Peripheral nerve sheath tumors (PNSTs) are frequently found in Danish cattle at slaughter. Bovine PNSTs share several gross and histopathological characteristics with the PNSTs in humans with heritable neurofibromatosis syndromes. The aim of the present study was to investigate a possible hereditary disposition to PNSTs in dairy cattle by statistical analysis performed on data from 567 cattle with PNSTs. Furthermore, a preliminary genome-wide association study (GWAS) was performed on DNA isolated from 28 affected and 28 non-affected Holstein cows to identify loci in the bovine genome involved in the development of PNSTs.PNSTs were significantly more common in the Danish Holstein breed than in other breeds with 0.49% of Danish Holsteins slaughtered during an eight-year-period having PNSTs. PNSTs also occurred significantly more frequently in the offspring of some specific Holstein sires. Examination of three generation pedigrees showed that these sires were genetically related through a widely used US Holstein sire. The PNSTs included in GWAS were histologically classified as neurofibroma-schwannoma (43%), schwannoma (36%) and neurofibroma (21%) and derived from Holstein cows with multiple PNSTs. A single SNP on chromosome 27 reached genome-wide significance.Gross and histological characteristics of bovine PNSTs are comparable to PNSTs in humans (schwannomatosis). Danish Holsteins are genetically disposed to develop PNSTs but the examined materials are insufficient to allow determination of the mode of inheritance. SMARCB1 is involved in the pathogenesis [Several abattoir surveys of neoplasms in cattle have shown that bovine peripheral nerve sheath tumors (PNSTs) are among the three most common neoplasms in cattle -5. Bovinogenesis .A disorder resembling NF1 has been described in four Holstein cows from the same herd . The cowpost mortem inspection. Moreover, a preliminary genome wide association study (GWAS) on 28 cows with confirmed PNSTs and 28 cows with no pathological evidence of PNSTs was performed to identify loci in the bovine genome involved in the pathogenesis of PNSTs.The aim of the present study was to investigate a possible hereditary disposition to PNSTs in cattle. Therefore we performed statistical analyses on data from 567 slaughtered dairy cattle diagnosed with PNSTs at post mortem inspection. At the abattoir, specimens of neoplastic tissue from each animal were fixed in 10% neutral buffered formalin. In addition, samples from the spleen and PNSTs were stored at – 20°C. Spleen samples of 28 unaffected Holstein cows aged ≥ 9 years were also frozen and used as controls in the genetic analyses. Carcasses with PNSTs underwent deboning to disclose all neoplasms, and the ear tag number of the animal and the location of the PNSTs were recorded.The tissue specimens for microscopical examination and genetic analysis derived from 28 slaughtered Holstein cows diagnosed with PNSTs at the 2O2 in TBS (pH 7.6) for 15 min at room temperature and with Ultra V block  for 5 min at room temperature, respectively. The slides were incubated for 24 h at 4°C with primary antibodies to CNPase  diluted 1:800; S100  diluted 1:5000; and NF  diluted 1:6000. The detection system Ultra Vision ONE, HRP polymer was applied in accordance with the manufacturer’s instructions (Lab Vision Thermo Fisher Scientific). The chromogen was 3-amino-9-ethylcarbazoloe (AEC-red) (Lab Vision Thermo Fisher Scientific), and the sections were counterstained with Mayer’s hematoxylin. Slides were given two 5 min washes in TBS at pH 7.6 before addition of each reagent. Normal bovine peripheral nerve tissue was used as positive controls. Negative controls with the primary antibody replaced by 1% bovine serum albumin in TBS, 5% normal swine serum in TBS, or with a nonsense monoclonal (matching isotype) or polyclonal antibody of the same concentration as the primary antibody were run in parallel.The formalin fixed specimens were processed conventionally and embedded in paraffin. From each sample, 2–3 μm sections were cut and stained with hematoxylin and eosin (HE) for histological assessment. For immunohistochemistry, sections were mounted on adhesive-coated slides , processed through xylene, and rehydrated in ethanol. Antigen retrieval was done by boiling in a microwave oven (700 W) twice for 5 min in Tris-EDTA buffer , pH 9 (S100 and NF); or 0.01 M citrate buffer, pH 6 (CNPase). Endogenous peroxidase and unspecific protein binding were blocked with 0.6% (v/v) Hmodel PNST = age sire, and model PNST = age grand-sire , where ‘age’, ‘sire’ and ‘grand-sire’ were defined as class variables. Additionally, a model including the production traits milk yield and weight at slaughter was applied.In the period 2003–2010, the unique ear tag number of all cattle diagnosed with PNSTs at the Danish Crown slaughterhouse in Tønder, Denmark was registered. A total of 669 animals were registered as having PNSTs, and the following data were obtained from the Danish Cattle Database on all animals: age, sex, breed, herd location at birth, herd location immediately before slaughter, sire, paternal and maternal grandsires, date of latest calving, number of lactations, details of milk production  during the preceding 305 days, and weight of carcass. Data on cattle with PNSTs were compared to data on all cattle slaughtered at the abattoir in 2003–2010 . The statistical analyses were restricted to animals aged 5–12 years being of the Holstein, Red Danish Dairy and Jersey breeds . However, all breeds were included in the statistical analysis of the effect of sex. When analyzing the effect of sire, the analyses were limited to Holsteins, due to the low occurrence of PNSTs in the other breeds, and the dataset was reduced to sires with more than five affected offspring aged 5–12 years. Furthermore, the age of the offspring was included in the model as a significant difference could be due to the longer life expectance of the offspring of some bulls in comparison with other bulls. Data were analyzed by the Chi-square test, Fisher’s exact test, or the General Linear Model procedure . The GLM procedure was used applying the SAS model statements were P = 0.05) were included in subsequent analysis. All samples had less than 10% missing genotype calls. The threshold for genome-wide significance was set by a permutation test using 100,000 permutations. Multidimensional scaling (MDS) analysis was carried out using PLINK [Genomic DNA from 28 cases and 28 controls was isolated from the spleen using the salting out procedure  with modng PLINK  and usedThe 28 Holstein cows included in the genetic analysis all presented with multiple PNSTs that were confined to the brachial nerve plexus 21), intercostal nerves (21)  during 2003–2010. Of these, 562 were Danish Holsteins and five were Red Danish Dairy cattle. The remaining cases were either beef cattle or crossbreds, while no cases were recorded in Jersey cattle. The statistical analyses were restricted to the Holstein and Red Danish Dairy breeds (n = 567) when relevant.2 = 223.62, df = 2, P < 0.0001).The animals surveyed included the three most common Danish dairy breeds: 115,248 Holsteins, of which 0.49% had PNSTs; 10,045 Red Danish Dairy, of which 0.05% had PNSTs; and 19,139 Jersey, of which none were affected. Thus, PNSTs were significantly more prevalent in the Holstein breed than in the other breeds . Figure The mean age at slaughter of cattle with PNSTs was 8.69 years SD = 2.08) and was significantly higher in affected than non-affected cattle (χ.08 and wP = 0.7297).PNSTs were almost exclusively seen in females (99.7% of the cases), but this was probably caused by culling of males before PNSTs were macroscopically detectable or even before the usual age of tumor development. In cattle aged 5–12 years, there was no significant effect of sex . By comparing the least squares means, four Holstein bulls appeared to have a higher prevalence of affected offspring than others. The prevalence of affected offspring for these four bulls was between 0.52% and 2.30% of the offspring slaughtered at the age of 5–12 years during the study period. Examination of three generation pedigrees showed that three of the four bulls were genetically related though a widely used US Holstein sire in generation three. In addition, a statistically significant effect of maternal grandsire was seen  as five bulls had a relative higher prevalence of affected offspring than others (1.10%-2.67% of the offspring slaughtered at the age 5–12 years). Three of these also had the widely used US Holstein sire in their pedigree in generations 1–3.A statistically significant higher number of affected offspring of some sires was observed even after correction for age . The genomic inflation factor was 1.18, hence genomic correction (GC) was applied.P-values was performed in PLINK using the options ‘--model’ and ‘--fisher’. Four SNPs were identified with point wise P-values (EMP1) of 0.000999 (Table GC) and after correcting initial raw P-values for multiple hypotheses testing by permutation (EMP2). EMP1GC = 7.88 × 10−6; EMPBonferroni = 0.049; EMP2 = 0.02298; Benjamini Hochberg False Discovery Rate (FDRBH) = 0.049. The neighboring SNP (ARS-BFGL-NGS-65900) also stands out compared to other SNPs on chromosome 27 but did not reach genome wide significance level  . In compAnalysis of pedigree data in the present study failed to show a clear Mendelian inheritance of PNSTs. However, a statistical significant effect of sires and maternal grandsires was found. Phenotypic information on PNST in the grandsires was not available. Some of the sires were rather closely related through a common ancestor, but this may simply be by chance, as some breeding lines are very frequently represented in the Holstein breed worldwide. As the incidence of PNSTs increases with age, it is possible that some of the animals included in the statistical analyses would have developed PNSTs if allowed to live longer. Thus, a Mendelian inheritance might have been identified if all the animals had been slaughtered at the age of 12 years.The GWAS identified a single SNP at chromosome 27 associated with PNST. Additionally, this SNP and the neighboring SNPs were the only two SNPs in the study that stood out from the rest. The test for association to every other SNPs had a p-value close to 1. The result, however, still has to be interpreted with caution as a GWAS with so few animals has very low power. Hence, the association reported here can only be taken as an indication on the presence of a genetic locus on chromosome 27 affecting PNST in Holstein dairy cattle and must be followed up by more powerful studies.Bovine PNSTs morphologically resemble schwannomatosis in humans. Danish Holstein cattle have a significantly higher prevalence of PNSTs than the other Danish dairy breeds as well as there were significant effect of sire and grand sire on the prevalence in the Holstein breed thus indicating a hereditary disposition. However, more animals need to be examined in order to determine the mode of inheritance and the involvement of specific loci or genes in the pathogenesis of bovine PNSTs.


