Assuming half-sibling, the pedigree-based model was limited to estimating the additive genetic variances which, in turn, were grossly overestimated as they were confounded by very minor dominance and major additive-by-additive epistatic genetic variances. In contrast, the implemented genomic pairwise realized relationship models allowed the disentanglement of additive from all nonadditive factors through genetic variance decomposition. The marker-based models produced more realistic narrow-sense heritability estimates and, for the first time, allowed estimating the dominance and epistatic genetic variances from OP testing. In addition, the genomic models showed better prediction accuracies compared to pedigree models and were able to predict individual breeding values for new individuals from untested families, which was not possible using the pedigree-based model. Clearly, the use of marker-based relationship approach is effective in estimating the quantitative genetic parameters of complex traits even under simple and shallow pedigree structure.The open-pollinated (OP) family testing combines the simplest known progeny evaluation and quantitative genetics analyses as candidates’ offspring are assumed to represent independent half-sib families. The accuracy of genetic parameter estimates is often questioned as the assumption of “half-sibling” in OP families may often be violated. We compared the pedigree-  Don) (Picea glauca (Moench) Voss × P. engelmannii Parry ex Engelm.] (Pseudotsuga menziesii (Mirb.) Franco]  (P. sylvestris L.) (Open-pollinated (OP)  family testing is, by far, the simplest and most economical means for screening, evaluating, and ranking large numbers of candidate parent trees. Thus, OP testing combines the simplest known field experimental design in pedigree testing as candidate trees enter the test as maternal parents and their offspring are assumed to represent independent half-sib families. OP testing has been widely implemented for several tree species throughout the world,  D. Don) , interioEngelm.] , Douglas Franco] , westerntris L.) .i.e., partial pedigree) is positioned between the “no pedigree” provenance testing  is superior to the former yet somewhat limited compared to the latter  which can be used to substitute the A-matrix  for estimating genetic parameters can be circumvented in the so-called “pedigree-free models” using the G-matrix. As already demonstrated in earlier cases, the G-matrix can provide relatively accurate genetic variance components and breeding value estimates without the need for elaborate mating designs  have become available for model and nonmodel species  overcome the drawback of the average numerator relationship matrix (A-matrix) as genomic data will unravel any undetectable hidden relatedness such as full-sibs, self-sibs, and self-halfs that inflates the estimated additive genetic variance (vs. absent QTL)  proHere, we used 214 white spruce OP families grown on one site  in a randomized complete block design, replicated over six blocks (replications) with each OP family represented by five-tree row plots within each of the six blocks  phenotypic and genotypic data used are available online from the Dryad Digital Repository: doi:10.5061/dryad.6rd6f , u is the vector of random additive genetic effects following u ∼ N, where A is the average numerator relationship matrix and r is the vector of random replication effect following r ∼ N, where rxfis the vector of random replication × family interaction effects following rxf ∼ N, where e is a vector of the random residual effects following e ∼ N, where X, iZ, jZ, and kZ are incidence matrices relating fixed and random effects to measurements in vector y.The variance components from pedigree-based analysis (ABLUP) were obtained by solving the following mixed model:A is substituted by the marker-based relationship matrix addG. The extended model for the dominance terms are performed as follows:d is the vector of the random dominance effect following d ∼ N where axa is the vector of random additive × additive epistatic interaction effects following axa ∼ N, where dxd is the vector of random dominance × dominance epistatic interaction effects following dxd ∼ N, where axd is the vector of random additive × dominance epistatic interaction effects following axd ∼ N, where The variance components from the analysis using the marker-based additive relationship matrix (GBLUP-A) were obtained from the model described above but the average numerator relationship matrix Narrow-sense heritability was estimated as ectively . The anaF, where F = L-1/2VL-1/2 using the asymptotic variance–covariance matrix of estimates of variance components V and its diagonal matrix L (Models were compared using the Akaike Information Criterion (AIC) estimates obtained from each analysis , PBV is the individual additive breeding value of the validation population obtained using the mth model  and nth cross-validation scenario , σ is the standard deviation. SEM for the correlations was computed using the following equation:σ is the standard deviation of the Pearson correlations and n is the number of replicates.Prediction accuracy within and consistency between models was evaluated using the mean Pearson correlation from the five replications. Specifically, the correlation values for each replication were calculated as:The data used are available from the Dryad Digital Repository: doi: 10.5061/ dryad.6rd6f . Overall, narrow-sense heritability was reduced by 65% for height and 50% for wood density when the genomic relationship matrix GBLUP-A was employed  and wood density (1 and 2–5%), leaving most of the within-replication effects residing within the residual terms . The greemployed , highligDiscussion). Including dominance variance in the models increased the AIC values for the models, indicating that GBLUP-AD models were overfitted compared to GBLUP-A models  of breeding values (BV) between the ABLUP and GBLUP-A models, all of the SEPs for height and wood density BVs were smaller for GBLUP-A compared to ABLUP as all SEPs were below the 45° reference lines, clearly indicating the superiority of the GBLUP-A model . GBLUP-ACross-validation prediction accuracies (Pairwise model comparisons (A-matrix) is used to estimate the genetic variance components for forest tree progeny test populations. The estimated genetic variance components  often are mating design-dependent and the mating scheme determines which component can be obtained. In most cases, this approach is incapable of disentangling the within-family genetic from within-family coenvironment effects. This is even more problematic in OP family screening as separating additive from nonadditive genetic variances is limited by shallow pedigrees and lack of connectedness among the tested families; furthermore, as shown in G-matrix) among these individuals. In turn, the G-matrix can be used as a substitute to the A-matrices to estimate more accurate and precise genetic variance components as the G-matrix represents the realized pedigree as well as having the capacity to exploit the Mendelian sampling/segregation within families  has recently been explored  genetic components requires elaborate mating designs with large numbers of interconnected full-sib families coupled with the inclusion of replicated clonal material , (2) discerning whether full-sibs, self-sibs, and self-halfs existed within the studied 214 OP families, (3) the ability to estimate among-family relationships . The observed reduction in the additive genetic variance between the two models (ABLUP vs. GBLUP-A) resulted in concomitant increase in the residual error terms and hence considerably reduced narrow-sense heritability estimates for height (0.25 vs. 0.16) and also for wood density (0.61 vs. 0.30) along with improvement in the model fit based on improved AIC values (vs. GBLUP-A).It is interesting to note that the estimated additive genetic variances for the three realized genomic relationship matrix-based analyses  were lower than those of the average numerator relationship matrix (ABLUP) , an obseC values . AdditioIt is noteworthy to mention that the present study is based on data collected from one site, thus there is a chance that the estimated genetic parameters could be upwards biased due to the genotype × environment confounding effects specific to this particular site or year. However, results from similar analyses for the same species and attributes for a set of 25 OP families planted in replicated trials over three sites in British Columbia were consistent with those reported here with the added benefit of estimating the additive and dominance × site (environment) interactions .Table S1).The observed overall trend in genetic variance decomposition persisted when the dominance genetic variance was estimated using the alternative genotypic approach proposed by Additionally, estimating the dominance genetic variance is only feasible when full-sib families are available (Table S1). When we removed the dominance genetic variance from the GBLUP-ADE model, the revised models (GBLUP-AE) produced better model fit for height  and wood density , confirming that dominance variance was negligible . Similar magnitude of the additive × additive epistatic variance to that of the additive variance, per se, was also observed in loblolly pine .The model that included the additive, dominance, and epistatic variances (GBLUP-ADE) offered better partitioning of the variance complements, as the additive × additive epistatic variance became extremely pronounced and accounted for 11 and 52% of the total variance for height and wood density, respectively (gligible . Intereslly pine . The powlly pine . Howeverlly pine . This inThe subject of genetic epistasis is controversial as all variance components, including epistasis, are dependent on the allele frequencies in the studied population. Thus, epistasis could have an allusive and unique effect across different scenarios . The rolvs. the GBLUP-ADE/GBLUP-AE (see details in the interaction plots of When ABLUP is used to estimate the genetic variance components from either half- or full-sib families, the above factors are barely considered, except those that were captured through common ancestry. As indicted above, the OP/half-sib structure is incapable of estimating the dominance and the epistatic genetic variances. This situation was clearly demonstrated in the study by We feel that our results have important and immediate implications for tree improvement programs in forestry as most programs are long-term and resource-dependent . The con


