls with a highly significant p-value, ranging from 2.55×10−9 to 1.19×10−23 for the RA vs. 58C comparisons and from 1.23×10−9 to 1.64×10−22 for the RA vs. NBS comparisons. By contrast, the successful models were unable to separate the NBS and 58C groups, and the p-values of the comparisons were always non-significant  and a borderline p-value for RA vs. NBS comparison (p<3.36×10−3), the p-values resulting from permutation testing of the model from the second pathway were borderline for RA vs. 58C comparison (p<2.63×10−3) and significant for RA vs. NBS comparison (p<08.5×10−4) respectively.Despite the high fitness values of the models obtained from the cT-cell receptor signaling pathway yielded statistically borderline fitness values when comparing RA against 58C and NBS (p<5.83×10−8 and p<8.03×10−8 respectively). Once again the comparison between the two control groups had a non-significant p-value. In permutation testing, the original case-control p-values appeared to be of borderline statistical significance for both the RA vs. 58C comparison (p<1.11×10−3) and the RA vs. NBS comparison (p<1.61×10−3). We suggest the model derived from this pathway may also be in moderate association with RA.The successful model from the Fc epsilon RI signaling, Fc gamma R-mediated phagocytosis and regulation of autophagy pathways are not considered to be in association with RA because they did not produce significant fitness p-values and the p-values resulting from the corresponding permutation tests were non-significant as well.Finally, the successful models derived from the p-value. In addition, the results of all permutation tests were non-significant   see . In threOverall, these results indicate that the final models generated by KBAS are not just simple classifiers capable of learning the differences between two arbitrary groups of individuals. Instead, their classification power is a function of the biological relevance of criterion used to select the initial sets of SNPs: SNP sets derived form pathways that are more biologically relevant to the trait of interest will lead to more accurate and powerful models. This feature is specially important when one aims to test and rank alternative hypotheses about the trait under consideration.Fc gamma R-mediated phagocytosis pathway were statistically associated to rheumatoid arthritis .Out of 72 total SNPs in these 12 models, two of them lie within the MHC region on 6p21  which is a known hot spot for several autoimmune disorders. None of the other SNPs present in the successful models or the genes to which these SNPs belong is among RA-associated loci in previously published genome-wide association studies. There is also no evidence of linkage-disequilibrium between theses SNPs and other RA-associated SNPs according to the HapMap LD data. This indicates that the results generated by KBAS are not simply a rediscovery of strongly associated individual SNPs. Instead, our method is able to elucidate the joint contribution of previously unknown sets of SNPs to the genetic architecture of rheumatoid arthritis.As seen in vs. CTR using each of these twelve models, along with their pairwise interaction terms (66 terms).To evaluate the impact of the twelve successful models previously concluded to be in association with RA on the risk of being affected by the disease, and to investigate potential interactions among them, a multiple logistic regression model was fitted by regressing the disease state on the score variables produced by comparing RA Antigen processing and presentation and Phagosome pathways. Moreover, the interaction terms of the interaction between the cytokine-cytokine receptor interaction and leukocyte trans-endothelial migration pathways and between the cytokine-cytokine receptor interaction and T-cell receptor signaling pathways were also kept in the fitted regression model.The multivariate model obtained from the stepwise selection procedure contained the score variables related to all twelve pathways except for those related to the p-values smaller than 10−4, and the covariates of the included terms were statistically significant with p-values smaller than 0.0028. All covariates were positively correlated with the disease susceptibility with odds ratios between 1.652 and 2.859, except for the two aforementioned interaction terms which were negatively correlated with odds ratios of 0.266 and 0.182 respectively. The c-statistics for the model was 0.687 and the p-value of Hosmer-Lemeshow test for the fitted model was non-significant (p>0.05), indicating model’s goodness-of-fit. The fitted regression model had overall model p-value was determined and used as the replication criteria. The significance thresholds for interpreting the results were the same as used for the RA vs. CTR analysis.To test if the detected significant association between the twelve immune system related pathways and RA can be generalized to other cohorts, the scores related to each of theses successful models were calculated in the NARAC dataset, and their distributions were compared between case (NARAC-A) and control (NARAC-C) groups. After performing 100,000 rounds of permutation testing over each of the models, the significance of the primary fitness p-values ranging from 5.85×10−15 to 7.17×10−25 and permutation test p-values less than 10−5. In addition, three models derived from chemokine signaling, leukocyte trans-endothelial migration and natural killer cell mediated cytotoxicity pathways resulted in permutation test p-values of 0.03463, 0.0031 and 0.00793 respectively, and therefore can be considered replicated at the significance level of 0.05. None of the models derived from the remaining 16 pathways gave rise to a significant p-value in the permutation tests. Due to the different genotyping platforms, a number of SNPs present in the successful models were replaced by new ones to conduct the replication study, as explained in Method Evaluation section. As seen in The disease state was also regressed on the overall score variable computed based on the all 44 SNPs present in the replicated models, to evaluate the applicability of this single score variable in predicting the disease risk. Further details are provided in Results S1 and vs. CTR, this risk ranges from around 18% when the score class is lowest to around 75% when the score class is highest. For model related to the NARAC-A vs. NARAC-C comparison’s model, the disease risk rises from around 2% for the lowest score class to around 75% for the highest score class. This indicates that the scores obtained from the total set of these 44 SNPs can be used as a predictor to estimate the probability by which an individual may develop the disease.To illustrate how an increase in the value of the overall score variable influences the risk of disease development, the range of values corresponding to each overall score variable was discretized into 12 bins, and for each bin the posterior probability of being affected was calculated. As shown in vs. CTR) on the overall score variable derived from the entire set of 57 SNPs present in the nine CD-associated models. Disease risk-Score class diagram for the CD vs. CTR comparison.The applicability of the KBAS method to other diseases was tested in Crohn’s disease (CD) using the same set of 24 pathways used for RA analysis. Detailed results are provided in Results S2. As seen in The method we presented in this paper provides a framework for extending genome-wide association studies to situations in which a phenotype is caused by a number of concurrent genetic factors. Its main purpose is to measure how well a multi-SNP model is able to classify case and control subjects for which genotype data are available. Biologically, multi-SNP models may implicate cases in which functional relationships exist among genetic factors of interest. These relationships might be for instance in the form of interaction among functionally redundant elements or physically interacting biomolecules, or of the concurrent occurrence of two or more hypomorphic mutations in different steps of a particular pathway AND B] OR [A AND C] OR [B and C]. However, since the main effect of each individual locus is small, subjects harboring single mutations do not develop the phenotype. Defining a score variable results in integrating small association signals arising from individual risk loci into an overall association signal capturing the joint effects of contributing loci. Moreover, since the score variable is computed independently on each subject, different combinations of loci can contribute to the same score variable distribution in parallel to each other, leading to a more accurate representation of the differences of case and control groups.Multi-SNP models that define a score variable over loci they contain are able to take into account the joint effects of loci individually conferring small risks to the phenotype under investigation, and the different combinations of trait influencing loci which is of considerable importance in capturing the genetic heterogeneity underlying a complex trait. For example we can imagine a case in which a hypothetical phenotype is produced by concurrent mutations in any two out of three loci involved in a particular pathway . Therefore, subjects having mutations in loci A and B show the same phenotype as subjects having mutations in loci A and C or loci B and C. This can be formally described using the following logical statement: [A Since KBAS employs a Genetic Algorithm-based search engine, it enjoys high flexibility and efficiency in searching through an extremely large solution space. On the other hand, like with any other method relying on heuristic search algorithms, this does not ensure that the successful models are the absolute best ones. Our method is instead meant to be used in a hypothesis-based fashion: its purpose is not to discover the “best” set of markers that explains a phenotype; something that is computationally unfeasible since it would require testing all possible combinations of a given number of markers; but to confirm or invalidate the hypothesis that a user-provided set of markers is associated with the phenotype. The method