Improved performance of crossbred animals is partly due to heterosis. One of the major genetic bases of heterosis is dominance, but it is seldom used in pedigree-based genetic evaluation of livestock. Recently, a trivariate genomic best linear unbiased prediction (GBLUP) model including dominance was developed, which can distinguish purebreds from crossbred animals explicitly. The objectives of this study were: (1) methodological, to show that inclusion of marker-based inbreeding accounts for directional dominance and inbreeding depression in purebred and crossbred animals, to revisit variance components of additive and dominance genetic effects using this model, and to develop marker-based estimators of genetic correlations between purebred and crossbred animals and of correlations of allele substitution effects between breeds; (2) to evaluate the impact of accounting for dominance effects and inbreeding depression on predictive ability for total number of piglets born (TNB) in a pig dataset composed of two purebred populations and their crossbreds. We also developed an equivalent model that makes the estimation of variance components tractable.For TNB in Danish Landrace and Yorkshire populations and their reciprocal crosses, the estimated proportions of dominance genetic variance to additive genetic variance ranged from 5 to 11%. Genetic correlations between breeding values for purebred and crossbred performances for TNB ranged from 0.79 to 0.95 for Landrace and from 0.43 to 0.54 for Yorkshire across models. The estimated correlation of allele substitution effects between Landrace and Yorkshire was low for purebred performances, but high for crossbred performances. Predictive ability for crossbred animals was similar with or without dominance. The inbreeding depression effect increased predictive ability and the estimated inbreeding depression parameter was more negative for Landrace than for Yorkshire animals and was in between for crossbred animals.Methodological developments led to closed-form estimators of inbreeding depression, variance components and correlations that can be easily interpreted in a quantitative genetics context. Our results confirm that genetic correlations of breeding values between purebred and crossbred performances within breed are positive and moderate. Inclusion of dominance in the GBLUP model does not improve predictive ability for crossbred animals, whereas inclusion of inbreeding depression does. Crossbreeding is primarily and intensively applied in meat production systems , especiamentclass2pt{minimr than 1 , and ther than 1 , 6.One of the major genetic bases of heterosis is dominance , 8. At tGenomic evaluation has been successfully used in purebred , 14 and Recently, several studies , 20 haveThus, the current study had the following objectives: (1) to show how genomic inbreeding can be meaningfully included in GBLUP, even for crossbred animals; (2) to estimate the variance components of additive and dominance genetic effects by using data on total number of piglets born (TNB) in two Danish purebred and one crossbred pig populations using the trivariate GBLUP model; (3) to show how to derive, from variance component estimates, estimated genetic correlations of breeding values between purebred and crossbred performances in each pure breed, and also correlations of allele substitution effects between the two pure breeds; and (4) to evaluate the impact of dominance effects from genomic information on genomic evaluation by comparing accuracies of estimated genomic values in different cross-validation scenarios.We begin this section with a short presentation of the data used in the study, with the aim of defining the notation for the methodological developments that follow. For this study, all datasets were provided by the Danish Pig Research Centre. Data from three Danish pig populations were analyzed simultaneously: Landrace (L), Yorkshire (Y) and their reciprocal crosses (LY). Only data on TNB data for the first parity of sows in the three populations were used. In total, there were 2126, 2218 and 5143 genotyped sows with own records on TNB for L, Y and LY, respectively. Instead of using original records, corrected phenotypic values of TNB were used as dependent variables for the trivariate GBLUP model, because the pre-correction for non-genetic effects, such as herd-year-season, month at farrowing, and service sire was more accurately achieved on a larger dataset . Among the crossbred animals, 7407 LY had a Landrace sire and a Yorkshire dam, while 3567 LY had a Yorkshire dam and a Landrace sire; L and Y populations were from nucleus farms and LY from a commercial farm. The litters of purebred sows were both purebred and crossbred litters. The relationship between LY-L and LY-Y are comparable since, in both cases, parents of the F1 animals are in the purebred datasets; further details about the model used for the pre-correction are in . All theThe pedigrees for both purebred and crossbred sows were available and all crossbred animals were traced back to their purebred ancestors until 1994 by the DMU Trace program , as was For the “full genomic dataset”, purebred sows were genotyped with the Illumina PorcineSNP60 Genotyping BeadChip , while tInbreeding can be defined as the proportion of homozygous SNPs across all loci for each animal, as suggested by several authors . If thed the vector of dominance marker effects, the following prior distribution is plausible:μd is the overall mean of dominance effects, which should be positive if there is heterosis due to dominance. A typical model for genomic prediction is that in Toro and Varona [y contains phenotypic values; Xβ stands for fixed effects and random effects other than additive and dominance effects; a is the vector of “biological” additive SNP effects, d is the vector of “biological” dominance SNP effects for each of the markers; matrix Z has entries 1, 0, −1, for SNP genotypes AA, Aa and aa, respectively, while matrix W has entries 0, 1, 0 for SNP genotypes AA, Aa and aa, respectively. e is the vector of overall random residual effects.Theory and evidence of directional dominance  suggest that dominance effects of genes (here associated to markers) should have a priori a positive value for traits that exhibit inbreeding depression or heterosis. If we call d Varona :1\documea and d to have zero means, which is not true for d when directional dominance exist. Defining Typically, genetic models require mentclass2pt{minimh = W1 contains the row-sums of W, i.e. individual heterozygosities . Inbreeding coefficients f can be calculated as:N is the number of SNPs. Then, the prior means The term μ), while the term The term Z and W are as above; A trivariate model based on “biological” (genotypic) additive and dominance effects of SNPs , 32, andNote that “biological” is used here to refer to the genotypic additive and dominance values of the SNPs, to distinguish them from the traditional treatment of quantitative genetics in terms of “statistical” effects  .u and v are vectors of genotypic additive and dominance effects and therefore cannot be directly compared to breeding values and dominance deviations in the pedigree-based genetic evaluation. In addition, f is a vector of genomic inbreeding coefficients and b is a population-specific inbreeding depression parameter per unit of genomic inbreeding, respectively. Note that there is potentially inbreeding depression at the level of the crossbred animals, although, first, the numeric values of the vector f should be smaller since crossbred animals have a higher level of heterozygosity, and second, the estimates of the inbreeding depression parameters (b) do not need to be identical across the three populations, which thus gives considerable flexibility.The above equations can be reformulated to genotypic values of individuals instead of SNPs, in order to be compatible with the classical GBLUP model and animal breeding software, such as BLUPF90  and DMU u, the variances within each breed are:u are:In terms of the genotypic additive effects u are:Z contains elements 1, 0, −1 for the three genotypes, and is defined across the three breeds, The variance components Y in Eq.  cannot bY in Eq. . To fit G-matrix of GBLUP [u in the following way:G0 are variance components associated to the genotypic additive effects u. This structure (a Kronecker product) is compatible with animal breeding software for BLUP and REML and the variance–covariance component G0 can be estimated in a straightforward manner. Then, the (co)variances of additive genotypic effects of SNPs across populations can be obtained as:v are altered in a similar way:D0 contains variances and covariances associated to the genotypic dominance effects v and W contains elements 0, 1, 0 for the three genotypes, and is defined across the three breeds To construct a relationship matrix similar to the classical of GBLUP , Vitezicof GBLUP  introduca et al. , makes iZ and W, their crossproducts and the inverses of G and D were built using own programs. Genetic parameters were estimated by using average information REML with software airemlf90 [Matrices iremlf90 . Standariremlf90 .The additive and dominance (co)variances of genotypic effects of SNPs, either within breed or between breeds, were calculated using Eqs.  and 8),,8), resppi and qi are allele frequencies for SNP i; indices L and Y denote the breeds Landrace and Yorkshire, respectively. For crossbred performance of say, Landrace, the allele substitution effect is Consider the allele substitution effect rding to , the add animals  as follog an F2) .The additive genetic covariances between purebred and crossbred performances within breeds L variances of additive genetic effects u were:A0 were variance components associated to genetic additive effects and not the genotypic additive effects in Eq.  were included in the training population, while the remaining 2716 sows  were included in the validation population. Predictive ability of crossbreds was measured as the correlations  samples  was applFor comparison, the predictive ability of crossbred animals was also investigated in a model without inbreeding depression effects, for all three scenarios. The predictive ability was measured as the correlation Gen_ADM scenario. For all scenarios, the additive genetic variances for purebred performance  to 0.95 (0.06) (Gen_AM) for