Canalization is defined as the stability of a genotype against minor variations in both environment and genetics. Genetic variation in degree of canalization causes heterogeneity of within-family variance. The aims of this study are twofold: (1) quantify genetic heterogeneity of (within-family) residual variance in Atlantic salmon and (2) test whether the observed heterogeneity of (within-family) residual variance can be explained by simple scaling effects.2, implying that the within-family variance of the most extreme high families is expected to be approximately three times larger than the extreme low families. For cross-sectional data, DHGLM with an animal mean sub-model resulted in severe bias, while a corresponding sire-dam model was appropriate. Heterogeneity of variance was not sensitive to Box-Cox transformations of phenotypes, which implies that heterogeneity of variance exists beyond what would be expected from simple scaling effects.Analysis of body weight in Atlantic salmon using a double hierarchical generalized linear model (DHGLM) revealed substantial heterogeneity of within-family variance. The 95% prediction interval for within-family variance ranged from ~0.4 to 1.2 kgSubstantial heterogeneity of within-family variance was found for body weight in Atlantic salmon. A tendency towards higher variance with higher means  was observed, but heterogeneity of within-family variance existed beyond what could be explained by simple scaling effects. For cross-sectional data, using the animal mean sub-model in the DHGLM resulted in biased estimates of variance components, which differed substantially both from a standard linear mean animal model and a sire-dam DHGLM model. Although genetic differences in canalization were observed, selection for increased canalization is difficult, because there is limited individual information for the variance sub-model, especially when based on cross-sectional data. Furthermore, potential macro-environmental changes  may make genetic heterogeneity of variance a less stable trait over time and space. In livestock and aquaculture production systems, individuals that can perform well in different environments and against different background genetics are preferred. In evolutionary genetics, the term canalization describes the stability or buffering ability of a genotype against minor variations, not only in the environment but also in the genetic make-up .In animal breeding, genetic differences in phenotypic stability can be detected as genetic heterogeneity of (within-family) residual variance, where a low variance indicates stable performance across environmental factors. Genetic heterogeneity of residual variance has been estimated for different traits in a number of land-based species, e.g., litter size in sheep , pigs 33, mice  and rabbThe presence of genetic heterogeneity of residual variance suggests that selection to change residual variance is possible, based mainly on family information. Thus, large families will be an advantage to study the genetic heterogeneity of variance. In fish species, both sexes are usually highly fecund, with a potential for large full- and half-sib families. The aims of this study were twofold: (1) quantify the genetic heterogeneity of (within-family) residual variance for body weight in Atlantic salmon and (2) test whether the observed heterogeneity of (within-family) residual variance can be explained by simple scaling effects. We also discuss the data structures that are best suited for estimating variance heterogeneity and individual breeding values for residual variance.http://www.aquagen.no/). Descriptive statistics of the dataset are in Table The analysis was restricted to year-class 2008 of Atlantic salmon from the AquaGen breeding program  family effects, e.g., effects due to common rearing, maternal effects and potential dominance genetic effects.i is defined as  = . This shows that the variation of the most extreme high families is expected to be approximately three times larger than the extreme low families.For the variance sub-model, the estimated sire-dam genetic variances from DHGLM2 for the untransformed and transformed data were 0.04 ± 0.01 and 0.03 ± 0.01 (log- and square root), respectively. The sire-dam variance component is ¼ of the total genetic variance Pearson correlation coefficients between estimated breeding values for the mean and variance sub-models using DHGLM2 were all significantly different from zero, but differed substantially between transformations . Thus, transformation of the data makes estimated breeding values for the mean and variance more independent. This may also explain the somewhat reduced genetic variance of the variance model after transformation.The main result of this study is that substantial heterogeneity of within-family variance exists for body weight in Atlantic salmon. Furthermore, the iterative approach revealed that the DHGLM animal mean model (DHGLM1) resulted in severely biased estimates of variance components when employed with cross-sectional data, both when compared with a linear mean animal model and a sire-dam DHGLM (DHGLM2) model.Since genetic heterogeneity of variance exists between families, an equivalent genetic heterogeneity must also exist within families. Hence, an animal model should ideally be fitted in both the mean and the variance sub-models of the DHGLM. This would be of particular importance for datasets with repeated records on individuals, and such data structures would allow proper estimation of variances on an individual level. However, the current dataset contained cross-sectional data , which implies that the variance cannot be estimated on the individual level but only for groups of individuals (families). This may explain why any attempt to model the variance using an animal model did not converge, possibly due to the iterative approach used, where one iterates between the mean and variance sub-models and the models are thus allowed to interact. In earlier studies, more approximate non-iterative methods have been used ,10,18, wSince genetic variance in the classical linear mean animal model is estimated based on between-family variation in observed mean phenotypes, the estimated genetic variance is expected to be unbiased. Likewise, the estimated residual variance is expected to reflect the typical level of within-family variation. This would be the case even if the true underlying model includes genetic heterogeneity of residual variance, which was confirmed in a simulation study with 200 families of 40 individuals resulting from a perfect 2 sires × 2 dams mating system of 100 sires and 100 dams (results not shown). In principle, the DHGLM models are expected to give similar genetic variance estimates on the mean as the linear mean animal model, because these estimates are also based on observed between-family variation. Hence, in the real data analysis, the mean sub-models of the two DHGLM models are expected to give similar results as a linear mean animal model. This was indeed the case for the DHGLM2 model but the DHGLM1 model showed substantial deviations. Hence, the results of this study indicate that the DHGLM1 model is severely biased when the data does not contain repeated records. The two DHGLM models differed in the flexibility of the variance sub-model; in the DHGLM1 model, the Mendelian sampling variance is assumed homogeneous . For instance, a genetic variance of 0.17 in the variance model, as found for DHGLM2, can be expressed as a standard deviation of 0.41 (i.e. the square-root of 0.17), which implies that a unit standard deviation increase/decrease of the breeding value for the variance increases/decreases the residual variance by 51% and 36%, respectively, because the model is multiplicative and can be shown to be :ΔGv is the genetic gain on the underlying log scale of the variance. Hence, the genetic standard deviation of residual variance is an informative measure for two reasons: (1) it gives an idea of how large the proportional change in the residual variance would be for a unit standard deviation increase/decrease of the residual variance breeding values and (2) this proportional change does not depend on the phenotypic variance and can therefore be compared across experiments and species. The value of using the genetic standard deviation of residual variance was emphasized already in Mulder et al. [where r et al.  where thr et al. , but thiCommon environmental effects were not included in the variance sub-models. The main reason for this is that genetic and common environmental effects are difficult to disentangle, and more so with respect to the variance model, since there is only one variance group per family. In contrast, data with repeated records per individual will have one variance group per animal rather than one per family. In our case, the data structure makes the separation between genetic and common environment factors on the variance scale difficult, which was confirmed in the simulation study described above, where the DHGLM2 model was extended with a common environmental family effect in the variance sub-model. Although all the simulated heterogeneity of variance was due to genetics, the model distributed the dispersion effects more or less randomly over genetic and common environmental factors (varying between replicates). This confirms the low power of separating such effects in the variance model, despite a perfect mating system of 2 sires × 2 dams. Furthermore, a preliminary analysis of the real data also revealed that partitioning additive genetic and common environmental effects in the variance model was sensitive to transformation of data, while the mean model was rather robust in this regard. Judging by the results of the linear animal mean model, the common environmental effects were small and not very significant . Still, we cannot rule out the existence of common environmental effects acting on the variance, and if they exist, the estimated genetic variance of the variance sub-model is probably inflated.It may be argued that heterogeneity of within-family variances may, to some extent, be explained by simple scaling effects, i.e., variance may be a function of the expected mean. If this is the case, larger genetic and environmental variances should be expected for families with higher mean body weight. Yang et al.  studied The results of this study indicate that there is genetic heterogeneity of (within-family) variance for body weight in Atlantic salmon. Selection for decreased within-family variance may give more homogeneous stocks, which would be an advantage in commercial fish farming. Increased homogeneity is consistent with the concept of canalization, but according to theory, canalization may be due to varying sensitivity to both environmental and genetic perturbations, i.e., the Mendelian sampling variance may also differ between families. Our study does not prove the presence of heterogeneity of Mendelian sampling variance, nor does it rule out the potential existence of such effects. A complication for selection for increased homogeneity based on cross-sectional data, which is by far the most common data structure in aquaculture, is that the Mendelian sampling and micro-environmental residual effects are completely confounded, which implies that pure selection against micro-environmental sensitivity cannot be guaranteed.Genetic heterogeneity in sensitivity to micro-environmental change  is one form of genotype by environment interaction. However, genotype by environment interactions may also be present on the macro-environmental scale , potentially causing re-ranking among families. For example, some families may have highly variable phenotypes for one diet but more homogeneous phenotypes for another diet. Hence, one may expect substantial re-ranking of estimated breeding values for variance among cohorts. Such factors would complicate meaningful selection for altered environmental sensitivity in practical breeding programs aimed at providing genetic material for production systems over a wide range of macro-environments.2, showing that the variation of the most extreme high families is approximately three times larger than the extreme low families. A tendency towards higher variance with higher means  was observed, but heterogeneity of within-family variance existed beyond what could be explained by simple scaling effects. Since there were no repeated observations, the fitting algorithm biased the estimates of the variance components of the DHGLM animal mean model (DHGLM1), but not of a classical linear mean animal model and a pure sire-dam DHGLM (DHGLM2) model. However, selection for increased homogeneity of variance may still prove difficult, especially when based on cross-sectional data. Furthermore, potential macro-environmental changes may make genetic heterogeneity of variance a less stable trait over time and space.Substantial heterogeneity of within-family variance was found for body weight in Atlantic salmon, with a 95% prediction interval for within-family variance ranging from ~0.4 to ~1.2 kgThe authors declare that they have no competing interest.AKS initiated the study. JØ analyzed the data. The manuscript was drafted by AKS and JØ. LR provided the necessary R scripts for the analyses. All authors read and approved the final manuscript.


