Recent studies on dairy cattle have revealed the existence of a heritable variation in CH4 production that enables mitigation strategies based on selective breeding. We have exploited the available heritable variation to study the genetic architecture of CH4 production and detected genomic regions affecting CH4 production. Although the detected regions explained only a small proportion of the heritable variance, we showed that potential QTL regions affecting CH4 production were located within QTLs related to feed efficiency, milk-related traits, body size and health status. Five candidate genes were found: CYP51A1 on BTA 4, PPP1R16B on BTA 13, and NTHL1, TSC2, and PKD1 on BTA 25. These candidate genes were involved in a number of metabolic processes that are possibly related to CH4 production. One of the most promising candidate genes (PKD1) was related to the development of the digestive tract. The results indicate that CH4 production is a highly polygenic trait.The global temperatures are increasing. This increase is partly due to methane (CH The estimated global temperature increase in 2010 due to greenhouse gas (GHG) and aerosol emissions was 0.81 °C in relation to the pre-industrial era. The 0.11 °C of this increase was contributed by methane (CH4) emissions from direct livestock emissions2. Most of livestock CH4 emissions are caused by ruminants4. The CH4 emissions from ruminants are mostly due to enteric fermentation.The increase in the global temperature has a serious impact on the environment and humans. Some of these consequences may exceed adaptive capacities of some species, lead to water supplies shortage, melt the glaciers and increase sea level as well as trigger extreme climatic events4.In ruminants the enteric fermentation is a consequence of a normal digestive process. One of their stomachs, the rumen, is inhabited by rumen microorganisms, enabling digestion of feed that contains high amounts of fiber. One of the by-products of this digestive process converting the feed provided to the ruminants by the microorganisms is CH4 consists of carbon. When carbon is lost from the body it may no longer be used by the animal as a source of energy. Therefore, apart from its environmental impact, CH4 emission in ruminants has also a potential negative impact on the profitability of animal production6. Due to those potential consequences of CH4 emissions from ruminants, mitigation strategies are under investigations. Optional strategies range from adjusting the management to nutritional treatments7. These strategies may have a high impact on CH4 production. An additional strategy of mitigating CH4 production might involve selective breeding for lower emitters. Such a strategy could be possible in case of the existence of genetic variation in CH4 production and a favorable genetic association of CH4 and traits in the current breeding goals.The CH4 production is due to non-genetic factors , the genetic component (i.e. genetic variance) in CH4 production also exists13. However, information on the extent of genetic control over CH4 production and the genetic architecture of the trait is generally scant. For example, Manzanilla-Pech et al.14 performed GWAS on different methane phenotypes in beef cattle and validated the results on dairy cattle, whereas Van Engelen15 performed GWAS on Holstein cows using phenotypes predicted from milk and breath analyses.Recent genetic studies on dairy cattle revealed that while most of the variation in CH4 production both on a large scale and on individual animals has become available. Among others, high throughput measuring techniques are based on breath analyses, since approx. 90% of enteric CH4 is released during eructation events and by breathing5. Nonetheless, collection of such phenotypic records is still challenging and data sets are limited. This technique is promising as it is non-invasive, based on infra-red analyses of breath samples and measurements can easily be taken during milking or feeding19. The most common application of these techniques is in combination with automatic milking systems (AMS) enabling a relatively long measurement period (duration of the milking); additionally, several observations per cow per day may be collected from a large number of animals. This type of measurement set up enables collection of large volumes of data, which is a prerequisite for genetic analyses.Only lately the technology for measuring CH4 production in dairy cattle. Therefore, the objective of this study was to undertake a genome-wide association study using CH4 phenotypes measured by breath analyzers to unravel the genomic regions controlling CH4 production from dairy cattle.To our knowledge, to date no reports are available on genome-wide association analyses based on direct measurements of daily CH4 production was estimated independently for each level of 2nd order Legendre polynomials. As the first parameter explains most of the variation, only SNP detected with it will be presented and discussed in this study. The GWAS performed on daily CH4 production indicated 50 SNPs with BF > 10 associated with CH4 production in dairy cattle  in order to maximize feed conversion, the CH4 yield26 is the trait of interest (CH4 produced per kg of dry matter intake). Another way of expressing emission is CH4 intensity26, where produced CH4 is expressed per unit of product (milk or meat). Similarly to the residual feed intake, CH4 may be expressed as a difference between predicted and measured CH4 emission 29. For our analyses we have decided to use the phenotype applied most widely in the literature and the least influenced by other traits not strictly related to CH4 emission itself . Another reason is related with the fact that when calculating our CH4 production phenotype, we account for body weight, physiological status and milk production as described in Pszczola et al.13 following Madsen et al.28. Therefore, calculations of CH4 yield or CH4 intensity may have resulted in some potential overestimation of CH4 emissions due to double counting.Methane emission may be expressed in several ways depending on the aim of a given study4 production in dairy cattle, five most promising candidate genes were selected based on GO Term analysis  located within the region of a candidate QTL on BTA 4, is a member of the cytochrome P450 family 51 subfamily A. Based on GO Terms this gene is involved in two biological processes that could potentially affect CH4 production in dairy cattle. Those GO Terms are the lipid metabolic process and the steroid metabolic process31, which are confirmed by CYP51A1 and its family members being involved in the synthesis of cholesterol, steroids and other lipids32. Lipids (i.e. fatty acids) were previously reported to be related to CH4 production, including several studies that used fatty acids present in milk to predict CH4 production39.Based on the bioinformatics analysis of detected regions for CHis Table . The firPPP1R16B , a protein phosphatase 1 regulatory subunit 16B, is located within the candidate QTL region on BTA 13. For this gene two biological processes were found in GO Terms analysis that could link it to CH4 production. One of them, the establishment of the endothelial barrier, e.g. in the intestine, is defined as “… specific and selective control over the passage of water and solutes, thus allowing formation and maintenance of compartments that differ in fluid and solute composition”40. The other, the positive regulation of blood vessel endothelial cells41. The biological processes involving PPP1R16B suggest that this gene could affect the digestive process by controlling the passage of water within the intestine and providing blood vessels to the endothelial cells of the intestine. Being part of such processes, PPP1R16B could affect efficient use of feed and in this way control the amount of by-products (including CH4) produced during the process of digestion.The second gene, namely NTHL1, nth like DNA glycosylase 1, is located at 1,590,252-1,595,934 bp. Its GO Term is the metabolic process, which includes protein synthesis and gradation40. The process involving this gene suggests that NTHL1 may affect digestive processes and consequently also a number of their by-products, e.g. CH4, being released post feeding.The three other genes were all located within the largest detected candidate QTL region on BTA 25, comprising of four SNPs. The first of the genes, TSC2 , tuberous sclerosis 2, is the only candidate gene with a GO Term related to a cellular component, in that case lysosome40. Moreover, TSC2 has been very well studied in humans, as its mutation causes tuberous sclerosis and its product is believed to be a tumor suppressor32. In the case of dairy cattle the location of the TSC2 gene in lysosome, which contains hydrolytic enzymes and takes part in energy metabolism, suggest that it could be involved in digestion processes and degradation of metabolites, this may affect CH4 produced by a cow.The second of the above-mentioned genes, PKD1, encoding polycystein 1, a transient receptor potentially involved in channel interacting . Three biological processes were assigned to it in GO Term analysis, i.e. blood vessel development40, nitrogen compound metabolic process43 and the digestive tract development40. All three GO Terms indicate that PKD1 is involved in digestion processes either directly by affecting the development of the digestive tract, or possibly also blood vessels around it as well as metabolic processes of a nitrogen compound. All those functions, in general, indicate that PKD1 might be involved in emissions of greenhouse gases, not only CH4 but also nitrogen related.The last of the candidate genes on BTA 25 is 4 further functional studies such as gene expression or sequencing of the region of highest interest are required. However, this was outside the scope of this paper.To confirm that the candidate genes detected in this study are the actual causative mutations affecting CH4 production. Those QTLs were clustered in four groups of similar traits: feed efficiency, milk related, body size and health status  could be used for the association study. At this moment, however, CH4 production is the most widely reported trait in genetic studies regarding reduction of enteric CH4 emissions. For this reason we restricted our study to this trait.Next to the search for candidate genes, we have also looked for previously detected QTLs for traits potentially related to CH4 production and QTLs for feed efficiency traits  results in lower CH4 production. Unfortunately, in this study no data was available on individual feed intake of cows and therefore we were not able to verify this statement empirically.Firstly, the comparison indicated an overlap between the genomic regions controlling the CH4 production were also overlapping with QTLs for traits describing various aspects of milk production  showed a negative genetic correlation on the health of the cows and methane production and a very low positive genetic correlation with udder health62. Elliott-Martin et al. (1997), based on breath analyses, indicated that CH4 could be used to diagnose ketosis. Moreover, the health status of the animal is known to affect other traits such as dry matter intake or production, and therefore is likely to affect CH4 production. It is likely that a sick animal produces less methane due to a lower milk production; however, methane intensity (i.e. the amount of methane produced per kg of milk) would increase. Next to QTLs related to traits indicating the health status of the cow also QTLs indicating susceptibility to illness were found in the regions important to CH4 production.Finally, the QTLs detected previously for the health status of the cow  were also found in regions overlapping with SNPs detected in this study for CH4 production, it may be suggested that some of the detected regions in this study have a pleiotropic effect. This knowledge is very beneficial especially in