The Enhancing NeuroImaging Genetics through Meta-Analysis (ENIGMA) Consortium is a collaborative network of researchers working together on a range of large-scale studies that integrate data from 70 institutions worldwide. Organized into Working Groups that tackle questions in neuroscience, genetics, and medicine, ENIGMA studies have analyzed neuroimaging data from over 12,826 subjects. In addition, data from 12,171 individuals were provided by the CHARGE consortium for replication of findings, in a total of 24,997 subjects. By meta-analyzing results from many sites, ENIGMA has detected factors that affect the brain that no individual site could detect on its own, and that require larger numbers of subjects than any individual neuroimaging study has currently collected. ENIGMA’s first project was a genome-wide association study identifying common variants in the genome associated with hippocampal volume or intracranial volume. Continuing work is exploring genetic associations with subcortical volumes (ENIGMA2) and white matter microstructure (ENIGMA-DTI). Working groups also focus on understanding how schizophrenia, bipolar illness, major depression and attention deficit/hyperactivity disorder (ADHD) affect the brain. We review the current progress of the ENIGMA Consortium, along with challenges and unexpected discoveries made on the way. During the “Decade of the Brain” in the 1990s  spaces—was eased by the development of automated registration and alignment methods , for example  demonstrate accelerated gray matter loss with age  is altered; SNPs are thought to be point mutations that were not so damaging that evolution allowed them to be retained in a significant proportion of the population of a species. Within a population, SNPs can be assigned a minor allele frequency—the proportion of chromosomes in the population carrying the less common variant. Figure In a typical GWAS analysis, one might test ~2.5 million common SNPs in the genome, to see if any of these genetic variants are associated with a trait, such as a brain-derived measure, or a specific disease such as AD. Although not the only important type of genetic variation, SNPs can be measured using readily available genotyping arrays, and individually provide adequate statistical power as the variants are common enough to test their effects statistically. Because only selected SNPs capturing the variability of the genome are genotyped, many authors have argued that this genotyping technology is much less expensive than whole-genome sequencing. However, new technologies using low coverage sequencing with imputation may in some cases yield several times the effective sample size of GWAS based on SNP array data, and a commensurate increase in statistical power as described in Pasaniuc et al. .GWAS has had many successes. Many common polymorphisms have now been found that increase genetic risk for AD  must be functional in the human brain. This was one of many early studies to validate the intermediate phenotype strategy in psychiatry.Imaging may play a role in finding out how these genes create risk for illness through their impact on the brain, by comparing brain scans of carriers versus non-carriers. One such example is the CLU, CR1 and PICALM . The growing computational power to screen very large neuroimaging datasets—for the purpose of extracting meaningful features from them—made this an interesting and achievable objective. Advocates of “imaging genetics”—the genetic analysis of brain images , amygdala (r = .91), and intracranial volume (r = .99) for a cohort of data collected across investigators and matched scanners. Nugent et al.  brain function. Structural measures of the brain, from MRI, tend to have relatively high reproducibility across measurement methods, and are generally consistent with expert tracings of the same structures .Second, measures of brain volume, integrity, receptor distribution, or chemical composition, might be more directly related to the function of genes—both genes whose function is unknown, and known candidate genes—such as growth factors, transcription factors, guidance molecules, or neurotransmitters and their transporters. Many of these had already been implicated in the risk for psychiatric illness, and imaging offered the opportunity to study differences in brain connectivity or function, in carriers of genetic variants associated with disease risk. In the future, advanced MRI methods such as [At the same time, some seasoned geneticists were skeptical about imaging genetics. Concerns were raised about the costs of image acquisition, relative to a standard psychiatric diagnostic test. For a study to be feasible, the cost of data collection must be borne in mind, regardless of which method is ultimately more efficient in discovering genes and mechanisms contributing to brain disease.TOMM40, in linkage disequilibrium with APOE, the known risk gene for AD. Using hippocampal atrophy as a quantitative phenotype in a genome-wide scan, they assessed 381 participants in the ADNI (Alzheimer’s Disease Neuroimaging Initiative) study, to identify SNPs for which there was an interaction between the genotype and diagnosis on the quantitative trait. Variants in TOMM40 appeared to affect hippocampal volume differently in AD patients versus controls. Working with genetic-founder populations, some GWAS-based studies revealed genome-wide hits in relatively small samples; in the Saguenay Youth Study, genetic variations in the KCTD8 region were associated with brain size in a community-based sample of adolescent girls ;  for which MRI scans and GWAS data could be freely downloaded from approximately 800 people. The ease of access of the ADNI data, and the principle of broad dissemination of the genomic data with fairly few restrictions led to over 100 genetic studies of the ADNI data, many of them using GWAS designs . Even so, data from other elderly cohorts is needed to determine how well ADNI’s genetic findings generalize to other non-selected cohorts. ADNI deliberately selected participants who are predominantly Caucasian, and relatively free from drug or alcohol abuse and vascular disease. Genetic associations detected in ADNI may be stronger or weaker, or even not supported at all, in cohorts with different ethnic composition, or with other co-morbid health conditions. Because of this, it is important to recognize that some genetic associations may depend on the cohort studied, diagnostic or demographic criteria, and we should not expect all true genetic associations to be detectable in all cohorts.The ADNI dataset stimulated work in imaging genetics, as evidenced by the large number of published papers using the data , the significance of a genome-wide hit has to be at least 20 million to one, to account for the very large number of variants tested. Some have argued that neuroimaging studies reporting effects of candidate genes—such as 1A receptor gene have been related to amygdala volume in borderline personality disorder   was larger than that of CHARGE, but some of the constituent cohorts in CHARGE numbered over 2,800 individuals.The genotype at that locus was also nominally associated with expression levels of the positional candidate gene The first ENIGMA project demonstrated the feasibility of discovering statistically significant effects of “single letter” genomic differences in brain data worldwide, using imaging and genetic data collected using diverse protocols. Novel, harmonized data analysis and meta-analysis protocols were vital to the success of this project.First, all genotypic data was imputed to the HapMap3 reference dataset to correct for diversity of the genotyping chips . The imputation protocols (detailed at enigma.ini.usc.edu) and the standard reference datasets allow the consistent reporting of genotypes at the same set of genetic loci across cohorts. Imputation effectively adds prior knowledge to the data and may in this way also increase the power of a study. Not all ENIGMA cohorts are Caucasian: the GOBS cohort consists of Mexican-Americans and the NIMH cohort contains a significant number of African-Americans. As in any GWAS, population structure is taken into account during the statistical modeling of associations, to ensure that differences in SNP frequencies with ancestry are not picked up as spurious associations. Also in the imputation step, the appropriate reference populations are used for each individual, which may in some cases be Yoruban or Hispanic, as well as the CEU population that is used to represent Caucasians. However, it is not a computationally trivial task to impute very large samples of data from so many subjects. The successive refinement of reference panels means that re-imputing the same dataset to the most current standards is likely to further boost power.Second, the exchange of data between the ENIGMA and CHARGE consortia, for the Stein et al.  study, ihttp://enigma.ini.usc.edu/ongoing/gwasma-of-subcortical-structures/ and the DTI analysis protocols are available at http://enigma.ini.usc.edu/ongoing/dti-working-group/.Third, the effort to harmonize the analysis of imaging data involved development of new quality control procedures. Considerable time was devoted to checking outliers, testing of the histograms and statistical distributions of brain structure volumes, and checking the allele frequencies, genomic inflation factors, and other statistical summaries of the cohort data. The genetic and MRI analysis protocols used in ENIGMA2, including quality control steps, are available online, at In a project of such a scale, the need for adequate data curation is paramount. Several measures were assessed to determine whether structures had values in the expected range for volume, hemispheric asymmetry, etc. In the end, the large number of contributing authors and contributing sites made it easier to identify sites that had outliers in their genotypic or brain measurement data, partly because normative data were becoming available from all the other sites. All relevant demographic factors were controlled for at each site, including population structure that might lead to ancestry differences masquerading as true genetic associations to brain traits.Among these tests, we demonstrated that different, widely-used programs to measure regional brain volumes produced consistent results on a broad range of cohorts worldwide, based on data from young and old samples and mixtures of both . Subsequently, and after quality control at each site, the Many cohorts within ENIGMA have restrictions on data use and data access. Some preclude the sending of data out of the lab where the data were collected. Some restrict the sending of personally identifying information to any other site. A founding goal of ENIGMA was to not require cohort data to be shared outside the center that collected it, to avoid creating ethical and legal issues for the study sites. Although data sharing is a laudable goal in science, a more pragmatic compromise has been to send protocols to distributed sites and analyze summaries of the resulting data that lack personally identifying information. This also encourages maximum participation as each site retains fiduciary responsibility for their data