Common diseases like essential hypertension or diabetes mellitus are complex as they are polygenic in nature, such that each genetic variation only has a small influence on the disease. Genes operates in integrated networks providing the blue-print for all biological processes and conditional of the complex genotype determines the state and dynamics of any trait, which may be modified to various extent by non-genetic factors. Thus, diseases are heterogenous ensembles of conditions with a common endpoint. Numerous studies have been performed to define genes of importance for a trait or disease, but only a few genes with small effect have been identified. The major reasons for this modest progress is the unresolved heterogeneity of the regulation of blood pressure and the shortcomings of the prevailing monogenic approach to capture genetic effects in a polygenic condition. Here, a two-step procedure is presented in which physiological heterogeneity is disentangled and genetic effects are analyzed by variance decomposition of genetic interactions and by an information theoretical approach including 162 single nucleotide polymorphisms (SNP) in 84 genes in the sphingolipid metabolism and related networks in blood pressure regulation. As expected, almost no genetic main effects were detected. In contrast, two-gene interactions established the entire sphingolipid metabolic and related genetic network to be highly involved in the regulation of blood pressure. The pattern of interaction clearly revealed that epistasis does not necessarily reflects the topology of the metabolic pathways i.e., the flow of metabolites. Rather, the enzymes and proteins are integrated in complex cellular substructures where communication flows between the components of the networks, which may be composite in structure. The heritabilities for diastolic and systolic blood pressure were estimated to be 0.63 and 0.01, which may in fact be the maximum heritabilities of these traits. This procedure provide a platform for studying and capturing the genetic networks of any polygenic trait, condition, or disease. Essential hypertension refers to hypertension with no known cause, affects approximately 30% of the adult population, and is a major risk factor for stroke, coronary incidences, and end-stage renal disease  may be the most important genetic contribution to the variance of a trait, not the main effects  studies  framework using common physiological variables generally assumed to be related to cardiovascular conditions  into an ensemble of 14 physiological more homogeneous subpopulations, i.e., more accurate phenotypes were defined ] is χ2-distributed with 4 df and only interactions significant after correction for multiple testing were included in the analysis.Two-gene interactions are actually measures of the mutual information  were done in a classical case-control design in which each subpopulation were compared to each of the other subpopulations. Also, each subpopulation (“cases”) were compared to the remaining subjects (“controls”) in the study population. Significant two-SNP genotypes as evaluated by WMI (above) were analyzed in a case-control design in the entire population for diastolic and systolic hypertension separately.p-value of 0.05 were applied to all analysis, unless stated otherwise. The Python packages Numpy, Scipy and Powerlaw were used in programmed algorithms. Plots were generated by QtiPlot v 0.9.8.8 on the Ubunto Linux platform.Basic statistics were performed in SPSS v19.0 on a PC, or in LibreCalc on the Ubunto Linux platform. Bonferoni correction for multiple testing with a nominal A parallel, multi-threaded software package for variance decomposition, analyses of epistasis, mutual information analysis and topology of the networks is under development in Python and will be freely available shortly.N = 39) was not further evaluated as none of the subjects were allocated to this subpopulation with a probability above 0.3. All the remaining subpopulations did contain subjects with an allocation probability of 0.9 or above although the number subjects and valid SNPs (exclusion of SNPs not in HWE) declined with increasing allocation probability  did not show a consistent pattern and differs between the subpopulations. In some subpopulations, including subjects allocated with a probability of 0.7 or above, the number of interactions was highest, but this it not the case in all subpopulations Tables , S3. ResThe WMI was increased  when the allocation probability was increased for all MAF levels in all classes Tables , S3. HowSubpopulations 3, 8, and 11 differs from in this general analysis from the other subpopulations in several ways and will be treated separately below.Stratifying the population according to gender only provide little information about the networks. Although thousands of significant interactions were detected  only a few accounted collectively for 50% or more of the WMI, which is anyhow low compared to the subpopulations extracted by the LCA/SEM procedure Tables , 2. FourThe GALC (rs398607)/GALC(rs34362748) interaction was prominent in both gender and particular for diastolic blood pressure. The explained variance by this interaction in the gender partition was 8.7% or below. This SNP-combination was recovered in most but not all subpopulations although with very low information content (WMI). The prevalence of hypertension associated with this SNP-combination did not significantly differ from population prevalence of hypertension, however. The FABP2 (rs1511025)/FABP2 (rs1799883) interaction was recovered in some subpopulations, but all with very low WMI and none significantly influenced the prevalence of hypertension.Interestingly, the two dominating interactions in the subpopulations  were consistently detected regardless of MAF and allocation probability level except in subpopulations 3, 8, and 11  of the maximum amount of interaction encountered at a probability allocation threshold of 0.7 Tables , S3.R2 ~ 0.98), that is the larger the genetic influence of the two-SNP genotypes the lower phenotypic variance and hence a lower impact of non-genetic factors, supporting the assumption that the genetic network sets the level and the range of variation possible for an individual as well in a homogenous subpopulation. It could be expected that the relative epistasis was correlated to the genotypic variance too, but the correlation turned out to be were low (not shown). The two two-SNP genotypes with the highest genotype/phenotype variance (and lowest phenotypic variance) are the SPHK1 rs8176328/rs2247856 genotypes (distance 12 nt) and the ASAH1 rs1049874/rs1071645 genotypes (distance 1482 nt). This is consistently seen for all subpopulations except subpopulation 3 and partly subpopulations 8 and 11 . Slightly more than one third of the two-SNP WMIs (39.2% for diastolic blood pressure and 35.5% for systolic blood pressure) were private in the sense that they only occurred in one subpopulation Tables , S5. MosSubpopulation 3 showed a different pattern of interactions as the ubiquitous interactions were not captured. The number of valid SNPs i.e., non-monomorph SNPs which are in HWE was reduced significantly to almost half compared to the other subpopulations. The vast majority of SNPs were excluded because they “turned” monomorph and hence non-informative, which particularly included the SNPs defining the ubiquitous genotypes except the SPHK1 rs8176328. ASAH1 was not detected at all. Consequently the major source of information was missing and the information retained by the remaining SNPs was extremely low amounting to 1% or less compared to the other subpopulations . In contrast, the ubiquitous SPHK1/SPHK1 interaction was detected for diastolic blood pressure but not for systolic blood pressure though Tables , S5. HowThe ubiquitous SPHK1/SPHK1 interaction was highly significant for diastolic and systolic blood pressure and possessed high WMI values in subpopulation 11. In contrast, although ASAH1/ASAH1 interactions were detected by the WMI analysis, the ubiquitous combination above were not detected. The ASAH1/ASAH1 interactions was however “substituted” by a SMPD4  with high WMI. SMPD4 codes for the neutral membrane sphingomyelinase 3 generating ceramide, while ASAH1 codes acid ceramidase generating sphingosine in the salvage pathway . Subpopulation 8 was included in these calculation using a allocation probability threshold of 0.7 rather than 0.9, but still the curve fittings converged in a few iterations for the Boltzman and Gauss fits. The only difference was that the correlation between heritability and phenotypic variance showed a exponential decay (R2 ~ 0.98) in contrast to the remaining subpopulations, where the correlation was linear (R2 ~ 0.98). In contrast, subpopulation 3 did not fit into this general pattern. The heritability implied by the sphingolipid metabolism was only ~0.07, but still significant.The heritability of blood pressure regulation as a function of the WMI is plotted in Figure The two ubiquitous interactions defined by ASAH1 and SPHK1 were supplying the most information in all subpopulations except in subpopulation 3. These two genes are pivotal in the ceramide/sphingosine-1 phosphate rheostat: ASAH1 codes for acid ceramidase generating sphingosine and SPHK1 phosphorylate sphingosine to generate sphingosine-1 phosphate . Most of the classes do have α-values in this range, with a few classes outside this range for the nominal significant WMI ~xMI Table . HoweverThe degree sequences of the SNPs and genes for the WMI data sets show a similar pattern of distributions as for the WMI data sets themselves. The gene degree sequences for diastolic and systolic blood pressure are almost identical Table . SeveralIt should be kept in mind that the above conclusions are for the most part conjectural founded on the “naive” assumption that a higher degree of a gene equals importance. The real importance of a gene is the information it supplies by interaction with the other genes. Nevertheless, the above analysis is supportive of the conclusions obtained from the WMI analysis.All populations are heterogenous due to the vast genetic variation present, and all genes only operates in integrated networks Fenger, . A recenDetection of genes and extra-genic variations of importance relies heavily on the reliability and accuracy of the phenotypes. This is clearly seen by comparison of the gender-based partition with the physiologically modeled partition, where there was more than a 300-fold increase in genetic information provided by the interactions, and more than a 15-fold increase in the number of significant interactions when corrected for multiple testing Tables . Most inThe WMI introduced here is a measure of the amount of information that the interacting genes provide about the trait. This measure is tightly related to the relative genetic variance in particular including all two-SNP/gene interactions Figure . As can It was expected that the node degree sequences of the genes were distributed as a power law or Poisson distributed, but to the contrary only a small fractions of the genes were captured by the power law distribution. Most of the genes did not conform to any of several continuos distributions and appears totally random distributed. This trend is confirmed in analysis of effects sizes and variances in which the data sets on average contains more than 5000 samples. However, when only data corrected for multiple testing were included a bipartite structure appeared: the power law distributed data did only capture a fraction of the data, while the Poisson distribution did not fit the entire set of data (corrected for multiple testing); rather, the data set can be split in two components, one captured by the power law, the other by Poisson distributions (as in the famous and widely applied Erdös-Rényi random graph, Erdös and Rényi, The influence of the sphingolipid network on the blood pressure regulation was quite large, while the impact of the phosphatidate and redox networks seemed to be limited. Caution should be observed with this conclusion as the selection of genes, mostly from the sphingolipid metabolic network, may have been fortuitous. Other genes or combination of genes could harbor more information than the ubiquitous genotypes above, but the heritability will only increase marginally if at all considering the fits shown in Figure Only a few of the valid SNPs have previously been associated with any clinical condition Tables . Some ofThere have been contrasting views about the importance of epistasis in genetic systems. Crow argues that epistasis is unimportant in polygenic directional selection Crow,  suggestiGenerally, the physiological and biochemical interpretation of the interactions revealed in the present study are highly theoretical as both metabolic and functional interactions are possible. Most probably, many of the interactions, apart from the flux of metabolites in the networks, may include elements of stereogenic interactions of the components generating integrated complexes of enzymes Lehner,  located 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.