In particular, we consider (i) the theoretical foundations of ridge regression, (ii) its link to commonly used methods in animal breeding, (iii) the computational feasibility, and (iv) the scope for constructing prediction models with nonlinear effects . Based on a simulation study we gauge the current and future potential of ridge regression for prediction of human traits using genome-wide SNP data. We conclude that, for outcomes with a relatively simple genetic architecture, given current sample sizes in most cohorts  the predictive accuracy of ridge regression is slightly higher than the classical genome-wide association study approach of repeated simple regression . However, both capture only a small proportion of the heritability. Nevertheless, we find evidence that for large-scale initiatives, such as biobanks, sample sizes can be achieved where ridge regression compared to the classical approach improves predictive accuracy substantially.In recent years, there has been a considerable amount of research on the use of regularization methods for inference and prediction in quantitative genetics. Such research mostly focuses on selection of markers and shrinkage of their effects. In this review paper, the use of  In a mixed linear model such expectations are known as the best linear unbiased prediction (BLUP) . Therefore, MAP estimation of β in  can also be used as point estimator. Estimation using the posterior mode is known as maximum a posteriori (MAP) estimation. However, due to the normality of  of β in  is equivλ such that the RR estimator of SNP effects is equivalent to its BLUP . The elastic-net method preserves SNP selection, while allowing more than N of P SNPs to be selected. Taking a convex combination of the two norms hardly increases the computational costs of solving this problem, when compared to solving the LASSO problem ).Endelman  finds thEndelman  find in [ rrBLUP .t kernel [Morota and Gianola  compare t kernel , for thet kernel . Though t kernel ), current kernel . Thus, it kernel  finds lit kernel .Given the current evidence, KRR using an appropriate kernel  is a promising prediction technique, especially for traits where epistatic effects and dominance are expected to contribute to trait variation. De los Campos et al.  suggest K denote the matrix of similarities in the higher-dimensional feature space in the training set, such that an element of this matrix kij is given by k and let K21 be defined similarly for individuals in the test set versus individuals in the training set. Now, KRR prediction without confounders is given by MC is the projection matrix removing the effects of C.Regarding the computation of predictions using KRR, let d, given the GRMs, P−1XX⊤ and P−1X2X⊤, the matrices K and K21 can be obtained efficiently by adding a constant c to each element of the GRMs and by raising each resulting element to the power d. When c > 0 and d ∈ {1,2,…} are not fixed, these are additional hyperparameters which can be tuned via (N)CV.In the case of the nonhomogeneous polynomial kernel of degree An important question is under what circumstances can we expect RR to yield more accurate predictions than RSR? The answer to this question can help us assess the merits of RR in quantitative genetics. As discussed, prediction using RR is intimately related to the BLUP of the phenotype under a mixed linear model in which SNP effects are assumed to be all drawn from a normal distribution. This corresponds to idea of each SNP making a tiny contribution to phenotype. Therefore, it is reasonable to assume that RR will perform well when the SNP effects are as such. However, given that not all SNPs in existence are causally affecting the outcome, an open question is how does RR perform when only a subset of SNPs affects the outcome?Moreover, an important factor influencing predictive accuracy of a classical polygenic score is the training sample size. Therefore, RR is likely also to be very sensitive to the sample size. Finally, the more heritable a trait is, the easier it should be to detect the effects of SNPs. Thus, an additional question is how do RR and RSR perform under different levels of heritability?N), the number of genotyped SNPs (P), the fraction of SNPs exerting a causal influence (fC), and the SNP-based heritability (hSNP2).In short, we want to know the relative predictive accuracy of RR and RSR (i) for a wide range of trait architectures and (ii) under particular combinations of sample size and the number of genotyped SNPs. To answer this question we run a suite of simulations. In these analyses, we vary sample size of the training set  denotes the binomial distribution with a draws each with probability of success b and 𝒰 denotes the uniform distribution on the interval . This data generating process corresponds to a quantitative trait which is normally distributed and has only additive genetic variation to which common variants contribute .For a combination of sample size, the number of SNPs, trait heritability, and a fraction of causal SNPs chosen from the levels shown in Ntotal includes the individuals in the test set. The size of the test set is 10% of the size of the training set, hence, yielding Ntotal = ⌊1.1N⌋. Here, ⌊x⌋ denotes the nearest smaller integer.The total number of observations R = 21 independent runs (replications). In each run we simulate only one set of genotype data for Nmax = 22,000 individuals and Pmax = 500,000 SNPs. Given any combination of N and P listed in P weights of which some are zero, such that we attain the desired fraction of SNPs being causal. Moreover, by scaling these weights and the noise vector ε appropriately we can attain any specified heritability. The result is a four-dimensional phenotype array with individuals along the first dimension and the factors P, fC, and h2 along the remaining dimensions.In order not to be dependent on a single generated dataset, the entire simulation consists of N and P, not on h2 or on fC. Therefore, given N and P, when N ≤ P the eigendecomposition of the N × N GRM, P−1XX⊤, can be reused for all combinations of h2 and fC. Moreover, the approach has already been amended to reuse the eigendecomposition for different values of λ. Similarly, when N > P the eigendecomposition of P × P matrix P−1X⊤X can be reused. Since there only are 7 unique levels of N and 12 unique levels of P, RR prediction (i) for the 62,160 scenarios per replication reduces to computing 7 × 12 = 84 eigendecompositions and (ii) for each scenario to carrying out the matrix multiplications seen in  the constancy of the GRM and of P−1X⊤X over the 20 × 37 different combinations of h2 and fC and (ii) the properties of the eigendecomposition which enable the joint evaluation of the 151 values of λ we consider dramatically increases the CPU time of RR. In fact, we infer that the less efficient approach yields a CPU time that is at most a factor 20 × 37 × 151 = 111,740 larger than the 4.5 hours we attain . Even worse, when the naive RR approach is applied and also when P ≫ N, RR predictions cannot be obtained for datasets with more than 50,000 SNPs on the machine we use. Thus, using the efficient approach based on the GRM when N ≤ P and based on P−1X⊤X when N > P, combined with the smart use of eigendecompositions and constancy of GRMs over different combinations of fC and h2 we are able to reduce CPU times from several decades to several hours.In a typical run it takes 4.5 hours to predict using RR on a machine with 16 cores at 2.60 GHz per core with 64 GB RAM. The RSR predictions are generated alongside at virtually no costs in terms of CPU and memory. The computing time includes computation of the GRM, R2 of the RSR prediction with the outcome and the R2 of the RR prediction with the outcome. R2 is measured by the squared sample correlation coefficient between the polygenic score and the outcome in the test set. Our aim is to assess predictive accuracy of RSR and see whether it differs significantly from zero for a wide range of configurations. Moreover, we want to test whether RR provides a significant improvement compared to RSR. Therefore, the performance of RR is measured relative to RSR. That is, we take the log-ratio of the two, given by log(RRR2/RRSR2). This measure is continuously distributed over .In each run, for each combination of levels we compute the RRSR2/hSNP2; that is, ∞, +∞). The reason for dividing RRSR2 by hSNP2 is that we want to know what part of the genetic variation the polygenic score captures. If hSNP2 is low, for instance, 5%, we consider a polygenic score that attains an R2 of 4% to be more impressive than a risk score that explains 10% of the variation in a highly heritable trait . Note that we exclude observations with RRSR2 > hSNP2 as these are uninformative outliers; a polygenic score that “explains” more genetic variation than there actually is is simply wrong.We measure the absolute performance of RSR by the logit transformation of RRR2 denote the accuracy of RR in run r, given penalty λ, conditional on some N, P, fC, and h2. Now, let λ. Now, for this combination of N, P, fC, and h2 we take λ is tuned by setting it such that it maximizes the median R2 of RR over the runs for the given combination of levels. Based on this procedure, the optimal R2 of RR in run r is given λ that performs well in 21 independent samples. Hence, it is similar to a value that would result from CV; there is little scope for overfitting. Moreover, since the median is less sensitive to outliers than, for instance, the mean, we make our measure more robust by taking the median over the runs. The reason that we choose for this approach instead of CV is to reduce the computational complexity of the simulation procedure at the expense of having a slightly less elegant approach.Regarding the RR penalty, let RRR2/RRSR2) and of RRSR2. As can be seen, overall the combinations of levels and runs RR seems to outperform RSR on average by about 6%. However, there is much variation in the log-ratio. The lowest log-ratio is −22.2 and the highest is +20.7. Since this ratio is on a log scale this implies a tremendous difference in R2. The reason for this is that when either the nominator or the denominator of RRR2/RRSR2 gets close to zero, the log-ratio can attain a large value (in absolute terms). For this reason we excluded log-ratios outside the interval . This leads to a drop in the variance from about 0.4 to 0.04, only at the expense of losing 3.9% of the observed combinations of levels and runs. Moreover, the mean log-ratio hardly changes by removing the outliers. This reduction in variance allows us to display the results in a more insightful manner and ensures further inferences on the relation between our factors  and predictive accuracy are not influenced by aberrant observations. For RRSR2 we see that the average R2 of about 17% is significantly greater than zero.RRR2/RRSR2) over the combinations