Using single nucleotide polymorphism markers, we mapped quantitative trait loci associated with plant vigour in the F2:3 families and determined the allelic contribution of the two parents. Seventeen QTLs (quantitative trait loci) associated with vigour and six QTLs associated with the accumulation of ions  were mapped on the nine linkage groups of lettuce. Seven of the vigour QTLs had a positive effect from the crop allele and six had a positive effect from the wild allele across treatments, and four QTLs had a positive effect from the crop allele in one treatment and from the wild allele in another treatment. Based on the allelic effect of the QTLs and their location on the genetic map, we could suggest genomic locations where transgene integration should be avoided when aiming at the mitigation of its persistence once crop–wild hybridization takes place.With the development of transgenic crop varieties, crop–wild hybridization has received considerable consideration with regard to the potential of transgenes to be transferred to wild species. Although many studies have shown that crops can hybridize with their wild relatives and that the resulting hybrids may show improved fitness over the wild parents, little is still known on the genetic contribution of the crop parent to the performance of the hybrids. In this study, we investigated the vigour of lettuce hybrids using 98 FThe online version of this article (doi:10.1007/s00122-012-1897-4) contains supplementary material, which is available to authorized users. Gene flow between crop species and their wild relatives may result in the introgression of crop genes into wild genomic background, or in the formation of new species through novel combinations of crop and wild genes  and wild prickly lettuce (Lactuca serriola L.). Cultivated lettuce and wild prickly lettuce are interfertile species, the hybrids of which are viable and fertile (Lindqvist 2 progeny of a cross between L. sativa and L. serriola. We addressed the following questions: (1) how is the performance of the hybrids relative to the wild parent under non-stress and stress conditions? (2) Do crop alleles contribute an advantage or disadvantage to the crop–wild hybrids under non-stress and abiotic stress conditions ? (3) How are the vigour QTLs distributed along the genome, and what is the nature of their allelic effects?In this study, we investigated the contribution of the crop alleles to the performance of a crop–wild hybrid population derived from a cross between cultivated lettuce  with which it could even be considered to be conspecific , are completely cross-compatible and the resulting hybrids are also viable and fertile , and it represents a commonly occurring genotype among L. serriola in northwestern and Middle Europe . cDNA libraries from parental lines were sequenced with Illumina Genome Analyzer II. These ESTs sequences encode genes for disease resistance and plant development. In this way, more than 10,000 SNPs were developed from 3,950 ESTs in four parental pair combinations, namely Salinas × Valmaine, Pavane × Parade, Emperor × El Dorado and Thompson × Cisco (http://compgenomics.ucdavis.edu/compositae_SNP.php). To improve the conversion success rate of bio-informatically identified SNPs to molecular markers, potential SNPs were filtered to 1,083 SNPs that had been previously assayed and shown to be robust, were polymorphic in more than one of the four parental pair combinations, were not located in intron/exon splice sites, were limited to one SNP per contig, were candidate genes of interest, were evenly distributed based on previous mapping work and the ultra-dense lettuce map, and for which the surrounding sequence was suitable for oligonucleotide design for the Illumina GoldenGate assay. The selected 1,083 SNPs were converted into Custom GoldenGate Panels (OPA) for genotyping, using an Illumina BeadXpress assay. From the 1,083 SNPs, a customized OPA of 384 SNPs which were polymorphic between the F2 parental lines was made specifically for the population.The Compositae Genome Project at UC Davis Genome Center has developed single nucleotide polymorphism (SNP) markers from lettuce populations derived from crosses between closely related cultivars of 2 and parent lines using the QIAGEN DNeasy 96 Plant Kit  with slight modifications for dry plant tissue to obtain a minimum DNA concentration of 60 ng/μl. The DNA concentration was quantified using a NanoDrop 1000 Spectrophotometer V3.7 (Thermo Scientific). We genotyped 187 F2 individuals and the parents using the customized 384 SNP OPA in a BeadXpress assay. Out of the 384 SNPs, 355 were successfully scored in the 187 F2 and parental lines. 331 Markers were co-dominant, 16 were dominant for the L. serriola allele and 8 were dominant for the L. sativa allele. The genotypes for the 187 F2 individuals were used to build a genetic linkage map using JoinMap® 4   the “drought experiment” (March–April 2010), which comprised drought and control treatments and (2) the “salt–nutrient experiment” (June–July 2010), which comprised salt, nutrient deficiency and control treatments. Each F2 plant was represented by 12 F2:3 seedlings per treatment. The parents and the two additional lines were also replicated 12 times per treatment.FDuring first establishment, the seedlings were irrigated twice a week for 2 weeks with water supplemented with nutrients. Subsequently, the treatments were started at the beginning of the third week after transplanting of the seedlings, when the plants had four to five leaves. For the drought experiment, the plants in the control treatment were still watered twice a week, while the plants in the drought treatment were not given water at all. For the salt–nutrient experiment, the plants were again irrigated twice a week, but with added 100 mM of NaCl in the irrigation water. The plants under nutrient deficiency treatment received water to which no nutrients were added. The control plants received nutrients for the whole period of the experiment. Stress was applied for 3 weeks after which time the plants were harvested at the rosette stage, 35 days after transplanting. A photoperiod of 18 °C/16 h of light and 15 °C/8 h of darkness was maintained throughout the experiments by temperature control and application of artificial lighting as needed. However, high summer temperatures influenced the greenhouse conditions during the salt–nutrient experiment when outside temperature reached as high as 35 °C.