Gammarus concluded in a weak potential for genetic adaptation to cadmium (Cd), while others reported inheritable increased tolerance in Cd‐contaminated populations. Using quantitative genetics and selection experiments, this study sought to further assess the potential of Gammarus populations to genetically adapt to Cd. By combining the control of the reproductive cycle of this species in the laboratory and protocols of individual Cd exposure, we conducted half‐sib analyses to establish the genetic and environmental sources of variance in Cd sensitivity of neonates. Prior to experiments, computations allowed optimizing the experimental design in order to increase the power to detect additive genetic variance. The main findings are the existence of strong between‐brood variability along with weak heritability of Cd sensitivity within Gammarus populations. This study also revealed a significant maternal effect on individual Cd sensitivity. This sheds new light on the importance of maternal influence in microevolutionary processes occurring in contaminated environments.Deciphering evolutionary processes occurring within contaminated populations is important for the ecological risk assessment of toxic chemicals. Whereas increased tolerance to contaminants is well documented in aquatic animal populations, whether such phenotypic changes occur through genetic adaptation is still debated. In that sense, several studies with the freshwater crustacean  Indeed,G. fossarum, along with the fact that the conclusion on the absence of additive genetic variance in Cd sensitivity in this species can be disputed with regard to the lack of statistical power of the sib design employed  of the trait ‘Cd sensitivity’  between the different causal components of variance, namely (i) additive genetic variance (VA), (ii) nonadditive genetic variance, which includes both dominance effects (VD) and epistatic interactions (VI), and (iii) environmental variance (VE)  of Cd sensitivity, as well as a nongenetic maternal component within environmental influences. Two different naïve populations of G. fossarum from uncontaminated streams were tested because heritability of a given character is specific to a particular population under particular conditions  by means of computations before experiments, seeking to maximize the statistical power for VA detection. Overall, beyond the validation of the hypothesis of a weak potential for Gammarus populations to genetically adapt to Cd, the experimental design demonstrated an unexpected significant maternal effect on the distribution of individual Cd sensitivity within populations. This result sheds new light on the importance of maternal influence in transgenerational processes underlying evolution of tolerance to contaminants.This recent observation of increased Cd tolerance in field populations of s et al.  that allGammarus fossarum adults were collected at an upstream location of the Bourbre River, Isère, France , a population denoted ‘Tour’, which corresponds to the population used in our previous study , a 16‐h light/8‐h dark photoperiod, and a temperature of 12°C. They were fed ad libitum with conditioned alder leaves (Alnus glutinosa) and supplied weekly with Tubifex larvae.−1, by means of semistatic exposure in 50‐mL polypropylene tubes . The concentration of 20 μg Cd L−1 was determined from Chaumot et al. . Hence, in previous studies considering Gammarus juveniles from the Tour population  and with drilled groundwater mixed with osmosed water at constant conductivity (300 μS cm−1) and water hardness . For each experiment, juveniles were not fed during exposure and they were exposed at a predetermined age, taking into account their date of release from the maternal brood pouch.In exposure conditions, a random spatial distribution of replicates, populations, and/or conditions within experimental systems was applied in all experiments. Cd was provided by Sigma‐Aldrich . To assess offspring Cd sensitivity, the sensitivity of juveniles was assessed individually by measuring time during exposure to the lethal level of 20 μg Cd Lt et al.  with the−1 for 4 days during semistatic exposure, in replicates of ten pairs in 500‐mL polypropylene beakers. The test solution was renewed every 24 h from a common solution of a nominal 100‐μg Cd L−1 concentration prepared every 24 h. Animals were not fed during the exposure, and dead animals were removed every day. One hundred additional mating pairs were submitted to the same treatment except for Cd exposure in order to provide control genitors. Replicates were pooled after exposure in 6‐L tanks and maintained under control conditions for approximately 2 months. Spermatogenesis, embryogenesis dynamics, and female reproductive cycle are fully described in G. fossarum  that could arise during the rearing of juveniles in the laboratory until they reach sexual maturity . The first batch of juveniles (obtained 1 week after the selection of mating pairs) was constituted by individuals with unknown fathers (fertilization in the field before sampling), and the second batch (released 1 month later) by the offspring of the guarding males present when pairs were selected. After the first fertilization of females, males were randomly redistributed between beakers, so that females would be fertilized by a different male for the third brood. Thus, at the end, each female produced juveniles from three different males, and each male identified provided offspring from two different females. This controlled mating scheme gave rise to three batches of broods for each population yielding both paternal and maternal half‐siblings. Juveniles were exposed to 20 μg Cd L−1 beginning the day following their release from the maternal brood pouch. The same protocol as described for the offspring in the artificial selection experiment was followed.The same breeding protocol as described in Chaumot et al.  was usedVP) can be related to the observational components of variance in the different sib designs , common environment influences are restricted to the marsupial incubation period. Therefore, beside a residual environmental variance (VEw), we distinguished two components in the common environment variance (VEc): a maternal effect (VEm)  and a brood‐specific maternal effect (VEsm) .As detailed in Table S1, the causal components of phenotypic variance of Cd sensitivity , namelyHeritability was estimated from both the paternal and the maternal designs, from sire and dam components, respectively, as follows:The degree of similarity between sibs was also quantified by means of intraclass correlation coefficients. Hence, full‐sib correlations were calculated from the three designs as follows:from the full‐sib, the paternal half‐sib, and the maternal half‐sib designs, respectively. Paternal and maternal half‐sib correlations were also calculated from the paternal half‐sib and the maternal half‐sib designs, respectively, as follows:Standard errors of heritability estimates and intraclass correlation coefficients were calculated as described by Lynch and Walsh  for balaAll statistical procedures and computations were carried out with the R software (R Development Core Team σB‐FS) was affected by the reduction in the number of sibs tested per brood (from ten to three). This allowed setting the number of juveniles tested per brood to conduct further experiments. Thereafter, we similarly assessed the precision of the estimate of the sire effect (σS‐PHS) in the paternal half‐sib design for different numbers of sires tested considering different values of h2. The distribution of σS‐PHS estimates was established from 100 simulated datasets of paternal designs considering two mated females per male, respecting interbrood and residual variance estimated by Chaumot et al. .The experimental design for sib analyses was optimized based on the estimates of variance components of Cd sensitivity from the previous study conducted with the Tour population  for the three batches of each population separately. The model without a brood effect was fitted using the gls function from the nlme library using the REML method. For the paternal  half‐sib design, we built a model considering a random sire  effect, a random dam effect nested within the sire effect , and a residual environmental effect. The significance of the sire  effect was assessed by LRT between the full model and a nested model considering only one random brood effect. The possibility of an effect induced by the fact that