of runs and levels inside the range . This histogram confirms that there are long and thin tails. Most mass centers around zero. However, the empirical distribution is slightly skewed to the right, giving rise to the positive average log-ratio. The figure shows that RR often performs better than RSR. Given the fact that RR lies between RSR and OLS, this is not surprising. Using the penalty parameter λ, RR tries to find the optimum between these two extremes. RRR2/hSNP2) excluding observations for which RRR2 > hSNP2. The observations are smoothly distributed. A value of zero corresponds to an R2 equal to half the heritability. Thus, in a substantial proportion of the cases RSR captures more than half of the genetic variation.R2 of ridge regression and of RSR, with values outside the interval  truncated to corresponding extremes of this interval. This truncation is necessary in order for the figure not to be dominated by the outliers. For N ≪ P  the standardized simulated SNP data are such that X⊤X approaches the identity matrix and RR becomes equivalent to RSR . We see that for these data dimensions a trait with a heritability of 50% has a classical polygenic score which on average only explains 0.5% of the total phenotypic variation. Moreover, RR yields a relative increase of just 2.9%. This increase gives an absolute R2 of 0.51% for RR. This observation clearly illustrates that the so-called missing heritability [tability  is hard RRR2/RRSR2 for all replications and for all considered levels of factors, such as sample size. Moreover, in order to obtain the R2 of RSR as a benchmark we also fit a linear model, the logit transformation of RRSR2.To understand the relation between the various factors in the simulation study and the gain in predictive accuracy by RR we fit a linear model to the logarithm of the ratio N and the performance is nonlinear. The relation seems to exhibit an inverted U-shape. For this purpose, we include log(N) and its square as regressors. Moreover, the location of the peak depends on the number of SNPs, implying that the parameters of regressors related to sample size depend on P. Consequently, interactions between P and N are added to the model. By symmetry of P. Based on this argument we consider up to three-way interactions between the regressors.The results in the previous section indicate that the relation between sample size In addition, we see in many subplots of Both outcomes are modelled as a linear function of the aforementioned basic regressors. These regressors are reported in R2 of RSR than in the gain of RR relative to RSR is the following. In case both the R2 of RR and RSR are to a large extent influenced by our factors in a similar way, taking the log-ratio basically eliminates these common effects. What then remains is a measure over which the factors have less predictive power than over the absolute R2 measure.A likely reason for the fact that we can explain far more variation in the RRR2 and RRSR2 as well as RRSR2 for sample sizes between 100,000 and 500,000 individuals and the number of SNPs between 100,000 and 500,000. For heritability and the fraction of causal SNPs we use the ranges considered in the initial simulations. The resulting predictions of the gain in accuracy are displayed in the heatmap in Using the parameters estimates of the models we predict the log-ratio of RRR2/RRSR2 and RRSR2 are reported together with confidence intervals in P = 500,000, h2 = 50%, and N varies from 100,000 to 500,000. In the second group N = 500,000 and P varies from 100,000 to 500,000. In the last group P = N = 500,000 and h2 ranges from 25 to 75%.In addition, point estimates of R2 between 10% and 20% for sample sizes ranging between 100,000 and 500,000 individuals. All increases in accuracy are greater than zero at a 5% significance level. Moreover, RSR attains values of R2 ranging between 15% and 75%. As an example, in case of 200,000 individuals and 500,000 SNPs, for a trait with hSNP2 = 50% the R2 of RSR is expected to be 33.7% and the R2 of RR 37.3%.Results from R2 attained by RSR with the relative increase by RR yields expected values of the R2 of RR which in some cases surpass h2. In practice this cannot be true. In case a trait has an h2 of 50% it is not possible to consistently predict more than 50% of the phenotypic variation on the basis of SNP data. This seems to indicate that our estimates are somewhat optimistic. Nevertheless, for the ranges in which we actually simulated data  RSR is able to attain a substantial R2 when N ≈ P and RR is able to considerably increase the R2. For instance, at h2 = 50% and N = P = 20,000, with 200 causal SNPs the median R2 of RSR is 17%, and the median R2 of RR is 20%. This constitutes a relative increase in R2 of about 16%. As shown in N ≈ P. Hence, at the very least, the expectation that RR improves the R2 of RSR considerably for large samples  is not unreasonable.Regarding these findings, combining the P SNPs and an outcome observed for N individuals, even when P ≫ N. When the ridge penalty is equal to the ratio of the noise variance and the variance of random SNP effects in a mixed linear model, prediction using the weights from ridge regression is equivalent to the best linear unbiased prediction used in animal breeding, agricultural science, and more recently also human genetics.Ridge regression is a flexible technique that can be used to estimate the association between a set of Ridge regression can be perceived as a method that partially accounts for linkage disequilibrium between markers. For a sufficiently low penalty the method fully accounts for linkage disequilibrium and is therefore equivalent to the OLS estimator of the multiple regression problem using all SNPs jointly. On the other hand, for a sufficiently high penalty, in terms of predictions ridge regression ignores linkage disequilibrium and is therefore equivalent to the approach of a simple regression per SNP, which is common in a GWAS.N unknown weights and applying these weights to a measure of relatedness of individuals out of sample and in sample. Formulating ridge regression this way makes it a computationally efficient technique, even for a large number of SNPs.Using standard results from, for instance, machine learning and animal breeding, prediction using ridge regression can be shown to constitute solving an equation with As with multiple regression and GWAS predictions, ridge regression can account for the presence of confounding variables, such as age, gender, and population structure. Moreover, such corrections can again be implemented at low computational costs.N × N matrix only once. This expression allows the researcher to efficiently carry out procedures, such as cross-validation, to tune this parameter.When the shrinkage parameter is unknown ridge prediction can be formulated such that predictions for different values of this parameter can be generated in a single step, requiring the eigendecomposition of an Finally, ridge regression prediction is amenable to a wide array of advanced techniques. First, using the kernel trick from machine learning, nonlinear effects such as dominance and epistasis can easily be incorporated in the prediction model. Moreover, in a Bayesian spirit, results from earlier studies can be used to give a prior weight to SNPs in the ridge regression prediction. Similarly, when prior information is not available, in-sample information can be used to discount SNPs differently, yielding a heteroskedastic ridge regression prediction.Empirical findings so far seem to suggest that for current sample sizes the performance of plain vanilla ridge regression is very similar to that of the repeated simple regression approach used in a GWAS. This raises two questions. First, how do more advanced ridge regression approaches perform? Second, how will the plain version of ridge regression perform in upcoming large scale initiatives, such as biobanks?R2 in 21 independently simulated datasets is 0.5% for repeated simple regression and 0.51% for ridge regression. This resonates with the finding that the main determinant of predictive accuracy of the polygenic score is the sample size of the training set . As. AsR2 iN, P, trait heritability, and the fraction of causal variants, we are able to extrapolate the performance of ridge regression for large scale initiatives. For a sample size of 200,000 individuals and 500,000 SNPs, we find that in a trait with 50% heritability and with 5,000 causal variants the polygenic score of a GWAS is expected to explain 34% of the phenotypic variation, whereas ridge regression is expected to capture about 37%. Thus, in this scenario ridge regression is expected to capture about 75% of the genetic variation, whereas the classical approach captures 67%.However, by analyzing the difference in accuracy of the classical approach and ridge regression for different values of N ≤ 20,000). However, one thing that remains unchanged even under different specifications of the models that try to explain the accuracy of respective methods is that ridge regression outperforms the repeated simple regression approach in all large scale samples considered.However, these predictions are rather coarse. They depend highly on the model being fitted . This observation comes as no surprise; we extrapolate quite a bit outside the interior of the levels of the factors that were considered in the simulations (e.g., A final note is concerned with the independence of the loci. In the present simulations at most 500,000 truly independent markers were used. As a result, all carry their own idiosyncratic bit of information about the genetic relationship of individuals in the data. As is shown, however, by Yang et al. , in realN ≈ P, even when in fact P is far greater still than N. Such a proposition would need to be tested either in empirical work or by means of simulations using actual genotype data in which linkage disequilibrium is present.The findings of Yang et al.  illustraThe use of GWAS data for the prediction of complex traits based on sample sizes far below 100,000 individuals yields genetic risk scores with little predictive accuracy, regardless of whether one applies the classical GWAS approach or ridge regression. However, as sample sizes approach the “effective number of SNPs” we expect the polygenic risk score based on repeated simple regression to be able to explain a substantial proportion of the normal genetic variation. Moreover, under this scenario prediction using ridge regression is likely to outperform the classical GWAS predictions significantly. Bearing in mind that ridge regression is amenable to include nonadditive genetic variance in the prediction model it is therefore not unlikely that ridge regression will make an even more substantial contribution to the accuracy of polygenic scores in traits where epistasis and dominance are expected to play an important role.