breed L and from 0.43 (0.22) (Gen_ADM) to 0.54 (0.30) (Nogen) for breed Y. The Gen_AM and Gen_AMD, respectively. However, the standard errors were large, around 0.2 in both scenarios. For crossbred performance, Gen_ADM. This high correlation is a byproduct of assuming that additive biological effects in crossbred animals are the same regardless of the Yorkshire or Landrace origin of the allele. However, the same allele has potentially different effects in the respective Landrace or Yorkshire genetic backgrounds, and the difference is modeled through the correlations, hence the low values of Gen_AM, The broad sense heritabilities for purebred and crossbred animals, genetic correlations between breeding values for purebred and crossbred performances within pure breeds and correlations of allele substitution effects across the two breeds are in Table  0.07 0.0 to 0.08 Nogen to 0.056 in scenarios Gen_AM and Gen_ADM. Standard errors of Predictive abilities for crossbred pigs in the validation population are in Table Gen_AM and Gen_ADM) were slightly closer to 1 than that for the pedigree-based scenario (Nogen). Except for the Nogen scenario, standard errors of regression coefficients were around 0.39. For the Nogen scenario, the standard error was around 5 times larger than that for other scenarios. Overall, there was no clear trend towards a scenario with less bias.The regression coefficients of corrected phenotypic values on the predicted corrected observations for TNB are in the second row of Table Nogen, 0.045 in scenario Gen_AM and 0.046 in scenario Gen_ADM. In all cases, these are lower than the predictive abilities in Table For comparison, predictive abilities f) for each population and their estimated corresponding inbreeding depression parameters (b) in the different scenarios are in Table b), they were all negative  but not of the same magnitude across the three populations. Note that for the scenario Nogen, b was estimated based on the pedigree-based inbreeding coefficients. As a whole, breed L had the most negative b, while breed Y had the least negative b, regardless of the scenario. Thus, TNB was more negatively affected by inbreeding in breed L than in breed Y and population LY.Marker-based and pedigree-based inbreeding coefficient  than for crossbred animals (7.30 for LY). This could be the reason why the estimated additive genetic variances for purebred performance  , 22, 43.sults of , the lowThe ratios of estimated dominance genetic variances to additive genetic variances in the current study (5 to 11%) were generally a little smaller than in other studies on TNB. Vitezica et al.  reportedThe genetic correlation of breeding values between purebred and crossbred performances  showed higher predictive abilities than the pedigree-based scenario (Nogen). For the Nogen scenario, the relationship matrix was constructed based on a base population that was considered as a mixture of L and Y animals, which was not the case. Therefore, the results of the Gen_AM and Gen_ADM scenarios were more reliable than those of the Nogen scenario. Although predictive abilities were not significantly different according to the Hotelling-Williams t-test, the results from 1000 bootstrap samples still showed that the predictive abilities of about 90% of the crossbred animals would be higher when genomic information was available . Comparison of the predictive abilities that were estimated in the current study with those from a previous study [Scenarios in which genomic information was included . In terms of unbiasedness, there was no clear trend among the scenarios examined, regardless of whether genomic information was included or not. Overall, unbiasedness was not a problem in the current study because the regression coefficients in all scenarios did not significantly differ from 1.Inbreeding depression for litter size in pigs is a well-known phenomenon , 51, andThe correlation between breeding values and dominance deviations is of theoretical concern . HoweverWe present for the first time the use of genomic inbreeding in crossbred and purebred genomic evaluation. Estimates are biologically sound and are relevant even for crossbred animals. We also report for the first time, estimated correlations of allele substitution effects in the presence of dominance. For TNB, the dominance genetic variance accounts for only a small proportion of the total genetic variation (4 to 10%). A moderate, positive genetic correlation between breeding values for TNB for purebred and crossbred performances was confirmed. Inclusion of dominance in the GBLUP model did not improve predictive ability for crossbred animals, whereas inclusion of inbreeding depression effects did. An additive GBLUP model is sufficient to capture the additive genetic variances and for genomic evaluation. The GBLUP model  was appl


Wolbachia decreases under high temperature in incubators. It is also known that a high density of Wolbachia in the host body reduces the host emergence rate, while low densities fail to change reproduction rates. However, few studies have examined the density of Wolbachia in hosts in the field. Here, we focus on Wolbachia infection of the pale grass blue butterfly, Zizeeria maha (Lepidoptera: Lycaenidae), which is distributed throughout the Japanese islands. We examined the rate and density of Wolbachia infection in the bodies of butterflies at thirteen locations in Japan. At seven of these places, we collected butterflies in different seasons to determine seasonal differences in the infection rate and density and found that Wolbachia density has seasonal differences within the same population. Moreover, to determine whether Wolbachia density has a geographical cline, we compared the infection density of Wolbachia amongst all geographical populations. In addition, we determined the sequences of Wolbachia wsp and host mtDNA CO1 haplotypes of all populations. The results showed that Wolbachia density increased in early summer and decreased in autumn. Further, the density of Wolbachia infecting the same strain of Z. maha varied amongst populations, although no tendency in geographical cline was observed.Previous studies showed that the survival rate of  Wolbachia are endosymbionts belonging to the alpha-proteobacteria [Wolbachia. CI affects sperm [Wolbachia-infected individuals dominate the host population.bacteria . This babacteria  and causbacteria . These mbacteria –3. Of thts sperm , and thuWolbachia, even temperatures that they are normally exposed to in the fields. Some studies showed that high temperatures eliminated Wolbachia from Drosophila melanogaster, Tetranychus urticae, and other species, but these studies were conducted in the laboratory [Wolbachia infecting host bodies affects the success of the reproductive manipulation. In Culex pipiens, high Wolbachia density decreases the host emergence rate [Wolbachia density fails to manipulate host reproduction in Drosophila innubila [External environmental conditions significantly affect the infective states of hosts including the density of the endosymbionts inhabiting the host body. For example, high temperatures are not salubrious for boratory ,5–8. Mornce rate , but lowinnubila .Wolbachia. For examples, Mouton et al. (2007) compared Wolbachia densities between progenies of crosses of strains of a wasp with different densities of Wolbachia [Wolbachia density of their mothers. This suggests that Wolbachia density is maintained by the host genotype. On the other hand, it has been suggested that Wolbachia density changes with the season [Wolbachia density changes with the age of the host [Wolbachia infection rate in Curculio sikkimensis has a geographical cline, they did not reveal whether Wolbachia density has a geographical cline [Laboratory studies have shown that different geographical strains of some insects have different densities of olbachia . The F1 e season . In addithe host . Howeveral cline .Wolbachia differ in host populations that inhabit temperate zones in summer [Wolbachia density. This hypothesis expects that the abundance of Wolbachia is terminated or decreases in the host body in hot temperature regions, and Wolbachia density thereby varies amongst geographical populations. To verify this hypothesis, Zizeeria maha  is an ideal subject because the Wolbachia infection status has been studied in this butterfly, which inhabits the main island of Japan from north to south [Wolbachia infection status of the butterfly in geographically separated populations. Furthermore, it is easy to compare the Wolbachia density of wild-caught butterflies, which are obtainable from spring to autumn. In the present study, we collected Z. maha butterflies across different latitudes and longitudes, and verified the rates of Wolbachia infection and density for the different populations using qPCR.Previous laboratory studies suggested that infection rates and density of n summer . In the to south . This maWolbachia using multilocus sequence typing (MLST) have demonstrated the power to discriminate between Wolbachia strains [Wolbachia strain that infects Z. maha.Studies of  strains . Here, wZ. maha males at thirteen points with different latitudes and longitudes in the Japanese temperate region in 2014: Sendai , Tsukuba , Chiba , Osaka , Sumoto , Mimasaka , Niimi , Okayama , Mannou , Nakatsu , Saiki , Kagoshima , and Yakushima . The geographic distribution of each sampling point is shown in We collected eight to 31 Wolbachia strains that infected Z. maha.We collected flying adults by butterfly net, and the collected samples were almost all males  because almost all flying adults were male. Thoraces width of collected samples was measured their thorax width under a stereomicroscope. After that, the samples were stored in 99.5% ethanol. We investigated the ® 100 (Bio-Rad) 98ul+Proteinase K (TaKaRa). The samples were incubated three hours at 56°C (spinning samples from 6 to 8 times each 30 min) to dissolve protein, and then they were incubated in a heat block set at 100°C for 3 min. After that, the sample was cooled to 5°C, and stored at -20°C.DNA was extracted from each specimen’s abdomen (excluding the first to the third sternites). The whole abdomen including gonads and testes was crushed by a toothpick in an Eppendorf tube (1.5ul) with Chelexwsp primers to investigate Wolbachia infection [Wolbachia strains that