the case of production traits controlled by the same regions as CH4 production , which could serve as indicator traits for enteric CH4 production and eliminate difficult and time-consuming phenotyping. Our findings mostly match the study of Negussie et al.63, who reviewed literature on potential indirect traits for measuring CH4 production. Further evaluation of genetic relationships between CH4 and other traits is necessary to confirm relationships revealed by our study and before inclusion of CH4 to the breeding program can be made.Based on the several traits mentioned above that share the genetic background with CH4 production allows for good distinctions between SNP with large and small effects on a trait, as in each iteration a different combination of SNPs is given a large effect. Thus detected SNPs give a valuable indication for the genomic regions potentially involved in CH4 production in dairy cattle. This was confirmed also by bioinformatics post-analysis of detected regions with the functions of selected candidate genes and QTLs for other traits detected within those regions. However, the total genetic variance explained by significant SNPs was very low. This could be due to several possible reasons, i.e. (1) a low number of animals used in the study, (2) the accuracy of the collected phenotypes, and (3) the polygenic nature of the studied trait.The Bayesian method selected to perform GWAS for CH4 production. Taking into account the heritability of this trait at 0.2713, a higher number of genotyped animals would be needed to obtain a higher percentage of genetic variance explained by the detected SNP. Therefore, the analyses of a larger dataset (for both phenotypic and genomic data) may shed light on more specific SNPs with large effects However, generating a large data set by one project is difficult due to related costs (measuring and genotyping). Therefore, generating such a dataset by combining phenotypic observations and genotypes from various experiments could be a solution producing more reliable results in the future.Firstly, it should be noted that the analyzed dataset was relatively small, and therefore the power of the GWAS design was too low to detect a majority of SNPs associated with CH4 at the AMS during milking. To verify the accuracy of the sensor used in this study we validated the used sensor against sensors used in Respiration Chambers (the standard CH4 measuring technique). This comparison showed a high similarity between results generated by the two sensors when used in the AMS64. There are no studies comparing the performance of sensors used in the present study when installed in the Respiration Chamber. Several factors could lead to inaccuracies in the collected measurements such as occasional wind in the area of AMS or cows’ head movement. These factors were not controlled in this study. To account for these arguably random effects we measured CH4 for the individuals in the long period of time . The average repeatability of the analyzed phenotype was 0.25 as reported in Pszczola et al.13.Secondly, to obtain reliable GWAS results reliable phenotypes are needed. In our study we used a technique that measures CH65 and 9.5% in GWAS on teat number in pigs66. Based on the presented results it seems that CH4 production is also a highly polygenic trait and many different regions are involved in its regulation. It might not be, therefore, possible to detect all of them using GWAS.Thirdly, the greater data set and increased accuracy of the measuring method could not have been enough to explain more genetic variation if the analyzed trait was highly polygenic. In previous studies using the same methodology, but larger data sets, only 0.83% of the genetic variance was explained by SNP in GWAS on litter size in pigs4 production turned out to be a very polygenic trait in application to breeding practice, it may be more advisable to use the genomic prediction approach without specifying particular SNPs as being more important than others (e.g. genomic BLUP). In fact, de Haas et al.67, Lassen et al.68 and Wilson et al.69 performed genomic prediction type analyses while searching for correlated traits. The biggest challenge for the performance of genomic prediction with sufficient, reasonable or high accuracy of the estimated genotypic values is to create an adequately large reference population, which is likely to require cooperation between several countries.As CH4 production in dairy cattle and showed that SNPs associated with the trait of interest may be detected. However, CH4 data collection poses a challenge, leading to a lower power of the experimental design and prevented detection of a high number of SNPs with a large effect on CH4 production. Consequently, only a small proportion of the genetic variance was explained by the SNPs. Nonetheless, the candidate QTL region on BTA 25, where three candidate genes were identified, may be considered as a genomic region regulating CH4 production in dairy cattle. Furthermore, the comparison of the QTL regions affecting CH4 production with previously reported QTLs indicated common genomic regions between CH4 production and traits related to feed efficiency, milk related, body size and health status. The found candidate genes were also involved in a number of metabolic processes possibly related to CH4 production. One of the most promising candidate genes (PKD1) was related to the development of the digestive tract being the environment inhabited by methanogens and the site for methane production. In general, all the evidence shows that CH4 production is a polygenic trait.This study aimed at detecting genomic regions affecting CHAll research was approved by the Local Ethical Committee for Experiments on Animals in Poznan, Poland (Decision Number: 64/2012) and performed in accordance with the “Act on the protection of animals used for scientific purpose” of the Republic of Poland, which complies with the European Union Legislation for the protection of animals used for scientific purposes.4 production [g/d] used in this study were obtained from Pszczola et al.13, where all the detailed information on farms, measuring set-up and data processing can be found.The observations on CH4 production and analyzed in Pszczola et al.13, of which 287 were genotyped. The CH4 production was measured repeatedly on Farm1 during two periods: from 2014/12/02 to 2016/02/03, and from 2016/06/01 to 2016/09/17, and on Farm2 from 2016/02/05 to 2016/03/14. Cows were milked repeatedly during the experiment, in total 25,872 CH4 production observations were collected for the genotyped animals.In short, animals available for this study were 287 Polish Holstein-Friesian cows kept on two commercial farms in Poland. This was a subset of 483 cows phenotyped for CH4 production was measured using a non-invasive Fourier Transform Infrared Spectroscopy breath analyzer  during milking in AMS (Lely Astronaut A4). Concentrations of CH4 and CO2 measured during milking were converted to daily CH4 production in grams per day [g/d] following Madsen et al.28 and Pedersen et al.70. This calculation took into account the concentrations of CH4 and CO2, fat-protein corrected milk, live weight and duration of the pregnancy. Multiple daily outputs per cow were corrected for the diurnal variation in CH4 and averaged per cow per day.The CHCows were genotyped with the Illumina BovineSNP50 v2.0 BeadChip  at the Cattle Genetics Laboratory of the Polish Federation of Cattle Breeders and Dairy Farmers. Ear tissue samples used to extract DNA were collected in the course of a routine procedure within the breeding program. The genotyped SNPs were processed with following quality control checks: (1) being in Hard-Weinberg equilibrium, (2) having the minor allele frequency above 0.05, (3) not being monomorphic, and (4) having a call rate of above 0.95. Six cows were removed as they had the call rate below 0.9. After quality control and removing SNPs located on sex chromosomes and chromosome 0 (unassigned), 39,680 SNPs remained for the genome-wide association analysis.4 production, a multi-SNP genome-wide association analysis was performed with the application of the Bayesian Variable Selection method71. The method allows for a simultaneous estimation of the effects of all markers used in the analysis. The analysis was performed with the Bayz software72 on daily CH4 production using the model developed by Pszczola et al.13. The model was:4 stands for the daily CH4 production levels of a cow; µ is an n-vector equal to the mean; Xb is the design matrix of fixed effects of year-week of measurement and cow’s lactation number (levels 1 or 2+) fitted within the general lactation curve, which was modeled using 3rd order Legendre polynomials; and e is an n-vector of random residual effects assumed to be normally distributed Lk is a vector of individual random animal effect, which was modeled using 2nd order Legendre polynomials. The mapping of marker effects is constructed as a hierarchical model on random animal effects73. Firstly, the model accounts for genetic variance only. Secondly, at the next level the model allows disentangling permanent environmental (Note: this accounted for repeated observations of daily CH4 production per cow.) and genetic variances independently for each level of 2nd order Legendre polynomials. Here the Zu is a matrix with dimensions n by p, with n being the number of genotypes and p being the number of SNP coded as 0, 1, 2 copies of a specific allele vector; βijk is a p-vector with the random effects of markers; and εijk accounts for the permanent environmental effect assumed to be normally distributed To identify regions of the genome affecting CHπ1 = 0.001 was selected, thus on average only 1 in 1,000 SNPs was in the second distribution in each cycle. This resulted in only ~38 SNPs per cycle to have a large effect on the traits. The posterior means were calculated with 500k MCMC iterations with burn-in of 5k iterations to secure that all the SNPs were used74. Selecting a stringent prior provides a more precise distinction between SNPs with large and small effects on the trait75. If the SNP was not genotyped for a certain animal then Bayz assigned an average genotype to that position.For the marker effect the Bernoulli distribution was applied:π1 and π0 are the prior probabilities and 20, the SNPs with BF > 30 are described as a “very strong” association and with BF > 150 as “decisive”. The variance explained by significant SNPs was estimated as a fraction of the total genetic variance explained by all SNPs.The Bayes Factor (BF) was calculated for each SNP to determine the significant associations:2 was estimated in Haploview21 between the SNPs detected on one BTA and not further from each other than 500 kbp. The candidate gene search was performed with the BIOMART software available in Ensembl Bos Taurus UMD 3.132 by entering the position of a possible QTL region or one of the most significant SNPs with ±500 kbp. To limit the number of QTLs to the most promising as candidate genes for daily CH4 production the BIOMART database was also used to study Gene Ontology Terms (GO Terms) of those QTLs. Furthermore, the Cow QTL database of the Animal Genome project20 was used to find previously detected QTLs within the most promising regions detected here for daily CH4 production. This was done analogically as for the candidate gene search, i.e. by entering the position of a possible QTL region or one of the most significant SNPs with ±500 kbp.To confirm the potential QTL regions, also the linkage disequilibrium (LD) measured by r