P=2.3 × 10−26). We replicate this association in a second set of Pomak samples (combined P=2.0 × 10−36). We demonstrate significant power gains in detecting medical trait associations.Isolated populations are emerging as a powerful study design in the search for low-frequency and rare variant associations with complex phenotypes. Here we genotype 2,296 samples from two isolated Greek populations, the Pomak villages (HELIC-Pomak) in the North of Greece and the Mylopotamos villages (HELIC-MANOLIS) in Crete. We compare their genomic characteristics to the general Greek population and establish them as genetic isolates. In the MANOLIS cohort, we observe an enrichment of missense variants among the variants that have drifted up in frequency by more than fivefold. In the Pomak cohort, we find novel associations at variants on chr11p15.4 showing large allele frequency increases  with haematological traits, for example, with mean corpuscular volume (rs7116019,  Isolated populations can increase power to detect low frequency and rare risk variants associated with complex phenotypes. Here, the authors identify variants associated with haematological traits in two isolated Greek populations that would be difficult to detect in the general population, due to their low frequency. The study of isolated populations can help to increase the power of genetic association studies in search of low-frequency and rare variant associations with complex traits123456Under the auspices of the HELlenic Isolated Cohorts study (HELIC), we have collected samples from two isolated populations in Greece: the Pomak villages (HELIC-Pomak), a set of religiously isolated mountainous villages in the North of Greece, and the Mylopotamos mountainous villages (HELIC-MANOLIS) on the island of Crete. All samples have information on anthropometric, cardiometabolic, biochemical, haematological and diet-related traits and both cohorts form the substrate for medically relevant trait association studies.The HELIC-MANOLIS (Minoan isolates) collection comprises individuals from the mountainous Mylopotamos villages, including Anogia, Zoniana, Livadia and Gonies . Residents of the Mylopotamos villages have over the centuries preserved their customs, traditions and anthropological character. The Pomaks inhabit the regional units of Xanthi, Rhodope and Evros. The HELIC-Pomak collection comprises individuals from the Pomak villages located in the regional unit of Xanthi . The Pomaks represent a small minority of Muslims in Greece with uncertain historical originsThe aims of our study are twofold. First, we use genome-wide genotype data to genetically characterize the MANOLIS and Pomak cohorts and compare their allelic architecture to the general Greek population; we demonstrate that isolation caused extensive genetic drift in both isolates. Second, we evaluate the gains in power for complex trait mapping studies that can be afforded by studying well-characterized population isolates in two ways: we calculate power to detect loci that have drifted up in frequency in the isolates compared with the general Greek population highlighting significant theoretical gains in power for variants at the lower end of the minor allele frequency (MAF) spectrum. We then demonstrate this empirically by examining the biological role of these variants and their association with medically important complex traits. We find an enrichment of missense variants among alleles that have drifted up in frequency in the MANOLIS cohort and novel associations between haematological traits and alleles that have drifted up in frequency in the Pomak cohort.N=61 individuals from Kentavros, which is comparable to the size of other large villages; we observe that the subsampled Kentavros individuals do not form a distinct cluster  analyses including data from the general Greek population and from the 1000 Genomes Project cluster .The inbreeding coefficient (Fin) was higher in the Pomak and MANOLIS populations compared with TEENAGE  show that the two isolated populations have on average a much larger number (nROH) and length (cROH) of ROH than TEENAGE. The Pomak isolate displays higher ROH values with respect to the MANOLIS isolate . When uset al.We computed for each population the proportion of individuals that have at least one ‘surrogate parent’ for randomly chosen regions in the genome of varying lengthUsing the modified long-range phasing (LRP) methodThe extent of isolation of the Pomak and MANOLIS samples is further reflected in the fact that nearest neighbours (NNs), that is, genealogically closest individuals in the sample , are typTo estimate the age of co-ancestry, we fit a model of exponential decay of haplotype sharing around 100 randomly sampled locations across the genome . We findUsing a different approach that utilizes pairwise LD information161719Overall, the MANOLIS, Pomak and TEENAGE cohorts have similar allele frequency distributions . We calcPPARG (peroxisome proliferator-activated receptor gamma). Rs4135336 shows an increase in allele A frequency by 47-fold (from 0.0007 in TEENAGE to 0.033 in MANOLIS). This variant appears to be monomorphic in all European (EUR) populations from the 1000 Genomes Project except in TSI where it has been observed at a frequency of 0.01. It is, however, common in African (AFR) populations and has reached 0.14 frequency in the Yoruban (YRI) population.In the respective fold analyses, 517 (0.08%) variants displayed >10-fold increase in MANOLIS versus TEENAGE . The higCDH9 ) and CDH6 ) that shows an increase in allele G frequency by 59-fold (from 0.0007 in TEENAGE to 0.0423 in Pomak). This variant is observed at low frequency (0.01–0.03) in all EUR populations from the 1000 Genomes Project but is common in populations from East Asia (ASN), Ad Mixed America (AMR) and AFR observed at the highest frequency in YRI (0.22). Rs9958680, an intronic variant in SLC14A2 (solute carrier family 14 (urea transporter), member 2), shows an increase in allele G frequency by 56-fold (from 0.0007 in TEENAGE to 0.03897 in Pomak). This variant is monomorphic in all EUR and ASN populations from the 1000 Genomes Project, has low frequency (0.01–0.02) in AMR populations and is common in populations from AFR, observed at the highest frequency in the Luhya (LWK) population (0.18).A total of 261 (0.04%) variants displayed an increase of >10-fold in Pomak versus TEENAGE and two variants displayed an increase of >50-fold . The higTo investigate power gains for frequency differences at rare alleles we examined variants that had MAF<0.01 in TEENAGE. In all, 24,493 of the variants that overlap between TEENAGE and MANOLIS are rare in TEENAGE. Of these, 15,341 (62.6%) have risen in frequency in MANOLIS and 4,581 (18%) have reached MAF>0.01. In the latter, allele frequency increases in the range from 0.000038  to 0.06897  with a median increase of 0.01 . We calculated power  to detecr2=0.54) show genome-wide significant association with haematological traits. Rs16913631 allele A shows a 32-fold increase in frequency, from 0.0014 in TEENAGE to 0.0441 in Pomak. This variant appears to be monomorphic in all EUR populations from the 1000 Genomes Project but common (0.13) in AFR populations, observed at highest frequency (0.21) in LWK. Rs16913631 is associated with three haematological traits: mean corpuscular volume (MCV) in 965 Pomak individuals ; mean corpuscular haemoglobin concentration (MCHC) in 974 individuals  and the mean corpuscular haemoglobin (MCH) in 960 individuals  and MCH  for associations with medically relevant traits in the full set of Pomak and MANOLIS samples using GEMMAr2=0.68 with rs16913631 and r2=0.86 with rs7116019; P=3.45 × 10−29), MCHC  and MCH  suggesting that rs7116019, rs11035019 and its perfectly correlated proxy rs12274659 are part of the same signal. Conditioning rs11035019 on rs16913631 also resulted in a higher P value; however, the rs11035019 association with MCV still remained strong (P=8.8 × 10−13), which that cannot conclusively rule out the presence of two signals in this region.To determine whether the signal in chr11p15.4 region is because of a single or multiple independently associated variants, we tested the most highly MCV-associated index variant, rs11035019, conditioning on the two other most highly drifted variants, rs7116019 and rs16913631. Conditioning rs11035019 on rs7116019 resulted in attenuation of the signal (P<4.4 × 10−18).Previous reports have provided evidence for association of several variants with haematological and related traits at the 11p15.4 locus232425262728293031323334−36, 8.3 × 10−27 and 1.7 × 10−13 for MCV, MCHC and MCH, respectively (N=92) are spread across villages  is not in LD with the four highlighted variants (r2<0.0008) in the Ugandan cohort. Similarly, the most highly associated SNP with MCHC  is not in high LD with the four highlighted variants (r2<0.0007) in the Ugandan cohort.Motivated by the common frequency of the drifted alleles in African populations, we investigated association between variants in this chr11 region (1 Mb upstream and downstream of the most highly drifted variants) and MCV, MCHC and MCH in the Ugandan General Population Cohorts=0.005, 0.007 and 0.01 acting on carriers. Here the probabilities of reaching the observed 0.046 frequency were higher: 0.83%, 1.45% and 2.85%, respectively. We therefore conclude that positive selection is likely to have acted on the Pomak haplotype. If a 1% chance of reaching the observed frequency of 0.046 is used as a criterion, then a selective coefficient between 0.005 and 0.007 is suggested given the demographic model used here.The haplotype length shared by all Pomak chromosomes carrying the minor alleles of the three correlated variants  is ~1.8 Mb, which is unusually long given the allele frequency . This suSIPA1 , rs6659553 in POMGNT1  and two variants that are classified as deleterious in SIFTLSM14A (SCD6 homologue A) and rs2290959 in ACY3 (aspartoacylase (aminocyclase) 3).In the