infected Z. maha as host, Wolbachia MLST primers [wingless primers [wingless primers were used to investigate the phylogenetic relationships of samples. Wolbachia causes a selective sweep that shows confused genetic link between nuclear DNA and mitochondrial DNA. Accordingly, we selected wingless as a nuclear gene marker. Sequence analyses were carried out by Fasmac Co. Ltd. . Wsp, CO1, and wingless gene sequences were assembled using DNA Baser version 4.2 , and aligned by Mega 5 (Accession numbers: LC125171–LC125181).We used CO1 primers  to confinfection . To inve primers , CO1 [16 primers . CO1 andwsp or CO1 primer pair. After that, PCR products were diluted 10 times in 10 steps. For real-time qPCR, we used iQ SYBR Green Supermix  and followed the supplier’s protocol. Then, we obtained standard curves of CO1 and wsp from the standard sample. Next, we amplified each sample DNA by qPCR on CO1 and wsp primer pairs, and qPCR cycles were fitted by each standard curve. Then we obtained copies of each CO1 and wsp gene. We considered that the butterfly cells were approximated by CO1 gene copies. Therefore, to evaluate Wolbachia density, each gene copy number was calculated by a standard curve, and wsp was normalized to CO1. All primers are shown in electronic supplementary We developed qPCR primers from analyzed DNA sequences. We amplified the sample of Sendai No. 1, which was the standard of qPCR in this study, by PCR of each Wolbachia infection rates amongst each geographical population, Fisher’s exact test was used. Wolbachia densities in each population were tested by a Kruskal-Wallis rank sum test, and followed by a Steel-Dwass test (referenced by http://aoki2.si.gunma-u.ac.jp/R/src/Steel-Dwass.R). To determine the relationship between Wolbachia density and collection season, we used a linear model from the eight points that were collected over several months. In each model, collection month and Wolbachia density were used as explanatory and response variables, respectively, for the eight points. Then, the models were tested by ANOVA. To investigate the correlation between latitude or longitude and Wolbachia density, we used the Pearson product-moment correlation coefficient. All statistical analyses were performed using R version 3.1.2 [To compare on 3.1.2 Z. maha.Our butterfly collection sites did not require specific permissions to catch the invertebrates. Moreover, this butterfly is not protected by any law. Further, we do not conflict with any guideline of PLoS ONE because we used only the butterfly Wolbchia infecting the butterfly, i.e., to examine the control of reproduction by Wolbachia infection, seven females collected from Okayama City in 2015 were allowed oviposit on the leaves of Oxalis corniculata. The larvae hatched from the eggs were divided into two groups, i.e., larvae were provided leaves grown in DW with 0.5% tetracycline (Tc) or without tetracycline (C), namely in DW only. Larvae were reared in the laboratory at 25°C, RH 60%, and 16L:8D dark-light cycles, and a laboratory population was established. Adults emerging via pupae from these larvae were reared in a hydroponic culture system  in which Oxalis corniculata were planted. The larvae of the 1st and 2nd generations were reared on food including tetracycline (Tc) or not including tetracycline (C). Then, the larvae of 3rd and 4th generations were reared on Oxalis corniculata alone to eliminate the effect of tetracycline.To determine the type of At the fourth successive generation, reciprocal crossing was conducted; i.e., females of Tc groups were paired with Tc and C males, and females of C groups were paired with Tc and C males. Each pair was allowed to copulate for two weeks for all crosses. The numbers of eggs oviposited by these females (n = 3 for each cross) and hatching rates were counted.Wolbachia strain did not differ amongst the Z. maha populations (LC125171–LC125176). The Wolbachia alleles revealed by the MLST analysis included coxA 14, fbpB 4, ftsZ 36, gatB 39, and hcpA 40. Therefore, the Wolbachia type was identified as ST41 by Wolbachia MLST Databases (https://pubmlst.org/wolbachia/). In the host genotype, the CO1 sequence differed only in Sendai (LC1251810). Similarly, the wingless sequence differed from other populations in Kagoshima (LC125179) and Tsukuba (LC12577). Numbers of infected adults with the numbers collected and tested for Wolbachia density, indexes of density of Wolbachia infection, and body sizes of Z. maha are shown in the Wolbachia infection rates were not significantly different amongst populations in all monthes examined (P > 0.05). However, Wolbachia infection density significantly differed amongst populations collected in October .MLST revealed that the Wolbachia density, we compared Wolbachia densities by collection month using a Steel-Dwass test. As a result, Wolbachia density significantly differed between two seasons in each population in 2014 . Then we examined whether the same seasonal change in Wolbachia density occurred in each population. Statistical analysis showed that Wolbachia density increased in early summer and decreased in autumn. However, there was a significant difference in the effects of month and population for each population, and the month × population interactions was also significantly different .To investigate whether the change of season affected P < 0.001, Fisher’s exact test). The results indicate that the Wolbachia strain infecting Z. maha causes cytoplasmic incompatibility.The numbers of eggs oviposited were 906 for C females×C males, 849 for C females × Tc males, 689 for Tc females × C males, and 809 for Tc females × Tc males. Eggs successfully hatched were 810 (89.4%), 733 (86.3%), 3 (0.4%), and 705 (87.1%) for C × C, C×Tc, Tc × C, and Tc×Tc, respectively  to early summer (July) than in late summer (Aug), and it decreased during late summer and autumn (Sept and Oct)  to autumn (0.27) in Kagoshima, and from late summer to autumn the difference was around two times in Tsukuba and Okayama. Accordingly, the seasonal fluctuation of Wolbachia density in hosts might be affected by the environment around the host habitat. It has been reported that Wolbachia density varied significantly between seasons within a population by annual observation of D. innubila [Wolbachia density were older than individuals that had a high density [Z. maha is short (about one to two weeks in laboratory conditions), and the change of generations is about one month [Wolbachia density).MLST conducted in the present study revealed that the  species , 20 and  species . No seasand Oct) . Compareinnubila . Unckles density . Howeverne month . TherefoWolbachia densities in Z. maha were significantly different amongst populations, a geographical cline of Wolbachia density was not observed. In the present result, the “geographical cline of Wolbachia density hypothesis” was dismissed. By median Wolbachia density, the highest population (Niimi) was 137 times higher than the lowest population (Tsukuba) in October. Surprisingly, Wolbachia density has an extremely wide range in natural population and at least difference of six times in density in the present study. On the other hand, Wolbachia density had small range in previous studies in the laboratory . This result suggests that environmental factors are related to the seasonal changes of Wolbachia density in the Japanese temperate region. Hence, we suggest that temperature is the most significant factor in seasonal changes of Wolbachia density in populations in a temperate region.Although Wolbachia is a maternally-transmitted bacterium, seasonally-induced changes in Wolbachia density are likely more important in female insects than in males. However, we collected mostly males in this study, as described in the introduction. Therefore, additional studies using female samples are required. Because it is difficult to collect flying females in the field, analyzing samples of the larvae or pupae collected from fields is required in the future. However, we consider that it is suitable to use males in our study. Because of this, we revealed this Wolbachia strain was characterized as ST41, which causes CI. Furthermore, CI was caused by males.Given that Wolbachia density was revealed by several studies in the laboratory. For example, Wolbachia density in Aedes albopictus was changed by the host juvenile diet [Wolbachia density was reported only in females [Wolbachia density in Drosophila innubila [Wolbachia density is high, it strongly manipulates host reproduction. Why a good nutrient condition did not affect Wolbachia density is unclear. If Wolbachia density in Z. maha males is not also changed by nutrient conditions, it suggests efficient Wolbachia transmission from mother and environment included seasonal nutrients affecting Wolbachia density  reported that sudden male killing by Wolbachia did not manipulate Hypolimnas bolina. Similarly, Armadillidium vulgare have a resistance factor to feminization by Wolbachia [Z. maha does not suffer costs from Wolbachia infection, infection rates may change in the future. We considered further experimentation is required to unravel this issue. On the other hand, Wolbachia protect their host from virulent RNA viruses [Wolbachia of Z. maha is that it provides some benefit to the host.The present study confirmed that the rate of us study . This reolbachia . These r viruses –27. One Wolbachia density in Z. maha populations differs between seasons in the field and is higher in spring than in summer. However, the Wolbachia infection rate of this species did not change. This seasonal change may be prevalent in wild invertebrates infected by Wolbachia.In conclusion, our results provide the first evidence that S1 FigP < 0.05, Steel-Dwass test).An open circle above a box plot indicates an outlier. A different letter shows a significant difference ((TIF)Click here for additional data file.S2 FigWolbachia density of all individuals is plotted by longitude. A solid line shows a linear model of Wolbachia density by longitude. The grey zone shows the 95% confidence interval.(TIF)Click here for additional data file.S3 FigWolbachia density of each population was plotted by host thorax width. The solid line shows a linear model of Wolbachia density by host thorax width. The grey zone shows the 95% confidence interval.(TIF)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.