three batches of broods were exposed to Cd at three different dates was assessed by testing the significance of a fixed ‘batch effect’ on Cd sensitivity. As this ‘batch effect’ appeared to be significant, it as has been included as a fixed effect in mixed‐effect models for all half‐sib analyses.As in Chaumot et al. , the obsi.e., spermatogenesis in clean conditions) was compared to control offspring from unselected males. After the first fertilization event (16 days after the end of Cd exposure), the survival of Cd‐selected males was equal to 19.5%. After the second fertilization event (58 days after the end of Cd exposure), it was only equal to 12.5%. This corresponds to 64% survival between the two copulations, whereas it exceeded 85% for unselected control males. This postexposure mortality thus implied that the percentage of males selected for their Cd resistance was not 20% as expected, but between 12.5% and 19.5%. Nonetheless, postexposure mortality was rapidly stabilized after the first fertilization event . Finally, 42, 36, and 39 juveniles from the second batch of broods were exposed to 20 μg Cd L−1 for conditions C‐I, C‐II, and S‐20%, respectively, and 28, 20, and 26 juveniles were used as controls  for the three conditions, respectively. All mortalities occurred in exposed juveniles within 6 days of Cd exposure, and no mortality was observed in juveniles used as control during this time. Time–response curves , indicated that the precision of the σS‐PHS REML estimator (and therefore h2 detection) was substantially improved for h2 values above 0.2 when the number of tested sires increased from 10 to 30 and to a lesser extent from 30 to 200  for low values of h2 (here 0.1). From these findings, experiments were designed seeking to test at least 30 sires in paternal half‐sib designs. Overall, the survival of 713 neonates was individually monitored for the Tour population and 442 for the Bois population. For most of the broods, we obtained five juveniles, but incomplete broods were still included in the analysis because mixed‐effect models make it possible to analyze such unbalanced data . No significant brood effect was detected for the third Bois population batch (LRT: P = 0.29), along with a large 95% confidence interval associated with σB‐FS , but no significant interaction between batch effect and the between‐brood variability . This indicates that there was a variation in the average level of Cd sensitivity between batches, but that the between‐brood variability remained unchanged from the first to the third batch of broods. Therefore, half‐sib analyses were performed including a fixed batch effect in the mixed‐effect models. It should be noted that the median lethal time for juveniles did not change monotonously from the first to the third batch . This disqualifies any hypothesis of uncontrolled selection or depletion of genitors in laboratory conditions, which could induce increasing or decreasing Cd sensitivity in their offspring during the 3 months of the experiment.For both the Tour and Bois populations, linear mixed‐effect modeling of Cd sensitivity detected a significant fixed batch effect (P = 0.818). This is also reflected by the low tPHS and hPHS2 values (Table tFS−PHS (0.236) is more than twice tPHS (0.015) suggests that dominance (VD) and/or maternal effects (VEm and VEsm) contribute to the resemblance between full‐sibs. This substantial contribution of dominance and/or maternal effects is also shown by the significant dam within sire component (σD−PHS), which is much greater than the sire component (Table P = 0.01) (Table σD−PHS) estimate is equal to 0.23 and leads to a hMHS2 of 0.417 (±0.190) and a tMHS of 0.104 (±0.047). This higher resemblance between maternal half‐sibs than paternal half‐sibs (tMHS >> tPHS) suggests that maternal effects are a significant source of variation. Furthermore, the sire‐within‐dam component estimate is large (0.28), with a relatively low 95% confidence interval, which, when VA is null, indicates that VD and/or VEsm also contribute substantially to the total variance . Unfortunately, the genitors from the Bois population were difficult to maintain under laboratory conditions, and some mortality arose during the experiment, resulting in half‐sib designs with a weak statistical power. Indeed, only seven sires were successfully mated with two different dams, and only ten dams were successfully mated with three different sires. Not surprisingly, the analysis of distribution of offspring Cd sensitivity failed to detect either a significant sire effect or a significant dam effect (Table S2), comparable to what was obtained by Chaumot et al. .per se. Indeed, false‐negative detection could arise because only males were selected, potentially leading to a dilution of the frequency of resistance genes by the influx of susceptible alleles from unselected females (Hoffmann and Hercus Heterandria formosa) after only one generation of selection. These authors reported this rapid response for two of three selection lines, while the third selection line only showed an elevated resistance to Cd in the second generation. A false‐negative case could also be that the number of individuals on which we applied the selection pressure  may have been insufficiently large to contain the rare resistance alleles from the field population in case of a major gene determinism of Cd sensitivity , thus resulting in a higher selection intensity than expected. Only selected males were used and not females, to avoid the influence of a nongenetic transgenerational effect of maternal Cd exposure that could bias the evaluation of the response to genetic selection. For the same reason, we tested only the offspring produced by the second fertilization operated by males after their exposure, thus resulting from gametes produced in clean conditions. All of the juveniles used as controls during Cd tests survived for the three conditions, including the S‐20% juveniles. This indicates that direct effects of parent Cd exposure on juvenile fitness were avoided because of the protocol developed. In these conditions, we observed no elevated resistance to Cd in S‐20% juveniles, and so selection for Cd resistance in the Tour population appeared inoperative, at least in the first generation. This negative result is not conclusive σS‐PHS value estimated here for the Tour population is unlikely to be observed  for heritability values >0.2. Therefore, we can conclude that heritability in the Tour population is weak if not null. Furthermore, it appears that a substantially higher number of families would have been needed to detect a low sire component if present. Indeed, as calculated from the simulations for heritability equal to 0.1 and for a design including 400 sires  as well as dominance (VD) and/or a brood‐specific maternal effect (VEsm) were substantial. As classically applied to data obtained from diallel analyses , which accounts for 9% of the total variance of juvenile Cd sensitivity. Despite the fact that a significant maternal effect has been revealed, the residual variance VEw appeared to be quite high. As exposure conditions and organisms were well standardized, this variance is unlikely explained by environmental variance. This high residual variance rather results from stochasticity in death event during exposure. As reviewed by Ashauer and Brown , the substantial similarity recorded between full‐sibs could only be explained by shared nonadditive genetic features or by maternal effects (during egg production and brooding). Hence, we detected a significant dam component in the maternal half‐sib design that was not recorded in Chaumot et al. , indicatnd Brown , the assnd Brown  tested tG. fossarum populations, because we did not observe a response to selection for Cd resistance, and because we confirmed that the heritability of Cd sensitivity was low. Nonetheless, these levels of acute Cd exposure tested in our study (20 μg L−1) can only be recorded in hot spots of metallic contamination, such as rivers impacted by mine drainages, for example, 15 μg L−1 in the Lot watershed . This led to relatively low estimations of h2 (0.23 and 0.06 depending on the temperature). Hence, despite the fact that our findings should not be abusively generalized to environmental conditions, they are in line with the fact that tolerance to contaminants of field populations cannot result solely from genetic adaptation, but also stems from acclimation  .Click here for additional data file.