+, K+, and Cl−) for salt and control treatments of the salt–nutrient experiment was measured. Because ion content is measured based on dry matter, the 80 °C-dried shoots were dried again at 100 °C for 24 h. The 12 plants per line per treatment were pooled, ground to fine powder, well mixed, and about 30 mg of dry matter was measured with the precise weight recorded. The ground samples were ashed at 545 °C for 5 h, diluted in 3 M formic acid and further diluted 1,000 times with extra-pure water. The diluted solutions were used in ion chromatography analysis on an 881 Compact IC pro  × 100/fresh weight]. The ion content .Broad sense heritability of family means of the traits was estimated for each treatment separately as the proportion of the total variance accounted for by the genetic variance using the formulaIn order to effectively model genotype by environment interaction  through QTL by environment interaction (QTL × E), each trait was analysed individually using the single trait—multiple environment option of the programme. Genome-wide association between markers and traits was decided based on a significance level of 0.05 corrected for multiple tests using the Li and Ji method (Li and Ji Epistasis was tested for the detected QTLs Holland . Each QTPgenotype < 0.001), and there was significant genotype × treatment variation (Pgenotype × treatment < 0.001). Broad sense heritability of family means of the traits ranged from moderate to high , however, heritability is consistently lower for all the stressed conditions and particularly so for drought and nutrient deficiency. Crop–wild hybridization released genetic variance: even when the means of the parents were not significantly different, heritability was relatively high as observed for dry weight under control (H2 = 0.90) and drought conditions (H2 = 0.66) and for relative moisture content under nutrient deficiency conditions (H2 = 0.89) . In addition, the mean for the L. serriola parent always fell within the range of the minimum and maximum values of the F2:3 families for all the traits and under all the treatments . The lack of correlation between ion content and dry weight indicates that the accumulation of ions in the shoots is not related to the biomass of the plants under salt treatment.Plant height positively correlated with biomass, except under salt treatment where fresh weight was negatively correlated with plant height . Three of these markers could not be placed on the map and the remaining five mapped on LG3 where they spanned a continuous segment of 76 cM, with a bias towards the crop allele . The details about the detected QTLs under control and stress conditions are shown in Table + content, indicating that the vigour of the hybrids was not mainly due to the heterozygous genotypes. QTL by environment interaction  was significant for all the vigour trait QTLs and Cl− content QTLs. This non-additive QTL effect from one treatment to another was due to the presence of a QTL in one treatment and its absence in another or to a differential QTL allelic effect characterized by unequal or opposite allelic effect from one treatment to another.Seventeen QTLs were mapped for vigour traits  and six QTLs were mapped for ion content traits  is consistent with the close relatedness of L. serriola and L. sativa and the complete fertility between the two species (Ryder and Whitaker Interspecific crosses have been reported to result in high pre-zygotic segregation distortion in progeny (ranging from 22 to 90 % of the markers) and to be associated with reproduction barriers  of L. serriola, a recent large-scale population genetic study on crop–wild gene flow using microsatellite data on a large genebank collection and samples of wild L. serriola from all over Europe has shown that the two species are still for the largest part genetically distinguishable  . This suggests that dominance is not the most important genetic basis behind the improved vigour among F2:3 families. Conversely, epistasis as a result of non-additive effect of genotypes at two QTLs was significant for the traits under stress and control conditions. Despite the proven importance of epistasis on polygenic traits Below is the link to the electronic supplementary material.


Association mapping studies offer great promise to identify polymorphisms associated with phenotypes and for understanding the genetic basis of quantitative trait variation. To date, almost all association mapping studies based on structured plant populations examined the main effects of genetic factors on the trait but did not deal with interactions between genetic factors and environment. In this paper, we propose a methodological prospect of mixed linear models to analyze genotype by environment interaction effects using association mapping designs. First, we simulated datasets to assess the power of linear mixed models to detect interaction effects. This simulation was based on two association panels composed of 90 inbreds (pearl millet) and 277 inbreds (maize).Based on the simulation approach, we reported the impact of effect size, environmental variation, allele frequency, trait heritability, and sample size on the power to detect the main effects of genetic loci and diverse effect of interactions implying these loci. Interaction effects specified in the model included SNP by environment interaction, ancestry by environment interaction, SNP by ancestry interaction and three way interactions. The method was finally used on real datasets from field experiments conducted on the two considered panels. We showed two types of interactions effects contributing to genotype by environment interactions in maize: SNP by environment interaction and ancestry by environment interaction. This last interaction suggests differential response at the population level in function of the environment.Our results suggested the suitability of mixed models for the detection of diverse interaction effects. The need of samples larger than that commonly used in current plant association studies is strongly emphasized to ensure rigorous model selection and powerful interaction assessment. The use of ancestry interaction component brought valuable information complementary to other available approaches. Linkage mapping and association mapping are two complementary methods that are widely used to study the relationship between genotype and phenotype. Linkage mapping or y mapping is genery mapping. This hiy mapping.One major pitfall of this method is that the genetic background of the populations could produce confounding effects which bias the statistical analysis and inflate the rate of false positives . MethodoAssociation mapping is especially powerful for common alleles and for moderate to large effects ,17. Assoi.e. the effect of single factors with no interactions). To date, only a few association mapping studies reported tests of interaction effects (e.g. [The number of association studies performed in plants is currently increasing (see reviews -23). Howts e.g. -28). Int. Inti.e.ts  framework  is the mThe aim of the present study was to investigate the use of a mixed linear model in an association mapping framework to identify genotype by environment interactions and interaction with population structure.The commonly used mixed model in plant association mapping studies is:, Z were 0/1 incidence matrices relating y to β, α and u vectors respectively. The variance of the