Although GS improves estimated breeding values and genetic gain, in most GS models genetic variance is estimated from training samples with many trait-irrelevant markers, which leads to severe overfitting in the calculation of trait heritability. In this study, we demonstrated overfitting heritability due to the inclusion of trait-irrelevant markers using a series of simulations, and such overfitting can be effectively controlled by cross validation experiment. In the proposed method, the genetic variance is simply the variance of the genetic values predicted through cross validation, the residual variance is the variance of the differences between the observed phenotypic values and the predicted genetic values, and these two resultant variance components are used for calculating the unbiased heritability. We also demonstrated that the heritability calculated through cross validation is equivalent to trait predictability, which objectively reflects the applicability of the GS models. The proposed method can be implemented with the Mixed Procedure in SAS or with our R package “GSMX” which is publically available at  Markers , which are in linkage disequilibrium (LD) with quantitative trait loci (QTL), are used for indirect selection of genetic determinants of traits of interest. Linear regression models can be used to assess the association between the traits and the markers using training sample in which the phenotypes and genotypes are known for each subject7. Phenotypic values are regressed on the genotypic values of markers, and statistical hypothesis test is performed on each marker. Criterion, such as threshold in p value or in the logarithm of the odds ratio (LOD score), are used for detection of markers/QTL with significant effects8. The selected markers are used to form a linear genetic model  which will be used for the recurrent selection process. Two criterions are commonly used for evaluating the performance of the genetic models built from training samples, i.e., heritability and predictability10. The heritability is defined as the proportion of variance that can be explained by the genetic model, which is equivalent to the R2 in linear regression analysis. The heritability for the training sample can be conveniently calculated with analysis of variance (ANOVA). Whereas, the predictability for the training sample is defined as the squared correlation between the observed phenotypes and the predicted phenotypes that are calculated using the genetic model under consideration. If the size of the training sample is larger than the number of the markers (a requirement for regular linear model), the heritability and predictability are actually measuring the same quantity. Note that the heritability and the predictability associated with a genetic model only reflect the genetic structure for the population from which the training sample has been drawn; much lower levels of heritability and predictability may be obtained if this genetic model (developed from training sample) is applied to a sample which comes from a distinct population, for example, a population with very different genetic background.Plant breeding is to produce desired characteristics by changing the traits of plants. Traditionally, we directly selected plants with desirable characteristics for propagation. In the past two decades, molecular techniques have been used for indirectly selection13. In many MAS or QTL mapping studies, the number of markers is much larger than the number of individuals, i.e., p ≫ n, where p is the number of markers (or parameters in the regression models) and n is the sample size. Under this circumstance, the least squares estimation does not work; likewise, ANOVA cannot be directly applied to the data. Rather, sophisticated strategies should be used to reduce the dimensionality of the analysis. To fit ANOVA, one can first reorganize the data by categorizing subjects in the sample into groups based on their genotypes ), and then analyze the variances between these groups (or lines). Note we used ‘reorganization of data’ to represent rearrangement of the data using a newly defined independent/predictive variable, i.e., we used the RILs (groups defined based on genotypes) as an independent variable for the ANOVA analysis. Nevertheless, samples with similar genotypes may be placed into different groups, yielding too many groups (or parameters) for the model and therefore overfitting the data. This is similar to the situation where too many ‘leaves’ are used to overly fit a ‘tree’ classification model. Therefore, the heritability calculated using this strategy through ANOVA is likely to be overestimated. Alternatively, variable selection strategies can be used in regression models to substantially reduce the number of parameters by assuming that most markers are irrelevant17. However, it has been commonly accepted that quantitative traits are determined by many genes including some major genes as well as a large number of genes with small effects. Major QTL only explain part of the total variation; on the other hand, significant portion of variation is attributed to many QTL with small or even tiny effects across genome which usually do not survive the statistical selection criterion. ‘Complete modeling’ by considering all QTL on the genome including those with small effects has potential to improve the performance of the genetic models. It is worthy of noting here that the heritability calculated through ANOVA using reorganized data is no longer equivalent to the predictability calculated using regression models since ANOVA analyzes the parameters that are derived from the genotypes rather than genotypes themselves. However, correlations are expected between the heritability from ANOVA (with rearranged data) and the predictability from regression models.With the emergence of the low-cost but high-throughput sequencing technologies, we can easily increase the number of markers and their density to enjoy increased resolution of QTL mapping19. Models including random effects  are used to reduce the dimensionality of the analysis. In GS, the effects of all markers, including the markers with major effects as well as many more markers with small effects, are first estimated from training sample, and then are used to form a genetic model for predicting genetic values for unphenotyped individuals. It has been indicated that GS models are more predictive and potentially more effective than classical MAS schemes or use of pedigree; therefore, the studies on GS become more and more popular. However, in GS analyses, the whole-genome markers are used to fit the regression model and estimate the covariance (kinship) between individuals in the training set; such information is subsequently used to calculate the parameters including variance components which are used to calculate trait heritability. The majority of the loci on the genome are neutral to the trait of interest; only causative loci  are contributing to the variation of the trait. Including the large number of the neutral loci in the regression model likely overfits the data. In the current study, we used intensive simulated studies to demonstrate that the genetic variance is overestimated using regular GS settings and trait heritability is thereafter exaggerated. In order to realistically reflect the applicability of the GS models that are developed using training samples, cross validation should be used to control such overfitting. In the study, we proposed a simple algorithm to calculate unexaggerated trait heritability in GS analysis. Our new method echoes the previous studies where cross validation has been used to reduce the bias of estimation of the predictability (or prediction accuracy) due to the environmental sampling error, genotypic sampling error, or both21. Compared with the previous efforts, our focus is to provide an effective control on the overfitting of heritability incurred by the excessive non-relevant markers included in the GS analysis, which has been overlooked in the literature. In the new method, a simple solution was proposed to estimate genetic covariance and eventually trait heritability using the variance of the genetic values predicted through cross validation. Hence, the aims of the study include (1) proof of the overfitting due to the inclusion of a large number of trait-irrelevant loci in the GS analyses and the similar overfitting in ANOVA approaches, (2) demonstration of effective control of such overfitting by the new method, and (3) showing that the heritability is equivalent to the predictability (or accuracy of prediction) when such overfitting is controlled. The proposed new method provides an accurate estimation of trait heritability or trait predictability, and objectively reflects the applicability of the GS models when they are applied to independent populations. The algorithms can be conveniently implemented using the Mixed Procedure in SAS or can be implemented using a newly developed R package “GSMX” (https://cran.r-project.org/web/packages/GSMX/index.html). The proposed method in this study has been demonstrated by a series of Monte Carlo simulation experiments and a real data analysis in rice.Genomic selection (GS) provides solutions to ‘complete modelling’. GS is a form of MAS in which genetic markers covering the whole genome are used so that all QTL are in linkage disequilibrium with at least one marker20. Mixed model is commonly described using the following regression modely is the observed response (univariate) of n individuals, X is a n × q design matrix for the fixed effects β (q × 1 vector), Z is an n × p design matrix for the random effects γ (p × 1 vector), and ε is an n × 1 vector of random errors. The random effects are assumed to be independently and normally distributed, as indicated by y is y isMixed model is a specially designed method to include fixed and random effects in a single regression model. Fixed effects represent factors that experimenters directly manipulate and are often repeatable, whereas random effects represent the outcome due to random selection of a sample from the entire population (sources of random variation)The variance components, Numerous algorithms can be used to maximize the above likelihood functions and get the REML or ML estimates of the parameters.e.g., G-BLUP23, BayesB10, and MIXTURE24) may be used for estimation of the genetic effects and development of a prediction model; however, BLUP based method generally gave the higher prediction accuracy due to the fact that a complex trait is usually explained by many genes21. In the study, we mainly focus on the BLUP approach on the basis of mixed model. In the general situation, if covariance among genomic loci and covariance of residual errors are considered . In genetics, the heritability of the trait under study is defined asNote that the estimation of this relationship matrix (or kinship matrix) The Henderson’s mixed model Eq.  becomes1The variance-covariance matrix of the BLUE and BLUP isSuppose we hope to utilize the GS model developed as above to predict the genetic values of a new cohort of individuals . Let The variance-covariance matrix is also partitioned similarly,Let To predict the trait values or genetic values in the test sample, we use the conditional expectation of Information used for the prediction mainly comes from We often name the sample that is used for developing GS model as training set. In literatures, the variance components  and the test set is used for model evaluation regarding the predictability of the model. Thus, the test set does not contribute to model development at all; rather, the test set provides an objective evaluation on the performance of the model that is developed solely on the training set. In k-fold cross validation, data are randomly partitioned into k equal portions. Each time, k-1 portions are used to develop the model ; whereas, the remaining 1 portion is used for test. This process is repeated until each portion has been exactly used for once as test set. After k-fold cross validation, each subject has an observed phenotype and a predicted phenotype. The predicted phenotype is the value calculated when the subject is included in the test set during the cross validation. Figure σ2) as in regular GS settings, we propose using the predicted genetic values  and the difference between the observed phenotype and the predicted genetic values to calculate the genetic variance and the residual variance, respectively, which are thereafter used to calculate the heritability  which are treated as new synthetic markers.The rice data used in the study includes 210 recombinant inbred lines (RILs), for each of which four traits  have been replicated 4 times in different years and different locationsK and the identify matrix for residual (e) are specified in the general linear covariance structure