MANOLIS cohort we found a significant enrichment of missense variants among those variants that have increased in frequency above a fold change of 5, and all higher thresholds examined . We alsoP=0.00707); Fhom and high-density lipoprotein ; Fhom and homeostatic model assessment β-cell function ; Fhom and MCH ; and Fhom and MCV  show consistently that they bear the genomic characteristics of genetic isolates. The extensive haplotype sharing in the isolates is further corroborated in the LRP analysis where for the 15q25 region we observe that with as little as 300 individuals analysed per population 88% of Pomak individuals and 79% of MANOLIS individuals have at least one ‘surrogate parent’ compared with 6% in the general Greek population. In the Icelandic population, the sample size required to reach such a high proportion of individuals with at least one surrogate parent is ~6,300 sampleset al.In our investigation of inbreeding effects on quantitative traits, we found the most significant association between height and genome-wide homozygosity in the Pomak population isolate. This inverse association is consistent with previously reported findings in other isolated populations49P=2.0 × 10−36, P=8.3 × 10−27, P=1.7 × 10−13 for the three traits, respectively. Rs7116019 is located at the 3′ end of the TRIM68 gene that functions as an ubiquitin E3 ligase and can act as a coactivator of androgen receptor depending on its ubiquitin ligase activity24252729303132HBB  gene, HbO-Arab (E122K), has been reported to have drifted up in frequency in the Pomak population and appears to have originated on a local haplotype about 2,000 years agoWe find novel genome-wide significant association between rare variants that have drifted up in frequency in the Pomak population and MCV, MCHC and MCH at 11p15.4, which encompasses the β-globin locus. We pooled genotypes at rs7116019 across the discovery and replication data sets and repeated the association analysis appropriately accounting for sample relatedness; we find stronger evidence of association in the combined Pomak set: P<10−4 in the Ugandan cohort that are not in LD with the four highly drifted loci. The complexity of chr11p15.4 as a risk locus for haemoglobinopathies, haematological and related traits is likely because of population-specific, trait-associated variants2323262834It is noteworthy that the associated variants are monomorphic in other European populations but have risen to high frequency in African populations. The prevalence of certain haemoglobinopathies is high in the Mediterranean region and AfricaPPARG, which encodes a member of the peroxisome proliferator-activated receptor subfamily of nuclear receptors. PPARG is thought to regulate adipocyte differentiation and glucose homeostasis. Variants in PPARG have been associated with type 2 diabetes, obesity, atherosclerosis, cancer and hypertension5657P<5 × 10−8) in the type 2 diabetes DIAGRAM meta-analysisr2<0.2) with rs4135336. Similarly, we do not find this variant to be in LD with body mass index-associated variants from the GIANT studyNonsynonymous variants in the human population are less frequently observed than expected based on the overall mutation rateWe evaluated power gains in detecting low frequency and rare variant associations afforded by studying the isolates. For an effect size of 1 s.d. (explaining 2% of trait variance for a variant with frequency of 0.01), the increase in power ranges from 0.4 to 100% with a median increase of >64%. The MCV-associated A allele of rs7116019 has increased in frequency to 0.044 in the Pomak population, empowering its discovery with genome-wide significance in a sample size of less than a thousand individuals. Ten times as many samples would be required to achieve 80% power to detect the observed effect in a nonisolated European population such as TEENAGE .It has been well documented that the use of genetically isolated populations can empower the identification of rare variants associated with complex traits, mainly through reduced allelic variability and genetic driftHELIC. This work utilized data from 1,364 HELIC-MANOLIS and 1,883 HELIC-Pomak samples. The HELIC collections include blood for DNA extraction, laboratory-based haematological and biochemical measurements, and interview-based questionnaire data. The study was approved by the Harokopio University Bioethics Committee, and informed consent was obtained from human subjects.TEENAGE. The TEENAGE (TEENs of Attica: Genes and Environment) study comprises 857 adolescents of Greek origin randomly recruited from public secondary schools located in the wider Athens area of Attica in GreeceP<0.0001. A total of 754 unrelated individuals and 655,511 SNPs passed QC in the MANOLIS data set; 567 unrelated individuals and 643,679 SNPs passed QC in the Pomak data set. Genotyping and QC of the TEENAGE cohort were performed as above (except for genome-wide heterozygosity exclusion thresholds that were set at <32% or >35%) and have been described in detail elsewhereDNA samples from the MANOLIS and the Pomak collections were genotyped using Illumina HumanOmniExpress BeadChips  at the Wellcome Trust Sanger Institute, Hinxton, UK. Genotypes of both cohorts were called together using the Illuminus genotype calling algorithmN=754 in MANOLIS, N=567 in Pomak and N=707 in TEENAGE cohorts) were used for all statistical analyses described herein except for trait association analyses that were performed on the full set of samples passing QC in the isolates Methods, Supplementary Methods, N=1,282 for MANOLIS and N=1,014 for Pomak).Unrelated samples .We examined population structure by performing MDS analyses in PLINKFhom, Fin and ROH were calculated using PLINKWe estimated the proportion of individuals with a surrogate parent for random regions in the genome by using the method proposed in ref. r2) between genotypes for 97,885 autosomal SNPs from four random chromosomes  using PLINK1617N=567) of individuals per population was considered. The genetic distance of pairs of markers was derived from HapMap recombination mapsWe estimated Ne of the three cohorts in two ways: by using estimates of haplotype sharing based on the modification of the LRP methodTo examine genetic drift in the population isolates, we compared the allele frequencies of all variants in each of the two isolates against their respective allele frequency in the general Greek population in two ways: for each pairwise comparison we calculated the absolute difference and the fold difference in allele frequencies for 652,812 overlapping variants in MANOLIS versus TEENAGE, and for 642,011 variants in Pomak versus TEENAGE. We inspected genotype calling intensity plots for signals showing the strongest allele frequency differences (top 30 in each of the comparisons) and excluded badly clustering variants. We investigated the biological role of these variants and the closest gene to which they reside and examined their association with HELIC study measured traits.N=1,282) and Pomak  cohorts were carried out using GEMMA v0.94  and focused on variants lying in coding sequence, specifically variants called as missense, synonymous, nonsense, frameshift or overlapping an essential splice site. We found insufficient numbers of variants falling into each of the latter three categories; therefore, we limited further analysis to missense and synonymous variants only. To test for enrichment of missense and synonymous variants we used incrementally increasing thresholds of the fold change in allele frequency , and at each threshold we computed a contingency table comparing the number of missense and other variants found at a fold change higher than the threshold. We focused this analysis on fold changes in order to primarily capture relevant changes in allele frequency for low frequency and rare variants. We used odds ratios to quantify enrichment and Fisher’s exact tests to compute the significance of the result.Linear regression was used to examine association of Fhom and F_ROH38Cohort collection: G.D., A.-E.F., C.K., E.T., M.K., R.N.N., A.K., M.S., E. Zengini., V.M., A.A., M.G., V.-E.K. and E. Zeggini. Phenotype cleaning: A.-E.F., K.H., A.M., N.W.R., I.T. and E. Zeggini. Genetic data analyses: K.P., K.H., D.K.X., V.C., G.R.S.R., L.S., A.G., I.T., S.F., I.N., Y.X., M.M., Y.C., C.T.-S., M.S., G.McV. and E. Zeggini. Bioinformatics: G.R.S.R., K.P., K.H, S.F. and E. Zeggini. Manuscript drafting: K.P., K.H., D.K.X., V.C., G.R.S.R., L.S., Y.X., M.M., C.T.-S., S.F. and E. Zeggini.How to cite this article: Panoutsopoulou, K. et al. Genetic characterization of Greek population isolates reveals strong genetic drift at missense and trait-associated variants. Nat. Commun. 5:5345 doi: 10.1038/ncomms6345 (2014).Accession codes: The HELIC-MANOLIS genotype data (Illumina Human OmniExpress) have been deposited in the European Genome-phenome Archive (EGA) under the accession code EGAS00001000687.Supplementary Figures 1-12, Supplementary Tables 1-13, Supplementary Notes 1-4, Supplementary Methods and Supplementary References