random effect u is expected to be Var(u) = K V, where K is the kinship matrix and V is the genetic variance. In the rest of this paper, we will use a simplified notation:where y is the vector of phenotype, β is a fixed effect other than SNP or population structure, α is the vector of a given SNP fixed effect, v is the vector of population structure fixed effects, u is the vector of polygenic background effects, and e is the residual error vector . Q is thY is the phenotypic trait, μ is the intercept, E is a fixed effect other than population structure effect or SNP effect , Q is the fixed effect of population structure, S is the fixed effect of a SNP (or any gene polymorphism). Q is set by matrices of population membership . K is the polygenic background random effect and e is the random residual of the model. K is set by a matrix of kinship relationship between individuals.In this canonical form, the linear mixed model has mainly been used so far to measure the main effect of genetic polymorphism (and other covariates) on the phenotype. We first developed an extension of this model to fit gene by environment interaction (S × E). The term for S x E in the model is as follows:If the environmental variable (E) is set as a random effect, the S × E term has to be set as random too. But, in this study, we consider the case where both S and E are fixed effects, so the interaction could be set as a fixed effect and will contribute to the mean structure. Note that this second model assumes the absence of interaction between population background and environment, so that no term was included for such interaction.Next, we developed a full extension of the model to fit two and three way interactions between factors:Q × E is the effect of interaction between ancestry and environment; Q × S is the interaction between SNP and ancestry; and Q × S × E is the three way interaction between ancestry, SNP and environment. All interactions are considered as fixed effects. Here, interaction between environment and genetic background is taken into account based on Q, and background effects linked to kinship are included only as random main effects.i the original  phenotype of an individual i. Considering a binary causative polymorphism (for instance presence/absence of a SNP), a simulated phenotype yi, can be assigned to each individual i as follows:A basic model of genotype-phenotype association consists in simulating datasets characterized by the main effect of a single locus on the trait. Such an effect could be added on real phenotypic scores from a structured panel, so that the generated phenotype is linked to a real genetic background. With this scheme, there is no longer any need to simulate background matrices. So let us consider a panel of n individuals. We denote pG is the standard deviation of the original trait across the whole panel; r is the genetic effect ratio ; and ϵi is a random variable that adds noise to the trait. The random variable S follows a Bernoulli distribution with P(S = 1) = q, q being the expected frequency of the causative allele. The random variable ϵ follows a normal distribution with a mean of 0 and a variance σϵ2. The variance σϵ2 is set to satisfy a given trait heritability h2 = σG2/ (σG2 + σϵ2). Note that the simulated SNP effect is independent of population structure and kinship relationship between individuals.where S is a random variable with possible values “1” and “0”, standing respectively for the presence or the absence of the causative allele; σHereafter, this basic simulation scheme was extended to generate data patterns with genotype by environment interactions and/or background interactions.1 and E2  is taken into account to obtain an equal mean phenotype (y) between the two environments Ei. The effect ratio r varied across iterations from 0 to 1.5 ; λ varied from 0.05 to 1 ; q was set at 0.05, 0.25 and 0.5, respectively; and h2 was set to 0.25 and 0.75, respectively. The values of r and λ where chosen in the respectively defined ranges with regular spacing, to allow assessing the trends of power variation with respect to these parameters. The parameter σG was fixed at the value of the standard deviation of the original trait in each panel (σG = 6.83 days for pearl millet and σG = 8.72 days for maize). Population size was set at the value of original panels (n = 90 for pearl millet and n = 277 for maize), so that all available individuals were included. For each combination of parameters, the simulation was replicated a thousand times for pearl millet and a hundred times for maize. The lower number of iterations for maize allowed simulations to be run in a reasonable timescale. So in this step, around 12 million individual genotype-phenotype data points were simulated for maize and around 40 million for pearl millet. The simulation parameters are summarised in Table The simulation was performed based on the two inbred panels described below (pearl millet and maize). Field experiment-based phenotypic scores (flowering time) from each panel were used to set the original phenotypic values p0. P0 was one of the populations in the panel. The SNP and the background marker were not linked. Two environments, E1 and E2, were considered. We modelled the effect of the SNP on each individual phenotype so that this effect increased in the second environment only for individuals simultaneously carrying the causative allele at the SNP and the background marker Bk  was greater than a value randomly selected from a uniform distribution with the range 0-1. Given this approach, the expected frequency of the marker Bk in the sample was q0, the ancestry coefficient averaged from all individuals. At each iteration, the probability of an individual having the marker equals the ancestry of this individual in P0. The final phenotype was simulated using the following model:We considered two loci in a structured panel of n individuals: a randomly distributed SNP with a frequency expectation q and a background marker (Bk) linked to the ancestry in population P2 was set at 0.25 and 0.75, respectively. For each combination of parameters, a thousand samples were generated for pearl millet panel and a hundred samples for maize, as in equation 2. The size of each individual sample was the same as in the original panel (n = 90 for pearl millet and n = 277 for maize). Among the populations comprising each panel, the population with the highest average ancestry  was defined as P0, to maximize sample size. We wrote scripts with the software R (version 2.7.2) to implement all the simulation schemes used.This simulation scheme is therefore basically identical to the previous one (Equation 2), except for the presence of Bk which makes the effect variation depend on ancestry. In the model, Bk was set as a binary numerical variable scoring the presence or absence of the background-dependent marker . The parameter r varied from 0 to 1.5  and λ varied from 0.05 to 2 ; q was set at 