for estimation of the variance components. The residual variance is fixed at 0.0001. Refer to online SAS User’s Guide for detailed instructions of using Mixed PROC (https://support.sas.com/documentation/). These SAS scripts need to be built in a MACRO to run a cross validation.The SAS scripts for implementation of GS using Mixed PROC is provided in below textbox. We first read in the dataset named ‘data’ that contains the phenotypic data (y) and dummy variable (X = 1) for individuals in the sample. The kinship matrix proc mixed data=data;class id;model y=X/noint solution outp=result_pred;random id/type=lin(1) ldata=k solution;repeated/subject=intercept type=lin(2) ldata=e;parms (1) (1) (0.0001)/lowerb=1e-5,1e-5,1e-5 hold=3;ods output SolutionR=blup_pred SolutionF=fixed_pred CovParms=covar_pred;run;σ2) are calculated using the entire data set. The results are presented in Table In the current study, genotype by environment (G × E) interaction was not considered; thus, for each trait, we treated the four observed phenotypic values for each RIL as four simple replicates. We first calculated the average of the 4 values of each trait for each RIL. Using SAS Mixed Procedure or R\GSMX, we first analyzed the averaged phenotype using the regular GS analysis . Note that the variances of genetics . Note that the ratio of the standard deviation of a genetic effect and the standard deviation of the residual was about 1/20 such that the overall heritability (accumulated from 1619 loci) was close to 50%. We calculated the correlation between the genotypes of each locus and the simulated phenotypic values; the 1619 loci were then sorted based on the strength of the association with the phenotype from the strongest association to the weakest association . The top 10% of the loci represent the most relevant QTLs (absolute correlation ranges from 0.20677 to 0.33090). We first analyzed the data only with the top 10% loci to calculate the heritability with or without cross validation and the predictability with cross validation , where i.e., by multiplying the genotypes and the genetic effects plus a random error which was independently sampled from a normal distribution, i.e., N. We chose different σg:σe ratios in order to simulate scenarios with various levels of overall or accumulated heritability (ranging from 0.2 to 0.8). Note that these overall heritability is equivalent to the heritability that is calculated using GS model without cross validation. Therefore, the overall heritability only reflects the property of the entire training set; however, it does not indicate how well the genetic model developed from this training set would predict when it is applied to an independent set. This is the main point that we hope to address in the study. For each of the 210 RILs, we simulated 4 simple technical replicates . We analyzed the data using three approaches: GS without cross-validation, GS with cross-validation, and ANOVA. Using GS analysis , we were able to analyze the 210 lines in each of the four replicated experiments separately, or analyze the average  of the four replicated measurements. When we analyzed the averaged phenotypes using GS analyses, the sample size appears to be 210; however, since the sample mean (sufficient statistic) is used for the GS analysis, the effective sample size for this analysis is actually 210 × 4 = 840. However, when we analyzed the 210 lines in each of the four replicated experiments separately, the effective sample size is only 210. The heritability without cross validation (H), the heritability with cross validation (Hcv), and the predictability with cross validation (Pcv) were calculated for each data analysis. In the ANOVA, all 840 phenotype values (210 lines × 4 replicates) were used to fit a linear regression model in R: Y ~ as.factor(line) + as.factor(replicate). The results from the three approaches are presented in Table We further did the following simulated study to demonstrate the deficiency of ANOVA analysis when compared with the GS analysis with cross validation. We also adopted the genotypes of the 1619 loci for each of the 210 RILs. Similarly, for each of the 1691 loci, we simulated a genetic effect from a normal distribution, The results in Table In the ANOVA analysis, we no longer analyzed the variance based on the genotypes of the markers; rather, we analyzed the variance between groups (or RILs) which represent a new independent variable derived from the genotype data. This gives a good explanation to the aforementioned observation (4). In addition, another type of overfitting is possible if more groups than necessary are used in the ANOVA analysis. For example, samples with similar genotypes may be placed into different groups (or RILs). We calculated the pair-wise correlations of genotypes between the 210 RILs. It shows that the absolute correlation coefficient ranges from 0.0000016 to 0.9539, with 8 absolute correlation coefficients greater than 0.8. An ANOVA model with more than necessary groups/parameters certainly overfits the data. This is analogous to the situation where too many ‘leaves’ or ‘branches’ are used to fit data with a ‘tree’ classification model. Therefore, the heritability calculated using ANOVA with reorganized data is likely to be overestimated.i.e., i.e., N. The ratio of the standard deviation of a genetic effect and the standard deviation of the residual was about 1/20 such that the overall heritability in this simulation was about 50%. For each of the 210 RILs, we simulated different numbers of simple replicates, i.e., 10, 50, 100, 500, 1000, and 5000 replicated measurements. We first analyzed each dataset using ANOVA. The heritability did not change as the sample size increases (Haov in Table We further demonstrated the limitation of ANOVA when compared to the GS analyses using the following simulated study. Like the previous simulation, we simulated a genetic effect for each of the 1619 loci. The genetic effects were sampled independently from a normal distribution,


Background: Poorer self-rated health (SRH) predicts worse health outcomes, even when adjusted for objective measures of disease at time of rating. Twin studies indicate SRH has a heritability of up to 60% and that its genetic architecture may overlap with that of personality and cognition.Methods: We carried out a genome-wide association study (GWAS) of SRH on 111 749 members of the UK Biobank sample. Univariate genome-wide complex trait analysis (GCTA)-GREML analyses were used to estimate the proportion of variance explained by all common autosomal single nucleotide polymorphisms (SNPs) for SRH. Linkage disequilibrium (LD) score regression and polygenic risk scoring, two complementary methods, were used to investigate pleiotropy between SRH in the UK Biobank and up to 21 health-related and personality and cognitive traits from published GWAS consortia.Results: The GWAS identified 13 independent signals associated with SRH, including several in regions previously associated with diseases or disease-related traits. The strongest signal was on chromosome 2  close to KLF7. A second strong peak was identified on chromosome 6 in the major histocompatibility region . The proportion of variance in SRH that was explained by all common genetic variants was 13%. Polygenic scores for the following traits and disorders were associated with SRH: cognitive ability, education, neuroticism, body mass index (BMI), longevity, attention-deficit hyperactivity disorder (ADHD), major depressive disorder, schizophrenia, lung function, blood pressure, coronary artery disease, large vessel disease stroke and type 2 diabetes.Conclusions: Individual differences in how people respond to a single item on SRH are partly explained by their genetic propensity to many common psychiatric and physical disorders and psychological traits. Key MessagesGenetic variants associated with common diseases and psychological traits are associated with self-rated health.The SNP-based heritability of self-rated health is 0.13 (SE 0.006).There is pleiotropy between self-rated health and psychiatric and physical diseases and psychological traits.There is considerable evidence that how individuals respond to one simple question asking them to evaluate their current state of health is a powerful predictor of future health outcomes. Poorer self-rated health (SRH) has been associated with increased mortality from all causes,N = 4233).et al.Evidence for the heritability of SRH comes from several twin studies,,Previous research suggests that perceptions of health are driven in part by psychological factors. There is evidence that people who are higher in the personality trait neuroticism—the tendency to experience negative emotions—are more likely to rate their health as being poor,The aim of the present study was to add substantially to the understanding of the genetic mechanisms and genetic architecture of SRH. Using the large UK Biobank genotyped sample, we conducted a genome-wide analysis of SRH, we estimated its SNP-based heritability and we studied its pleiotropy with physical and mental health and with personality and cognitive traits.The UK Biobank is a health resource facilitating the study of the origins of a wide range of illnesses.UK Biobank received ethical approval from the Research Ethics Committee (REC reference 11/NW/0382). This study has been completed under UK Biobank application 10279.Participants were asked the question, ‘In general how would you rate your overall health?’ Possible answers were ‘Excellent/Good/Fair/Poor/Do not know/Prefer not to answer’. We created a four-category SRH variable indexing how each participant rated their health ranging from ‘excellent’ to ‘poor’; excluding those that responded with ‘do not know’ or ‘prefer not to answer’. For the phenotypic correlations, LD score regression and polygenic profile score analyses used in this study, a higher score for SRH indicates a better health rating.,Participants completed 12 questions of the Eysenck Personality Questionnaire-Revised Short Form (EPQ-R Short Form)Education was measured by the question, ‘Which of the following qualifications do you have? (You can select more than one)’. Possible answers were: ‘College or University Degree/A levels or AS levels or equivalent/O levels or GCSE or equivalent/CSEs or equivalent/NVQ or HND or HNC or equivalent/Other professional qualifications e.g. nursing, teaching/None of the above/Prefer not to answer’. For the present study, a binary education variable was created to indicate whether or not a participant had a college or university-level degree; excluding those who responded with ‘prefer not to answer’. Previous studies have used similar binary variables as a ‘proxy-phenotype’ for cognitive ability.Intelligence was measured by a 13-item test with a time limit of 2 min, completed by 36 035 individuals. Six items were verbal and seven numerical. An example of a verbal question is ‘Bud is to flower as child is to?’ Possible answers were: ‘Grow/Develop/Improve/Adult/Old/Do not know/Prefer not to answer’). An example of a numerical question is ‘If 60 is more than half of 75, multiply 23 by three. If not, subtract 15 from 85. Is the answer?’ Possible answers were: ‘68/69/70/71/72/Do not know/Prefer not to answer’. The Intelligence score was the total score out of 13 items. The Cronbach α coefficient for the 13 items was 0.62.Phenotypic correlation coefficients were calculated between SRH, and neuroticism, education, intelligence and mortality in the UK Biobank. Cox proportional hazard ratios were calculated for all-cause mortality according to the SRH categories (Poor to Excellent).N = 49 979) or the UK Biobank axiom array (N = 102 750). UK BiLEVE samples were selected based on lung function and smoking behaviour from participants with self-declared European ancestry.http://biobank.ctsu.ox.ac.uk/crystal/refer.cgi?id = 155583] and the Axiom array [http://media.affymetrix.com/support/downloads/manuals/axiom_2_assay_auto_workflow_user_guide.pdf]. Before the release of the UK Biobank genetic data a stringent QC protocol was applied, which was performed at the Wellcome Trust Centre for Human Genetics (WTCHG). Details of this process can be found at [http://biobank.ctsu.ox.ac.uk/crystal/refer.cgi?id = 155580]. Before the analyses described below, further quality control measures were applied. Individuals were removed sequentially based on non-British ancestry , high missingness, relatedness, QC failure in UK Bileve and gender mismatch. A sample of 112 151 individuals remained for further analyses.A total of 152 729 UK Biobank samples were genotyped using either the UK BiLEVE . An imputation quality score of 0.1 was chosen, rather than the more commonly used 0.3–0.5, due to the relatively large sample size of UK Biobank. An imputation score of 0.1 on 150 000 individuals corresponds to an effective sample size of 15 000 individuals.An imputed dataset was made available in which the UK Biobank interim release was imputed to a reference set combining the UK10K haplotype and 1000 Genomes Phase 3 reference panels. Further details can be found at the following URL: . The ‘frequentist 1’ option was used to specify an additive model. Genotype dosage scores were used to account for genotype uncertainty.SNPTEST v2.5.1P < 5 × 10-8) were selected as index SNPs. Second, SNPs within 500 kb and in LD of r2 > 0.1 with the index SNP were included in the clump. SNPs from within this region were assigned to the clump if they had a P-value < 1 × 10-5. In addition, conditional analyses were performed using SNPTEST v2.5.1The number of independent signals for the genotype-phenotype analyses was determined using LD clumping, using the 1000 Genomes as a measure of LD between SNPs. First, SNPs with a genome-wide significant association with SRH . Individuals with imputation score < 0.8 and alleles with frequency < 0.01 were removed before analysis. Linear regression correcting for age, gender, assessment centre, genotyping batch, genotyping array, imputation quality score and 10 principal components was performed to identify associations between HLA alleles and SRH.Human leucocyte antigen (HLA) classical allele imputation was performed using HLA genotype imputation with attribute bagging (HIBAG).P < 2.76 × 10−6).MAGMAhttp://www.gtexportal.org] was used to identify eQTLs associated with the SNPs. Functional annotation was investigated using the Regulome DB databasehttp://www.regulomedb.org/]. Regulome DB was used to identify regulatory DNA elements in non-coding and intergenic regions of the genome in normal cell lines and tissues.For the 13 independent genome-wide significant SNPs identified by LD clumping, evidence of expression quantitative trait loci (eQTL) and functional annotation were explored using publicly available online resources. The Genotype-Tissue Expression Portal (GTEx) , three cis-eQTL associations were identified for the 13 independent genome-wide significant SNPs (IJE online). rs907662 on chromosome 1 potentially regulates Mannosidase, Alpha, Class 1A, Member 2 (MAN1A2), previously identified as being differentially expressed in type 2 diabetes patients compared with normal controls.http://www.regulomedb.org/] . This indicates that the SNPs within these annotation categories explain a greater proportion of the variance for SRH than would be expected based on the proportion of the total number of SNPs used for this analysis. SNPs in evolutionarily conserved regions showed enrichment, as they account for only 2.6% of the total number of SNPs but explain 39% of the heritability . Enrichment was also found in super enhancers, which contained 16.8% of the SNPs collectively explaining 27.9% of the heritability . SNPs within 500 bp of DNase hypersensitivity sites (DHS) also showed significant enrichment, accounting for 50% of the total SNPs and explaining a total of 84.2% of the heritability . A number of histone markers were also enriched, including the H3K27ac mark, , the H3K4me1 mark  and SNPs within 500 bp of the H3K9ac mark . The results of the cell type-specific histone marks are shown in IJE online. Histone marks that are present in the central nervous system were significantly enriched. These SNPs contain 14.8% of the total number of SNPs which collectively explained 42.8% of the heritability .The baseline model yielded eight significantly enriched functional annotations (IJE online). None of the gene-sets examined showed statistical significance once correction for multiple comparisons had been applied. To test for pleiotropy between SRH and health-related, personality and cognitive traits, we present LD score regression and polygenic profile analyses. For the purpose of these two analyses, a higher score for SRH indicates a better health rating.IJE online). Better SRH showed positive genetic correlations with intelligence, education, longevity, anorexia nervosa and forced expiratory volume in 1 s (FEV1) (rg = 0.11 to 0.59). Negative genetic correlations were found between better SRH and neuroticism, BMI, ADHD, major depressive disorder, schizophrenia, systolic and diastolic blood pressure, coronary artery disease, ischaemic stroke and type 2 diabetes (rg = -0.16 to -0.46).LD score regression was performed to obtain genetic correlations between SRH in UK Biobank and the summary results of the 16 GWAS consortia and three UK Biobank traits  . Higher polygenic profile scores for neuroticism, BMI, ADHD, major depressive disorder, schizophrenia, diastolic and systolic blood pressure, coronary artery disease, large vessel disease stroke and type 2 diabetes were associated with lower levels of SRH (standardized β between -0.07 and -0.009). The results showed very little change when individuals with self-reported clinical diagnoses of cardiovascular disease (N = 5300), diabetes (N = 5800) and hypertension (N = 26 912) were removed from the corresponding analyses . The results including all five thresholds can be found in IJE online.The results of the polygenic risk score analyses are shown in 1, systolic blood pressure, coronary artery disease, large vessel disease stroke and type 2 diabetes) alongside the same covariates as described previously. Due to the high phenotypic correlation between systolic and diastolic blood pressure, only systolic blood pressure was included in the model. This tested the extent to which including all significant polygenic profile scores in a multivariate model would improve the prediction of SRH and discover which polygenic scores contributed independently. This was done by subtracting the r2 value of the model only including the covariates from the model with both covariates and polygenic profile scores. All polygenic profile scores remained significant, after FDR correction (P < 0.032), in this multivariate model, and together accounted for 1.03% of the variance in SRH . A 1-SD increase in BMI polygenic risk score, based on 90 SNPs, was associated with a 0.12-SD increase in BMI. A 1-SD increase in BMI polygenic risk score was associated with a 0.026-SD decrease in SRH. A genetically determined increase in BMI of 0.58 kg/mIn the present and other studies, a single item of SRH is associated with mortality. Such SRH items are widely and successfully used in health research. Given their predictive validity, it is of interest to discover the causes of people’s differences in SRH. Here, in analyses of the large UK Biobank sample together with results from many GWAS consortia, we discovered many new genome-wide significant genetic variants associated with SRH. A robust estimate of the SNP-based heritability of SRH in the UK was provided (13%), which is close to that previously reported (18%) using this method in the US-based Health and Retirement Survey.KLF7, MAN1A2),,TC4F, NRXN1, AUTS2),,,BSN),SAMD12, ZNF652),ASXL3, AUTS2),,HLA-DQA1 which was associated with SRH in our gene-based analysis, has previously been associated with coeliac disease.,The present study identified novel genes/loci associated with individual differences in SRH. These include genes previously associated with diabetes . This indicates that even in self-rated healthy individuals, a higher polygenic profile score for systolic blood pressure, coronary artery disease and type 2 diabetes is associated with lower health ratings.The results of the present study indicate that genetic variants associated with better SRH are associated with a lower genetic risk of neuroticism, but a higher genetic risk of anorexia nervosa. From a previously published positive phenotypic association between anorexia nervosa and neuroticism,This study shows that the SRH measure, consisting of only one question, is able to reflect the genetic variants of traits and disorders, such as intelligence, personality, cardio-metabolic disease and psychiatric disorders, associated with actual health. Genetic variants associated with higher levels of intelligence and lower levels of cardio-metabolic diseases are associated with better health ratings. This supports the theoretical construct of bodily system integrity, a latent trait indicating individual differences in encountering health and cognitive challenges from the environment.The strongest association found in this study is between SRH and the polygenic profile score for BMI, accounting for 0.45% of the variance. Mendelian randomization indicated that higher genetically determined BMI leads to lower SRH, although we cannot exclude a causal effect in the other direction. When combining the polygenic liabilities for multiple traits and disorders in a multivariate model, the polygenic liabilities together double the amount of variance to 1%. This implies that SRH may be affected by risk alleles unique to each trait and disorder.A strength of this study is the large sample size of UK Biobank, permitting powerful and robust tests of pleiotropy between SRH and many health-related traits. Other strengths include that all individuals were of White British ancestry, minimizing population stratification. Genotyping and quality control have been performed in a consistent way across the whole sample. The use of summary data from many international GWAS consortia allowed a detailed examination of pleiotropy between SRH and a wide range of health-related traits, showing many novel estimates of genetic correlations between traits.P < 1 x 10-5. The summary data from the GWAS studies curated to perform LD score regression and create polygenic profile scores often originated from consortia studies, which involve meta-analyses across data sets with substantial heterogeneity in sample size, genome-wide imputation quality and measurement of the traits. For the polygenic profile analyses, we might have overestimated the effects because of possible overlap of individuals in UK Biobank sample and some of the cohorts within some of the GWAS consortia. We were unable to quantify the exact overlap, but the number of overlapping individuals is probably small and we judge that this will have a minor effect on the results. Because the analyses were restricted to individuals of white British ancestry, we are unable to generalize the results beyond that group. Therefore, these analyses should be replicated in large samples of individuals with different backgrounds. For the majority of traits we were unable to distinguish between type I pleiotropy (a single locus directly influencing multiple phenotypes) and type II pleiotropy (a single locus influencing a cascade of events). The findings from this study are not necessarily transferable to other populations, as SRH is influenced by social and cultural components.The present study has some limitations; several of the genome-wide significant hits are single SNPs rather than in a peak. These SNPs should be treated with particular caution until they are replicated in an independent sample, which is currently not available. The clumping method used to derive independent regions for DEPICT analyses relied on the 1000 Genomes data as a reference panel, whereas the UK Biobank genotypes were imputed to the UK10K haplotype and 1000 Genomes reference panels. Therefore, we may have failed to include regions which only contained non-1000 Genomes SNPs with Measuring people’s overall health is difficult, because the state of the body and mind can be disrupted in many ways, and people’s perceptions of the same objective bodily state can differ. Notwithstanding this complexity, the response to a single subjective question about whether a person is in good or poor health has proved valid and useful in health research. The present study has been able to identify many genetic contributions to SRH, confirming the complexity of the contributions to the phenotype and also its partial foundations in genetic differences. The mechanisms by which the genes contribute to SRH have still to be determined. The single subjective item of SRH picks up the contributions from many background systems, including mental and physical health, as well as cognitive abilities and personality.IJE online.This work was supported by the University of Edinburgh Centre for Cognitive Ageing and Cognitive Epidemiology, part of the cross-council Lifelong Health and Wellbeing Initiative (MR/K026992/1). Funding from the Biotechnology and Biological Sciences Research Council (BBSRC) and Medical Research Council (MRC) is gratefully acknowledged. This research was conducted using the UK Biobank Resource. A.M.M., J.M.W. and I.J.D are supported by Wellcome Trust Strategic Award 104036/Z/14/Z. W.D.H. is supported by a grant from Age UK (Disconnected Mind Project).Conflict of interest: None declared.Supplementary MaterialsClick here for additional data file.Supplementary Table S2-S15Click here for additional data file.Supplementary Table S16-S18Click here for additional data file.