Pre-eclampsia is a common pregnancy disorder that is a major cause for maternal and perinatal mortality and morbidity. Variants predisposing to pre-eclampsia might be under negative evolutionary selection that is likely to keep their population frequencies low. We exome sequenced samples from a hundred Finnish pre-eclamptic women in pools of ten to screen for low-frequency, large-effect risk variants for pre-eclampsia. After filtering and additional genotyping steps, we selected 28 low-frequency missense, nonsense and splice site variants that were enriched in the pre-eclampsia pools compared to reference data, and genotyped the variants in 1353 pre-eclamptic and 699 non-pre-eclamptic women to test the association of them with pre-eclampsia and quantitative traits relevant for the disease. Genotypes from the SISu project (n = 6118 exome sequenced Finnish samples) were included in the binary trait association analysis as a population reference to increase statistical power. In these analyses, none of the variants tested reached genome-wide significance. In conclusion, the genetic risk for pre-eclampsia is likely complex even in a population isolate like Finland, and larger sample sizes will be necessary to detect risk variants. Pre-eclampsia is a common and complex vascular pregnancy disorder. It is characterized by hypertension and proteinuria, and often involves impaired placental development14Genetic factors contribute to pre-eclampsia susceptibility. Heritability estimates for pre-eclampsia range between 0.54 and 0.68, consisting of both maternal and fetal contribution610111213151618Because pre-eclampsia is a major cause for both maternal and fetal mortality, preterm birth and fetal growth restriction320th century  case-control cohort that was collected from five Finnish university hospitals during 2008 to 2011The first individually Sequenom genotyped sample consisted of 180 pre-eclamptic and 180 healthy pregnant women, including the 100 pre-eclamptic cases originally exome sequenced, and additional study subjects from the FINNPEC cohort. The exclusion criteria for the controls were any pregnancy complication in the current pregnancy, pre-eclampsia in any pregnancy, chronic hypertension and pregestational diabetes mellitus.The second individually genotyped sample set included 1353 pre-eclamptic and 699 non-pre-eclamptic women. These also include all the samples from the first Sequenom genotyping, all of which except the family samples were re-genotyped in the second run. All the women, except for the ten family cohort members, were selected from the FINNPEC cohort. The inclusion criterion for the cases was pre-eclampsia, and for the controls non-pre-eclamptic pregnancy. The exclusion criteria for the controls were pre-eclampsia in any pregnancy, small-for-gestational age (SGA) infant or placental insufficiency, gestational hypertension, chronic hypertension and placental ablation.All study participants have provided a written informed consent. The study protocols have been approved by the Coordinating Ethics Committee of the Hospital District of Helsinki and Uusimaa, and the methods were carried out in accordance with the approved guidelines.Variant data from a hundred Swedish scoliosis caseshttp://www.sisuproject.fi/) and at the time of the analysis contained exome sequence data from over 6100 Finns. The data set was utilized as a reference unselected for the pre-eclampsia phenotype as this information was not available for the sequenced individuals.The Sequencing Initiative Suomi (SISu 3.0) data set was utilised in the Sequenom phase 2 association analysis as population specific reference data to increase the statistical power. The SISu database is available online . By using three reference data sets we were able to obtain comprehensive picture of the variant frequencies in the Finnish and European populations, and also to estimate relevance of those variants that were absent in the population-specific reference data SISu. The variants with pre-eclampsia_MAF/reference_MAF ratio ≥1.5 in all the available comparisons were selected. In addition, five variants that were close to the cut-off or had high ratio in one or two of the comparisons were included. The following procedures were also utilised. Variation located in the genes listed in the papers by Fuentes Fajardo Two rounds of Sequenom genotyping were performed. The purpose of the first round was to verify the presence and enrichment of the selected variants individually in the original exome-sequenced samples, whereas the second round was conducted to test the association of the variants with pre-eclampsia.2 = 1 and D′ = 1 in the 1000 Genomes FIN and CEU populations, and rs12462506 tagged rs3745601 with r2 = 0.96 and D′ = 1 in the 1000 Genomes FIN population. The rest of the SNPs were left out, because of issues in assay design. In total, 48 variants were genotyped. The first, the second and the third iplexes contained 24, 17 and 7 variants, respectively. For the second genotyping run, 28 variants were selected for genotyping in two iplexes. In addition, rs6025 in F5 was included to the panel to investigate if the previously found association between the variant and pre-eclampsia1516Of the 59 variants selected based on the exome sequencing, 46 were directly fitted to three Sequenom iplexes. In addition, two of the variants were captured through tagging SNPs. Rs117741116 tagged rs139702277 with rAssociation of the variants with pre-eclampsia was evaluated by chi-square test in the PLINK software v1.07A standard linear regression model in the PLINK software was applied for testing association of the genetic variants with quantitative traits relevant for pre-eclampsia in the FINNPEC cohort. The quantitative traits utilized in the association testing included the highest systolic blood pressure, the highest diastolic blood pressure, proteinuria and relative birth weight of the baby. An additive model was applied in the analyses.http://pngu.mgh.harvard.edu/~purcell/gpc/cc2.html). With a pre-eclampsia prevalence of 0.05 and a risk allele frequency of 0.05, our cohort of 1353 pre-eclamptics and ~6800 controls (the non-pre-eclamptic FINNPEC controls and the SISu (3.0) data unselected for the pre-eclampsia phenotype combined), was estimated to be sufficient to detect an effect size of 1.65 for risk heterozygote and 3 for risk homozygote with power of 0.80 when α < 5 × 10−8. Under the aforementioned parameters, for the variants with a risk allele frequency of 0.01, we could detect effect sizes of 2.52 and 5 for the risk heterozygote and homozygote, respectively.Statistical power was calculated with Genetic Power Calculator using the “case-control for discrete traits” moduleClinical characteristics of the study participants are presented in The sequencing provider delivered a total number of 299 to 482 million reads in each sample pool. Over 98% of the reads could be mapped to the reference genome hg19. Per pool on average, 90% and 80% of the SureSelect target regions were covered by a depth of at least 30x and 60x, respectively, and the average depth of the target regions per pool was between 95x and 277x, the average of all pools being 220x. Eight of the ten pools had average coverage over 200x in the enrichment regions. The total number of variants called was 2,308,376. The main filtering strategy applied to these variants is illustrated in The first round of Sequenom genotyping was carried out in a sample set of 180 cases and 180 controls including the 100 exome sequenced samples. The purpose of this step was to verify the presence of the variants in the original samples and the MAF difference between pre-eclamptic women and general population. All assays had a success rate >95%. Of the 48 variants that were genotyped, three were monomorphic. After excluding these variants, correlation coefficient between the MAF estimates from the exome sequencing and the MAFs obtained from the Sequenom genotyping for the exome sequenced samples was 0.94, showing that we were able to estimate MAFs in the exome sequencing fairly accurately. Four of the variants were not in HWE in the controls. Twenty-eight variants that had OR ≤0.65 or ≥1.3 were selected for the second round of Sequenom genotyping in a larger case-control cohort. The results of the first Sequenom round are shown in NRTN; p-value = 0.0314, OR (95% CI) = 0.69 (0.48–0.97)), but the variant did not pass differential missingness test between the cases and controls. None of the association tests reached genome-wide significance. Full results are shown in In the second round of genotyping all the variants except failed rs6681 were successfully genotyped. After excluding 17 cases and 5 controls with more than 2 failed genotypes, the genotyping rate for the variants in the remaining individuals was over 96%. Concordance rate of the genotypes in the 350 individuals included in both Sequenom runs was 0.9992. Three individuals with at least one discordant genotype between the runs were excluded. Association of the variants with pre-eclampsia was first tested in the Sequenom genotyped FINNPEC case-control sample set. Three variants deviated from HWE in the FINNPEC controls and were omitted. In the association analysis, one of the genotyped variants was nominally associated with pre-eclampsia  data, and tested association of the genotyped variants with pre-eclampsia in this combined data set. Three of the variants deviated from HWE in the controls in these data, and were excluded from the analysis. Furthermore, the X chromosomal variants were excluded as the SISu data contain both males and females. In the association analysis in the merged data, we detected nominal association of four variants . None ofF5 gene and has previously been connected to pre-eclampsia1516The variant rs6025, which is located in the TP53BP1 showed nominal association  with the highest systolic blood pressure, and rs61747120/T in ZFR2 with proteinuria , both in the pre-eclamptic women. In addition to those two SNPs, there were several other variants associated with the highest systolic or diastolic blood pressure, relative birth weight of the baby or proteinuria in the pre-eclamptic patients, the non-pre-eclamptic controls or the whole case-control sample set  and relative birth weight of the baby . However, none of the SNPs were associated with the quantitative traits at the genome-wide significance level.Assuming an additive model of genetic inheritance, we investigated the association between the genotyped SNPs and quantitative clinical characteristics of pre-eclampsia . Among tmple set . Rs22915In this first attempt to screen exome-wide for low-frequency, moderate or large-effect risk variants for pre-eclampsia in a Finnish founder population, we did not find any genome-wide significantly associated risk variants. Whereas many complex diseases such as type 2 diabetes or cardiovascular diseases often have onset at midlife or later, pre-eclampsia affects women at their reproductive years, or if the phenotype of offspring is considered, already during the fetal period. Consequently, the disease decreases reproductive success, and there is a reason to hypothesise that pre-eclampsia risk variants are under negative evolutionary selection, which would keep their population frequencies low. A couple of GWA studies have assessed the role of common variation in pre-eclampsia susceptibility18The DNA samples were exome sequenced in pools of ten in order to maximise the number of sequenced samples while maintaining the sequencing costs low. With this strategy we were able to perform cost-effective exome-wide screen for pre-eclampsia risk variants, but the approach also has several limitations, such as missing information on individual genotypes and on exact MAF of each variant in the study sample. We were able to estimate MAFs from the pooled exome-sequenced samples fairly accurately: correlation coefficient between our estimates and the 1000 Genomes European data was 0.972 when the sequencing depth was at least 30x per pool. We however acknowledge that variants with biased MAF estimates were prone to be selected for the Sequenom genotyping, whereas some truly enriched variants could have been missed. In the association analysis we utilized the large SISu data as a population specific reference to increase statistical power of the analysis. Both the FINNPEC data and the data sets contributing to the SISu project have been collected to represent the Finnish population. However, population substructure within Finland39There are several possible explanations for not identifying pre-eclampsia risk variants in this study. Our screening did not cover non-coding regions, and also structural variation was omitted from the analysis. Furthermore, variants in low-coverage regions could have been missed. At the time of the exome sequencing data analysis robust variant callers with ploidy setting were not available. Utilizing a caller assuming a diploid genome might have caused us to miss some candidate variants. Some risk variants may have been lost due to choices made in the filtering. As shown previously, variant annotations are much dependent on a transcript set and annotation software utilized, and often there are several plausible annotations for a single variantTP53BP1, rs61747120 in ZFR2, rs113926353 in ANO9, and rs142394560 in TMTC1), or with proteinuria and relative birth weight of the baby in the pre-eclamptic cases (rs2291516 in RGL3). These variants or genes have not previously been linked to pre-eclampsia or any other pregnancy disorders. TP53BP1 encodes a protein involved in DNA damage response and cell cycle regulationTP53BP1 have shown a suggestive association with blood pressure4548TP53BP1, TMTC1 and RGL3ANO9 most abundantly in skin and digestive tract and ZFR2 in adrenal gland, cerebral cortex and testis ( http://www.proteinatlas.org/). A larger sample size would have been needed to state anything conclusive about the role of the variants in these genes in the risk of pre-eclampsia.Although we could not detect any robust risk variant for pre-eclampsia in this study, we mention here five missense variants nominally associated either with the disease phenotype .