and its curation and integrity. Nevertheless, there is a growing perception of the community that data sharing is one fundamental building block of reproducibility in science, and a rapidly expanding number of imaging datasets are being shared thus facilitating discoveries. New ways of acknowledging data acquisition are being developed concurrently  polygenic scoring, which determines how much of the phenotypic variance can be explained by common SNPs in aggregate . This interface allows a user to input any gene (or SNP) that they are interested in, and query its effects on a wide variety of brain measures. The current dataset also allows targeted studies of individual genes, enabling research groups, even if they are not involved in human studies, to assess the possible impact on the brain of genes they are studying (via the ENIGMA-Vis search tool).In the aftermath of ENIGMA1, several investigators requested access to the GWAS meta-analyzed results, and the meta-analyzed data were made available online through an interactive website named ENIGMA-Vis  and were also associated with measures of hippocampal volume and function.In one study, Bulayeva and colleagues , all the way to new functional experiments in neuronal cell lines or animal models. This kind of follow up study is crucial, given the difficulties of obtaining robust functional variants from GWAS studies.ENIGMA2 is a follow-on study from ENIGMA1, in which the volumes of all major subcortical structures are subjected to genome-wide association analysis , the square-root of the heritability of the endophenotype (he2), and their genetic correlation (ρg):The ERV balances the strength of the genetic signal for the endophenotype and the strength of its relation to the disorder of interest. It is defined using the square-root of the heritability of the illness  Working group was recently initiated. It already includes structural MRI data from 1,850 patients and 3,483 controls. Data analysis is currently in progress.An additional working group on attention deficit/hyperactivity disorder is currently being formed, ENIGMA-ADHD, which will analyze data from more than 1,500 cases (children and adults) with the disorder and over 2,000 controls.An even more recent extension is a developing ENIGMA-Addiction working group that will analyze data relevant to addiction phenotypes including case-control comparisons across a variety of substances, and going beyond this to examine the influence of comorbidities, gender and stages of disorder. The ENIGMA meta-analytic approach will be used to aggregate data from case-control and developmental cohorts to examine the relative contribution of various genetic and brain correlates to risk for early onset substance misuse, transition to regular use, susceptibility to dependence, and individual differences in relapse vulnerability.  We will also examine variants common to all addictive behaviors, and attempt to identify those that might be specific to homogeneous addiction profiles.  To date, a pooled sample of 8,000 participants with neuroimaging, genetics and addiction phenotypes has been identified; their data will be re-analyzed to address these questions.https://pgc.unc.edu/), to identify shared biology between brain characteristics and disease. A collaboration between ENIGMA and the PGC is now underway to study these relationships.Clearly, these studies aggregate data from cohorts that are heterogeneous in terms of duration of illness, disease etiology, medication history, demographics, exposure to potentially neuroprotective substances such as lithium, and many other factors. But part of the richness of the ENIGMA efforts is that they afford sufficient power to begin to see which of these factors—including geographic factors, perhaps—affect disease expression in the brain and the universality, or otherwise, of the biomarkers of brain disease. Based on these findings, a key direction for ENIGMA is to see how genes that affect the brain relate to genes that affect risk for psychiatric illness . Also, common causal variants may account for around 23 % of the risk for schizophrenia . In principle, ENIGMA could be used to study rare variants as well, but a range of complementary approaches are always necessary.APOE risk gene for Alzheimer’s disease shows a difference between European and Asian populations. So far, people in Africa and Asia are under-represented on the ENIGMA map; we are therefore keen to include samples from these continents.Second, the geographical diversity of ENIGMA is higher than that of most neuroimaging studies, but there may be important ethnic differences in allele frequency that complicate the generalization of results to all human populations. This limitation is not specific to ENIGMA, and its consortium structure could be expanded geographically to assess ethnic differences in factors associated with disease and their relationship to brain structure. Ethnic differences in genetic effects are well known: the meta-analysis of the effects of the Third, the need for multivariate analysis has long been known in the neuroimaging field—no serious neuroscientist would predict diagnosis from a single pixel or voxel in an image—the multivariate pattern of signals is paramount. Methods to access and recover the maximum amount of pertinent information in an image dataset are only just in their infancy in the fields of genetics and neuroimaging—partially due to the lack of sufficient data to test competing methods, until recently . But more recently, Rose and Donohoe  performe3 or by 1.2 % of the average hippocampal volume per risk allele. Bearing in mind that the cause of the effects is quite different, the effect of ENIGMA’s top hippocampal SNPs on hippocampal volume is approximately 5 % of the mean effect of Alzheimer’s disease, around one-third of the effect of schizophrenia, and around 40 % of the effect of bipolar disorder. If such effect sizes are typical, sample size requirements will generally be larger in genetic association studies than in neuroimaging studies of disease effects on the same phenotypes, but not vastly larger.It is interesting to compare the effect of ENIGMA’s top SNPs with the effects of common psychiatric and neurological conditions on hippocampal volumes. In a recent meta-analysis , and these effects have been confirmed in smaller cohorts by comparing brain images from carriers and non-carriers  associations. Paus et al.  noted thOne testable hypothesis is that GWAS would be more powerful and efficient if we select imaging phenotypes in a principled way; if this is true, it may be possible to perform GWAS with consistently replicated hits, that do not require tens of thousands of subjects to reject the null hypothesis. In fact, the ENIGMA working groups each aim to find heritable brain measures that maximize case–control differentiation, for studies of disease. This will help us to prioritize the future targets of study for influential genes. Although ENIGMA is data-driven, that does not mean that we cannot use patterns in the findings to design more targeted approaches that prioritize phenotypes and genetic loci for follow-up analyses.www.brainspan.org).One such analysis  is considered on its own, and each genetic variant is considered on its own. Recent multivariate analyses can cluster voxels in the brain—or SNPs on the genome—to empower analyses, sometimes with both forms of clustering occurring at once (Hibar et al. COMT and MTHFR polymorphisms on prefrontal dopamine signaling, suggesting that in schizophrenia patients, the MTHFR 677 T allele exacerbates prefrontal dopamine deficiency. Andreasen et al. (A further line of work studies the “interactome”: it is now possible to search pairs or sets of SNPs for interaction effects in images (Hibar et al. n et al.  used a mExpanding the study of interactions to the whole genome, Kam-Thong et al.  presenteIn conclusion, when the next round of ENIGMA studies has been completed, there will be a scaffolding of credible genetic variants on which to build and test new models of macroscale brain development, the implications of those variants for neuropsychiatric disease, and a new basis to probe the genetic architecture of the living human brain.


GIBS) or sometimes on linkage analysis relationships (GLA). Here, we propose a novel method to predict GEBV based on a genomic relationship matrix using runs of homozygosity (GROH). Runs of homozygosity were used to derive probabilities of multi-locus identity by descent chromosome segments. The accuracy and bias of the prediction of GEBV using GROH were compared to those using GIBS and GLA. Comparisons were performed using simulated datasets derived from a random pedigree and a real pedigree of Italian Brown Swiss bulls. The comparison of accuracies of GEBV was also performed on data from 1086 Italian Brown Swiss dairy cattle.Genomic prediction is based on the accurate estimation of the genomic relationships among and between training animals and selection candidates in order to obtain accurate estimates of the genomic estimated breeding values (GEBV). Various methods have been used to predict GEBV based on population-wide linkage disequilibrium relationships (GROH achieved consistently more accurate GEBV (0 to 4% points higher) than GIBS and GLA. The bias of GEBV prediction for simulated data was higher based on the real pedigree than based on a random pedigree. In the analyses with real data, GROH and GLA had similar accuracies. However, GLA achieved a higher accuracy when the prediction was done on the youngest animals. The GIBS matrices calculated with and without standardized marker genotypes resulted in similar accuracies.Simulations with various thresholds of minor allele frequency for markers and quantitative trait loci showed that GROH as a novel method to estimate genomic relationship matrices and predict GEBV based on runs of homozygosity and shows that it can result in higher or similar accuracies of GEBV prediction than GLA, except for the real data analysis with validation of young animals. Compared to GIBS, GROH resulted in more accurate GEBV predictions.The present study proposes  GIBS matrix), where the relationships are reflected by the actual proportion of shared marker alleles that are IBS, as a deviation from expected IBS allele sharing in the population. With an animal model similar to the classical mixed model, best linear unbiased prediction (BLUP) of the GEBV can be achieved by replacing the pedigree-based numerator relationship matrix with the GIBS matrix (G-BLUP) [With the development of high-throughput genotyping technologies and the reduction of genotyping costs, genomic selection (GS) has become a practical and effective tool for animal and plant breeding ,2. In ge(G-BLUP) ,6.GLA matrix) that contains IBD probabilities within a known pedigree and that depicts this LA information. Thus, based on a limited number of generations within the known pedigree, GEBV can be predicted using the GLA matrix [Habier et al.  and LuanA matrix .GLA matrix, marker alleles are IBD if they can be traced back to common ancestors in a clearly defined base generation. The probability of IBD is based only on pedigree information and the inheritance of marker alleles