Triticum aestivum) yield potential (YP). A significant bottleneck for increasing YP is achieving increased biomass through optimization of radiation use efficiency (RUE) along the crop cycle. Exotic material such as landraces and synthetic wheat has been incorporated into breeding programmes in an attempt to alleviate this; however, their contribution to YP is still unclear. To understand the genetic basis of biomass accumulation and RUE, we applied genome‐wide association study (GWAS) to a panel of 150 elite spring wheat genotypes including many landrace and synthetically derived lines. The panel was evaluated for 31 traits over 2 years under optimal growing conditions and genotyped using the 35K wheat breeders array. Marker‐trait association identified 94 SNPs significantly associated with yield, agronomic and phenology‐related traits along with RUE and final biomass (BM_PM) at various growth stages that explained 7%–17% of phenotypic variation. Common SNP markers were identified for grain yield, BM_PM and RUE on chromosomes 5A and 7A. Additionally, landrace and synthetic derivative lines showed higher thousand grain weight (TGW), BM_PM and RUE but lower grain number (GM2) and harvest index (HI). Our work demonstrates the use of exotic material as a valuable resource to increase YP. It also provides markers for use in marker‐assisted breeding to systematically increase BM_PM, RUE and TGW and avoid the TGW/GM2 and BM_PM/HI trade‐off. Thus, achieving greater genetic gains in elite germplasm while also highlighting genomic regions and candidate genes for further study.One of the major challenges for plant scientists is increasing wheat ( Triticum aestivum) is one of the most globally important crops with 750 million tonnes produced each year   spring wheat germplasm. We also combine this data with genotypic data through genome‐wide association studies (GWAS) to identify marker‐trait associations (MTAs) allowing the identification of genomic regions of interest that will help to elucidate the genetic basis of biomass accumulation and RUE in wheat.The 150 elite lines were evaluated during two consecutive years under similar and optimal growth conditions with a shorter cycle during Y17 probably associated with higher temperatures registered Table . The pop2, Stems per m2 7 days after anthesis (A7), grains per square metre (GM2), Infertile SPKL per SP, SpikeL, BM_A7, LI_InB and LI_A7 were adjusted using DTA as COV. The results from the analysis of variance (ANOVA) for most traits indicated significant variations among genotypes, environments (years) and genotype × environment interactions where year was the least significant factor  explained 56.3% of its variability  could be anchored to the Refseq‐v1.0 reference genome, including 509 to unassigned contigs. The chromosomal and sub‐genome distributions of the total array SNPs and of those that were polymorphic in our panel can be seen in Table R2) for all intrachromosomal SNP loci for each chromosome . The A genome showed an average R2 of 0.097, 31.7% of pairwise comparisons were significant and 1.17% of marker pairs were in complete linkage. The B genome showed an average R2 of 0.107, 34.2% of pairwise comparisons were significant and 2.17% of marker pairs were in complete linkage. The D genome showed an average R2 of 0.132, 34.3% of pairwise comparisons were significant and 3.45% of marker pairs were in complete linkage. Chromosome 1 had the highest average R2 (0.134) and highest proportion of pairs in complete LD (4.9%) with chromosome 7 showing the lowest for these metric with 0.081 and 0.6% respectively. A chromosomal breakdown of LD can be found in Table The extent of LD and the average trend of LD decay rate were estimated based on pairwise LD squared correlation coefficients  as described, with most evidence suggesting k2 and some evidence for k3. Each accession was assigned to lineage 1 (gold) or lineage 2 (purple) based on their membership coefficient , while the rest were products of pre‐breeding, namely crosses between elite lines and landraces (11), synthetic hexaploids 26) or product of recent crosses involving landraces, synthetic hexaploids and elite lines 14). Similarly, a phenotypic distinction was observed, where most of the synthetic derivative lines and landraces derivatives appeared distributed in the area of BM_PM, RUET, TGW and Height  from 2 or 4 repetitions for each measured trait over two growing seasons. In total 94 MTAs were identified Tables  and S7. In total, 927 unique genes within a 1 Mbp region (±1 Mb of each locus) of the 94 MTAs were identified. From those, 38 promising candidates were identified for further validation and are presented in Table et al., et al., et al., et al., et al., et al., et al., et al., et al., et al., et al., per se, nor necessarily high final biomass, but for different sources of expression for yield potential traits including RUE at different growth stages, traits which when combined strategically in physiological pre‐breeding crosses, would be expected to be complementary in terms of yield and final biomass  of our markers. However, we also demonstrate a novel pleiotropic MTA on 3D that suggests a link between phenological development and spikelet number, an occurrence that has been linked previously with allelic diversity of Ppd‐1 effecting spikelet formation  that will be tested in the near future.The development of a high‐density physical map with the wheat 35K array and comparative genomics provide a powerful tool in searching for potential candidate genes in wheat. Bioinformatics analysis of the mapped SNP markers in the important MTA regions for yield and yield components identified a large number of candidate genes. Many of these genes were associated with photosynthetic machinery. However, since a number of biological processes are associated with these candidate genes, more detailed experimental analyses will be needed to confirm their roles in determining yield potential‐related traits.The High Biomass Association Mapping Panel (HiBAP) consists of 150 wheat spring types  agronomically acceptable including elite high yield material, pre‐breeding lines crossed and selected for high yield and biomass, synthetic derived lines and appropriate checks. The panel is the result of systematic screening under field conditions of CIMMYT genetic resources that allowed the identification of elite genotypes with favourable expression of traits of interest. These traits were biomass/RUE at different growth stages including final aboveground biomass, high biomass 7 days after anthesis, high biomass at booting stage, high biomass at canopy closure and high RUE at pre and post anthesis. In the selection of the panel, extremes in phenology and plant height were discarded. Therefore, the material has a restricted range of maturity to avoid confounding effects associated with extreme phenology, and restricted plant height to avoid confounding effects on biomass expression. The 150 lines were evaluated in two consecutive growing seasons .et al., All of the field experiments were carried out at IWYP‐Hub  situated at CIMMYT's Experimental Station, Norman E. Borlaug (CENEB) in the Yaqui Valley, near Ciudad Obregon, Sonora, Mexico , under fully irrigated conditions. The soil type at the experimental station is a coarse sandy clay, mixed montmorillonitic typic caliciorthid, low in organic matter, and slightly alkaline (pH 7.7) in nature (Sayre 2 (GM2) and the variables derived from those where four replicates were scored. Phenology of the plots was recorded along the cycle using the scale for growth stages (GS) developed by Zadoks et al. , grain number per ms et al. , followi2 from two beds, starting at least 50 cm from the end of the plot (or the previous harvest) to avoid border effects. A subsample of fresh biomass was weighted and oven‐dried at 70 °C for 48 h for constant dry weight measurement. At physiological maturity, a sample of 100 (Y16) or 50 (Y17) fertile shoots was taken randomly from the harvested area to estimate yield components and HI. The sample was oven‐dried, weighed and threshed to allow calculation of HI, spikes per square metre (SM2), GM2, number of grains per spike (GSP) and grain weight per spike (GWSP). Grain yield was determined in 3.2–4 m2 using standard protocols  or 42 (Y17) days after emergence (BM_E40), at initiation of booting stage according to plot phenology (BM_InB), approximately 7 days after anthesis (BM_A7) and after physiological maturity (BM_PM). Samplings for BM_E40, BM_InB and BM_A7 consisted of total aboveground tissue in 0.4 met al., Percentage of rapid spike growth period (RSGP) was calculated as the difference between DTA and DTInB divided by the total length cycle (DTM). Percentage of grain filling (PGF) was calculated as the number of days between anthesis and physiological maturity divided by DTM. Radiation use efficiency was estimated as the slope of the linear regression of cumulative aboveground biomass on cumulative intercepted PAR . DNA purity was assessed using a NanoDrop 2000  and quantified fluorometrically using the Quant‐iT™ assay kit . The SNP markers were generated using the 35K wheat breeders array  (Allen R2)  curve was fitted using statistical program R . The physical distance at which LD fell below the population critical LD threshold was used to determine the interval size of identified molecular trait associations markers (MTAs). The extent of marker pairs in LD and the mean R2 values were calculated for each chromosome and sub‐genome.To estimate the level of linkage disequilibrium (LD) between markers, the square of the determination coefficient  1–10 with nine independent replicates for each k value. The most likely value of k was determined for each population using structureHarvester.py ] value between each k value was used to predict the likely number of subpopulations. A consensus Q matrix was created from the independent STRUCTURE replicates using Clummpp 1.1.2  within the distance LD decayed below that value in this population (8 Mbp).The population structure of the panel was determined using STRUCTURE 2.3.4  >3 was chosen, as used by multiple studies of this size   was estimated using the MIXED procedure from META R 5.1 , σ2 =error variance, σg2 =genotypic variance and σge2 = G × Y variance. Phenotypic correlations (rp) between traits were simple Pearson correlations. Genetic correlations among traits (rg) were calculated for cross‐year means using the equation from ¯ is the adjusted mean of all pairwise genotypic covariance between trait j and j’ and σg(j)σg(j′)¯ is the average of all pairwise geometric means among the genotypic variance components of the traits.Adjusted means were calculated for each trait by combining data from 2 years using DTA as covariate (fixed effect) when its effect was significant with the exception of phenology or phenological derived traits. The analysis of variance was conducted with the GLM procedure from META R 5.1  and days to maturity (DTM).Figure S2 Boxplots of the best linear estimated predictions (BLUEs) of the main traits measured in HiBAP during 2 years of evaluation (Y16&Y17).Figure S3 Linkage Disequilibrium Decay depicted as a scatter plot of pairwise SNP LD (R2) and pairwise physical distance across the hexaploid wheat genome.Figure S4 GWAS results using 9267 SNPs markers in HiBAP for yield traits based on BLUEs means obtained from the combined analysis from Y16 and Y17.Figure S5 Venn diagram exhibiting the number of total and common MTA's detected for different traits.Table S1 Growing conditions and main agronomical characteristics of the trial grown for 2 years in northeast Mexico under full irrigation conditions.Table S2 Phenotypic correlations among the 31 traits presented in this study.Table S3 Genetic correlations among the 31 traits presented in this study.Table S4 The distribution of the 35K Axiom Wheat Breeders Array loci on the Refseq1.0 Chinese Spring wheat physical map.Table S5 The distribution of 35K Axiom array SNPs that were polymorphic in the HiBAP panel.Table S6 Linkage Disequilibrium/Decay statistics for the HiBAP panel.Table S7 Summary of GWAS results from the trial evaluated during 2 years in northeast Mexico under full irrigation conditions.Table S8 List of selected candidate genes found for the evaluated traits using GWA mapping.Click here for additional data file.