0.05, 0.25 and 0.5, respectively; hThe data simulating gene by environment interaction (Equation 2) were fitted using model 2. The model with two and three way interactions (model 3) was used to fit the data including the corresponding interactions (Equation 3). Model components were estimated using the REML method . The fixResults of independent field experiments were available for two panels (maize and pearl millet). Maize data came from Cornell University . Pearl millet data came from the Institut de Recherche pour le Développement .trial to refer to the replicate of the field experiment at a given sowing date. All trials were conducted at the same location . Three of these trials (2005-2006) and the experimental design are described in detail in a previous paper [PHYC locus . For this dataset, we use the term us paper . The sixus paper ,45. Popuus paper . We compus paper . For canribed in ).trial to refer to the maize experiment in a given year of experimentation at a given location. In this study, only seven trials were used, due to missing data in the eighth trial. For each inbred, the best linear unbiased predictor (BLUP) from each trial was used. Ancestry estimates were also available from a previous study which clustered maize inbreds into three populations: NonStiffStalk (NS), StiffStalk (SS) and Tropical (TS) populations [Vgt1 locus was also available from a previous study [The maize panel contained 277 inbred lines. Flowering phenotype (days to silk) was recorded in eight environments in the United States . Hereaftulations . Kinshipulations  and calculations . The genus study . One inbA common set of five competing models were defined to fit each of the maize and pearl millet datasets Table . All fiv2 = 0.75). Also, the power to detect the interaction was more sensitive to the coefficient λ; this was expected because λ measures the increase in the effect of the SNP from the first environment to the second. The power was very low for the detection of gene by environment interactions when low heritability was combined with low allele frequency and/or low effect size. The global pattern of power variation with the parameters  was consistent for both datasets (maize and pearl millet), but the maize sample performed globally better than the pearl millet sample in terms of absolute power. So in the maize sample, environmental interactions underlined by common alleles with relatively strong effects were still detectable at h2 = 0.25 and also the detection of rare alleles (q = 0.05) was better than that in pearl millet . The precision of estimation of fixed effects by this model was generally good with respect to the actually expected effects .We used the simulated data to measure the power of mixed linear model to detect gene main effect and gene by environment interaction Figure  = 0.75. 2) on the power was globally similar to the impact described in the case of the gene by environment interaction. However, here, the power to detect the interactions appeared to be more sensitive to the value of differential effect between environments (λ). Thereby, even in the best allele frequency and heritability conditions  in both panels .We measured the power of MLM to detect two and three way interactions between SNP (S), ancestry (Q) and/or environment (E) . For the other SNPs, the main effect was significant while none of interaction effects were significant , but not in others . We set mixed linear models to test for possible interactions  produced different results depending on the trial . A highly significant environment main effect was also highlighted (P < 10-26), as expected with contrasting environments. Note that the main effect term set for Vgt1 was not significant (P = 0.37). Instead, we observed a significant effect of interaction between this locus (Vgt1) and environment  and, respectively, for the oligogenic scenario (h2 = 0.5) [Previous association mapping studies in plants investigated the power of mixed linear model mainly in the simple case of main effects ,13,16,172 = 0.5) , making In the current study, we simulated data based on an explicit control on heritability, allele frequency and effect size, to investigate how these parameters impact the power of mixed model. Diverse patterns of G × E interactions occur in biological data . Our fir2 > 0.25). The framework will lack the identification of rare alleles or alleles affecting poorly heritable traits. The loss of power was more critical when higher order interactions were considered. One obvious statistical reason is that the power to detect higher order interaction  relies not on the allele frequency alone, but rather on the combination of the frequency of all variables involved in the interaction. As allele frequency is a proportion , this combination is necessarily lower than any of the original variable frequencies. Furthermore, these simulations suggest that the exhaustive study of trait architecture based on current plant association panels will suffer from the bias of discarding not only rare alleles but also alleles with very small effects, because the full level of power (>0.95) could be reached only with less realistic effect sizes. For instance, the effect size needed to reach 95% of the simulated interactions in the best cases (h2 = 0.75 and q = 0.5) corresponded approximately to about 0.4 or 0.5 fold the standard deviation of the trait , the improvement in power was in great part due to the effect of the larger sample size in maize (three times larger than the pearl millet sample). But despite this difference in the absolute value of power estimates, it is important to note that the pattern of power variation, as a function of allele frequency, heritability or effect size, was consistent for the two panels. To explore more parameters spaces in terms of genetic background configuration, allele frequency or sample size, the use of simulated panels based on theoretically defined parameters  will be more suited. But this is not implemented in the current study.Statistical limits to the analysis of complex interactions using small panels were revealed in when we used very low allele frequency for the smaller dataset (pearl millet data). The number of inbred baring the allele is then too low and the reliability of model components defined on the basis of rare combinations is statistically questionable. Taking all the simulation results together, it appears that no single parameter determines the power of the model and that the effects of all parameters might balance each other. For instance, a good allele frequency does not necessarily imply good power when heritability is insufficient, and reciprocally. In this connection, the power of the MLM framework for a particular set of data needs to be discussed with respect to the combination of data characteristics, instead of focusing on only one or two parameters. This will have implications for the design of association studies, in particular when