Phenotypic variation in natural populations results from a combination of genetic effects, environmental effects, and gene-by-environment interactions. Despite the vast amount of genomic data becoming available, many pressing questions remain about the nature of genetic mutations that underlie functional variation. We present the results of combining genome-wide association analysis of 41 different phenotypes in ∼5,000 inbred maize lines to analyze patterns of high-resolution genetic association among of 28.9 million single-nucleotide polymorphisms (SNPs) and ∼800,000 copy-number variants (CNVs). We show that genic and intergenic regions have opposite patterns of enrichment, minor allele frequencies, and effect sizes, implying tradeoffs among the probability that a given polymorphism will have an effect, the detectable size of that effect, and its frequency in the population. We also find that genes tagged by GWAS are enriched for regulatory functions and are ∼50% more likely to have a paralog than expected by chance, indicating that gene regulation and gene duplication are strong drivers of phenotypic variation. These results will likely apply to many other organisms, especially ones with large and complex genomes like maize. We performed genome-wide association mapping analysis in maize for 41 different phenotypes in order to identify which types of variants are more likely to be important for controlling traits. We took advantage of a large mapping population (roughly 5000 recombinant inbred lines) and nearly 30 million segregating variants to identify ∼4800 variants that were significantly associated with at least one phenotype. While these variants are enriched in genes, most of them occur outside of genes, often in regions where regulatory elements likely lie. We also found a significant enrichment for paralogous (duplicated) genes, implying that functional divergence after gene duplication plays an important role in trait variation. Overall these analyses provide important insight into the unifying patterns of variation in traits across maize, and the results will likely also apply to other organisms with similarly large, complex genomes. Natural phenotypic variation arises from a combination of genetic effects, environmental effects, and gene-by-environment interactions. A major goal of modern genetics is to tease apart these components, and especially to identify the genetic loci that govern variation in traits. In the past decade, genome-wide association studies (GWAS) have become a major tool to advance our understanding of genetic variation. While many genome-wide association studies (GWAS) focus on disease phenotypes, especially in humans e.g., , it is aBecause of the ability to create controlled crosses, model organisms provide powerful platforms to dissect this natural genetic variation. In recent years, large artificial populations have been created using several different organisms to leverage this power to dissect genetic traits  decays in maize. An empirical calculation of LD decay in NAM shows that most LD decays to below background levels within 1 kilobase of a given polymorphism, though the variance is large since some alleles are segregating in only one or two families . Due to We find that a large amount of functional variation is located outside of protein-coding genes, presumably in regulatory regions, and that these non-genic variants often have large phenotypic effects. We also find that genes identified by association analysis are enriched for regulatory functions and for paralogs; this latter implies that gene duplication followed by functional divergence  is likely to be a strong driver of normal functional variation.et al., in preparation); for this paper, we used them primarily to expand our pool of available phenotypes. Both raw metabolite data and best linear unbiased predictors (BLUPs) for each NAM line are included in The majority of phenotype data in this analysis was taken from existing studies on the maize Nested Association Mapping population  [12]–Unless otherwise stated, all analyses were performed with in-house bioinformatics pipelines written in SAS, R, Perl, or Java. Source code for the various scripts is included in The NAM population was planted in Aurora, New York, USA in May 2007. Samples were all taken within one week at the beginning of August (when most NAM lines are flowering) between 10:00 AM and 2:00 PM on the sampling date. Two samples were taken from each row (RIL), one from the end plant and the other from four middle plants . Tissue was punched in the base part of the first leaf below the flag leaf and immediately frozen in liquid nitrogen, then stored at −80°C until extraction.et al.et al.et al.∼50 mg (fresh weight) of tissue was extracted twice with 80% ethanol and once with 50% ethanol as in Geigenberger et al. http://www.vsni.co.uk/software/asreml). The final BLUPs are the result from controlling for several potential confounding factors, specifically: spatial effects within the field; the level of nitrogen, phosphorous and potassium in the soil before planting; the tissue sampling date and time; the researcher who performed the sampling; the batch effect of the plate samples were stored in; and the batch effect of the plate the measurements occurred in. BLUPs were also calculated for flowering time (defined as the time from sowing to when 50% of plants in a row are shedding pollen), correcting for the spatial field effects. Most metabolites correlate with flowering time, so we used Proc GLM in SAS (http://www.sas.com/) to regress the values for all 12 metabolites on flowering time. Partial correlation analysis (part of Proc GLM) was used to confirm that resulting values were significantly different, and a Holm-Bonferroni correction Best linear unbiased predictors (BLUPs) for each line within each trait were calculated using ASReml  Forward-regression genome-wide association was then performed with the NamGwasPlugin in TASSEL version 4.1.32 The input SNPs were a union of all SNPs in Hapmap1 and Hapmap2. A small portion of SNPs are duplicated between the datasets—that is, they were independently discovered in both studies—but in almost every case they have different (and sometimes conflicting) allele calls. Thus we made no attempt to merge such SNPs and instead let each original call be tested individually. After running GWAS, we found a single case of ambiguity in determining which SNP had been chosen by the model, due to two SNPs having identical positions and allele codings. In this case we retained both to maintain consistency with the input dataset.Zea mays reference genome (AGPv2). The B73 sample from Hapmap2 itself served as the null distribution to determine the cutoff corresponding to an empirical, genome-wide Type I error rate of 0.05. CNVs that had been previously identified within annotated genes by the same method Putative CNVs were determined by two methods. First, Hapmap2 sequencing reads aligned to the maize genome were counted in 2 kb-windows and compared to a high-coverage B73 sample with edgeR Independently, the mapped reads were also analyzed by CNVnator Since there were a total of three separate sources of CNVs in this analysis, a single genome region could potentially contribute to multiple CNVs and thus be tested multiple times per GWAS run. The contribution to each set of CNVs will be different, however, since each one depends on all regions within its limits and is then collapsed to a single score of 0 or 1.Zea mays Ensembl database (version 68). Since the VEP annotates effects relative to any gene model , it was run with both the “–most-severe” and “–per-gene” options to get lists of the worst overall effect per SNP and the worst per gene, respectively.  The two results were then combined with in-house Perl scripts to create a list of the worst overall SNP effect with respect to only those genes in the Zea mays 5b.60 filtered gene set (available at http://www.gramene.org).Putative SNP effects were determined by running all 28.9 million SNPs through the Ensembl Variant Effect Predictor (VEP) Polymorphisms classes were tallied for both the input SNPs dataset and for the GWAS-hit SNPs. Using the input dataset as the null, we then removed any categories with <5 expected counts in the GWAS dataset. Total counts in the remaining groups were then tested for significance by a Chi-square test using the Stats package in R Due to the possibility that linkage disequilibrium could distort the results from the above test, we also ran 1 million circular permutations of the hits to generate a null distribution of what would be expected by chance. Circular permutation in this case refers to keeping the order of all elements intact while randomly changing the “start” location along the chromosome. This maintains the structure of the original data while randomizing its relationship to genomic features. The resulting counts formed a normal distribution, which was used to extrapolate the p-values in 2) between a model with all identified SNPs and a model with all SNPs except those in the chosen category.Marginal variance explained by polymorphisms classes  was calculated by fitting linear models to each trait and comparing the difference in variance explained . The number of genes with paralogs in the GWAS hit dataset was compared to those in the maize filtered gene set and significance of the difference tested by a two-sided exact binomial test in R Maize paralogs were taken from an existing list Figure S12<0.2) in less than 100 base pairs. Rare variants segregating in just a few lines create a large variance in LD structure, however, as shown by the persistence of LD at higher percentile cutoffs.Linkage disequilibrium in NAM. Linkage disequilibrium (LD) in the NAM population was calculated for 10,000 random polymorphisms (A) and for all GWAS hits (B) based on expected contribution from the 26 founder genotypes. Lines show the distribution of polymorphisms at different percentile cutoffs (marked at left). Median LD, as marked by the 50% line, falls below background (r(EPS)Click here for additional data file.Figure S2et al. 2009), QTL support intervals for Northern leaf blight resistance (C) and leaf length (D) , and 6 cM windows of significant SNPs for stalk strength (E) . 