Gene-environment (GxE) interaction is one potential explanation for the missing heritability problem. A popular approach to genome-wide environment interaction studies (GWEIS) is based on regression models involving interactions between genetic variants and environment variables. Unfortunately, GWEIS encounters systematically inflated (or deflated) test statistics more frequently than a marginal association study. The problematic behavior may occur due to poor specification of the null model (i.e. the model without genetic effect) in GWEIS. Improved null model specification may resolve the problem, but the investigation requires many time-consuming analyses of genome-wide scans, e.g. by trying out several transformations of the phenotype. It is therefore helpful if we can predict such problematic behavior beforehand. We present a simple closed-form formula to assess problematic behavior of GWEIS under the null hypothesis of no genetic effects. It requires only phenotype, environment variables, and covariates, enabling quick identification of systematic test statistic inflation or deflation. Applied to real data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI), our formula identified problematic studies from among hundreds GWEIS considering each metabolite as the environment variable in GxE interaction. Our formula is useful to quickly identify problematic GWEIS without requiring a genome-wide scan. Gene-environment (GxE) interaction is one potential way to unravel the missing heritability problem –3. GenomThe severity of problematic behavior can be quantified by the median or mean of the chi-squared statistics for association from a genome-wide scan. For example, the genomic inflation factor constant λ is estimated by the median  or mean By assuming no genetic effect, we present a novel closed-form approximation to the mean of the genome-wide joint GxE interaction test statistics, which can be used to assess problematic behavior due to null model misspecification. The formula disregards characteristics of genetic loci, thereby enabling preliminary use before computing chi-squared statistics by genome-wide scan. We show that the approximation agrees well with the mean of the chi-squared statistics from various joint GxE interaction tests for GWAS data from the ADNI. Our approximation is also valid for marginal association tests. The approximation formula reveals that the joint GxE interaction test is sensitive to null model misspecification, whereas the marginal association test is not.The remainder of the paper is organized as follows. In the Materials and Methods section, we provide the proposed approximation formula, describe the real data application using SNP-GWAS data from ADNI for joint GxE interaction and marginal association analyses, and provide the setup of simulation studies to evaluate the performance of the approximation. In the Results section, we give the results from the real data application and simulation studies. In the Discussion section, we summarize the results and discuss about the proposed approach both theoretically and empirically.n samples are observed with phenotypic value  denoted by y1, …, yn, and L genetic variants, gl = T for l = 1, …, L, are to be tested for association with the phenotype. We introduce p variables, i  at the lth locus to be tested for association (i.e. Hl0), such as gl itself or an interaction between gl and an environment variable. Let q covariates (e.g. sex or age) of sample i to be adjusted in common for all L tests. We consider L hypothesis tests of the null hypothesis Hl0: βl = 0 under the following regression model for the conditional mean of yi with transformation,i = 1, …, n, where η is a monotone increasing function, and η is the identity function and yi follows a Gaussian distribution. The model reduces to the logistic regression model if η is the logit function and yi follows a Bernoulli distribution. The model under Hl0 , ωis are positive values specific to the regression model, and uT =  depends on y1, …, yn. The above tl in (p degrees of freedom (pdf).We study the chi-squared statistic for the score test of the above regression model . AccordiZ˜W˜l)Tu,where QZtl reduces to the score statistic for a logistic regression model by setting βl = 0. More generally, tl reduces to the score statistic for a more general regression model having loglikelihood function ℓ = ℓ(η) by setting ωi = −(∂2/∂2ηi)ℓ evaluated at the null hypothesis βl = 0. Furthermore, if ωi = 1 for all i, u = y, thenFor example, tic, see  for mathwl,i = gl,ixi can be written in matrix form as Wl = GlX, and also as Gl = diag. Then,  with an environment variable Ei considered for GxE interaction. For marginal association test, letting We specifically provide the form of  for joint1, …, tL. Two estimators for λ are the median of t1, …, tL divided by the theoretical median of Systematic inflation (or deflation) of test statistics can be quantified by the overall behavior of genome-wide test statistics. Under the presence of population stratification, empirical distribution from test statistics is inflated from  to λχ12 . This inribution  and the ribution . DeviatiL loci, g1, …, gL and to the marginal distribution of gl, respectively. If q = 1, the matrix inverse is just the reciprocal. Hence, the proposed approximation is a multi-dimensional extension of the approximation of the mean of a ratio by the ratio of means. In order to derive the above approximation, we impose the following assumption for each tested variant independently: gl,1, …, gl,n are independently and identically distributed whose all moments are finite, with mean and variance denoted by μl and gl are independent of u, Z, and X. Since the approximation applies separately for each l, each variant may have a different genotype distribution (i.e. different MAF), and variant frequencies may be correlated due to linkage disequilibrium. The above assumptions exclude the case where the tested variant gl itself causes systematically inflated test statistics, e.g., due to population stratification, cryptic relatedness, sample difference of genotyping efficiency, or a batch effect. In addition, we assume that p ≤ q and Z contains X. Without loss of generality, the first p columns of Z correspond to X, or Z = :q = :q, where Zp1: represents the first p columns of Z and Zp+1):q( are the remaining columns. Now we study the expectation of tl with respect to gl. Our approximation formula for the expectation of tl with respect to gl is:O(n−1) terms. The derivation is given in ith datum, ith residual from a regression of u on gl. As a result, by1L∑l==tapprox,where th=tapprox,where thon model  isTapprlapprox is close to one suggests that the null model is appropriate (or at least has no problematic behavior), and it is expected that the test statistics behave properly unless genetic variants cause problems in the test statistics. Checking systematic inflation or deflation by marginal association scan allows to check whether genetic variants cause problems. On the other hand, a large discrepancy from one suggests null model misspecification, in which case systematically inflated test statistics will be observed after genome-wide scan and the test is unreliable.The case where www.adni-info.org. ADNI is an ongoing, longitudinal study with primary purpose being to explore the genetic and neuroimaging information associated with late-onset Alzheimer’s disease (LOAD). The study investigators recruited elderly subjects older than 65 years. The cohort comprised about 400 subjects with mild cognitive impairment, about 200 subjects with Alzheimer’s disease, and about 200 healthy controls. Each subject was followed for at least 3 years. During the study period, the subjects were assessed with magnetic resonance imaging (MRI) measures and psychiatric evaluation to determine cognitive status at each time point. Study subjects gave written informed consent at the time of enrollment for imaging and genetic sample collection and completed questionnaires approved by Institutional Review Board (IRB) of each participating sites (http://adni.loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf). We obtained approval from the ADNI Data Sharing and Publications Committee for use of the data and analyzed the data anonymously.We illustrate the validity and usefulness of our approximation through application to a real GWAS dataset obtained from the publicly available Alzheimer’s Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). The ADNI was launched in 2003 as a public-private partnership, led by Principal Investigator Michael W. Weiner, MD. The primary goal of ADNI has been to test whether serial magnetic resonance imaging (MRI), positron emission tomography (PET), other biological markers, and clinical and neuropsychological assessments can be combined to measure the progression of mild cognitive impairment and early Alzheimer’s disease. For up-to-date information, see http://adni.loni.usc.edu/) which includes 620,901 SNPs for 757 individuals. We applied a quality control procedure by excluding SNPs with missing genotype rate > 0.05, HWE test P < 10−10, and MAF < 5%; the total number of remaining SNPs was 521,203.The ADNI-GWAS data were obtained from 818 DNA samples of ADNI1 participants using the Illumina Human 610-Quad genotyping array . The genlapprox well approximates lmean, while it is not guaranteed that the approximation is well for the latter dataset. To make the approximation workable, we considered adjusting for PCs as covariates . We also repeated the above analyses using the artificial genotype data for the ADNI data with the 757 samples.We considered the impact on the approximation when the real genotype data is replaced by simulated genotype data. We repeated the same analyses for the nine metabolites and five phenotypes on the ADNI 684 samples described above with the simulated genotype data rather than with the real genotype data, while phenotype, environment, and covariates were fixed. In the above simulation procedure, 10,000 unlinked loci were simulated using PLINK http://genetics.emory.edu/labs/epstein/software/robust-joint-interaction/”. Another solution to the systematic inflation of test statistics is to use the genomic control-adjusted p-values, i.e. chi-squared test statistics divided by a constant so that the median matches the expected value of one. We applied the genomic control-adjustment for the two examples.To see the impact of null model specification, we investigated the BMI—PC.ae.C38.2 and BMI—PC.ae.C40.3 pairs in detail. We considered sophisticating null modeling by applying a quadratic model rather than the linear model or removing outliers. Voorman et al. , Tchetgelapprox for joint GxE interaction and marginal association tests, we carried out extensive simulation