interactions are of interest.They are some parameters which could be more easily handled when planning a plant association study. For instance, the size of a panel can be extended with an appropriate sampling effort to reach a sample size favourable for the detection of effects. As revealed by the comparison of the pearl millet panel (n = 90) and maize panel (n = 277), considering a size of hundreds of individuals appear to be the minimum required to ensure a powerful design. However, even in this case, very small phenotypic effects or very low allele frequency also limit the performance of the MLM framework as already noted. To be able to detect rare alleles, the use of family mapping  could be recommended . Also, tFinally, the use of the present framework will be more suited for: 1) association mapping sample of several hundred individuals, 2) traits with high heritability, and 3) relatively common allele.Methods of model selection led to contrasting results for pearl millet  is actually expected in the light of our simulation study  and the environment, with a highly significant probability (P < 10-6). When we performed site by site analysis, this effect was also detected. The effect of the MITE insertion at this locus was in the same direction across all the environments examined, but the size and the significance of this effect was different between trial locations. The two types of interaction effects have important implications for the understanding of quantitative trait variation. More generally, interaction between biological and environmental factors impact trait stability, trait prediction, and trait architecture [The second type of interaction was an interaction between one locus . Nonetheless, other issues remained to be addressed. For example, it will be interesting to evaluate possible heterogeneous variance structure using mixed model framework.The present study is one of the first in plant to deal with genotype by environment interaction in a association mapping framework. It highlight the challenging issue about interaction study based on deep examination of important aspect of this issue (modelling of different types of interaction, model setting and model selection, model power, impact of data parameters like sample size and allele frequency, We used mixed linear model to discuss the statistical perspective of using association mapping panels to study interaction effects in plants. First, this study highlighted the need of large sample size to ensure best model selection and high power. Most of the association panels of plants species to date are composed of a fairly small number of individuals, so larger panels are to be recommended in the future to deal better with G × E interactions. Second, we showed a strong impact of data parameters on the power, with a drastic loss of power when allele frequency, heritability, or effect size, are low. This shortcoming reinforces the need of complementary methods to deal with rare alleles or alleles with small effects. However, we illustrated cases of success of the current mixed model framework by identifying, in the maize association mapping panel, two types of biologically interesting effects of interaction between genetic factors and environment. So the development of interaction studies based on this mixed model framework would contribute understanding quantitative trait variation, notably by taking into account key components of G × E interactions. This framework is complementary to the frameworks of association mapping developed to deal with multi-QTL ,55, and The authors declare no competing interest.MC and CM sequenced pearl millet panel. CM, AAS, and YV designed and supervised field trials for pearl millet. AAS participated in the design of the study and performed statistical analyses. AAS, ACT, and YV wrote the paper. YV coordinated and supervised the study. All authors read and approved the final manuscript.This file provides additional figures cited in the text. Figure S1 Power of mixed linear model to detect phenotypic effects including gene by environment interaction. Figure S2 Power of mixed linear model to detect phenotypic effects including 3-way interactions in the pearl millet sample. Figure S3 Power of mixed linear model to detect phenotypic effects including 3-way interactions in the maize sample. Figure S4 Model selection for the analysis of associations in a multi-trial design. Figure S5 Effect estimates of the Vgt1 locus on days to silk for each of the 7 environments. Figure S6 Model selection based on different criteria. Figure S7 Frequency of selection of competing models as a function of sample size in maize.Click here for fileTable S2 Expectation of minimum effect detected with a power of 95% in the model with three way interaction. Table S3 Model selection based on WLD. Table S4 Wald test for Vgt1 effect analyzed independently into each trial. Table S5 Formulation of information criteria. Table S6 Rate of selection of competing models by information criteria, at different values of effect size parameter r. Table S7 Significance of the effect of data parameters on the rate of success of information criteria.Minimum effect detected with a power of 95% in the model with gene by environment interaction. Click here for fileAssessment of methods for model selection.Click here for file


Recent advances in sequencing technologies set the stage for large, population based studies, in which the ANA or RNA of thousands of individuals will be sequenced. Currently, however, such studies are still infeasible using a straightforward sequencing approach; as a result, recently a few multiplexing schemes have been suggested, in which a small number of ANA pools are sequenced, and the results are then deconvoluted using compressed sensing or similar approaches. These methods, however, are limited to the detection of rare variants.In this paper we provide a new algorithm for the deconvolution of DNA pools multiplexing schemes. The presented algorithm utilizes a likelihood model and linear programming. The approach allows for the addition of external data, particularly imputation data, resulting in a flexible environment that is suitable for different applications.Particularly, we demonstrate that both low and high allele frequency SNPs can be accurately genotyped when the DNA pooling scheme is performed in conjunction with microarray genotyping and imputation. Additionally, we demonstrate the use of our framework for the detection of cancer fusion genes from RNA sequences. Recent advances in sequencing technologies have drastically reduced the cost of nucleotide sequencing ,2 and arMultiplexing pools are practical for sequencing a short genomic region in many individuals. As sequence capacity increases, it is likely that this technique will become even more practical in the future. Sequencing capacity is constantly increasing and therefore it is plausible that multiplexing pools will benefit