is traced within the pedigree. For genomic prediction based on the GIBS matrix, it is not possible to identify whether IBS marker alleles are IBD or not, since there is no defined base generation, which means that the GIBS matrix potentially depicts non-recorded relationships that occurred before the base generation of the known pedigree. Thus, a key difference between the GIBS and GLA matrices is the number of generations they take into consideration. For the GIBS matrix, this is limited by the age of the SNPs used, whereas estimates of IBD coefficients with the GLA matrix are based only on the known pedigree, and founders are considered to be unrelated. Because of selection, mutations that cause genetic variation in the trait of interest may be considerably younger than the mutations that underlie SNPs on the SNP chip that have a high minor allele frequency (MAF), which may be very old since they drifted to high MAF. Moreover, the GLA matrix may focus on too few generations [GROH, based on runs of homozygosity (ROH), which considers a range of relationship ages that is between that considered by GIBS and GLA.For genomic prediction based on the erations . Hence, GROH, IBD probabilities are calculated using a multi-locus measure of LD called ROH or haplotype homozygosity [Ne – 1)/2 Ne, where Ne is the effective population size [Ne, whereas ROH over small distances reflects the Ne in the more distant past. ROH can be used to measure multi-locus LD between a marker and a QTL. Compared to two-locus measures of LD such as r2, a major advantage of ROH is that it is generally a less variable indicator of IBD than r2, since the latter is known to be very variable [r2 is unaffected by the number of markers [For zygosity . ROH is zygosity . The proion size . Hayes eion size  found thvariable . The var markers .GROH. Using simulated datasets with various thresholds of MAF for markers and QTL, we compared the accuracy of GEBV prediction using GROH,GIBS based on (population-wide) LD, and GLA based on linkage analysis. In addition, we evaluated the accuracy of prediction of these methods using real data of deregressed EBV of 1086 Italian Brown Swiss bulls.In this paper, we propose a novel method to predict GEBV based on ROH, hereafter referred to as http://ihaiwtheoserv.umb.no/tools/xform/xform.tar.gz) was used to simulate populations according to Wright’s ideal population model, i.e. with random mating, uniform mutation rate and base pair position, drift/mutation balance, manageable effective size, SNP mutations that are accumulated through generations of spontaneous mutations and recombinations under random mating. The ideal populations had an effective size of 500, a 1:1 sex ratio and a mutation rate of 10−8 per base pair per meiosis. To maintain a reasonable computation time, only one chromosome of length 1 Morgan was simulated.A forward simulator ; Population 2 consisted of markers all sampled with a minimum MAF of 0.1 and QTL with a maximum MAF of 0.1 ; Population 3 consisted of markers with a minimum MAF of 0.1 and QTL sampled at random ; Population 4 consisted of markers sampled at random and QTL sampled with a maximum MAF of 0.1 ; Population 5 consisted of markers with a minimum MAF of 0.15 and QTL sampled with a maximum MAF of 0.05 . These five populations reflect the varying degrees to which SNPs can be selected for inclusion on the SNP chip based on high MAF and the variable low frequency of QTL due to selection.One thousand SNPs per chromosome and 30 QTL were sampled disjointedly (i.e. QTL loci could not be sampled as marker loci) from the genotypes created above. Five sampling strategies were used according to the SNP allele frequencies to obtain the following five populations in each dataset (Data I and Data II): Population 1 consisted of randomly sampled markers and QTL  and phenotyping data i.e. de-regressed proofs (DP) for three traits: milk yield (kg), milk fat yield (kg) and milk protein yield (kg). A detailed description of these data is reported in Luan et al. [To obtain the cross-validation datasets, the phenotypes of a defined number of individuals were masked. For the simulated data, in Data I we randomly selected 500 of 4500 individuals at a time for each replicate, without replacement, to produce nine non-overlapping cross-validation datasets, i.e., every phenotype was masked once. Therefore, a total of 90 cross-validation datasets were produced for 10 replicates. Similarly, in Data II we randomly selected 181 of 1086 individuals at a time to produce six non-overlapping cross-validation datasets for each replicate, resulting in 60 datasets. The GEBV of the masked individuals were predicted by the genomic prediction methods described in the next section. The correlation coefficient between the GEBV and true breeding values (TBV) was calculated and used as a measure of the GEBV prediction accuracy, and the deviation of the coefficient of regression of TBV on GEBV from 1 was used as a measure of bias. The mean and standard error of the prediction accuracies and biases in the 90 and 60 datasets for Data I and Data II, respectively, were calculated for each population and each prediction method.For the analysis with real data on 1086 Italian Brown Swiss bulls, two strategies were used to produce cross-validation datasets. The first strategy was the same as that applied to Data II, except that the GEBV were correlated to the masked DP, to obtain a measure of the accuracy of the GEBV (this measure does not have a maximum of 1 since the reliability of the DP is less than 100%). To obtain standard errors, the division into sets and GEBV predictions were replicated 10 times. The second strategy consisted of selecting the youngest bulls as the validation dataset. In practice, to obtain a validation dataset of reasonable size, we selected bulls born in the three most recent years in the pedigree . One hundred and sixteen young bulls were selected, and their GEBV were predicted using data on 970 older animals.Ne), which was assumed to be 100. An approximate estimate for the mutation rate at the markers, mm, is obtained by equating the average homozygosity of all markers to its expected value 1/(1 + 4Nemm). Here, we will also consider run of homozygosity probability ROH, where a putative focal position k which is in the middle between two consecutive markers forming a marker bracket, is also assumed to be IBS (with i < k < j). Since the focal position k is in the middle between two markers, there is no actual marker data at this position. Thus, ROH is the sum of the probability ROH and the probability that all positions except position k carry IBS alleles. Let ROH denote the probability that all marker alleles between positions i and j are IBS between two haplotypes, but the haplotypes are not IBS at positions (i−1) and (j + 1) . Bounded ROH probabilities can be calculated from unbounded ROH probabilities as [A run of homozygosity is defined as two haplotypes carrying IBS marker alleles from some position i through to some position j. Let ROH denote the probability of this occurring (without making any assumptions about marker identity at the border positions (i-1) and (j + 1)). The method to calculate ROH was described in detail by Macleod et al. . Brieflyities as :\documenInclusion of an extra position k among the IBS markers is straightforward:Now, given that we know that all actual markers are IBS between positions i and j and not IBS at positions (i−1) and (j + 1), the IBD probability at position k is defined as the probability that there has been no mutation at this position since its coalescence:k), which is chosen such that the a priori IBD probability at position k is close to 0.5, i.e. 1/(1 + 4Nemk) ≈ 0.5, in order to give the marker data ample opportunity to change the a priori probability either towards 0 (few or no IBS markers in the vicinity of k) or towards 1 (k is in the middle of a long stretch of IBS markers).Here, we need to make an (arbitrary) assumption about the mutation rate at position k  is added to the diagonals to make GROH positive definite.IBD probability PIBD is calculated and averaged over all marker brackets in the genome, with the focal position k in the middle of each bracket. The averaged PIBD of all combinations of genotyped animals are stored in a ROH-based relationship matrix, called GROH is implemented in the LDMIP software (http://ihaiwtheoserv.umb.no/tools/ldmip) [hap haplotypes that resemble the haplotype with a missing marker based on the highest PIBD probability at every position k. Next, it uses the Viterbi algorithm [hap haplotypes without mismatches between the current and the proposed haplotype and with the fewest number of switches between the Nhap haplotypes. I.e., the algorithm finds a mosaic of the Nhap haplotypes that most closely resembles the current haplotype, and uses this mosaic to impute the missing markers. Because marker phase is often unknown (i.e. a heterozygous genotype is not known to be ‘1 2’ or ‘2 1’), the Viterbi algorithm is actually applied to resolve both haplotypes of an individual simultaneously, resulting in a mosaic (as explained above) for each of the two haplotypes and resolving the phase of heterozygous genotypes (‘1 2’ or ‘2 1’). For this, the Viterbi algorithm considers Nhap2 combinations of the Nhap haplotypes that were selected based on PIBD. Based on some preliminary testing, we found Nhap = 40 as a suitable tradeoff between accuracy and computing time. The LDMIP algorithm also yields probabilities of paternal and maternal inheritance at the marker alleles for all animals in the pedigree [GLA by setting up such a relationship matrix at all marker positions and averaging across positions [The calculation of PIBD and s/ldmip) . Programlgorithm  to find,pedigree , which cositions ,9.The model used to predict GEBV with IBS, LA and ROH information can be expressed as:y is a vector of phenotypes (DP) for a trait; μ is the overall mean; Z is a design matrix linking the animals to the phenotypes; a is a vector of additive genetic effects of the animals and e is the vector of random residuals. It is assumed that a(.) ~ N σ(.)2) where (.) refers to ROH, LA or IBS and σ(.)2 is the additive genetic variance associated with G(.).where G(.) is GIBS. Two ways to set up the GIBS matrix were used here. The first was to construct the GIBS matrix with standardized marker genotypes (GIBS-STD) as GIBS-STD = XX’/Nm, where Nm is the number of markers and X is a matrix of the standardized marker genotypes, gij is the genotype of animal i for SNP j, with gij = 0, 1 or 2 for genotypes “0 0”, “1 0” or “1 1”, respectively, and pj is the frequency of allele 1 of SNP j. Standardization is such that the mean and the variance of Xij are 0 and 1, respectively [GIBS matrix was as in VanRaden [GIBS − NSTD = YY ’/∑(2pj(1 − pj), where Y is a matrix of non-standardized marker genotypes, i.e. For GEBV prediction based on IBS relationships, VanRaden , where mG(.) is GLA, the LA-based genomic IBD relationship matrix. For a detailed description about models for GEBV prediction based on LA relationships, see Luan et al. [G(.) is GROH, the ROH-based genomic IBD relationship matrix. To implement the models, GIBS-STD, GIBS-NSTD, GLA and GROH were inverted