experiments. Simulation scenarios are described in To study the behavior of Baseline scenario. This is a baseline for comparison. Other scenarios are a slight modification of the baseline scenario.Association among environment, covariate variables and/or genotypes . The aim is to assess the influence on the proposed approximation of association among environment, covariate variables and/or genotypes. Scenarios 1a, 1b, and 1c consider the association between covariate/environment variables and genotypes, which may arise due to population stratification or genetic architecture. Scenario 1d considers the association between environment and covariate variables.lmean from one. Scenarios 2a and 2b consider that the null model misses the covariate associated with genotypes, for example, adjustment for population stratification is not applied or inadequate. Scenario 2c considers that the null model misspecifies the functional form of the environment variable. Scenarios 2d and 2e consider the presence of outlier(s).Misspecified null model . The aim is to assess the impact of the misspecified null model on the approximation. It is expected that the misspecification deviates the value of Environment/covariate variable distribution . This scenario is intended to investigate the approximation performance under several kinds of environment and covariate variables. We consider four scenarios, considering continous (e.g. age), binary categorical (e.g. sex), and ordinal categorical (e.g. questionnaire score) variables.Genotype distribution . This scenario is intended to evaluate the impact of the distribution of the genetic variants. Scenario 4a considers the correlation between genetic variants due to linkage disequilibrium, while scenarios 4b and 4c consider the different allele frequency spectrum.bG, bZ, and bGE denote the parameters of genotype, covariate and GxE interaction effects on the phenotype. Then, the four scenarios are given as triplets : ,  ,   and  . For the scenarios under the presence of any genotypic effect,  =  and , we considered three genotype codings, additive, recessive, and dominant. We repeated the simulations 200 times to compare lapprox with lmean. Two sample sizes, n = 1000 and 10000, were considered. To evaluate the discrepancy between lapprox and lmean, we summarized mean and standard deviation in the 200 simulation runs. In some scenarios, the magnitude of lmean varied with sample size. Thus, we considered the ratio lapprox/lmean, which is useful to quantify how well lapprox approximated lmean while excluding the impact of the sample size. We considered four effect size scenarios. Let lmean and lapprox for joint GxE interaction and marginal association tests for each of five quantitative phenotypes and nine metabolites set as an environment variable on the ADNI dataset with 684 non-Hispanic Caucasian samples showing no population stratification. The top left and right panels in lapprox approximated lmean well as seen by that all points were gathered around the diagonal line. In the top left panel, there were cases where lmean showed a large discrepancy from one, and two of them are further investigated below. On the other hand, all points in the top right panel were concentrated around one, that is, the means of the chi-squared test statistics from marginal association test were all made closer to one. This behavior differs from that of the joint GxE interaction test, in which the target environment variable xi plays an important role in determining the test statistic distribution, and dependence of lapprox on xi cannot be ignored. In lapprox is close to one if n → ∞ when xi = 1 for all i with p = 1 , which in turn implies that the mean of the chi-squared statistics is approximately one irrespective of what the null model is used.lmean observed in the top left panel means the presence of systematic inflation in genome-wide test statistics. Middle left panel of lapprox and lmean for the phenotypes with Box–Cox transformation based on normality. However, systematic inflation still appeared. On the other hand, the Box–Cox transformation optimized in terms of the closeness of lapprox mitigated the systematic inflation as seen in the middle right panel of The case with large lapprox will not always be close to one for models other than Gaussian unless the null model is correctly specified. Nevertheless, lapprox for marginal association tests was close to one in a real GWAS data application.The bottom left and right panels in lapprox was derived under the assumption that each of genetic variants is an independently and identically distributed random variable, and also is independent of phenotype, environment, and covariates. Therefore, the scaled mean of test statistics computed from genotype data, simulated under the assumptions above, with other variables  being fixed, must be close to lapprox. The results with the artificial genotype data for the 684 samples are given in The proposed lmean and lapprox for joint GxE interaction and marginal association tests with the five phenotypes and nine metabolites as the environment variable on the ADNI dataset with 757 samples showing population stratification as seen in lapprox often underestimated lmean for lower lmean). Results for binary phenotypes were in panels in the third row, and the similar deviations were observed. The left and right panels in the second row of lapprox’s underestimation of lmean. For binary phenotypes given in the bottom panels, lapprox’s underestimation was resolved similarly. lmean and lapprox, which is the expected behavior since the simulated genotype data was generated under the assumption that lapprox is derived. It in turn implies that some of the assumptions for lapprox were violated in the cases of The results with the artificial genotype data for the 757 samples are given in lapprox from one suggests that the specified null model is problematic. Here, we investigated two analyses that showed large discrepancy of lapprox from one as described in the Materials and Methods section. lmean was 1.61. A scatter plot of BMI versus the environment variable  =  and  satisfy the above assumptions except in scenarios 1a, 1b, 1c, 2a, and 2b. In such cases, the approximation of lapprox to lmean was well as the ratio lapprox/lmean was close to one. On the other hand, in scenarios  =  and , phenotypes are associated with genotypes, and hence the assumptions are not satisfied. In such cases, there is no guarantee that lapprox approaches to lmean even if n is increased. Actually, there were several scenarios showing the ratio lapprox/lmean for n = 10000 that was more different from one than that for n = 1000. We provide brief summaries not mentioned above.Here, we provide the results of joint GxE interaction and marginal association tests from various simulation studies. Tables bG, bZ, bGE) =  and  under the presence of the association between covariate and environment variables, the assumption for the derivation of lapprox holds, that is, genotypes are not associated with phenotype, covariate/environment variables. Indeed, lapprox approximated lmean well. On the other hand, in scenario  =  under the presence of the association between genotype and covariate/environment variables, the assumption for the derivation of lapprox does not hold. Nevertheless, lapprox well approximated lmean. Scenarios  =  and  correspond to the presence of the genetic effect, meaning that the approximation is not guaranteed. Actually, lapprox was deviated from lmean in many cases. The magnitude of deviation differed depending on the setup of environment/covariate variables. The results of scenario 1d in Association among environment, covariate variables and/or genotypes . In scenarios , no deviation between lapprox and lmean was observed when no genotypic effect exist  =  and ), but lapprox was close to one while lmean deviated from one in other cases  =  and ). The misspecified functional form of the null model (i.e. scenario 2c) gave larger lmean, and lapprox could approximate the inflated lmean. The existence of outlier(s) tended to give large lmean just as in Figs lmean in scenario 2d (i.e. one outlier) was larger than that in scenario 2e (i.e. ten outliers).Misspecified null model . In some scenarios, bG, bZ, bGE) =  and ), the approximation of lapprox to lmean looked well. Under the presence of the genetic effect  =  and ), where the approximation is not guaranteed, lapprox was deviated from lmean as expected. The magnitude of deviation differed depending on the setup of environment/covariate variables.Environment/covariate variable distribution . Under the absence of the genetic effect . The difference in MAF distribution gave no much difference in the approximation as our derivation does not require specific MAF distribution. Correlation between genotypes did not alter the approximation in terms of mean values of lmeans were less deviated from one compared with the results on quantitative phenotypes . This simplification enabled us to derive a closed-form formula. On the one hand, our theory does not cover the presence of population stratification, which is the limitation of our approach. Indeed, we observed situations where the approximation failed in the presence of population stratification . Intereslapprox quantifies problematic behavior based on the extent of the discrepancy from one, as with the genomic inflation factor. For example, we can roughly judge that null models having lapprox within the range  or  are not a problem, so that a genome-wide scan can be safely conducted.The statistic bG, bZ, bGE) =  and ). In real GWAS, we sometimes encounter the situation where the marginal association test gives a very limited number of loci being genome-wide significant while other loci follow the expected null distribution , implying that the majority of loci have approximately no genetic effect on phenotype. In such cases, we expect that the approximation works well.In derivation of the approximation formula, we imposed the technical condition of no genetic effect on phenotype, covariates, and environment variables. This assumption may not necessarily hold in real GWAS data. However, as seen in the real ADNI data application, the approximation worked well in most of the cases. The simulation studies also showed that the approximation worked under the scenarios with no genetic effect on phenotype  are unavailable and the genetic variants caused the problem, e.g. due to population stratification as in the ADNI data with 757 samples , Asian (Asian), Hawaiian/Other PI (Hawaiian or Other Pacific Islander), Black or African American (Black), White (White), More than One Reported (More than one), Unknown or Not Reported (Unknown).PCs were computed by the EIGENSOFT package using GWAS data with 757 ADNI samples. The first and second PCs for the 757 samples were provided. Ethnic group label for each individual is taken from PTRACCAT object in (EPS)Click here for additional data file.S2 Figlapprox > 1.5 was computed for the ADNI 684 non-Hispanic Caucasian samples. Phenotypes: HEIGHT , BMI , WholeBrain , and MMSE ; Metabolites as environment variables: C10.2, C10.2, C4, C5, PC.aa.C42.6, PC.ae.C38.2, PC.ae.C40.3, PC.ae.C44.3, C10.2, C5.DC‥C6.OH., C5.DC‥C6.OH.