whole-genome sequencing in the future. We note that in Erlich et al  the use In this paper, we present an alternate scheme for sequencing using overlapping pools which, unlike all previous approaches, is able to quantify both rare and common variation. The key idea underlying our scheme is that we formulate the pooling problem within a likelihood framework that provides several advantages over previous methods. Our scheme is flexible and can be applied to a wide variety of applications. We demonstrate this by applying the scheme to two very different applications, each of which takes advantage of the likelihood framework within our approach and is difficult to solve using previously proposed combinatorial methods.The first application we consider is obtaining highly accurate genotype information for a set of individuals. Currently, genotype microarrays are the most accurate method for measuring individual genetic variation at a base-pair level at variable locations across the genome (Single Nucleotide Polymorphisms: SNPs). A typical array will collect up to 900,000 or more genotype calls at common SNPs across the genome. Using imputation techniques and a reference dataset such as the HapMap  or the 1The second application we consider in this work is to rapidly screen for fusion genes in cancer samples. Fusion genes play an important role in cancers and are caused by genomic rearrangements in a tumor that create new genes consisting of several exons from one gene followed by several exons from a second gene. Our application considers the sequencing of RNA obtained from cancer tumors with paired-end reads. The read pairs of interest are ones that span exon boundaries with each read of the pair coming from a different exon. The majority of such read pairs will map to the same gene when aligned to the reference genome and. However, read pairs from fusion genes will map to two exons from different genes. One potential approach in identifying fusion genes is to search for read pairs that contain reads mapping to different genes. The main drawback of this approach is that it leads to a very high level of false positives making it difficult to distinguish actual fusions from experimental artifacts. Our application will mix RNA from a large number of cancer tumors into overlapping pools and utilize the likelihood framework to decode which fusion genes come from which samples. In order to accomplish that, we extended the basic overlapping pool model to consider different levels of expression for each gene. This can be estimated from the data. Our decoding scheme is based on a likelihood formulation which presents novel computational challenges compared to previous approaches. Each possible configuration (genotype assignment or gene-fusion assignment) is assigned a likelihood and the goal of the algorithm is to identify the most likely decoding. We identify good solutions for the problem by formulating a related problem as a linear program which we can efficiently solve. We note that these results are just the first steps in applying this framework to multiplexing sequencing pools and it is likely that better optimization algorithms and better designs of pooling schemes can lead to more substantial savings.We first report the results of applying our approach to genotyping individuals to obtain both common and rare variation using combining overlapping sequencing pools with genotyping and imputation. In this set of experiments, we utilize the 1958 Birth Cohort from the Wellcome Trust Case Control Consortium  data whiFor our experiments we consider a total of 100 individuals mixed into 36 pools which is a reduction of the total number of sample preparations necessary by 1/3. We use a very high coverage of 150 per individual within a pool for our experiments under the assumption that the bottleneck is not the coverage, but the number of pools, each which requires a single sample preparation step. We assume a sequencing error of 0.005. We measure the accuracy of the predictions by comparing the predicted genotypes to the true genotypes and only call a prediction correct if the genotypes are correct for all 100 individuals. We note that this is a very high standard and only 1 of our 100 SNPs have a correct imputation prediction. Our method has very high accuracy significantly improving over imputation. Table We also apply our scheme to predict the genotypes without the imputation for rare variants such as those not found in the reference. The only difference in our methodology is that in the optimization problem, for the imputation vector we use a zero vector since we expect most individuals will not have the variant. This problem is actually much easier than the case of common alleles and we get perfect accuracy for the parameters above.We evaluate our approaches ability to detect cancer fusion genes using a similar simulation framework. In this application, RNA from different tumors is is mixed into overlapping pools and sequenced. In each pool we search for reads which cross exon boundaries from different genes and are evidence of fusion genes. Counts of these fusion genes in each pool are then decoded to identify the samples which contain the fusion genes.We simulate this process by generating reads in a similar fashion to the genotyping without imputation simulations. We assume that we have 100 cancer samples where either 1, 2 or 3 of the samples contain a specific fusion gene. We assume a sequence error rate of 1% and vary the coverage and number of pools in our experiments. A difficulty in this application is that each individual has a different level of expression for each gene. We simulate this by randomly selecting an expression level in the range such that the concentration of the fusion gene in the RNA will differ by up to a factor of 10. Table In this paper we have described a flexible framework for overlapping pool sequencing and two applications of this framework. We presented some results showing the bounds on the performance of decoding rare and common variants (in Methods). We argue that due to information theoretic bounds, common variants are impossible to decode without the addition of external information; we propose to use imputation results as possible external information. In practice, it is often the case that such information is given, as many of the samples have already been genotyped through the massive effort of genome-wide association studies; in addition, current cost of genotyping has reduced considerably and is negligible compared to sequencing costs .Our decoding framework is likelihood based framework and is general enough to account for different types of data and error models. Particularly, we demonstrate how our method can be extended to the case where there are different unknown concentrations of each variant in each sample as motivated by the cancer fusion gene detection example. We note that our approach to detect fusion genes using RNA