and were then used in ASReml [For GEBV prediction based on LA relationships, n et al. . For GEBn ASReml  to prediGROH in 90 simulated datasets of Data I and in 60 datasets of Data II and compared them with GEBV based on GIBS-STD, GIBS-NSTD and GLA relationship matrices. Means and standard errors of the accuracies and biases of the GEBV are in Tables We evaluated the accuracy and bias of the GEBV obtained by GROH than with GLA, GIBS-STD and GIBS-NSTD, although the differences were not always statistically significant. Accuracies of GEBV based on GIBS-STD and GIBS-NSTD were similar. Accuracies of GEBV were higher and biases lower with Data I , the older and more distant relationships contributed more to the accuracy of GEBV, which favors GIBS and thus the accuracy obtained with GIBS was higher than with GLA for Data I.In this study, we proposed lls used . Thus, iGLA and GIBS depended on the simulation scenario. If QTL were randomly sampled, the older and more distant relationships were important because this scenario allows old QTL mutations to still contribute to the genetic variance. Matrix GIBS can capture such relationships and hence achieved higher accuracy than GLA for that scenario. If QTL were sampled with a maximum threshold of MAF, then mainly recent QTL mutations contribute to the genetic variance. This implies that recent family relationships are important for the accuracy of GEBV and that more distant relationships contribute little, as indicated by the fact that GLA achieved higher accuracy than GIBS for this scenario , the results in Table io Table .GROH achieved higher accuracies than GLA and GIBS in all cases. In cases where older and more distant relationships are important , the regression coefficient b should be estimated from the data, which can be achieved by fitting the A and GIBS-STD matrices jointly in a variance component estimation model.Similar to the way both marker and pedigree information are used in matrix d et al.  proposedGLA, followed by GROH and GIBS. A possible explanation may be that the three methods capture different relationship ages. Matrix GLA only focuses on the known pedigree, for which the relationships of young animals can be well-defined. With GIBS, uncertain relationships between ancestors prior to the known pedigree may deteriorate the ability to capture relationships between young animals. Matrix GROH captures information on relationships for ages that are intermediate between those of GLA and GROH, and thus achieves an intermediate accuracy.Accuracies were lower for prediction of young animals than for random cross-validation datasets. This may be due to the fact that the Mendelian sampling component of their TBV, i.e. about half of the total variance of the TBV, is uncorrelated to any of the training records. The results for the group of young animals in the real data show that the highest accuracy was obtained with Ne). If Ne is small, common ancestors tend to be in the recent past and recent family relationships tend to dominate the population structure. It is expected that GLA performs better than GROH. If Ne is large, distant family relationships occur frequently and the performance of GLA deteriorates. Thus, it is expected that GLA will perform worse than GROH in a population with a large Ne and when the training population consists of a mixture of different breeds. In the analysis with real data, GLA was found to give higher accuracies than GROH, while in the simulation study with Ne = 500, GROH performed better. This suggests that the Italian Brown Swiss bull population has a smaller Ne than 500, which is also suggested by its small number of sires (21). Goddard et al. [Ne. Thus, GROH is expected to result in higher accuracies of prediction than GLA when variation in relationships is small, such as between breeds.The performance of the methods also depends on the effective size of the population , which also resulted in the higher cross-validation accuracies in the real data. This high reliability of the de-regressed proofs resulted in accurate estimation of chromosomal segments in the linkage analysis, while the low heritability of the simulated trait implies that the long-term, LD-based genetic effects also need to be estimated to achieve high cross-validation accuracy.The simulated and real data results were quite different even when the real pedigree was used in the simulations. The changes in allele frequencies between markers and QTL introduced in Table GROH, to predict GEBV based on runs of homozygosity. Through computer simulations, we showed that the accuracy of GEBV was higher with GROH than with GIBS and GLA. In the analyses of real data, accuracies obtained with GROH and GLA were similar and for the youngest animals, they were highest with GLA. The accuracies obtained with the LD matrix calculated with or without standardizing marker genotypes were similar.The present study proposes a novel method,


Tachycineta bicolor) over 4 years in southern Québec (Canada) to assess the relationships between those four candidate genes and two phenological traits related to reproduction (laying date and incubation duration) and also determine the importance of GxE in this system. Our results showed that NPAS2 female genotypes were nonrandomly distributed across the study system and formed a longitudinal cline with longer genotypes located to the east. We observed relationships between length polymorphism at all candidate genes and laying date and/or incubation duration, and most of these relationships were affected by environmental variables . In particular, the positive relationships detected between laying date and both CLOCK and NPAS2 female genotypes were variable depending on breeding density. Our results suggest that all four candidate genes potentially affect timing of breeding in birds and that GxE are more prevalent and important than previously reported in this context.Monitoring and predicting evolutionary changes underlying current environmental modifications are complex challenges. Recent approaches to achieve these objectives include assessing the genetic variation and effects of candidate genes on traits indicating adaptive potential. In birds, for example, short tandem repeat polymorphism at four candidate genes  has been linked to variation in phenological traits such as laying date and timing of migration. However, our understanding of their importance as evolutionary predictors is still limited, mainly because the extent of genotype–environment interactions (GxE) related to these genes has yet to be assessed. Here, we studied a population of Tree swallow ( Current environmental changes, such as climate warming, severely impact natural populations by generating new and/or modifying already existing selective pressures Parmesan . To copeMicrotus ochrogaster; reviewed in Fondon et al. A candidate gene approach tests statistical correlations between phenotypes and specific a priori relevant genetic components  to link phenotypic variations to gene variants , Johnsen et al. Ficedula hypoleuca), Kuhn et al. Hirundo rustica, Caprioli et al. Buteo buteo) population, STR length polymorphism in three other candidate genes, NPAS2, ADCYAP1 and CREB1, has been recently reported for the first time in relationship to reproduction timing  long-term study in southern Québec (Canada) to investigate the relationship between length polymorphism at all four candidate genes  and phenological traits related to reproduction (laying date and incubation duration). Tree swallow is a small migratory passerine, and while laying date for this species has advanced in North America during the last decades . Birds were individually identified with an aluminum band (US Fish and Wildlife Service), and females were assigned to an age class, second year (SY), or after second year (ASY), based on feather color . Time periods showing the strongest correlations with temperature were different for laying date  and incubation duration  and are referred hereafter to April and May temperatures, respectively. We only considered first breeding attempts in our analyses, that is, first reproductive event that occurred in a nest box and first record of breeding attempt of both female and social male (if known) within a reproductive season .The study system in southern Québec (Canada) covers an area of 10,200 kmwww.sequences.crchul.ulaval.ca) to assess the concordance between targeted genes and PCR products. CLOCK, NPAS2, and CREB1 showed sequences highly similar  to those previously published  with GenePop 4.0 . The full model included latitude and longitude , breeding density (% of occupied nest boxes on each farm), temperature (°C), sex and all two-way interactions with sex as explanatory variables. As April and May temperatures were highly correlated within years (r > 0.83), we decided to average these values to a mean temperature. Year was not included in this model because there was no difference in genetic structure among years (see AMOVA results). All explanatory variables were standardized  and the final model was determined by sequentially removing the least significant term from the model based on its P-value until all remaining variables were significant (α = 0.05) (Crawley r) for 10 distance classes of 10 km : 42.2 (21.1) km) in three datasets: females only, males only, and all individuals. Two-tailed 95% confidence intervals were obtained based on 999 permutations. Individuals observed on more than one farm  were randomly assigned to a single location.To assess how genetic variation distribution was related to environmental and spatial variation, we used two approaches. First, we used a linear model implemented in the software R  for all candidate genes separately , and differences between distributions would suggest nonrandom mating.Genetic variation can also be nonrandomly distributed between mating pairs. To assess the presence of nonrandom mating, we computed the distribution of pairwise genetic relatedness estimator , we restricted our analyses to laying date and incubation duration . Using linear mixed models, we assessed the relationship between candidate genes and both laying date and incubation duration. As both females and social males showed significant adjusted repeatability for laying date  and incubation duration , only clutches with both parents known and genotyped were included in these analyses to disentangle their genotypes relative impact on these traits . Full models included as fixed effects: male and female genotypes (continuous), female age class (SY or ASY), relevant environmental variables , and all two-way interactions between female age class or environmental covariates and genotypes  to test GxE and genotype–age interactions. Female identity, male identity, and year were included as random effects. Explanatory variables were standardized , and analyses were performed using lme4 package  was most frequent (61.6%), a result similar to the observation of Dor et al. (P > 0.39), neither within years (P > 0.13) nor in female age classes (P > 0.19). However, a closer look within sexes suggested a deviation in males at NPAS2  that was not significant after Bonferroni correction for multiple comparisons.We successfully genotyped