(EPS)Click here for additional data file.S3 Figlapprox). Bottom left: joint GxE interaction test (binary phenotype created by dichotomizing quantitative phenotype). Bottom right: marginal association test (binary phenotype created by dichotomizing quantitative phenotype).Joint GxE interaction and marginal association tests are carried out on ADNI-GWAS data for 684 non-Hispanic Caucasian samples where only the real genotype data was replaced by simulation with 10000 loci independently generated under linkage equilibrium, where MAFs are set by uniform distribution on  (ADNI684sim) Phenotypes, covariates and environment variables in real data are fixed. Five phenotypes—height (HEIGHT), body mass index (BMI), whole brain (WholeBrain), intracranial volume (ICV), and mini mental state exam (MMSE)—and nine environment variables: lysoPC.a.C16.0, PC.ae.C38.2, PC.ae.C40.3, C10, PC.aa.C40.5, PC.ae.C36.3, SM‥OH‥C14.1, SM‥OH‥C22.1, and SM.C24.0. Top left: joint GxE interaction test (quantitative phenotype). Top right: marginal association test (quantitative phenotype). Middle left: joint GxE interaction test . Middle right: joint GxE interaction test (quantitative phenotype after Box–Cox transformation optimized in terms of (EPS)Click here for additional data file.S4 Figlapprox and lmean, for which population stratification exists, for joint GxE interaction and marginal association tests on ADNI-GWAS data for 757 samples showing population stratification (ADNI757). Five phenotypes—height (HEIGHT), body mass index (BMI), whole brain (WholeBrain), intracranial volume (ICV), and mini mental state exam (MMSE)—and nine metabolite variables: lysoPC.a.C16.0, PC.ae.C38.2, PC.ae.C40.3, C10, PC.aa.C40.5, PC.ae.C36.3, SM‥OH‥C14.1, SM‥OH‥C22.1, and SM.C24.0. Results are shown without and with adjustment for top 10 principal components (PCs). Top left: joint GxE interaction test with adjustment for top 3 PCs (quantitative phenotype). Top right: marginal association test with adjustment for top 3 PCs (quantitative phenotype). Left in the second row: joint GxE interaction test with adjustment for top 5 PCs (quantitative phenotype). Right in the second row: marginal association test with adjustment for top 5 PCs (quantitative phenotype). Left in the third row: joint GxE interaction test with adjustment for top 3 PCs (binary phenotype created by dichotomizing quantitative phenotype). Right in the second row: marginal association test with adjustment for top 3 PCs (binary phenotype created by dichotomizing quantitative phenotype). Bottom left: joint GxE interaction test with adjustment for top 5 PCs (binary phenotype created by dichotomizing quantitative phenotype). Bottom right: marginal association test with adjustment for top 5 PCs (binary phenotype created by dichotomizing quantitative phenotype).Comparison between (EPS)Click here for additional data file.S5 FigJoint GxE interaction and marginal association tests are carried out on ADNI-GWAS data for 757 samples where only the real genotype data, which showed population stratification, was replaced by simulation with 10000 loci independently generated under linkage equilibrium, where MAFs are set by uniform distribution on  (ADNI757sim). Phenotypes, covariates, and environment variables in real data are fixed. Five phenotypes—height (HEIGHT), body mass index (BMI), whole brain (WholeBrain), intracranial volume (ICV), and mini mental state exam (MMSE)—and nine metabolite variables: lysoPC.a.C16.0, PC.ae.C38.2, PC.ae.C40.3, C10, PC.aa.C40.5, PC.ae.C36.3, SM‥OH‥C14.1, SM‥OH‥C22.1, and SM.C24.0. Results are shown with adjustment for top 3 and 5 principal components (PCs). Top left: joint GxE interaction test without PC adjustment (quantitative phenotype). Top right: joint GxE interaction test with adjustment for top 10 PCs (quantitative phenotype). Left in the second row: marginal association test without PC adjustment (quantitative phenotype). Right in the second row: marginal association test with adjustment for top 10 PCs (quantitative phenotype). Left in the third row: joint GxE interaction test without PC adjustment (binary phenotype created by dichotomizing quantitative phenotype). Right in the third row: joint GxE interaction test with adjustment for top 10 PCs (binary phenotype created by dichotomizing quantitative phenotype). Bottom left: marginal association test without PC adjustment (binary phenotype created by dichotomizing quantitative phenotype). Bottom right: marginal association test with adjustment for top 10 PCs (binary phenotype created by dichotomizing quantitative phenotype).(EPS)Click here for additional data file.S6 Fig(EPS)Click here for additional data file.S7 Fig(EPS)Click here for additional data file.S1 Tablelapprox computed for joint GxE interaction on ADNI-GWAS data for 684 non-Hispanic Caucasian samples, where sex and age are adjusted for, with respect to five quantitative phenotypes, height (HEIGHT), body mass index (BMI), whole brain (WholeBrain), intracranial volume (ICV), and mini mental state exam (MMSE), and 117 metabolite variables as environment variable.(CSV)Click here for additional data file.S2 TableAdditional quantitative phenotype simulation results.(PDF)Click here for additional data file.S3 TableAdditional binary phenotype simulation results.(PDF)Click here for additional data file.S1 AppendixDetails of theoretical results and simulation studies.(PDF)Click here for additional data file.S2 Appendixlapprox to compute lapprox using phenotype, environment and covariate variables as input.R code for simulation studies, including a function (R)Click here for additional data file.


Genomic selection has the potential to increase genetic gains by using molecular markers as predictors of breeding values of individuals. This study evaluated the accuracy of predictions for grain yield, heading date, plant height, and yield components in soft red winter wheat under different prediction scenarios. Response to selection for grain yield was also compared across different selection strategies- phenotypic, marker-based, genomic, combination of phenotypic and genomic, and random selections., with maximum values reached when ~ 60% of the lines were used as a training panel. Predictions using related subpopulations also resulted in higher accuracies. Inclusion of major growth habit genes as fixed effect in the model caused increase in grain yield accuracy under a cross-validation procedure. Independent predictions resulted in accuracy ranging between − 0.14 and 0.43, dependent on the grouping of site-year data for the training and validation populations. Genomic selection was “superior” to marker-based selection in terms of response to selection for yield. Supplementing phenotypic with genomic selection resulted in approximately 10% gain in response compared to using phenotypic selection alone.Genomic selection was implemented through a ridge regression best linear unbiased prediction model in two scenarios- cross-validations and independent predictions. Accuracy for cross-validations was assessed using a diverse panel under different marker number, training population size, relatedness between training and validation populations, and inclusion of fixed effect in the model. The population in the first scenario was then trained and used to predict grain yield of biparental populations for independent validations. Using subsets of significant markers from association mapping increased accuracy by 64–70% for grain yield but resulted in lower accuracy for traits with high heritability such as plant height. Increasing size of training population resulted in an increase in accuracyOur results showed the effects of different factors on accuracy for yield and agronomic traits. Among the factors studied, training population size and relatedness between training and validation population had the greatest impact on accuracy. Ultimately, combining phenotypic with genomic selection would be relevant for accelerating genetic gains for yield in winter wheat. High-throughput genotyping technologies that generate large sets of DNA marker data at low-cost have accelerated the adoption of genomic selection (GS) in plant breeding programs . GS is aFusarium head blight (FHB) resistance [GS was initially implemented in animal breeding, particularly of cattle , 6 and hsistance , grain ysistance , yield, sistance , grain ysistance , and norsistance . The persistance . Factorssistance –21.R), as a measure of genetic gain for grain yield.Muleta et al.  recentlyH2) of grain yield in different environments used for GS are presented in Table H2 for the measured traits were 0.48 (grain yield), 0.63 (heading date), 0.47 (kernel weight spike− 1), 0.37 (kernel number spike− 1), 0.77 (thousand kernel weight), and 0.81 (plant height). Values of H2 for grain yield datasets across the three populations ranged between 0.33 (PA_ALL) and 0.85 (PA_Cluster3), with mean grain yield between 2.82 (NB_NPT) and 5.56 t ha− 1 (PA_Cluster3) (Table H2 for grain yield ranged between 0.40 (BLUP14) and 0.80 (BLUP15).Broad-sense heritability (0.15), 540 (SS0.10), and 270 (SS0.05) SNPs. Prediction accuracies for grain yield increased from 0.33 to 0.56 when SS0.10 was used for predictions . Using less markers, on the other hand, was not that successful for heading date, in which using SS0.15 and SS0.10 resulted in negative accuracies (− 0.01), probably resulting from using a smaller number of markers. For plant height, similar accuracies were observed for SS0.10, SS0.15, and whole genotype data (0.31), whereas using SS0.05 resulted in marginal decrease in accuracy (0.31 to 0.25). For the yield components, there was a 14–39% decrease in accuracy when using the marker SS for predictions. Using random SNP marker sets resulted in accuracies between 0.07 (heading date) and 0.46 (thousand kernel weight). Relative to the GWAS-derived markers, using the random SNPs caused a significant (P < 0.0001) reduction in prediction accuracies (0.34 vs. 0.55) for grain yield. In contrast, significantly higher prediction accuracies (P < 0.05) for random markers were observed for all the other traits except thousand kernel weight. Among the random marker sets, using RM1 (820 random SNPs) and RM3 (270 random SNPs) resulted in similar prediction accuracy (0.30).Average number of markers used for GS for each subset (SS) were 820 SS0.5, 540 S0.5, 