sequences can only detect fusion genes that are expressed in the tumor since we are sequencing RNA, but this is the case for a significant subset of the total fusion genes .We expect that with improved optimization algorithms and better designs of pooling schemes, we can achieve even more substantial savings.N individuals are to be sequenced for any application such as a disease association study, or fusion-gene detection. The most straightforward approach would be to barcode the individual and sequence them separately. When N is large, or when the desired coverage is high, this approach is infeasible due to budget constraints. A few methods have been suggested to tackle this problem using a set of overlapping pools [G = {ijg} of dimension N × m, where m is the length of the genome. ijg ∊ {0,1,2} is the number of occurrences of a genetic variant in position j of individual i - such variant could be a single nucleotide polymorphism (SNP), copy number variant (CNV), or a gene-fusion, as discussed in the introduction. The pooling based approach considers a {0, 1} matrix A of dimension T × N, representing a set of pools. Each row of A corresponds to a DNA pool; individual j participates in the i —th row if and only if ijA = 1. Thus, the matrix A provides a compact description of the study design. When the study is performed, under an error-free model, the pooling results are given as Y = AG. In principle, one can now decode the matrix by finding a solution to the set of equations AX = Y. In reality though the pooling results are not as accurate, and therefore current methods are using a rounded version of Y; for every i,j, we define ijc = 1 if ijy > 0 and ijc = 0 otherwise. Thus, if we replace the SUM operation by an OR operation then AG = C. Using this information, Erlich et al. [gij > 0. For the simplicity of the exposition, we will assume from now on that only one variant is considered, and so Y, C, and G are column vectors of length N.We consider the scenario in which a set of ng pools -11. Thesh et al. ,Prabhu eh et al.  and ShenN3 possible genotype vectors. The number of possible column vectors jC is 2T. Therefore, in order to be able to decode all individual genotypes we need T2 > 3N, or T >N. Even without rounding, the number of possible vectors jB is at most (2N)T, and therefore even in the error-free case we need (2N)T > 3N, or N)T ≥ 3N, or T ≥ —Nαlogα, and if we are using the full information given by the matrix B, we need A is chosen as a random matrix where each entry is 1 with probability 0.5, then the bounds given here are tight up to a constant factor (the proof is omitted from this version). Moreover, in [C one can decode low allele frequencies T = O(logN) suffices, which is consistent with the bounds we provide here. Since a random matrix provides a good decoding scheme in theory, we followed this intuition and generated a matrix A so that half of the entries in each row is 1 and the other half is 0. To obtain a better design matrix, we use local search; we repeatedly permute a random row and a random column and check to see if the Hamming distance between the permuted row/column and the other rows increased. If so, we keep the change, otherwise, we revert. After performing 1000 permutations, we result in a matrix whose rows and columns are farther apart, which improves our ability to decode.Unfortunately, by collapsing the data to a {0,1} matrix resolution is lost, and therefore there is no hope in decoding all genetic variants from the pools if the number of pools is not large. Note that for a given variant, there are over, in -11, it iG as a sum of the (rounded) imputation predictions I, iji ∊ {0, 1, 2}, and a set of imputation residual errors R, ijr ∊ {-2,1, 0, 1, 2}, where G = I + R. Then, the observed data can be represented as the pools’ results Y = AG, which is Y = AI + AR. Now, note that R is a sparse vector, and I is known; therefore, from a theoretical point of view, the above information theoretic lower bound does not hold on our case and there may be an algorithm that is able to decode the genotypes based on the sequencing and the imputation. In principle, we can solve for the imputation residual errors by solving the set of equations for AX = Y - AI. Once we obtain the residual vector, we can obtain the actual genotypes. In practice, as described below, we use the imputation dosage so our algorithm theoretically searches over the entire space, and not only over sparse vectors, but the search is pruned for vectors that are dense based on a likelihood model. As we show in the results section, this yields an improved imputation accuracy for high allele frequency SNPs.As described above, from an information theoretical point of view, decoding the genotype vector is only possible when the allele frequency is low and therefore the genotype vector is sparse. For this reason, both Erlich et al.  and ShenY and not C. As discussed above, this should allow us a gain of approximately log N factor in the number of pools needed, at least for higher allele frequencies. However, in order to do so, we need to explicitly model the sequencing errors. The error model may be different, depending on the application at hand. We will describe here the model we use for the detection of mutations . There are three main sources of noise that we include in the model:Our approach differs from previous approaches in that we are considering the matrix pooling noise is modeled as a normally distributed noise added to each non-zero element of A with mean 0 and variance p.σ Thus, we set1. There are slight differences in the concentration of each individual’s DNA in each pool. This L the length of the sequenced genomic region; if the total number of bases sequenced is λLN, then we expect that each base will be covered by λ reads on average. λ is often termed the expected coverage. We will denote the number of reads covering individual i by ir1, ir2 . Then, ijr is Poisson distributed, with mean mi. Prabhu et al. [i are approximately drawn from a Gamma distribution with α = 6.3 and β = λ/α for Illumina Solexa sequencers. We note that for a given variant it is easy to infer the value of im, since it is shared across all individuals in all pools. Thus, we have2. There is a variance in the coverage of any specific region in the genome. We denote by u et al.  showed tmi ~ Γ, rij ~ Poisson(im)ε for a substitution (1% is an acceptable estimate).3. The third source of error is sequencing error. The sequencing error rate depends on the location of the base in the read, but since the location of the base is uniformly distributed, we simply model the error rate by a constant probability Â of noisy pools and a pair of vectors ig, and the coverage im, followed by a Binomial distribution to model the errors as explained above. R0 corresponds to the reads with the major allele, while R1 corresponds to the reads with the minor alleles. Note that even if ig = 0, if ε > 0, then expected number of reads with the minor allele will be greater than 0 because of errors. The pooling results are given by , where kY = k.