more than 98.8% of the 925 breeders  captured between 2010 and 2013 , ADCYAP1 , and CREB1  in females; however, all results were not significant after Bonferroni corrections. No other correlations among pairs of genotypes for female or for males were significant . Finally, in the AMOVA, more than 99% of the total genetic variance was due to individual differences, suggesting no genetic structure among years or farms.CLOCK genotypes were weakly correlated with NPAS2 . A closer examination within each sex revealed a positive significant relationship with longitude in females . No relationships between genotypic and environmental variations were observed for CLOCK, ADCYAP1, and CREB1. Spatial autocorrelation analyses revealed no spatial structure in any of the candidate gene allele distributions . Pairwise genetic relatedness between observed and random mating pairs showed no significant different distributions for all genes .The final model suggested an effect of the interaction between sex and longitude on the genotypic distribution of NPAS2 , NPAS2 , and ADCYAP1  female genotypes were all nonsignificant.Laying date was a function of the polymorphism at three candidate genes Fig.. First, β = −0.076 ± 0.621, t = 1.22, P = 0.22). No significant relationships between incubation duration and genotypes were found for CLOCK and ADCYAP1 models, although a marginally nonsignificant effect was observed for the interaction between CLOCK male genotype and both longitude (P = 0.06) and May temperature (P = 0.08) (Table S4.5). Full models for laying date and incubation duration are detailed in Appendix S4.Incubation duration varied as a function of male genotypes at two candidate genes Fig.. NPAS2 mWe investigated the relationship between four candidate genes  and two phenological traits related to reproduction: laying date and incubation duration. We used 4 years of data for males and females and included in our statistical analysis gene–environment interactions (GxE) to account for potential confounding environmental effects. We observed relationships between length polymorphism at all candidate genes and laying date and/or incubation duration. Most of these relationships were affected by environmental variables , emphasizing the presence and importance of GxE in our study system and its potential role in explaining divergent results among previous studies  than in most previous reports from other species , the only exception being the study by Chakarov et al. .Number of alleles and heterozygosity observed for CLOCK, NPAS2, and ADCYAP1 genes in this study were similar to those reported in other bird species . Notably, CLOCK allele frequencies previously reported in a tree swallow population in Ithaca  by Dor et al.  were almv et al.  on raptor = 0.90), revealing a possible migration route from west to east within the study area. Taken together with our results, these observations suggest that earlier settlement dates could be related to shorter NPAS2 female genotypes.The presence of genetic variation in relation to space and/or environmental components can indicate underlying evolutionary processes, but also functional roles when observed at candidate genes .We found a positive relationship between CLOCK female genotypes and laying date, which supports the results previously reported in blue tits and barn swallows of earlier laying dates at smaller allele length , Mueller et al. Junco hyemalis thurberri), Peterson et al. We also found a correlation between ADCYAP1 female genotypes and laying date in interaction with latitude. In previous studies, ADCYAP1 longer genotypes were associated to greater migratory restlessness (blackcaps (Cygnus olor), Charmantier et al. Larus canus), Brommer and Rattiste Strix aluco), Brommer et al. Larus novaehollandiae), for example, significant additive genetic variance component and nonzero heritability for laying date were reported in males . The male component of genetic variation was rarely taken into account in previous studies of candidate gene variation effects on timing of reproduction : female h2 = 0.040, Husby et al. Parus major) and blue tits). Repeatability, the superior limit of heritability (Boake h2 = 0.86) showed smaller value in extra-pair young than within-pair young  still suggests the importance of one candidate gene–environmental interaction for laying date and incubation duration . Nonetheless, we believe that replicates should be obtained from other tree swallow populations and more species for a better understanding of the importance of GxE involving these phenological candidate genes.Importantly, some precautions are needed when interpreting GxE interactions because of potential publication bias favoring significant results, high false-positive rate when assessing multiple comparisons and rare replications of previous findings (Little et al. Finally, the detection of relevant GxE interactions is also dependent on the underlying neutral population genetic structure and the validity and reliability of the environmental variables used when testing for such effects. Here, a previous study on this tree swallow population showed no important genetic structure at neutral microsatellite loci (Porlier et al. Candidate gene approaches provide complementary information to quantitative genetic studies (Liedvogel et al.


Recently, one of the greatest challenges in genome-wide association studies is to detect gene-gene and/or gene-environment interactions for common complex human diseases. Ritchie et al. (2001) proposed multifactor dimensionality reduction (MDR) method for interaction analysis. MDR is a combinatorial approach to reduce multi-locus genotypes into high-risk and low-risk groups. Although MDR has been widely used for case-control studies with binary phenotypes, several extensions have been proposed. One of these methods, a generalized MDR (GMDR) proposed by Lou et al. (2007), allows adjusting for covariates and applying to both dichotomous and continuous phenotypes. GMDR uses the residual score of a generalized linear model of phenotypes to assign either high-risk or low-risk group, while MDR uses the ratio of cases to controls.In this study, we propose multivariate GMDR, an extension of GMDR for multivariate phenotypes. Jointly analysing correlated multivariate phenotypes may have more power to detect susceptible genes and gene-gene interactions. We construct generalized estimating equations (GEE) with multivariate phenotypes to extend generalized linear models. Using the score vectors from GEE we discriminate high-risk from low-risk groups. We applied the multivariate GMDR method to the blood pressure data of the 7,546 subjects from the Korean Association Resource study: systolic blood pressure (SBP) and diastolic blood pressure (DBP). We compare the results of multivariate GMDR for SBP and DBP to the results from separate univariate GMDR for SBP and DBP, respectively. We also applied the multivariate GMDR method to the repeatedly measured hypertension status from 5,466 subjects and compared its result with those of univariate GMDR at each time point.Results from the univariate GMDR and multivariate GMDR in two-locus model with both blood pressures and hypertension phenotypes indicate best combinations of SNPs whose interaction has significant association with risk for high blood pressures or hypertension. Although the test balanced accuracy (BA) of multivariate analysis was not always greater than that of univariate analysis, the multivariate BAs were more stable with smaller standard deviations.In this study, we have developed multivariate GMDR method using GEE approach. It is useful to use multivariate GMDR with correlated multiple phenotypes of interests. Genome-wide association studies (GWAS) have been successfully conducted to detect disease susceptibility genes for common complex human diseases by focusing on associations between single-nucleotide polymorphisms (SNPs) and phenotypes . While tT , the cell of combination is labelled as "high risk", otherwise, "low risk". MDR method shows greater power for testing high-order interactions compared with logistic regression analysis [Classic logistic regression can be used to analyze the gene-gene interaction . Howeveranalysis . Severalanalysis -16. One These GWAS methods are generally implemented in a univariate framework analysing one phenotype at a time even though multiple phenotypes of interest are collected from a study population. In particular, pleiotropy that occurs due to potential genetic correlation between multiple phenotypic traits plays a role in pathogenesis of correlated human diseases . JointlyIn this study, we have proposed multivariate GMDR method by extending GMDR method for the multivariate phenotypes. We construct GEE model with multivariate phenotypes to extend generalized linear models. The GEE approach is exceptionally useful method for the analysis of longitudinal data, especially when the response variable is discrete . Using tWe apply the proposed multivariate GMDR method to the Korean Association Resource study on blood pressure: systolic blood pressure (SBP) and diastolic blood pressure (DBP). A number of authors have investigated the genome-wide association studies on blood pressure and hypertension for Korean population -26 and fi  regarding a multivariate version of generalized linear model (GLM) which is implemented in GMDR. Let where The GEE estimators of hth column is i. By the chain rule,where Then the score equations for i is defined as:The expression, where B and DBPB, respectively. We defined the hypertensive case as HP = 1 if SBP ≥ 140 mmHg or DBP ≥ 90 mmHg, and HP = 0, otherwise. Several genome-wide association studies (GWAS) have been performed on blood pressure by treating blood pressure as a quantitative trait [1, HP2, and HP3. Among 7,546 subjects, 2,080 subjects did not follow up at time 2 or 3. Subject characteristics are summarized in Table B and DBPB, while a total of 5,466 individuals and 344,309 SNPs were included in the analysis of repeatedly measured hypertension status.Our primary outcomes are two types of blood pressure, systolic blood pressure (SBP) and diastolic blood pressure (DBP), and hypertension diagnosis of the Korean Association REsource (KARE) Consortium. The measurements of blood pressure were dichotomized at 140 mmHg for SBP and 90 mmHg for DBP, and denoted by SBPve trait -29. In tB and DBPB with covariate adjustment for recruitment area, age, sex, and BMI. The correlation between SBPB and DBPB is 0.48. The multivariate analysis with two binary phenotypes  was conducted using the GEE approach. For the repeatedly measured hypertension status HP1, HP2, and HP3, we fit logistic models for each HPi and fit the GEE model for three HPs simultaneously. The pairwise correlations range from 0.32 to 0.36. In the GEE model, we assumed two types of genetic effect: homogeneous genetic effect and heterogeneous genetic effect for multivariate phenotypes. However, when we compared the effect sizes and p-values of homogeneous model with those of heterogeneous model, there was no strong evidence for supporting the homogeneous genetic effect. So, we present the results of the GEE model with heterogeneous genetic effects for multivariate