540  from TP125 to TP150 as accuracy values hit a plateau. No significant differences between the mean accuracy of each training population size across traits were observed for TP100 and TP125 and for TP125 and TP150, whereas accuracy for TP25 was significantly lower (P < 0.05) compared to all other training population sizes.Increasing training population size resulted in increased accuracy across all the measured traits when validation population size was held constant and reached a maximum at TP150 , Q2 (N = 54 lines) and Q3 (N = 126 lines), with Q2 and Q3 being the most related based on population differentiation coefficient. On the average, using Q2 to predict Q3 (and vice versa) resulted in the highest accuracies, whereas using Q1 to predict Q2 resulted in the lowest accuracies for yield and yield components . Prediction accuracies of 0.09 and 0.10 were observed when Q1 was used as a training population to predict Q2 and Q3, respectively  and 0.25 (Q3/Q2). For kernel weight spike− 1, accuracies ranged between 0.04 (Q1/Q2) and 0.21 (Q3/Q1) whereas for thousand kernel weight, accuracy values ranged between 0.08 (Q1/Q2) and 0.37 (Q3/Q2).Previous STRUCTURE analyses  identifiPpd and vrn marker data were as fixed effect in the model , followed by PS (0.31 t ha− 1) and GS (0.21 t ha− 1)  was highest for RS and MS (both at 0.13) followed by GS (0.12), whereas PS and PS + GS exhibited the lowest σ2 at 0.03.Response to selection and GS 0.1 t ha− 1The impact of various factors on the accuracy of genomic selection for yield and agronomic traits were evaluated through cross-validations using a diverse panel of soft red winter wheat lines that are adapted to the southeastern region of the US. Effects of marker number, size of TP, relatedness between training and testing set, and the presence of fixed effect in the model were assessed under a ridge regression model (RRBLUP). In another scenario, independent predictions were conducted using the diverse panel to predict grain yield of biparental populations of SRWW. The effects of these parameters in the accuracy of GS are discussed below.P < 0.05) resulted in the best accuracies for yield [P < 0.05) and using them for predictions did not necessarily result in the highest accuracies; in some traits (e.g. for plant height and thousand kernel weight), using the marker subset SS0.05 resulted in lower accuracies. For heading date and the yield components, using marker subsets decreased accuracy, irrespective of heritability which suggests that these subsets might not have efficiently captured LD between markers and QTL. Using subsets of markers from association mapping resulted in significantly (P < 0.0001) higher accuracies relative to using random SNPs for predicting grain yield, whereas no significant differences was observed for thousand kernel weight. In other traits such as such as plant height and kernel number per spike, nonetheless, using random markers resulted in higher accuracies  for grain yield and component traits gave an 85% advantage over using the less related subgroup Q1. These results agree with previous studies that showed higher prediction accuracies for more related populations [Aside from TP size, the composition and relatedness of the training and validation populations significantly affected prediction accuracy. Using ulations , 28. In ulations . Close rulations . In contulations . RelatedPpd-D1 and vrn-A1 fixed effect in the model resulted in a general increase  in the accuracy of grain yield. Mason et al. [Lr34/Sr57/Yr18) increased accuracy for rust resistance in diverse wheat germplasm.Including n et al.  reportedn et al.  observedOverall, our results demonstrated the effects of different parameters in the accuracy of GS in soft red winter wheat through cross-validations. Training population size and its relatedness to the validation population were the major factors influencing accuracy. Fine-tuning of these parameters would help achieve optimal prediction accuracies towards improving genetic gains in plant breeding programs.N = 239 lines) to predict grain yield of biparental populations derived from the cross between parents belonging to the TP. Lower accuracies for grain yield resulted when NB (0.06–0.22) and PA (− 0.14–0.43) were used as VP compared to when predicting through cross-validations, which could be due to low relatedness between the populations. The prediction model used (i.e. RRBLUP) relies mainly on the genetic relationships between training and test populations [The goal of GS is to predict the performance of new lines before testing them in the field. With this, we were interested in evaluating prediction accuracies using a TP . However, the highest accuracy was observed when GS was coupled with PS, resulting to a 10% increase in R compared to using PS alone. Using both phenotype and breeding values for selections, Belamkar et al. [R, whereas using four or more significant QTL for MS might not be beneficial as there would be lower number of individuals being selected. Arruda et al. [R. Using simulations in maize double haploid populations, it was demonstrated that across different QTL number and trait heritability, the response to GS was 18–43% greater than response to MS, with an increase in R observed as heritability and the number of QTL increased [GS is a tool to complement PS in selecting “better” genotypes through estimation of breeding values of individuals . Within r et al.  observeda et al.  observedncreased . UltimatDifferent factors were observed to affect accuracy for grain yield and agronomic traits in soft red winter wheat, with training population size and the number of markers having the greatest effects. Inclusion of fixed effect in prediction model increased accuracy for grain yield under single population cross-validations. Ultimately, genomic selection could be exploited further with traditional PS to increase response to selection towards grain yield improvement and increasing genetic gains in plant breeding programs. The effects of the evaluated parameters should be considered when implementing genomic selection not only in winter wheat, but also for other important crops to improve genetic potential and facilitate the process of improvement. Altogether, results could be used as basis in designing and optimizing training population, selecting training and validation populations, and determining the ideal number of markers to be used for genomic selection.N = 239 lines). The TP was comprised of genotypes from the SunGrains® (Southeastern University Grains) Breeding Cooperative (www.sungrains.lsu.edu.index.shtml) which included lines from Arkansas, Georgia, Kentucky, Louisiana, North Carolina, and Virginia, among others; and other sources of germplasm adapted to the southeastern region of the US. Two additional biparental populations were used for independent validations: (1) a recombinant inbred line population  der00 lines ;) derive00 lines ;) and ‘B00 lines ;).iSelect assays [The TP and PA were genotyped using the Illumina® 9 K single nucleotide polymorphism (SNP) chip  whereas t assays  at the Ut assays  and implt assays  in R [50t assays  in R.ijk = μ + Entryj + Loci + Entryj x Loci + Blockk(Loci) + εijkl,Collection and analyses of the phenotypic data were described previously in . Brieflyi is the effect of the ith block; Entryj corresponds to the un-replicated genotypes; Loci is the effect of the ith location; Entryj x Loci is the effect of genotype-by-environment interactions; Blockk(Loci) is the effect of blocks nested within environments; and ε is the standard normal errors.where Y is the trait of interest; μ is the mean effect; Block− 1, kernel weight spike− 1, and thousand kernel weight were collected in eight environments in Arkansas and Oklahoma, U.S. between 2014 and 2015 planting seasons. Collection and analyses of the phenotypic data for the PA were described previously [Measured traits included grain yield, plant height, heading date, kernel number spikeeviously , 42. Theeviously  were useGrain yield data for NB was collected in five environments, including in Fayetteville (AR) during seasons 2015, 2016 and 2017 , and Newport (AR) during 2016 and 2017 (NPT16 and NPT17) in a randomized complete block design with two replications per site year except for FAY15 that had only one replication. Grain yield was recorded by harvesting whole plots, weighing the grains, and adjusting for 13% moisture. BLUP across all locations (NB_ALL), across Fayetteville (NB_FAY) and Newport (NB_NPT) were used for NB as VP dataset for genomic prediction.H2) was calculated by using the formula: e and r are the number of environments and replications. Genotype, environment, and genotype by environment interactions were considered as random effects. Variance components were estimated through PROC Mixed in SAS v 9.4.Broad sense heritability (Ridge regression best linear unbiased prediction (RRBLUP) model was used for genomic selection (GS) through the ‘rrBLUP’ package  in R. RRX is a full-rank design matrix for the fixed effects, β; Z is the design matrix for the random effects u, K is a positive semidefinite covariance matrix, obtained from markers using ‘A.mat’ which is an additive relation matrix function; residuals are normal with a mean of zero, with constant variance and u and ε being statistically independent [where ependent .Two GS scenarios were evaluated in this study: (1) a standard single population cross-validation scheme where the effects of different factors such as marker number, size of the TP, relatedness between TP and VP, and fixed effect on accuracy were evaluated; and (2) independent predictions, where the population in GS scenario 1 was used as a TP to predict grain yield in NB and PA.0.15 (P < 0.15), SS0.10 (P < 0.10), and SS0.05 (P < 0.05) derived from genome-wide association analysis were used to perform predictions to examine the effects of marker number on GS accuracy. To determine the marker subsets, a total of 10 different TP (N = 219 lines) and VP (N = 20 lines) sets were generated, and an independent association analyses using the GAPIT package [(K-PC) model (with number of PC = 3) was performed with each TP and the ABLUP dataset. This was done to prevent “inside trading” effect, which occurs when prediction accuracies are evaluated using QTL that were previously identified in the same group of lines, potentially resulting to overestimated accuracies [p-values corresponding to marker SS0.15, SS0.10, and SS0.05 from each cycle of GWAS. Mean accuracy for each round of GWAS-GS  for each marker subset was recorded. Model performance using marker sets chosen at random was also evaluated, wherein three different sets corresponding to the average number of markers for SS0.15, SS0.10, and SS0.05  were used for predictions.Subsets of markers with