Oryza sativa var. Swarna/O. nivara accessions were grown and evaluated for yield and related traits. Trials were conducted for consecutive three seasons in field conditions in a randomized complete block design with three replications. Data on yield traits under irrigated conditions were analyzed using the Additive Main Effect and Multiplicative Interaction (AMMI), Genotype and Genotype × Environment Interaction (GGE) and modified rank-sum statistic (YSi) for yield stability. BILs viz., G3 (14S) and G6 (166S) showed yield stability across the seasons along with high mean yield performance. G3 is early in flowering with high yield and has good grain quality and medium height, hence could be recommended for most of the irrigated locations. G6 is a late duration genotype, with strong culm strength, high grain number and panicle weight. G6 has higher yield and stability than Swarna but has Swarna grain type. Among the varieties tested DRRDhan 40 and recurrent parent Swarna showed stability for yield traits across the seasons. The component traits thousand grain weight, panicle weight, panicle length, grain number and plant height explained highest genotypic percentage over environment and interaction factors and can be prioritized to dissect stable QTLs/ genes. These lines were genotyped using microsatellite markers covering the entire rice genome and also using a set of markers linked to previously reported yield QTLs. It was observed that wild derived lines with more than 70% of recurrent parent genome were stable and showed enhanced yield levels compared to genotypes with higher donor genome introgressions.Advanced backcross introgression lines (BILs) developed from crosses of  Oryza to explore novel genes that can improve yield traits. Wild relatives were widely explored as donors for stress resistance and less exploited for yield improvement because of non-preferable agronomic traits linked with them. Wild rice genotypes provide a diverse range of allelic variation due to their adaption to a wide range of environmental conditions. Wild and related genotypes are valuable resources to explore novel variations to widen the genetic background of cultivated rice   to identify the yield potential of backcross introgression lines in comparison with existing popular varieties (2) to identify stable high yielding BILs and their parental genome percentage (3) to prioritize the component traits important for further genetic dissection and improvement.A panel of 14 BILs derived from Swarna/ Kharif -2013(E1), (Kharif -2014) (E2) and one dry season Rabi-2014(E3). Crop was grown in alkaline vertisol with a pH of 7.94 at irrigated field conditions. Details of meteorological conditions during the crop growth period are presented in Table Field experiments were conducted at Indian Institute of Rice Research, Hyderabad (17° 19′ N and 78° 29′ E) at an altitude of 549 m above mean sea level during two wet seasons O. sativa cv. Swarna and accessions of wild relative, Oryza nivara  (S lines) and 104 lines from Swarna / O. nivara (81832) (K lines), a panel of 14 BILs at BC2F8 generation were selected based on their preferable phenotypic traits  along with checks. As there is considerable variation in the duration among the BILs, per day productivity was computed to compare genotypes with different duration.−2, with 20 cm row spacing and 15 cm intra-row spacing with five rows of 21 plants each constituting a replication. Normal package of practice and fertilizer application was followed; weeds, insects, and diseases were controlled by using standard herbicides and pesticides as required to avoid yield loss. The experimental plots were arranged in a randomized complete block design with three replications each containing 105 plants. These same parameters were followed uniformly across the seasons.Seeds were sown in nursery beds, and 25 days old seedlings were transplanted, with single seedling per hill in all the field trials. The planting density was 33.3 hills mThese genotypes were screened for various yield contributing traits in all the seasons following Standard Evaluation System IRRI, . The obshttp://bbi.irri.org/products) and R  yield-stability statistic (YSi)  statistic was developed by Kang  Kang, , (2) Addi) Kang, , and (3)i) Kang, . These m by Kang  to be us by Kang  method ad Magari . SimultaYij. is the mean yield of ith genotype in jth environment, μ is the overall mean, δi is the genotypic effect, βj is the environment effect, λk is the singular value for PC axis k, δik is the genotype eigenvector value for PC axis n, βjk is the environment eigenvector value for PC axis k and εij is the residual error assumed to be normally and independently distributed , σ2 is the pooled error variance and r is the number of replicates.The AMMI model Gauch,  was usedGGE biplots display both G (genotype) and GE (genotype environment) variation Kang,  for geno*P < 0.05, **P < 0.01, ***P < 0.001.Sum of square percentage was computed as percentage of sum of squares of components of stability analysis of variance per total sum of squares to know the contribution of each component viz., genotype, environment and GEI. Correlation analysis was performed with Statistical Tool for Agricultural Research (STAR) using Pearson's correlation coefficient method. Significance levels are indicated as: 2, 10 pmol of forward and reverse primer and 1 unit of Taq DNA polymerase . PCR cycles were programmed as follows: initial denaturation at 94°C for 5 min followed by 35 cycles of 94°C for 45 s, 55°C for 30 s, 72°C for 45 s and a final extension of 10 min at 72°C. Amplified products were resolved in 4% metaphor agarose gels prepared in 0.5 X TAE buffer and electrophoresis was conducted at 120V for 2 h. Gels were stained with ethidium bromide and documented using gel documentation system . Amplified fragments were scored for the presence (1) or absence (0) for each primer genotype combination. The SSR genotypic data generated in the population were analyzed using the software, GGT ver.2.0. The graphical representations and comparisons were made among the 23 lines on linkage group basis and also the entire genome level on individual basis.Molecular screening was conducted to identify the presence of reported QTLs in the BILs and also to identify recurrent parent genome percentage. Leaves of 20 days-old seedlings were collected from the field and CTAB (Cetyl Trimethyl Ammonium Bromide) method was followed for DNA extraction ; GY (4.73 to 24.63); BY (0.33 to 2.10); PH (65.98 to 148.43); TN (6.12 to 20.70); GN (93.70 to 314.55); PL (18.09 to 25.19); PW (0.98 to 3.87); TGW (12.50 to 26.07); SF (60.57 to 97.57); BM (11.26 to 54.12); HI (0.20 to 0.55) and per day productivity (0.04 to 0.19) among the BILs under study  showed highest vigor in terms of tiller number consistently across the seasons. In terms of vigor, G6 and derived lines were better compared to checks. Productive tillers were highest in G1 at the time of harvest. Among the checks Tulasi and Sahbhagi Dhan showed comparatively higher vigor and BILs outperformed popular checks. G2 showed highest seedling vigor in paper towel screening method.The BILs were screened for seedling vigor in two seasons od ISTA, . SeedlinYSi)  Kang, , AMMI anYSi statistic. Similarly for bulk yield, G6 scored highest rank followed by G4, G7, G12, G3, G10, and G2. Among the BILs G6 and G3 showed non-significant stability variance and high average yield, so they may be considered for further multilocation trials. Number of genotypes selected based on YSi ranking varied among the traits. 9 genotypes were found to be superior based on YSi scoring for GY and PH; 8 for DTM, FG,TGW, BM, TDMPD;7 for BY, DFF, TN,PTN, GN,PL,SF, and YPD and 5 genotypes were selected based on high trait mean and stability for HI. G6 was found to be stable for 14 traits under study except DFF, TN, PTN, and BM followed by Swarna which was stable for 13 yield contributing traits. G14(7K) showed stability and high mean for 12 traits, G3(14s) for 11 traits, G2(148S) and G8(24K) for 10 traits and G7(248S) for 9 traits  showed high interaction but genotypes G2, G6, and G12 were identified with low environmental interactions and were considered best across the seasons for the trait. Based on AMMI analysis G10(3-1K) was the most stable genotype for BM; G6 and G3 for BY; G14 for DFF, DTM; G5 for FG, GN, TN; G3 for HI, GY, YPD; G2 for PH, TN, SF, 1000GW; G3 for PTN; G14 for TDM, TDMPD and G12 for TN. GGE biplot also showed similar results for stability of genotypes in trait expression across environments  appeared to be a favorable environment for BM and SF; E1 for BY, GN, PL, and E2 for PTN and GY. Genotypes G3(14S), G6(166S), and G9(250K) showed low interaction effects and hence they can be considered stable. In case of GY, G3, and G6 had high mean values and hence they can be recommended for all the environments. The genotypes with high interaction are suitable for specific environments, genotypes with high mean and positive interaction are suited for favorable environments and those with high mean and negative interaction are suited for unfavorable environments for the respective traits. A line that passes through the origin and is perpendicular to the O-axis in the biplots separates genotypes that yielded above the mean  that would possibly yield above average in all the seasons and genotypes that yielded below average . The released varieties Tulasi, MTU1010, Swarna and Sahbhagi Dhan used as checks performed well across the seasons.From the biplot graph of AMMI, it was inferred that interactions of environments are highly varied and all the three environments were highly