Pedigree errors and cryptic relatedness often appear in families or population samples collected for genetic studies. If not identified, these issues can lead to either increased false negatives or false positives in both linkage and association analyses. To identify pedigree errors and cryptic relatedness among individuals from the 20 San Antonio Family Studies (SAFS) families and cryptic relatedness among the 157 putatively unrelated individuals, we apply PREST-plus to the genome-wide single-nucleotide polymorphism (SNP) data and analyze estimated identity-by-descent (IBD) distributions for all pairs of genotyped individuals. Based on the given pedigrees alone, PREST-plus identifies the following putative pairs: 1091 full-sib, 162 half-sib, 360 grandparent-grandchild, 2269 avuncular, 2717 first cousin, 402 half-avuncular, 559 half-first cousin, 2 half-sib+first cousin, 957 parent-offspring and 440,546 unrelated. Using the genotype data, PREST-plus detects 7 mis-specified relative pairs, with their IBD estimates clearly deviating from the null expectations, and it identifies 4 cryptic related pairs involving 7 individuals from 6 families. Mis-specified pedigree relationship and cryptic relatedness often occur in family and population data. The potential causes of such errors are numerous, including undocumented nonpaternity, nonmaternity, adoption, mating between relatives, sample duplication or swap. It is well known that such errors, if undetected, can affect the accuracy or power of both linkage and association studies, as well as have adverse effects on other aspects of the analyses such as population stratification -6.Genome-wide marker data can provide accurate information on the genetic relatedness among individuals. For linkage scans, a number of statistical methods have been proposed and implemented, including RELCHECK , RELATIVThere are 3 main differences between PREST-plus and PLINK. First, PREST-plus uses the maximum likelihood-based IBD estimation method, which has more statistical power, whereas PLINK relies on the method-of-moments approach, which is computationally more efficient. Second, PREST-plus identifies both pedigree errors and cryptic relatedness in linkage or association studies with family data, population sample, or both, whereas PLINK is primarily suitable for detecting cryptic relatedness in GWAS with population sample. Third, PREST-plus provides a formal hypothesis testing framework, which can be useful when a potential error has been being identified, whereas PLINK provides point IBD estimation only ,6. The GThe relatedness between a pair of individuals can be summarized by the IBD probability distribution, m and where lgorithm ,16,17. Ilgorithm  estimateG are compatible with the null putative relationship type, 0 R. HoweveThe methods considered here focus on global estimation of IBD distribution, which is powerful and efficient to distinguish distinct relationships, for example, full-sibs versus unrelated. However, such global methods are not adequate to distinguish similar relationship types, for example, second-cousin versus unrelated. To this end, the recent local estimation methods  providePedigree errors and cryptic relatedness often occur in sample despite the best practice in data collection. Genome-wide marker data, collected for linkage or association studies, can provide accurate genealogy information between individuals. Using the GWAS SNP data, PREST-plus analyses the GAW18 sample that had been previously "cleaned," and it identifies 7 clearly mis-specified relative pairs in the 20 SAFS families and 4 cryptic-related pairs in the set of putatively unrelated individuals.The authors declare that they have no competing interests.Study design: LS. Analysis: AD and LS. Manuscript drafting: LS and AD. All authors read and approved the final manuscript.


Language difficulties have historically been viewed as integral to autism spectrum conditions (ASC), leading molecular genetic studies to consider whether ASC and language difficulties have overlapping genetic bases. The extent of genetic, and also environmental, overlap between ASC and language is, however, unclear. We hence conducted a twin study of the concurrent association between autistic traits and receptive language abilities. Internet-based language tests were completed by ~3,000 pairs of twins, while autistic traits were assessed via parent ratings. Twin model fitting explored the association between these measures in the full sample, while DeFries-Fulker analysis tested these associations at the extremes of the sample. Phenotypic associations between language ability and autistic traits were modest and negative. The degree of genetic overlap was also negative, indicating that genetic influences on autistic traits lowered language scores in the full sample (mean genetic correlation = −0.13). Genetic overlap was also low at the extremes of the sample (mean genetic correlation = 0.14), indicating that genetic influences on quantitatively defined language difficulties were largely distinct from those on extreme autistic traits. Variation in language ability and autistic traits were also associated with largely different nonshared environmental influences. Language and autistic traits are influenced by largely distinct etiological factors. This has implications for molecular genetic studies of ASC and understanding the etiology of ASC. Additionally, these findings lend support to forthcoming DSM-5 changes to ASC diagnostic criteria that will see language difficulties separated from the core ASC communication symptoms, and instead listed as a clinical specifier. Autism Spectrum Conditions (ASC) are neurodevelopmental conditions characterized by atypical social and communication abilities, and by repetitive, restricted patterns of behavior and interests . Twin stSince the pioneering work of While candidate gene studies yielded some initially promising findings, associations between ASC and variants associated with language impairment have yet to replicate in genome-wide association studies e.g. . FurtherThe aim of the present study was hence to investigate the extent to which traits characteristic of ASC and language ability share genetic and environmental influences with one another using the classical twin design. One twin study to date suggested that autistic traits at age 8 and expressive language in early childhood share limited genetic and environmental influences with one another in the general population  and at tWe hence explored the aetiological associations between autistic traits and four different receptive language skills in a general population twin sample. We also aimed to test whether similar associations would emerge across three core autistic trait domains , and whether similar associations would be present at the extremes of the general population. While language impairments are not universal in ASC, a considerable proportion of individuals with ASC do appear to present with language difficulties, particularly in pragmatic domains. We hence hypothesized that autistic traits and receptive language would share a considerable degree of their aetiological influences with one another in the full sample and at the extremes. We also hypothesized that communication atypicalities characteristic of ASC would display the strongest degree of aetiological overlap with receptive language.The Twins Early Development Study (TEDS) is a population-representative, longitudinal, community sample of twins born in England and Wales between 1994–1996 . ParentsParents completed the Childhood Autism Spectrum Test (CAST ), compriReceptive language abilities were assessed using four internet-based, self-report measures. Internet-based testing offers the considerable advantage of allowing vast data to be collected. Validity of the in-person forms of these tests is described below; as such only indirect information on validity of the internet versions is available. Similar internet-based measures in mathematics and reading abilities administered to the TEDS sample at age 12 correlated with results obtained from the in-person versions of the tests . In all The Figurative Language subtest of the Test of Language Competence FL;  requiresThe Making Inferences subtest of the Test of Language Competence [Pragmatics; Participants completed the Listening Grammar subtest of the Test of Adolescent and Adult Language Syntax; . ParticiParticipants completed a multiple-choice adaptation of the vocabulary subtest of the Wechsler Intelligence Scales for Children [Vocabulary; ph). One twin was randomly selected per pair when computing these correlations to account for the non-independence of twin data.Phenotypic associations in the full sample were explored using Pearson correlations between the measures  and non-additive genetic influences (‘D’), arising from interacting alleles within loci. Environmental influences are also estimated, and include shared (‘C’) environmental influences, which are common to both twins in pair, heightening their similarity, and nonshared (‘E’) environmental influences, which differ between twins and create cross-twin dissimilarity.Analyses began with cross-twin correlations, which indicate the extent of genetic and environmental influences, derived separately for MZ and DZ twins. MZ twins are assumed to share all of their segregating DNA code, while DZ twins are assumed to share ~50%. When MZ cross-twin correlations exceed DZ cross-twin correlations, A is indicated; E is indicated where the MZ correlation is less than unity. C is implicated if the DZ cross-twin correlation is at least half the MZ statistic. Where the DZ cross-twin correlation is less than half the MZ statistic, D is implicated.ph between traits. If the MZ cross-trait cross-twin correlation exceeds the DZ cross-trait cross-twin correlation, A influences on covariance are implied. Influences of E on covariance are indicated if the MZ correlation is less than the phenotypic correlation, while C is indicated when the DZ cross-trait cross-twin correlation is greater than half the MZ statistic. D is implicated when the DZ cross-trait cross-twin correlation is less than half the MZ statistic.Cross-trait cross-twin correlations, which correlate one twin’s score on one measure with their co-twin’s score on another, assessed etiological contributions to covariance between phenotypes. Cross-trait cross-twin correlations cannot exceed rg) is calculated, and falls between −1 and 1. Wherer rg = 1 or −1, all additive genetic influences are common to two phenotypes, while if rg = 0, then all these influences are independent across phenotypes. Shared environmental (rc),non-additive genetic (rd), and nonshared environmental (re) correlations were also computed, and operate in the same manner.Structural equation twin model fitting was used to estimate A, C, D, and E. A Cholesky decomposition, presented