100,000 circular permutations were performed to determine the significance of overlap between the previous results and our GWAS hits; the resulting empirical p-values are in the upper-right of each graph. (Since parts (A) and (B) are continuous scans, a LOD-score cutoff of 15 was used to specify QTL intervals.) All overlaps are significant at p<0.01. It should be noted that the lack of perfect overlap is largely due to the different statistical strengths of joint linkage and GWAS, and similar results are seen in the previous NAM studies that used both methods.Agreement between identified polymorphisms and known QTL. Quantitative trait loci (QTL) for key traits from previous studies in NAM were compared against polymorphisms found in the current analysis (black dots). Gray bars show the results of genome-wide joint-linkage scans for days to anthesis (A) and days to silk (B) (Buckler (EPS)Click here for additional data file.Figure S3Site frequency spectra for intronic and synonymous SNPs. The site frequency spectra for all SNPs annotated as either synonymous or intronic in the input dataset  are plotted. The spectra are nearly identical, with only a slight enrichment for rare variants among the intronic SNPs.(EPS)Click here for additional data file.Table S1Category counts.(DOCX)Click here for additional data file.Table S2GO term analysis.(DOCX)Click here for additional data file.Dataset S1Metabolite data. Raw data and best linear unbiased predictors (BLUPs) for the metabolite data used in this analysis.(ZIP)Click here for additional data file.Dataset S2Chromosome-specific residuals. Existing best linear unbiased predictors (BLUPs) for each inbred line were used to fit a joint-linkage model across all chromosomes. The hits from this model were then used to create chromosome-specific residual values by accounting for all markers except those on the chromosome in question. (See (ZIP)Click here for additional data file.Dataset S3Bioinformatic scripts. This file contains the various bioinformatics scripts that were used to perform the NAM-GWAS analysis and the subsequent analyses that form the basis for this paper.(GZ)Click here for additional data file.


Genetic relatedness is currently estimated by a combination of traditional pedigree-based approaches  and, given the recent availability of molecular information, using marker genotypes . To date, GRM are computed by genome-wide pair-wise SNP (single nucleotide polymorphism) correlations.Bos indicus) and Tropical Composite (Bos taurus by Bos indicus) populations, the clustering inferred by NCD was comparable to that based on SNP correlations using standard principal component analysis approaches. One of the versions of the CRM modestly increased the amount of explained genetic variance, slightly reduced the ‘missing heritability’ and tended to improve the prediction accuracy of breeding values in both populations when compared to both NRM and GRM. Finally, a sliding window-based application of the compression approach on these populations identified genomic regions influenced by introgression of taurine haplotypes.We describe a new estimate of genetic relatedness using the concept of normalised compression distance (NCD) that is borrowed from Information Theory. Analogous to GRM, the resultant compression relationship matrix (CRM) exploits numerical patterns in genome-wide allele order and proportion, which are known to vary systematically with relatedness. We explored properties of the CRM in two industry cattle datasets by analysing the genetic basis of yearling weight, a phenotype of moderate heritability. In both Brahman  contains supplementary material, which is available to authorized users. All genomes are equal, but some genomes are more equal than others“Accurate measures of genetic relationships among individuals are needed to accelerate artificial selection for genetic improvement  and to rhttp://www.gzip.org). If the data compression relating the two genomes is strong, then they are deemed to be closely related and are awarded a short distance. Applying this process systematically across a genotyped population can be used to build a compression relationship matrix (CRM), analogous to a GRM. In a preliminary study, we explored the application of NCD to two sheep populations, one that included multiple breeds [GRM are essentially computed by genome-wide SNP genotype similarities (e.g. correlations) among all pair-wise combinations of individuals . These ce breeds  and anotFST), and consistent with phylogeography. Genome-wide CE can be considered as reflecting patterns in both allele order and allele proportion that are known to differ systematically between breeds, but to be shared among closely related individuals. These shared patterns among individuals could include, but not be limited to, genome-wide heterozygosity and runs of homozygosity [Prior to that, we explored a basic measure of within-genome compression efficiency (CE) by expressing the SNP genotype file sizes in bits before and after data compression by the gzip tool. Plotting these CE values relative to heterozygosity  yielded zygosity . SimilarBos indicus and Bos taurus progenitors, which are sub-species that arose from independent domestication events and last shared a common ancestor more than 200,000 years ago [Here, we studied two animal populations of commercial relevance to Australian agricultural production that have matching phenotype data for yearling weight, a complex phenotype of moderate heritability, one Brahman (BB) and one Tropical Composite (TC). These populations have recorded pedigrees that show the presence of both full-sib and half-sib individuals. Furthermore, these populations represent historically admixed populations that were founded from contributions of both ears ago . For theears ago  and the Bos indicus cattle .Animals, phenotypes and genotypes used in this study were a subset of those used in . BrieflyHet) across the whole genome:B and SA indicate the genotype file size expressed in bits before and after compression by gzip, respectively. The underlying principle of CEh is the same as for any genetic clustering method: the closer the match in the numerical patterns present in two genotype files is, the closer is the inferred genetic relationship between them. No attempt was made to discriminate DNA segments that were identical by descent from those that were identical by state.First, we computed animal-to-animal relationships that could be ascertained from genotype data using the basic CE approach corrected for heterozygosity (CEh), as described in . This aphttp://www.gzip.org) as our real world compressor. The application gzip is based on the lossless data compression algorithm DEFLATE that was originally described by [The main weakness of CEh is that two genotype strings can have the same CE and heterozygosity despite being different (e.g. 0000000000 and 2222222222). It is not clear how common this phenomenon is in real population genetic data, but it has the potential to confound some of the observed clustering. To address this, we used normalised compression distance (NCD)  to develribed by . NCD onlx and y based on their respective SNP genotype sequence is:Z(xy) represents the size of the compressed file that contains both SNP genotype sequences to be compared and Z(x) and Z(y) are the sizes of the compressed file with the separate SNP genotypes for x and y, respectively.As previously reported , the forRelationship matrices are based on estimates of similarity, but through NCD we have computed ‘distance’ not similarity. Therefore, the construction of the CRM from all pair-wise NCD values first requires conversion of the compression distance to an equivalent similarity measure. While distance and similarity share commonalities they are not equivalent. In practice, there are numerous ways of inter-relating them. Here, we explored two approaches, producing two different CRM (CRM1 and CRM2) from the same NCD input.d) to similarity (s) conversion law of Shepard [i and j  covered the 0–1 interval observed for correlation , where di,j is the NCD between the i and j individual pair. This method proved to have a scaling issue which can bias estimates of genetic parameters. This problem was overcome through computation of CRM2 (described below).The first method (CRM1) made use of the universal distance ( Shepard . We usedThe second method (CRM2) attempted to better ground the NCD in established genetics—that is, an expectation of relatedness of 1 for self–self pairs, 0.5 for full sibs and 0.25 for half-sibs. This expectation is governed by the laws of inheritance and the likely molecular outcomes of meiosis when applied to a diploid mammalian genome. CRM2 used a linear conversion method defined as follows:This linear method has the appealing feature of yielding an average value of 1 for self–self pairs, including a spread around 1 that reflects inbreeding. This result shows that the CRM2 matrix is scaled in a manner more suitable for the estimation of genetic parameters. The remaining values approximate 0.5 for full sibs, 0.25 for half-sibs and so on. Similar to GRM but unlike NRM, these values were not pre-defined by pedigree expectation but derived from the SNP genotype data. Therefore, they are likely to more accurately capture the observed variability that is inherent to the process of meiosis that gives rise to each individual compared to its relatives.The third compression-based relationship matrix (CRM3) was entirely independent of the NCD approach described above. The aim of CRM3 was to produce another set of genetically sensible relatedness values, through application of a two-step