phenotypes in both of blood pressures and repeatedly measured hypertension status.To compare multivariate analysis with univariate analysis, we first separately fit a logistic regression model for each dichotomized blood pressure measurement SBPB and DBPB analysis, we selected the top 50 SNPs for each SBPB and DBPB. From these 100 SNPs, we chose 35 SNPs using a p-value criterion (< 1 × 10-4) from the GEE model. In a similar manner, we chose 34 SNPs for HP1, HP2, and HP3 by selecting the top 50 SNPs for each HPi using the same p-value criterion from their GEE model.To perform gene-gene interaction analysis using GMDR analyses, we first selected SNPs with strong marginal effects in univariate models and among those, we select the ones with strong effects in multivariate models. For SBPB and DBPB, and their multivariate analyses. For SBPB and DBPB, the Manhattan plots are given in Figure B  and three SNPs for DBPB  were selected at the 10-5 significance level. For multivariate GEE analysis for , six SNPs were selected: rs17045441, rs1378942, rs12942470, rs1549022, rs927833, and rs2111464. Among these six SNPs selected from multivariate GEE analysis, four SNPs were also found by univariate analysis but two SNPs (rs1378942 and rs2111464) were not. A gene CSK in which SNP rs1378942 is located has been reported as a hypertension susceptibility gene in the Korean population [We report results of GWA studies of dichotomized SBPpulation ,26 and apulation .1, HP2, and HP3. First, the logistic regression model was fit for each HPi and multivariate analysis for  was performed by GEE model. Manhattan plots are given in Figure -5 significance level , five for HP2 , and seven for HP3 , and three for multivariate HPs . However, none of the identified SNPs were commonly observed by all three univariate analyses  which is average of sensitivity and specificity was chosen at each fold. To choose the final model, we considered cross-validation consistency (CVC) among a set of best combinations.We present GMDR results to discover gene-gene and/or gene-environment interactions. For univariate GMDR analysis, logistic regression models for dichotomized SBPB, 4.21E-05 for DBPB, and 3.26E-05 for multivariate phenotypes. The best two-locus model of DBPB included one SNP, rs1378942, in CSK and another SNP, rs11866964, in ZNF423 implying that the interaction between CSK and ZNF423 genes was identified as a significant contributor to dichotomized DBPB. The test BAs of the one-locus models (two-locus model) for these SNPs were 0.545 and 0.549 (0.566) for rs1378942 and rs11866964, respectively. The best two-locus model from the multivariate GMDR included rs7555790 in PEX14 gene and rs11077135 in A2BP1 gene. The test BA of the one-locus models (two-locus model) for these SNPs were 0.526 and 0.532 (0.546), respectively. It seems that the contribution was from the joint effects of two genes rather than their main effects. The graphical descriptions for test BA are given in Figure B and DBPB in both one and two-locus models. The distribution of test BA for multivariate GMDR is more concentrated than those of SBPB and DBPB.Table 1, HP2, and HP3. For these hypertension phenotypes, 34 SNPs selected from the preliminary analysis were included to GMDR mechanisms. All possible one and two locus models were fit for 34 SNPs. Not surprisingly, all different SNPs were identified in one-locus model. For the comparison between GMDR methods and classic method of logistic and GEE models, we report the p-values from the logistic models and GEE model for the identified SNPs from GMDR methods in one-locus models: 1.02E-05 for HP1, 1.59E-05 for HP2, 6.33E-06 for HP3, and 8.50E-05 for multivariate phenotypes. The identified SNPs by GMDR methods also have significant p-values from the classic methods. The best two-locus model from multivariate GMDR included rs7791839 in CCDC129 gene and rs7168365 in WDR72 implying that the interaction between CCDC129 and WDR72 genes was identified as a significant contributor to the repeatedly measured hypertension status. Box plots and density plots of test BA for GMDR and multivariate GMDR of HPs are given in Figure B and DBPB, the test BA for multivariate GMDR had a smaller deviation in the both one-and two-locus models.The results of the univariate GMDR and multivariate GMDR are summarized in Table B and DBPB with the results from the GMDR of HP1 including the same individuals and candidate SNPs (Table B or DBPB, we can directly compare the performance of multivariate GMDR and univariate GMDR through those analyses. Multivariate GMDR and GMDR yielded the same best two-locus model. However, multivariate GMDR shows slightly better test BA than GMDR. Box plots of test BA for multivariate GMDR and GMDR from those two analyses are given in Figure We presented the results of univariate and multivariate GMDR by the same phenotypes in the previous two sub-sessions. However, those comparisons are not significantly meaningful to describe the usefulness of multivariate GMDR. Here, we compared the results from multivariate GMDR of SBPPs Table . BecauseIn this paper, we have developed multivariate analysis for discovering gene-gene interaction, namely multivariate GMDR. Our multivariate GMDR analysis was developed by utilizing a GEE approach to multivariate phenotypes. Many studies emphasized the importance and the increase of power for multivariate analysis in GWAS -35. AlthThough real GWAS data analysis, we investigated the properties of multivariate GMDR. Firstly, the result of multivariate GMDR does not always coincide with that of GEE approach. That is, the best SNP set selected by multivariate GMDR does not always have the smallest p-value from GEE model. In our analysis, note that the SNP set selected by multivariate GMDR still tends to have quite a small p-value. Secondly, the test BAs of the multivariate GMDR is not always larger than those of univariate GMDR. As shown in Figures The proposed multivariate GMDR can be extended in many different ways. The modified version BAs which takes account for the distributional difference is expected to improve the performance of multivariate GMDR. The testing procedure using the modified BAs under the null distribution would enable us to demonstrate the increase of power of multivariate GMDR. A prediction score is defined as the sum of elements of the score vector from GEE model. We are currently working on several different weighting schemes for accounting various relationships between phenotypes. The weighted prediction score is also expected to improve the performance of multivariate GMDR. In the future studies, all these extensions will be evaluated through extensive simulation studies.The authors declare that they have no competing interests.JC and TP designed the study and JC carried out statistical analysis. TP coordinated the study. JC and TP wrote the manuscript. All authors read and approved the final manuscript.


Mixed models are commonly used for the estimation of variance components and genetic evaluation of livestock populations. Some evaluation models include two types of additive genetic effects, direct and maternal. Estimates of variance components obtained with models that account for maternal effects have been the subject of a long-standing controversy about strong negative estimates of the covariance between direct and maternal effects. Genomic imprinting is known to be in some cases statistically confounded with maternal effects. In this study, we analysed the consequences of ignoring paternally inherited effects on the partitioning of genetic variance.We showed that the existence of paternal parent-of-origin effects can bias the estimation of variance components when maternal effects are included in the evaluation model. Specifically, we demonstrated that adding a constraint on the genetic parameters of a maternal model resulted in correlations between relatives that were the same as those obtained with a model that fits only paternally inherited effects for most pairs of individuals, as in livestock pedigrees. The main consequence is an upward bias in the estimates of the direct and maternal additive genetic variances and a downward bias in the direct-maternal genetic covariance. This was confirmed by a simulation study that investigated five scenarios, with the trait affected by (1) only additive genetic effects, (2) only paternally inherited effects, (3) additive genetic and paternally inherited effects, (4) direct and maternal additive genetic effects and (5) direct and maternal additive genetic plus paternally inherited effects. For each scenario, the existence of a paternally inherited effect not accounted for by the estimation model resulted in a partitioning of the genetic variance according to the predicted pattern. In addition, a model comparison test confirmed that direct and maternal additive models and paternally inherited models provided an equivalent fit.Ignoring paternally inherited effects in the maternal models for genetic evaluation can lead to a specific pattern of bias in variance component estimates, which may account for the unexpectedly strong negative direct-maternal genetic correlations that are typically reported in the literature.The online version of this article (doi:10.1186/s12711-015-0141-5) contains supplementary material, which is available to authorized users. Genetic evaluation based on mixed models  has becoinsulin-like growth factor 2 (IGF2) gene in pig [Genomic imprinting , 8 is the in pig , 13. Imue in pig  also repe in pig . Studiese in pig  and bovie in pig  have alse in pig , 19 and e in pig  confirmeMaternal effects can be statistically confounded with maternal inheritance, as noted by Hager et al. . Furthero” and “m” to differentiate between direct and maternal components, respectively. In addition, capital letters are used to identify different individuals. Under this model, the phenotypic values of individuals A and B are defined as:Consider a model with direct and maternal additive genetic effects. Hereafter, we use the subscripts “μ is the general mean, aoX and amX are the direct and maternal additive genetic effects, respectively, and eX is the residual for individual X = {A, B, AD, BD}. According to this notation, AD and BD stand for the dams of A and B, respectively.where A and B is:Information for the estimation of variance components estimation originates from covariances between relatives. Under the model with maternal effects described above, and assuming independence of the residuals, the covariance between the phenotypic values of individuals σa2, σm2, and σam are the direct additive genetic variance, the maternal additive genetic variance, and the direct-maternal genetic covariance, respectively, and r represents the additive relationship between individuals X and Y. In this context, the main sources of information to estimate maternal parameters are the observed correlations between phenotypes of full sibs (FS), maternal half sibs (MHS) and dam-offspring (DO) pairs. Equated to their expectations under the maternal model, the following expressions are obtained:where Now, let:A little algebra shows that under condition  the prevA and B) under the condition set by Equation  is the gametic