here as a mathematically equivalent correlated factors solution , was fita1 and a2 are A for the first and second phenotype respectively, rg is the genetic correlation between them, and rph is the phenotypic correlation. The extent of C, E, and D influences on the phenotypic correlation can be calculated in a similar manner.An additional statistic is bivariate heritability, which estimates the proportion of the phenotypic correlation explained by additive genetic influences, and is calculated:2 distributed, with degrees of freedom (df) equivalent to the difference in number of parameters between two models, enabling a statistical comparison of fit. Significant χ2 results indicate that a given model is a poorer fit relative to the comparison model. Akaike’s Information Criterion (AIC), calculated χ2 - (2 × df), further assessed model fit. Lower values reflect better fitting models. Each model was fitted with estimates equated across sexes and quantitative sex limitation, which assumes the same etiological influences operate to differing extents in each sex.Fits of Cholesky decompositions were compared with that of saturated models of the observed data using the likelihood-ratio test. The -2LL fit statistic was calculated for each model. The difference in -2LL between two models is χThe best fitting full model was selected using AIC. Within the best-fitting model, nested models were tested by dropping certain parameters by constraining them to equal zero. Nested models were tested with likelihood-ratio tests.The CAST and its three subscales were log transformed for positive skew. Two language measures, Pragmatics and Vocabulary, were also skewed, and hence log transformed see . The meaData from extreme-scoring groups within the sample were analysed to test the degree of genetic overlap between extreme autistic traits and language difficulties. All scales were z-transformed. Probands were defined on the basis of scoring within the highest 5% of the CAST distributions, or the lowest 5% of the language ability distributions. Subsequently, more extreme thresholds were employed; the highest 2.5% of the CAST distributions and lowest 2.5% of the language score distributions.Phenotypic group correlations measure the relationship between two phenotypic scores in extreme-scoring groups. They were calculated by dividing the mean proband z-score on one measure with the mean proband z-score on the measure used to select probands. These estimates provide an indication of the extent of the phenotypic association between the measure used to select probands and proband quantitative scores on the second measure of interest.2g), the genetic contribution to extreme scores, was then estimated by fitting the following regression equation to the data:C is co-twin scores on the measure of interest, β1P is the coefficient for proband scores on the same measure, β2R is the coefficient for zygosity, and A is the regression constant. β2R equals twice the difference between the transformed MZ co-twin mean and transformed DZ co-twin mean, and is an estimate of h2g. This should not exceed the transformed MZ co-twin mean, but may in the instance that non-additive genetic influences operate. Whenever this occurred, h2g was constrained to equal transformed MZ co-twin mean.DeFries-Fulker extremes analysis estimates heritability of extreme scores through regression-based analyses of means . Scores DeFries-Fulker analysis can be extended to examine genetic overlap between extreme scores on two measures . Proband2.xy), which indicates the degree of genetic influences on the selection variable that also influence the outcome variable. h2.xy is bi-directional, in that it could, for example, be used to explore the relationship between the CAST and TOAL using the CAST as the selection variable and TOAL as the outcome, and vice-versa.Bivariate DeFries-Fulker analysis also estimates bivariate heritability  to be calculated, which estimates genetic overlap between extreme scores [xyβ is bivariate heritability using the first variable of interest as the selection variable, yxβ is the reverse, and xβ and yβ are h2g estimates for each phenotype. All regression equations included sex and age.Calculating he scores :(βxy×βySee P < 0.01). The mean phenotypic correlations between the CAST subscales and language measures were −0.08 , −0.06 (RRBI), and −0.18 , −0.15 , and −0.16 (Vocabulary) (ph), suggesting E influences. Modest C influences were also implicated.Twin correlations are presented in 2160 = 216.02, p < 0.01, AIC = −103.98; all fit statistics are provided in An ACE model with quantitative sex limitation best fit the full-scale CAST and language data, χg) ranged from 0.01 to −0.18, suggesting few common A influences on language and autistic traits. Non-shared environmental correlations (re) was also low, ranging from −0.08 to −0.01. Shared environmental overlap (rc), however, was higher (−0.43–−0.99), although confidence intervals were wide , while was E modest (0.28–0.32). Etiological overlap between the social subscale and language was low, rWithin the highest 5% of the CAST distribution, phenotypic group correlations with the language measures were similar to the full sample: −0.13 (FL), −0.14 (Syntax), and −0.15 (Pragmatics and Vocabulary). In the highest 5% of the CAST subscale distributions, these ranged from −0.07–−0.17. Within the highest 2.5% of the CAST distribution, phenotypic correlations were −0.11 (FL and Vocabulary), −0.12 (Pragmatics), and −0.13 (Syntax). Within the highest 2.5% of the CAST subscales, these values fell between −0.06–−0.17.2g) estimates were substantial for the CAST and its subscales, ranging from 0.69 to 0.76, and modest for the language measures, ranging from 0.18 to 0.55.Transformed means are presented in the supplementary materials. Across all measures in both extreme-scoring groups, the transformed DZ co-twin means regressed towards the population mean to a greater extent than the transformed MZ co-twin means, suggesting genetic influences on extreme scores. Group heritability (h2.xy) suggested the proportion of the modest phenotypic group correlations that could be explained by additive genetic influences ranged from none to the entire phenotypic group correlation. There was evidence of non-additive genetic influences on some phenotypic group correlations. Across all CAST subscales and language measures, rg was modest. In the 5% extreme-scoring group, the highest estimate was 0.32 (CAST Communication – Vocabulary), while the lowest was 0.01 . In the 2.5% analysis, rg fell between 0  and 0.26 (CAST Communication – Vocabulary). The results of the DeFries-Fulker analyses are fully presented in the Bivariate heritability (hWe aimed to examine the concurrent association between autistic traits and receptive language skills in a general population sample. The historically advocated link between ASC and language led us to expect relatively strong phenotypic and etiological associations. Contrary to this, all four language measures displayed weak etiological and phenotypic links with autistic traits, which extended across three autistic trait domains and to the extremes of the general population. This pattern extended to communication atypicalities characteristic of ASC, which were expected to show stronger overlap with language.As mentioned previously, the historic link between ASC and language has motivated some molecular genetic studies to question the role of variants thought to associated with language in ASC e.g. . In our There are two further possibilities regarding these findings. First, they could be taken as adding evidence to the fractionable autism triad hypothesis . This hyAlternatively, these findings could be taken as quantitative genetic support for the separation of language difficulties from the ASC phenotype. In the DSM-5 , languagA notable exception to these findings was shared environmental overlap, which was substantially higher than additive genetic and nonshared environmental overlap. However, it is important to note the wide confidence intervals around the shared environmental correlations see , which oAs with any study, our research was not without limitations. Autistic traits were assessed by a single rater; future research should test whether these findings extend to self- and teacher-reported autistic traits. Some researchers question the extent to which findings from twins generalize to singletons. However, recent studies suggest that twinning does not elevate autistic trait scores . AdditioIt is a limitation that the internet-based versions of the language tests used here have yet to be extensively validated. While Our large sample meant that administering in-depth clinical assessments was not feasible. This was not, however, necessarily a limitation; trait-based questionnaires can complement research with clinically based samples by enabling the large samples required to perform twin modelling to be studied, whilst avoiding biases associated with clinical samples. There is also evidence of continuity between heritability of autistic traits in the general population and in extreme-scoring groups, including those scoring at a comparable level with diagnosed samples .In addition, our findings do not necessarily apply to ‘syndromic’ ASC. Syndromic cases of ASC are associated with a known genetic cause , and oftIn conclusion, general population variation in autistic traits and receptive language ability are caused by largely different etiological factors. Additionally, quantitatively defined language difficulties appear to be caused by different additive genetic influences to extreme scores on autistic trait measures. This suggests that molecular genetic studies of ASC and language impairments will produce largely discrepant findings. Furthermore, these findings lend support to the imminent removal of language impairments from the core ASC symptoms, instead being listed as a clinical specifier.Supplementary Tables 1-6