process: an initial window-based CE step and a subsequent correlation step. To achieve this, we produced a matrix with as many columns as sets of 50 consecutive SNPs that can be built from the genotype file, and as many rows as animals in the analysis. Individual cells in this matrix contain the CE value for each window for each animal. This matrix was then used as input for a correlation analysis so that, for each pair of animals, the correlation across their respective CE values was used as a measure of relatedness. Animals that had sets of SNPs that compressed in the same way along their respective genomes were awarded high correlations.Z is the  matrix of genotypes and pi is the frequency in the population of the B allele for the ith SNP. ZZT represents the number of shared SNP alleles between all pairs of individuals and the division of ZZT by The construction of the GRM was based on the correlation between genotypes and was computed according to the methodology developed in :\documeng values .The computations of NRM, GRM, CRM1, CRM2 and CRM3 are schematically summarised in Fig. The encrypted genotype profiles are awarded the following genome-wide CE; 30, 27, 23, 20 and 32 %, respectively for Animals 1 to 5. On the one hand, Animals 1 and 5 have the most regular genotypes, resulting in the highest CE and on the other hand, Animals 3 and 4 have the most irregular genotypes, resulting in the lowest CE. A plausible pedigree graph is given in b of Fig. The NRM reveals that Animal 1 is the sole inbred animal since it results from a parent-offspring mating. The GRM reveals that Animals 2 and 4 are the most inbred and captures the strong (parent-offspring) relationship between Animals 1 and 2  and Animals 3 and 4 . The GRM also captures the most distant relationships , i.e. of Animal 2 with Animals 3 and 4, which are unrelated based on the NRM.Based on this genotype file, we can also compute the NCD matrix  of consecutive SNPs and CE can then be computed for each window by animal combination. Here, we have four windows of 7, 7, 7, and 9 consecutive SNPs giving rise to the CE matrix h of Fig. y is the vector of yearling weight observations, X in an incidence matrix relating observation in y with the vector of fixed effects in β  [r, the number of random components fitted in the model. Z is an incidence matrix relating observations in y with the vector of random additive effects in ur which are assumed to be normally distributed with zero mean and variance Cr is the relationship matrix based on either the pedigree (NRM) or markers , and ur. Finally, e is the vector of random residual effects assumed to be normally distributed with zero mean and variance I denotes an identity matrix and We used mixed-model equations and the Qxpak.5 software  for the mentclasspt{minimaTwelve models were explored: one each  with a single additive effect from either relationship matrix , and then an informative subset of combinations of the above models. These 12 models are defined in Tables Using yearling weight, we compared the performances of NRM, GRM, CRM1, CRM2 and CRM3 according to the resultant genetic parameters, EBV and prediction accuracies. For the computation of accuracy, 20 % of phenotypes were randomly set to missing values. The reported accuracy was the average of 20 random splits of the data . Estimates of breeding values based on NRM, GRM, CRM1, CRM2 and CRM3 were compared and the accuracy of the resulting predictions was computed from the correlation between the EBV and the adjusted phenotypes (Table Cmiss) using the formulae of [Models 5, 6 and 7  can estimate the fraction of missing heritability  are a possible source of compressible patterns in genomes with high heterozygosity. Based on its improved performance, all remaining analyses were performed using the Indicine SNP chip.In Fig. Tables For relationships corresponding to NRM values of 0.25 , the average GRM were equal to 0.196 and 0.201 for BB and TC cattle, respectively. Self–self relationships were equal to 0.997 and 0.987 for BB and TC cattle, respectively.The relationship between GRM and NCD for each pair of individuals is plotted in Fig. A distinct cluster with an increased NCD was observed in the BB population Fig. . This waNext, we attempted to identify genome properties that were responsible for the similarities and differences between the GRM and NCD measures of relatedness. To answer this question, we overlaid the average Zebu contribution   of each The impact of the two NCD mapping approaches (CRM1 and CRM2) on the estimate of similarity from the same NCD value is in Fig. We explored the computing time required for each population. For the BB population and once the relationship matrices have been built, the mixed model that contained a single additive effect took 31 s for the NRM, 4 min and 6 s for the GRM and 4 min and 10 s for the CRM2. The longer time taken for the models with either GRM or CRM2 reflects the higher density of these marker-based relationship matrices. However, the computing of NCD, which is required for CRM1 and CRM2, consumed substantially more time than the pair-wise correlations required for GRM. In our implementation, it took 102.6 and 162.4 h to compute the NCD matrices for BB and TC, respectively. The reason being the DEFLATE algorithm included in the gzip tool was not incorporated into the UNIX script, so we had to resort to numerous input and output operations that call on the compression function of GZIP externally.Computational demands aside, the relationship matrices based on NCD were highly related to the GRM based on the strong negative correlation between pairs of individuals  Tables , 5. FurtOverall, estimates of genetic parameters were quite similar for GRM and CRM2 Tables , 2. It sFST and CEh revealed a high positive relationship (r = 0.75), which confirmed the relevance of using CE to detect putative selected genomic regions in cattle. Genomic windows on the X chromosome consistently displayed high values for both metrics, which confirms previous results observed for populations that include Bos indicus and Bos taurus ancestry [The comparison between ancestry . A likelancestry .FST and yielded a positive relationship , immune function (BCL2) and fatness (ATP5H)  two subunits of the mitochondrial ATP synthase, the F1 catalytic core complex coded by ATP5B on BTA5 and the membrane-spanning F0 complex coded by ATP5H on BTA19  Table . It is aIt is well established that shared patterns of allele composition can be used to infer genomic relationships between individuals. Since both GRM and CRM are based on genome-wide similarity, it is not surprising to detect a close relationship between these two approaches. NCD shows merit as an alternative or complementary measure of genomic relatedness to GRM. Overall, short NCD distances reflect high co-sharing of genome-wide heterozygosity, runs of homozygosity and compositionally complex haplotypes, which may not be identified by other approaches. Collectively, these genomic features have implications for inbreeding, population structure and the identification of signatures of selection.The quadratic relationship between NCD and GRM implies that NCD is particularly well adapted to discriminate closely related individuals. This conclusion is borne out by current and past data. Previously, we found that NCD can separate some full-sibs from half-sibs in cases where GRM cannot . This obAny measure of genomic similarity  needs to be clearly grounded in the biology of meiosis for it to provide meaningful estimates of genetic parameters. That is, it must yield the expected relationship values of ~1 for self–self pairs, ~0.5 for full-sibs and ~0.25 for half-sibs. These values are implicit  for correlation-based measures of relationships, but not for NCD. In this regard, the linear transformation that we used for CRM2 was superior to the quadratic transformation  of CRM1.Other authors have explored various options for optimising estimation of genomic relationships. For example,  found thPreviously, we reported that by sliding a CE-based population-level window along genomes, we could identify haplotypes that are likely the result of recent positive selection . ObviousINHBE and INHBC), which have been previously identified as associated with fertility traits in tropically adapted cattle [In this study, we applied the compression-based sliding window analysis to two bovine populations. Analysis of genomic windows with the largest difference in CE between the two populations successfully identified regions with major effects on production traits in tropically adapted cattle . The topd cattle . The preBos taurus chromosome 5 (BTA5) (between 56.2 and 56.5 Mb; Fig. FST and may constitute novel findings.Inspection of the genome-wide profile revealed that nearly all extreme genomic regions were characterised by a greater CE in BB cattle, well above the genome-wide average CE Fig. . This suIn a commercial context, broiler chicken and dairy cattle breeding populations have small effective population sizes, high levels of inbreeding and both use genomic prediction as part of their modern breeding strategies, as discussed in . We antiNCD clusters a genome in a manner that is broadly similar to correlation-based approaches. Unlike GRM, NCD exploits patterns that are present in haplotypes and unlike ROH-based methods, NCD can identify and exploit haplotypes that have a more complex genotype composition. In this study, CRM2 has been validated by the fact that we show that it has a tendency to reduce the missing heritability and increase the phenotype accuracy for a moderately heritable complex trait in two bovine populations. The fine-grained resolution that NCD appears to possess may lend itself to situations for which the capacity to discriminate very closely related individuals is of particular value. A sliding window version of the analysis aimed at detecting sweeps identified regions caused by introgression of taurine haplotypes.