relationship [A and B (Ap and Bp) and σs2 is the variance caused by paternally inherited gametic effects. Stated the other way around, the existence of paternally inherited variation that is not accounted for by the maternal model will tend to be assigned to the remaining variance components according to Equation  and two generations of 5000 phenotyped individuals that comprised 2500 males and 2500 females. Phenotypic records were generated for the individuals of the last two generations based on the following model:y is the vector of phenotypic data, μ is the general mean, set to 100 units, ao and am are vectors of the direct and maternal genetic effects, s is a vector of paternally inherited gametic effects, and e is the vector of residuals, while Za, Zm and Zs are incidence matrices. Covariances between genetic (ao and am) and gametic effects (s) were assumed to be zero andwhere I is the identity matrix and σe2 is the residual variance. The variances of the direct and maternal additive genetic effects are:where A is the numerator relationship matrix andwhere s):For the paternally inherited gametic effects . Ethical approval for animal care and use was not required for this study since all data was field data from the Yield Recording System of the Pirenaica breed; furthermore, data was recorded by the stockbreeders themselves, under standard farm management, with no additional requirements.In addition to the simulated scenarios, we analysed data for phenotypic records on the Pirenaica beef cattle breed. The Pirenaica breed is a meat-type beef population from northern Spain with an approximate census of 20 000 individuals that are typically reared under extensive conditions . The datAn additional simulation study was performed based on the same scenarios as described in the previous section, but using genealogical information of the Pirenaica beef cattle breed and replacing each phenotypic record by a simulated value. The aim was to replicate the same structure of relationships between individuals of the real dataset.Although a realistic implementation of all potential genetic sources of variation in the same hierarchical mixed linear model may result in non-estimable functions, the description of the full model is essential to understand the simplified parameterizations that are used below. The full statistical model is:y is the vector of phenotypic data, b is the vector of systematic effects, consisting of the general mean for the simulated dataset and the two sexes and 16 age-groups of dam age of parity for the Pirenaica beef cattle data, and ao, am, s and d are vectors of direct additive genetic, maternal additive genetic, paternal gametic and maternal gametic effects, respectively. Finally, p and h are vectors of random permanent maternal (9224 levels) and herd-year-season (2781 levels) environmental effects (not included in the simulated datasets), e is a vector of residuals, and X, Za, Zm, Zs, Zd, Zp, and Zh are incidence matrices that link the effects with the phenotypic data. Variances and covariances for random sources of variation were defined as follows:where σp2 and σh2 represent the variances of the permanent maternal and herd-year-season effects, σd2 is the variance of maternal gametic effects, and σsd is the covariance between paternal and maternal gametic effects. All other parameters were defined previously. Note that under a pure direct additive model:where y = Xb + Zaao + e,Model A: y = Xb + Zss + e,Model S: y = Xb + Zaao + Zss + e,Model AS: y = Xb + Zss + Zdd + e,Model SD: y = Xb + Zaao + Zmam + e,Model AM: y = Xb + Zaao + Zmam + Zss + e,Model AMS: A number of models based on reduced parameterizations of this full model were fitted to both the simulated and the real data:zpp and zhh.When the Pirenaica beef data was used, all models also included the terms For statistical analysis, we applied a Bayesian approach through a Gibbs sampler . The priy = , where yi is the ith datum and y-i is the vector of data with ith datum deleted, the conditional predictive distribution has a probability density equal to:Models were compared using the pseudo log-marginal probability of the phenotypic data . If we cθ is the vector of parameters. Therefore, p(yi|yi-) can be interpreted as the probability of each datum given the rest of the data and is known as the conditional predictive ordinate (CPO) for the ith datum. The pseudo log-marginal probability of the data (LogCPO) is then:where The collection of conditional predictive densities is equivalent to the marginal probability of the data . A MonteN is the number of Markov chain Monte Carlo (McMC) draws, and θj is the jth draw from the posterior distribution of the corresponding parameter. The interpretation of the results of this test is that the larger is LogCPO, the higher is the marginal probability of data and, thus, the better is the relative fit.and In Scenario 1, all genetic variation was generated as direct additive; there were no maternal genetic or paternally inherited effects. The average posterior mean estimates of variance components and ratios of components of variance are in Table Scenario 2 . Average posterior mean estimates are in Table Scenario 5 included direct and maternal additive genetic, and paternal gametic effects. Direct and maternal additive genetic effects with variances of 500 and 250 were generated, with a strong negative correlation between them (−0.707). The paternally inherited variance was 250. The average posterior mean estimates are in Table 2d) was equal to 0.367, but with Model AS, it was only equal to 0.174, whereas the posterior mean estimate of paternal gametic heritability was 0.379, which increased to 0.505 with Model S that did not take direct additive genetic effects into account. Model SD returned the highest posterior mean estimate of the paternal heritability (0.463), a lower value for maternal heritability (0.130) and a very low estimate of the direct-maternal genetic correlation (0.059). The standard maternal animal model (AM) produced a very large posterior estimate of direct additive heritability (0.471), along with a smaller posterior estimate of maternal heritability (0.157), and the correlation between direct and maternal effects was strong and negative (−0.734). Finally, with Model AMS, both heritabilities fell to very low values (0.045 and 0.056) and a significant proportion of the genetic variation was assigned to the paternal gametic effects (0.436). The results of the comparison of models based on LogCPO showed that Model SD had the best predictive ability, followed by Models AM and ASs. Model AMS was next, and Models S and A showed the worst fit.The results of the analysis using real data on the Pirenaica beef cattle breed are in Table We present a theoretical development that shows that the structure of the (co) variance components assumed by the standard maternal animal model is partially confounded with a model that considers a paternal gametic effect. Meyer and Tier  postulatThese results were confirmed by the simulation study. When simulation and estimation models were analogous, the Bayesian analysis was able to provide suitable estimates of the variance components. Furthermore, when the true simulation structure of the (co)variance components was included in the estimation model together with other variance components, the procedure correctly estimated the true parameters, whereas estimates of the non-simulated variance components were small. However, the presence of paternal gametic effects (Scenarios 2 and 3) and their absence in the estimation model resulted in an overestimation of the direct additive genetic variance, as previously described by other authors , 22. FurMore generally, when any relevant variance component in the simulation model was not considered in the estimation, substantial biases on the variance component estimation were noted. For example, ignoring a true direct additive genetic effect while assuming paternal and maternal gametic effects in the estimation model, led to the absorption of close to half of the additive genetic variance by the paternal gametic variance and half by the maternal gametic variance. In addition, the increase in the estimate of the covariance between paternal and maternal gametic effects was also of this magnitude. This distribution of the direct additive variance followed the pattern described in Equation  and was The model comparison test that we performed provided support to our main argument. To illustrate this point, in Scenarios 2 and 3, where paternally inherited effects were included in the simulation model, the goodness of fit of Model AM was very close to that obtained with Models S and AS, which mimicked the respective simulation models. Moreover, under Scenarios 4 and 5, Model SD performed almost as well as Models AM or AMS, which replicated the true simulation models. Clearly, the constraint imposed by Equation  explainsIt should be emphasized that the constraint imposed by Equation  is not aet al. [This latter explanation helps to understand the results of the analysis of the Pirenaica beef cattle dataset. Estimates of variance components obtained from Model A were concordant with previous results obtained in the same  and otheet al. , 19, whiinsulin-like growth factor 2 (IGF2) gene involved in fetal growth [IGF2 gene has also been shown to affect meat quality traits in beef cattle [IGF2 have been associated with carcass traits [Many studies have reported negative estimates of the genetic covariance between direct and maternal additive effects for beef cattle populations –6. Severl growth , 39 or pl growth , 12, 40 l growth . Genomicf cattle , 43 and s traits  and bodys traits .Furthermore, a wealth of evidence on the role of parental inheritance in fetal and early growth in mammals supports the imprinting hypothesis , 47. ThiFinally, other causes that can explain overestimation of paternal gametic variance are a large difference in allele frequencies between sires and dams or the presence of significant dominance variation. However, these are not relevant for close populations and that include few full-sib relationships, respectively. In future studies, a very promising alternative to distinguish between paternally and maternally inherited effects arises from the use of molecular information that may contribute to better discriminate between paternal and maternal alleles.Ignoring paternally inherited effects in genetic evaluations with maternal animal models can lead to a specific pattern of bias in the estimates of variance components. This phenomenon may account for the unexpectedly strong negative direct-maternal genetic correlations that are reported in the literature. In addition, we showed that the existence of paternal effects may play a role in the explanation of the partitioning of genetic variation in growth traits and possibly in some other relevant traits in livestock production. The main implication of this study is that the presence of relevant paternally inherited variation should be investigated when the maternal animal model provided negative correlation estimates between direct and maternal effects. In addition, in those cases, applying maternal animal models should be done with caution.