varying levels of significance, namely, subset SS package  in R undcuracies . Whole gTo test the effect of training population size on the accuracy for the evaluated traits, 50 different subsets of 25, 50, 75, 100, 125, and 150 lines were sampled as TP at a constant VP size of 60. Mean accuracy for each TP size was recorded.Q values derived from STRUCTURE [Ppd-D1) and vernalization requirement (vrn-A1) were included in the model as fixed effect, either individually or in combination. GS accuracies with or without the presence of the fixed effect were compared under 10-fold cross-validations for TP size = 144 lines under different datasets- BLUP for all environments (ABLUP), BLUP for 2014 site-years (BLUP14), BLUP for 2015 site-years (BLUP15), BLUP for northern environments  and BLUP for southern environments .The effects of relatedness between the training and validation population were evaluated by grouping the lines based on corresponding membership coefficient, TRUCTURE  and perfN = 239 lines) was used to predict grain yield in the PA (N = 157 lines) and NB (N = 100 lines) biparental populations using RRBLUP model. Datasets used for the training set were BLUP across all environments (ABLUP), across northern (NBLUP) and southern locations (SBLUP). Simple matching coefficients between the training and validation populations were calculated using the nominal clustering ‘nomclust’ package and simple matching ‘sm’ function in R to evaluate relatedness between the training and validation populations.The TP . Selection strategies included phenotypic selection (PS), marker-based selection (MS), genomic selection (GS), random selection (RS), and a combination of PS and GS (PS + GS). Mean for grain yield under PS (μPS) was calculated based on the top 25 highest yielding lines; μMS was equal to the mean grain yield of the lines having the favorable alleles for three loci, wsnp_Ex_c2723_5047696 (3B), wsnp_Ex_c13849_21698240 (4B), and wsnp_Ex_c48922_53681502 (4B), previously identified to be significantly associated with grain yield in the TP [GS was equal to the mean of lines having the highest estimated breeding values (top 25 lines) in 10 different rounds of GS under a 10-fold cross-validation in RRBLUP, with TP size =144 lines; μRS was computed based on a function to generate 25 random selections, 10 different times and calculating the mean for these selections; μGS + PS was equal to the mean of the lines with the highest grain yield and estimated breeding values.Response to selection,  R = H2S , where Ha et al. , equal tn the TP ; μGS wasAdditional file 1: Table S1. Accuracy of genomic selection for measured traits across different training population sizes at a constant validation population size (N = 60 lines). Table S2. Accuracy of genomic selection across different marker subsets (SS) from association mapping using BLUP across all environments (ABLUP) dataset. Table S3. Accuracy of genomic selection for grain yield and yield components using inferred subgroups Q from STRUCTURE analyses. Table S4. Accuracy using fixed effect (Ppd-D1 and vrn-A1) in genomic selection model for grain yield in soft red winter wheat. Table S5. Accuracy of genomic selection for grain yield using the “NC-Neuse-Bess’ and “Pioneer 26R61-AGS2000′ mapping populations as validation sets.


Humans vary in their ‘natural ability’ related to sports performance. One facet of natural ability reflects so-called intrinsic ability or the ability to do well with minimal training. A second facet of natural ability is how rapidly an individual adapts to training; this is termed trainability. A third facet is the upper limit achievable after years of prolonged intense training; this represents both intrinsic ability and also trainability. There are other features of natural ability to consider, for example body size, because some events, sports, or positions favor participants of different sizes. In this context, the physiological determinants of elite endurance performance, especially running and cycling, are well known and can be used as a template to discuss these general issues. The key determinants of endurance performance include maximal oxygen uptake  Over the past 50 or so years, the key physiological determinants of endurance exercise performance have emerged. These include maximal oxygen uptake mentclass2pt{minimData on these three variables can be modeled to predict performance, and there are field tests that incorporate several of these variables that are also highly predictive of performance. For example, in the early 1990s I took emerging evidence that humans run the marathon at a pace similar to their running speed at lactate threshold, and calculated a theoretical upper limit, at least at that time, for the ‘fastest’ potential marathon performance by men . This moformance . This la2. Additionally, the physiological determinants of The basic idea underpinning these factors is that they interact in a predictable way. Before I go on, I want to share two sets of assumptions related to the physiology behind moglobin . In othemoglobin , 6. Effimentclass2pt{minimTherefore, with this general perspective as a background, I will next try to ask what is known about the genetic contributions to the major physiological determinants of endurance exercise performance. A key question then is what constitutes ‘genetic’. One approach is to focus on the heritability of key traits related to athletic performance. These are typically statistical arguments based on the correlation of a given trait between family members, most notably mono- or dizygotic twins. If the correlation between monozygotic twins is greater than the correlation between dizygotic twins then the interpretation is that this similarity is due primarily to greater similarities in the DNA of monozygotic twins than dizygotic twins . For \dotraining , 9.While the observations highlighted above suggest there is a strong genetic component to training, specific DNA variants associated with entified –13.The issue of limits of genetic ‘causation’ is also part of a general trend in genomic research for complex human traits that has accelerated in recent years following the completion of the human genome project. In the late 1990s and early 2000s, it was generally assumed that a limited number of gene variants would explain much of the risk of developing common non-communicable diseases. The idea was that once these variants were identified, a host of new approaches to diagnosis, prevention, and therapy would emerge. Unfortunately, this vision has not been realized and hundreds of gene variants with small effect sizes have been associated with complex non-communicable diseases. Importantly, their role in the diagnosis, prevention, and therapy for these diseases remains obscure. These larger issues related to genomics and complex disease-related traits have been discussed in detail elsewhere .Another way to think about endurance performance is via the so-called oxygen transport cascade Fig. . In thisA number of genome-wide association studies (GWAS) have been conducted in an effort to understand the role of DNA variants in lung function. The vast majority of these have focused on lung volumes, and there is little information on diffusing capacity. The take-home message from these studies is that there are a large number of potential common DNA variants that explain a tiny fraction of interindividual differences in lung function. Additionally, when so-called gene scores  are constructed, lung function values in individuals in the highest quartile or quintile versus the lowest quartile or quintile frequently differ by only a few percentage points. These differences typically account for < 0.1 L of a given lung volume and are within the limits of the test–retest validity of spirometry . Thus, terations .After the lung, the next step in the oxygen transport cascade is cardiac output. The right ventricle of the heart pumps blood through the lungs where it is oxygenated and returned to the left side of the heart, which delivers it to the systemic circulation. A hallmark of elite endurance performance is a high maximum cardiac output driven almost exclusively by a very large stroke volume . To datehis time . AdditioIn addition to cardiac output, red cell mass or total body hemoglobin are also important physiological determinants of }V˙O2max , 21.Once the blood leaves the left ventricle and enters the peripheral circulation it is delivered to the tissues. A key determinant of pressure . This ispressure . If at lOne of the fundamental adaptations to endurance exercise training is the increase in mitochondrial density seen in trained skeletal muscle. When this was initially observed by John Holloszy in the mid-1960s, it was a revolutionary finding that initiated the era of exercise biochemistry –26. Subs muscles . As is t muscles . Again, While twin studies show that skeletal muscle fiber type is highly heritable, there is ongoing discussion about so-called fiber-type transformation in humans in response to prolonged intense training –31. In tThere are a number of potential limitations to the perspectives outlined above. The most obvious is that very large cohorts of subjects (perhaps numbering in the hundreds of thousands) in conjunction with the phenotypes of interest and DNA sequence information are simply not available for the key steps in the oxygen transport cascade discussed in this review. For this sort of cohort to be a reality, beyond a blood test for genotyping, detailed measurements of gas exchange at rest and during submaximal and maximal exercise would be needed. Measurements of cardiac output and red cell mass would also be needed, as would serial measurements of blood lactate during graded exercise. Muscle biopsies to assess fiber type, mitochondrial function, and capillary density would also be essential. The financial and logistical barriers to such a research program seem formidable to say the least.However, if such a cohort ever did emerge, it seems likely, based on the data from other phenotypes, that very large numbers of variants with very small effect sizes  would emerge . AdditioA final cautionary note is that for many complex human phenotypes, genetic association studies can have reproducibility issues, and also require diverse ethnic cohorts. The classic example of the reproducibility problem comes from studies of depression where a recent report found essentially no significant and reproducible genetic associations for depression .The above discussion of the oxygen transport cascade shows that while there is evidence, based on family and twin studies, for a genetic component of genotype , 39. Addgenotype .The obvious question is why? One emerging concept is that there are many potential genetic pathways to a given phenotype . This co