interactive for most of the yield traits. E3 (Kharif (wet season) seasons under study but another genotype appeared to be best for Rabi (dry season). So these traits are showing seasonal variation and genotypic performance depends on environmental conditions. Traits like bulk yield, productive tiller number and grain yield showed no seasonal dependence on genotypic performance.Genotypic evaluation was conducted and based on GGE biplot which-won-where pattern and adaptation showed specific genotypic adaptation to limited environment conditions or the adaptability of genotypes for each environment Figure . The samRabi season and Tulasi to Kharif season. The analysis indicated that G3, G12, and G4 were suitable BILs for cultivation in irrigated environment as they had the highest ranking in biplot and in predicted means.The polygon was drawn joining cultivars that are located farthest from the origin so that all other cultivars are contained in the polygon. Perpendicular lines to the sides of the polygon divide the biplot into sectors. Each sector has a vertex cultivar which is present in the corner of the polygon. The vertex cultivar is the best performing cultivar in the environments that share the sector with it. Vertex genotypes are G3, G4 and G7 at E1, E2 and E3 respectively. In case of checks, it is inferred that cultivar Sahbhagi Dhan is suited to Multiple correlations between different yield and yield related traits was conducted for all the three seasons Figure  and it wAll the BILs were screened using universal core genetic map for rice  and G6(166S) as the most stable BILs with high yield performance. The percentage of explanation of genotype on phenotype was high for 1000 grain weight and plant height and environment effect was high for tiller number, days to flowering and grain yield and interaction effect was high for bulk yield and filled grains per panicle. DRR Dhan 40, an elite BIL and recently released variety showed yield stability with high mean performance and the mega varieties which were used as checks also showed yield stability across the seasons. It was observed that wild derived lines with about 70% of recurrent parent genome were more stable and showing enhanced yield levels. Thus, more emphasis should be devoted in future breeding programs to pre breeding and to develop genotypes with wider adaptation. Stability analysis and GEI may be further extended widely for stress resistance, quality as well as nutrient composition for precise identification of superior genotypes.The study showed the importance of genotype × environment interaction and stability analysis for evaluation of genotypic yield potential. Wild introgression lines derived from The authors declare that the experiments comply with the current laws of the country in which they were performed and in compliance with ethical standards.DB, SN conceived and planned the work. Phenotypic and genotypic screening was performed by JB, AR, RY, KB, SM, MS, DB, RP, and GP. DS, DB, analyzed the data. DB wrote the manuscript. DS and SN revised and proofread the manuscript. Facilities provided at Indian Institute of Rice Research by VB.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


One of the main goal in phytopathology is to better understand the molecular basis of plant–pathogen co-evolution through the identification of effectors and effector targets that play a role in natural phenotypic variation. Fortunately, next generation sequencing (NGS)—which can measure genetic variation at hundreds of thousands of markers across a genome, including for non-model organisms—is now helping to reach this goal. Among all possible strategies using NGS data, we expect that genome-wide association studies (GWAS) have the most potential to revolutionize the field of phytopathology. In contrast to QTL mapping, GWAS use outbred populations to capture the standing genetic variation, thus characterizing the raw material for evolution. By examining the natural phenotypic and genetic variation, association mapping can elucidate the genetic basis underlying complex traits. In the two decades since association mapping successfully detected common variants for human complex diseases  thaliana. Even for this selfing species with an extent of linkage disequilibrium (LD) over a distance of 20 kb, Atwell et al. (Pseudomonas (P.) syringae , and confirmed the contribution of these loci to the natural variation of resistance of A. thaliana against P. synrigae. Subsequent studies reported more bacterial resistance loci in A. thaliana  for identifying traits related to plant–pathogen interactions, has been demonstrated for various species including both host plants and pathogens. Paving the way, a few recent studies detected significant associations targeting resistance or (a)virulence loci. The first GWAS targeting phenotypes related to plant–pathogen interactions were done in the model species l et al.  demonstrOverall, these findings demonstrate that GWAS is a successful method in the field of plant–pathogen interactions. In addition, when conducted with a sufficiently high-density marker map single-gene resolution of GWAS reaches far beyond the resolution of QTL mapping.Based upon the premise that the contribution of a genetic variant to the phenotype is expressed, association mapping measures the significance of the association between the phenotype and the genotype. A detailed discussion of the statistical aspects of GWAS is beyond the scope of this article, a thorough discussion can be found in Balding . Apart fSample size must be considered because greater statistical power is obtained when increasing the sample size . The measure of LD is fundamental to predict the resolution of association studies. Lastly, to clarify how many significant markers are dragged along with the putatively causal marker, LD also should be well described in genomic regions covering top significant markers. The worst-case scenario is when there is a group of significant markers in “complete” LD. In that situation, complementary sequencing approaches using larger sample size may help to identify among associated markers which one(s) is causal. Complementary sequencing approaches also are beneficial when performing GWAS using RAD (Restriction site associated DNA)-sequencing that partially surveys the genome. Indeed if the LD drops quickly between adjacent  markers, additional sequencing should be performed to call more variants in the region and identify the ones with the lowest associated P-values.When carefully examined, LD greatly helps to improve the power of the study. Pairwise LD, as measured in association studies, corresponds to the non-random association of alleles at two loci. It is usually estimated from the coefficient correlation RGWAS are now emerging in phytopathology; however, the vast heterogeneity of species that are under study and the lack of a uniform design for all systems remains a challenge. Thus, thorough analyses of GWAS are necessary to positively impact the reliability of this approach in the field of phytopathology.., inversions, translocations within and between chromosomes) are not rare in micro-organisms and have been largely neglected so far. In our opinion, structural variants likely contribute to the potential of plant pathogen evolution and thus should be carefully examined. Hartmann et al.  because we observe the most significant difference of disease symptoms between the two alleles at that position, within a given region. For instance, for a haploid species with two alleles “A” and “B” at the site, the phenotypic value varies the most significantly between the two groups “A” vs. “B.” Once we have this result, however, additional work to elucidate the molecular function associated with the SNP needs to be conducted to support causality . This step, the so-called “functional validation” is commonly feasible in micro-organisms. This resource should be better exploited to examine fully the molecular function hidden behind a top significant marker.A. thaliana against X. campestris pv. campestris by GWAS  can be constructed in several genetic backgrounds and phenotypic effects of each mutation can be quantified. We think this strategy should be prioritized for a better understanding on the molecular mechanisms associated with plant pathogen evolution. Using GWAS and reverse genetics one demonstration of the molecular co-evolutionary dynamics between host and pathogens was done  What molecular variants contribute the most to the standing phenotypic variation? (2) What is their phenotypic effect? (3) Are they regulatory or coding? (4) Are there many loci in action with small effects? (5) What molecular functions are associated with the phenotypic differences among individuals? (6) What evolutionary forces are maintaining this variation?Importantly, GWA has limitations that may vary depending on the species and the phenotype under study and it is not trivial to perform a successful GWAS with good statistical power to detect causal variants. Even if molecular variants with large phenotypic effect are often discovered, certainly many more variants that contribute to the phenotypic variation remain to be found. The ability to detect these variants will require alternative strategies. We suggest that using very large sample sizes and combining population genomics with population transcriptomics and epigenetics should greatly contribute to elucidating the complex genotype-phenotype map in plant pathogen interactions.AG conceived and wrote the article with significant intellectual input from all authors: JC, ML, and LG.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.