does not require or stipulate a specific way of selecting markers: if the provided set does not contain a sufficient number of “relevant” ones, the algorithm will simply fail to find an appropriate combination of markers, and will report that the corresponding hypothesis is not supported by the available data.This is clearly observed using the two sets of pathways we selected for this study, the first one containing pathways known to be relevant to the immune system, and the second one containing pathways unrelated to the immune system, used as negative controls. For instance, while on the first set of pathways KBAS was able to produce multiple replicated RA-associated models with remarkable classifying efficacy, none of the pathways in the second set gave rise to a successful model capable of significantly separating cases from controls see , 3 and 4vs. CTR . KBAS will then use the score variable obtained by combining these values to classify study subjects as affected or unaffected.Table S1The number of genotyped and validated SNPs in each functional role class for the test and control pathways analyzed in this study.(DOC)Click here for additional data file.Table S2The list of SNPs included in the successful models showing strong or moderate association with rheumatoid arthritis. SNP positions refer to version GRCh37 of the human reference sequence.(DOC)Click here for additional data file.Table S3The list of SNPs from NARAC study replacing the SNPs from WTCCC study for replication of the results.(DOC)Click here for additional data file.Table S4Simple regression of disease-state on the overall score variable derived from the entire set of 44 SNPs present in the replicated RA-associated models (comparing RA vs. CTR).(DOC)Click here for additional data file.Table S5Simple regression of disease-state on the overall score variable derived from the entire set of 44 SNPs present in the replicated RA-associated models (comparing NARAC-A vs. NARAC-C).(DOC)Click here for additional data file.Table S6The p-values associated with the pairwise comparisons of the CD group and the two control groups using successful models derived from immune system related pathways. The fitness p-values measure the fitness of each successful model retrieved by Genetic Algorithm engine. They are calculated by comparing original case and control datasets using corresponding successful models. Randomization-test p-values measure the significance of fitness p-values of their corresponding successful model by comparing permuted case and control datasets. According to Bonferroni’s correction, a fitness p-value <6.944×10−9 and a randomization test p-value <0.00104 were considered significant. The p-values of the models showing strong or moderate association with Crohn’s disease are in bold.(DOC)Click here for additional data file.Table S7The p-values associated with the pairwise comparisons of the CD group and the two control groups using the successful models derived from negative control pathways.(DOC)Click here for additional data file.Table S8The p-values associated with the comparisons of the CD and CTR groups using successful models derived from pathways under consideration. According to Bonferroni’s correction, a fitness p-value <6.944×10−9 and a randomization test p-value <0.00208 were considered significant. The p -values of models showing significant association with Crohn’s disease are in bold.(DOC)Click here for additional data file.Table S9The list of SNPs included in the successful models showing association with Crohn’s disease. SNP positions refer to version GRCh37 of the human reference sequence.(DOC)Click here for additional data file.Table S10Multivariate regression of disease-state on the score variables derived from the successful models showing association with Crohn’s disease (comparing CD vs. CTR).(DOC)Click here for additional data file.Table S11Simple regression of disease-state on the overall score variable derived from the entire set of 57 SNPs present in the CD-associated models (comparing CD vs. CTR).(DOC)Click here for additional data file.Table S12Comparative summary of pathway associations with rheumatoid arthritis and Crohn’s disease. (+) indicates that the successful model retrieved from the pathway is in strong association with the disease in the corresponding comparison, (−) indicates that the successful model retrieved from the pathway is not associated with the disease in the corresponding comparison, and (+/−) indicates that the successful model retrieved from the pathway is in borderline association with the disease in the corresponding comparison.(DOC)Click here for additional data file.Methods S1Description of the method used to perform logistic regression analysis and to illustrate Disease risk-Score class diagram.(PDF)Click here for additional data file.Results S1Description of additional results regarding the analysis of rheumatoid arthritis (RA) dataset.(PDF)Click here for additional data file.Results S2Description of the results regarding the analysis of Crohn’s disease (CD) dataset.(PDF)Click here for additional data file.