Poa secunda J. Presl) was assessed over the intermountain western United States in relation to source population climate. Common gardens were established at two intermountain west sites with progeny from two maternal parents from each of 130 wild populations. Data were collected over 2 years at each site on fifteen plant traits associated with production, phenology, and morphology. Analyses of variance revealed strong population differences for all plant traits (P < 0.0001), indicating genetic variation. Both the canonical correlation and linear correlation established associations between source populations and climate variability. Populations from warmer, more arid climates had generally lower dry weight, earlier phenology, and smaller, narrower leaves than those from cooler, moister climates. The first three canonical variates were regressed with climate variables resulting in significant models (P < 0.0001) used to map 12 seed zones. Of the 700 981 km2 mapped, four seed zones represented 92% of the area in typically semi-arid and arid regions. The association of genetic variation with source climates in the intermountain west suggested climate driven natural selection and evolution. We recommend seed transfer zones and population movement guidelines to enhance adaptation and diversity for large-scale restoration projects.Genetic variation for potentially adaptive traits of the key restoration species Sandberg bluegrass ( In the U.S., exotic species and native cultivars have been extensively used over large geographic areas for restoration. Over the last 20 years, there has been an increasing emphasis on the use of local native plant germplasm to maintain local adaptation and ecological relationships when restoring landscapes Erickson . AlthougAs climate varies across the landscape, it is reasonable to expect that heritable genetic traits in growth and development will evolve Turesson . GenecolPinus contorta Dougl. ex Loud.) are rare. Common gardens are way to assess genetic variation among populations with a relatively large number of seed sources  have lead to monocultures that can competitively exclude desirable native species , a perennial, facultative apomictic bunchgrass  assess genetic variation in morphological, phenological, and production traits, (ii) visualize genetic variation as a function of source population climate though regression modeling and GIS mapping, and (iii) develop seed transfer zones to enhance establishment and sustainability of Sandberg bluegrass within restoration plantings over large geographic areas.Poa curtifolia (Scibner), a serpentine endemic from central Washington state, represented a separate evolutionary lineage. In this study, germplasm collections corresponded to Poa sandbergii from Cronquist et al.  for the time period spanning 1981–2010. There were 21 climate variables designated by Wang et al.  and the Oregon State University's Central Oregon Agricultural Research Center (COARC) in Powell Butte, OR (hereafter PB). The cultivars were supplied by Benson Farms Inc.  and Western Reclamation Inc. . Central Ferry is a low elevation (209 m), relatively warm site in the Snake River Canyon and PB a cooler, higher elevation (941 m) site in the high desert of central Oregon. The 30-year (1981–2010) mean annual temperature at CF was 12.0 and at PB it was 9.2°C. The 30-year norm for precipitation at CF is 352 mm and for Powell Butte 269 mm.In winter, 2008 seeds from the 130 wild accessions and the 9 cultivars were germinated in boxes  containing water-saturated vermiculate. The boxes were placed at room temperature (∽20°C) and seeds allowed to germinate. Germinates were planted into 5 × 5 × 5 cm containers in flats holding 36 containers of Sunshine #5 plug mix  and grown under greenhouse conditions for 6 weeks. Seedlings were watered and fertilized as needed to promote optimal growth. The plants were placed in a lath house for 2 weeks before transplanting.Seedlings were transplanted at CF on April 8 and at PB on April 22, 2008. Plants were spaced 0.6 m apart in rows separated by 1.5 m at CF; at PB, all plants were spaced 0.6 m apart in all directions. At PB, soil moisture conditions were dry so supplemental irrigation (≈10 mm) was applied the day after transplanting. No fertilizer or additional irrigation was applied at either site.The 139 germplasm sources were randomized in six complete blocks at both common garden sites. Within each block, wild collections from each source were represented by two families. Thus, there were 6 individuals for each family for a total of 12 from each source population at each site. For cultivars, two plants from each source were included also giving 12 individuals from each source. At each garden site, there were 1668 plants. In 2009 and 2010, after the establishment year, each plant was evaluated for phenology, production, and morphology traits at each site as defined in Tablesas/stat version 9.2 as described in Littell et al. , and their interaction were tested using block within site as a random effect.For wild populations, variance components for source population, family within population, and residual error was computed using PROC MIXED for each site and year combination. The percentage of total phenotypic variance attributed to each factor was calculated.sas/stat version 9.2) to assess the relationship between plant traits measured in common gardens and source population climate variables similar to St. Clair et al. , indicating reasonable correspondence between traits in both magnitude and direction, data where averaged over environments.Because there were 15 plant traits measured at each site and year, there was a potential to use 60 traits in the canonical correlation analysis, 15 for each of the 4 year-site combinations. Such a high number of potential traits complicate the identification of a small set of canonical variates that explain a high fraction of the variation suitable for modeling with climate variables. Consequently, to simplify the modeling, the number of traits used in canonical correlation was reduced using Pearson correlation analysis of traits for each year–site combination to determine the magnitude and direction of interactions. If the correlations coefficient was highly significant and positive (P < 0.01) as composite plant traits were used for regression modeling and mapping trait variation with seed source climate. Additionally, representative production, phenology, and morphology traits that correlated with canonical correlation scores were also regressed on climate variables and models mapped. Regression modeling between plant traits and climate variables was completed using sas proc reg sas/stat version 9.2. The objective was to find models with the highest predictive value with the fewest number of model parameters  . Raster layers comprised of the relevant climate variables were converted to trait values by multiplying each climatic variable by each associated regression coefficient in the model and summing the results. A mapping contour interval corresponding to the 99% confidence level at regression model means was calculated using the regression model error term. To avoid extrapolation beyond the data, mapping was confined to the range of the observed canonical scores for each trait value.Spatial mapping of plant traits and canonical variates predicted from regression models was completed using the grid algebra function  of the P < 0.01), the second and third variates into high and low categories over the range of the scores. The resulting rasters were then overlaid  were also observed in seven of the 15 traits in 2009 and nine of 15 traits in 2010. For all traits except the leaf length to width ratio, the garden site × source population interaction was also significant (P < 0.01). Thus, populations differed for plant traits depending on site and source, indicating a degree of plasticity , averaging 81% for cultivars and 71% for the wild collections. Leaf length × width also differed between groups and was 18% higher for cultivars both years. Dry weight differed between cultivars (26.9 g per plant) and wild populations (20.0 g per plant) only at CF in 2009. Within cultivars, however, there was a range of dry weight with McIntyre, Wallow, Klamath, and Paulina producing more than Reliable and Duffy Creek in 2009 and more than Mountain Home and Reliable in 2010 (P < 0.01); other cultivars were intermediate.In most cases, the cultivars as a group did not differ from wild populations (data not shown). Survival, however did differ between groups both in 2009 and 2010 (P < 0.01). The average correlation between traits was r = 0.57 , with correlations associated with morphology somewhat higher (r = 0.65) than phenology (r = 0.54) and production (r = 0.53). Although the prevalence of garden site × population interactions indicated plasticity  variates that together explained nearly two-thirds of the variation  or highly significant (P < 0.01) correlations were observed for continentality (TD) and the annual heat-moisture index (AHM) in 11 of the 15 plant traits , indicating more survival in gardens of plants from warmer, dryer source populations with large seasonal changes in temperature than those from wetter, more moderate temperatures Table. For morP < 0.0001) with R2 values between 0.27 and 0.71  was associated with its relatively high and frequent correlation with climatic variables  and higher leaf area . Plants with the highest leaf to width ratios (relatively narrower leaves) were from dry areas with typically lower dry weights, such as the central Columbia Plateau, the lower Snake River Plain, and the eastern Central Basin and Range. But plants with higher leaf to width ratios were also from wetter areas such as the Klamath Mountains that supported higher plant dry weights .Maps of plant traits revealed populations from warmer and drier areas, such as the Columbia Plateau and much of the Central Basin and Range, usually had less dry weight, earlier heading, and smaller, more narrow leaves Fig.. Most of1), middle (M1), and low (L1), and variates 2 and 3 into high (H2 and H3) and low (L2 and L3) sections, resulted 12 seed zones , covered only 298 km2 and was almost indiscernible at our mapping scale. Four zones represented nearly 92% of the mapped area: 212 (dark green) with 26.6%, 222 (light green) with 35.5%, 312 (brown–orange), with 10.2%, and 322 (tan) with 19.3% , mesic (740 mm), semi-arid 367–431), and arid 237–301)  Á. Löve) had higher dry weight and more inflorescences than wild collected material from the intermountain west, the apparent result of agricultural selection. In our experiment, cultivar survival was 10% higher and leaf area was 18% higher than the wild populations as a whole (P < 0.01), suggesting direct or inadvertent selection for those traits. Cultivar survival would be desirable for establishment and might relate to seedling vigor, a trait highly valued in plant material development (Leger and Baughman P < 0.01). We did not see the generally high dry weight and inflorescence number for cultivars that St. Clair et al. . Larson et al.  scores regressed on climate of 0.28 and 0.51. Erickson et al.  models, and Johnson et al. (Achnatherum hymenoides (Roem. & Schult.) Barkworth), regression models with canonical variates and climate ranged from 0.16 to 0.43  Maxim.) from the first PC and climate with a R2 of 0.86. Thus, our regression models for Sandberg bluegrass were comparatively strong and an appropriate basis for seed zone development.Regression of canonical traits with climate resulted in models with r et al.  found R2n et al.  reportedn et al.  reportedIn this experiment, we used transplants to promote establishment for whole-plant evaluation. In doing so, we were unable to examine establishment traits such as germination and emergence. Given that genetic variation in whole-plant traits was linked to climate perhaps differences in seed recruitment would also be linked. Espeland and Hammond  found Sain situ application on relatively large-scale restoration projects. As the scope for future selective adaption and evolution depends on the availability of genetic variation (Sgrò et al. Depending on the needs of land managers, there are many cases when smaller scale restoration maybe desired for specific needs. More mapping detail could be achieved by dividing the range of canonical variates into more sections. This rapidly increases the number of zones and also the complexity of maps and the cost of additional collection and seed increase. In the current seed zone map as in similar studies (St. Clair et al. in situ genetic variation across the landscape.Genecological studies provide information regarding the ability of plant populations to evolutionarily respond to climate variation. Here, we show that Sandberg bluegrass expresses distinct multivariate phenotypes that likely evolved across environmental gradients that were, at times, quite small. Our research supports preferential use of restoration seeds that are appropriately sourced. Although seeds that are juxtaposed geographically are often used when local, specific adaptation is a concern, we show that adaptation on a climatic scale may be used to inform seed source choices, especially in larger scale restoration. The seed zones developed will provide guidance for the choice of genetic resources for restoration, and compared to using a limited number of cultivars, promote