ÂRThe above procedure produces a matrix Y, we need to find a decoding algorithm that estimates G from Y. To do so, we define a likelihood model which can evaluate each putative solution. Our likelihood model takes into account both the error model, as well as population genetics data and external information when available. We decompose the likelihood L into several functions, and take their product as a composite likelihood.Given the pooling results n0, n1, n2 are the genotype counts in G. Using Bayes law we haveWe first note that the overall allele frequency HWPr(Pools | G) is equivalent to maximizing HWPr(G | Pools). We denote Assuming no prior information, we observe that maximizing j in pool i are Poisson distributed with ijλGjÂ (or ijλÂ(2 j- G)). Since the sum of Poisson distributions is Poisson distributed, we have that nfoise(G). In order to find the concentration values Âij we need to use external information. One such possibility could be to genotype small set of SNPs across the population and use those as the ground truth in order to tune the values of ij.Â These SNPs provide a set of linear equations for the values Â; for each pool we have one equation per SNP, and the number of variables is N. Therefore, genotyping as many as O(N) SNPs and using a least squares approach guarantees an accurate estimate of ij.ÂWe compute the probability of the observed reads in the pools given G based on the noise model. Note that the only unknown in the noise model is the concentrations of the individuals in the different pools. This is true since the coverage in any given region can be easily estimated. Assume that λ is the coverage. Then, the number of reads with the minor allele (or major) contributed by individual j, we can assume that there is a given probability hi(0), ih(1), hi(2), where ih(j) is the probability that individual i has iG = j. We can now use the imputation results for our likelihood model, by writing Due to the bounds given on the possibility for detection, it is clear that without external information we will not be able to do much better than detecting rare SNPs. One natural choice for external data could be the genotypes of the individuals using microarrays. Today’s genotyping technology is extremely cheap compared to sequencing, and the genotyping of thousands of individuals is feasible within a given study. The genotype information, however, provides the information about less than a million SNPs and another million CNVs across the genomes, while many other genetic variants are left unmeasured. To cope with this, imputation methods have been developed, in which nearby SNPs are used to impute unmeasured variants using the linkage disequilibrium structure of the genome ,20. HoweÂG = Y. We can therefore solve the following linear program:We use a linear program to bound the possible errors of each of the pools. If the coverage for the SNP is λ, we have that the pools should roughly satisfy λl1 distance between λÂG and Y as well as returning a solution G which is close to the imputation prediction I. β is a parameter that trades off the relative importance of being close to the imputation vector compared to being consistent with the pools. Note that if jY is distributed as Poisson with expectation jµ for which j - µjY = jx, thenThe linear program provides a lower bound on the best possible Therefore, we get that ije be the normalized expression level of a particular variant j (in this case a fusion gene). Whether or not an individual i has the variant j is encoded as G = {ijg}, ijg ∊ {0, 1}. We define the matrix H = {ijeijg} as the concentrations of the samples and the results of the pools (assuming no noise) will then be Y = AH instead of Y = AG as in the genotyping application. In this application, we can also assume that the matrix G is sparse, but in order to perform the decoding, we must also estimate ije for the non-zero values of ijg.In order to detect gene fusions, we make several changes and extensions to the model presented above. The major additional complication in detection of fusion genes is that each sample may have a different expression level for a particular fusion gene. Even if we include the same amount of RNA from each tumor into each pool, the relative concentration of each gene will differ in each sample. However, this concentration is approximately constant across pools. Let ije because they are constant across pools, however this introduces additional complexities in the optimization. We take advantage that fusion genes are very rare and most fusion genes are not shared across tumors. We constrain our optimization to allow for a maximum of k tumors to contain a given sample. We note that we only need to estimate the values of ije corresponding to non-zero elements of ijg. To perform the optimization we enumerate over all ije values.It is possible to estimate A* be a matrix consisting of the only the columns of A corresponding to the non-zero entries of the genotype vector. If x is a vector which has a length the same as the number of non-zero elements in the genotype vector, the solution to A * x = Y will be an approximate estimate of the values for ije. We can incorporate errors by adding a vector of all 1s to A* and appending a term to x corresponding to the amount of errors expected in each pool. For the top 100 estimates obtained by using the pseudo-inverse, we then perform a grid search over the values of ije using the likelihood function described above.Since optimizing the likelihood function for each possible genotype vector is computationally impractical, we solve a linear program as a method to quickly eliminate poor solutions. Let The authors declare that they have no competing interests.D.H., N.Z., B.P., E.E. and E.H. developed the method. D.H., N.Z., B.P. performed the experiments. D.H., E.E. and E.H. wrote the manuscript.


The timing of associations between common genetic variants and changes in growth patterns over childhood may provide insight into the development of obesity in later life. To address this question, it is important to define appropriate statistical models to allow for the detection of genetic effects influencing longitudinal childhood growth.t random errors, semi-parametric linear mixed models and a non-linear mixed effects model. Of the four methods, the semi-parametric linear mixed model method was the most efficient for modelling childhood growth to detect modest genetic effects in this cohort. Using this method, three of the 17 loci were significantly associated with BMI intercept or trajectory in females and four in males. Additionally, the obesity-risk-allele score was associated with increased average BMI  and rate of growth  throughout childhood.Children from The Western Australian Pregnancy Cohort  Study were genotyped at 17 genetic loci shown to be associated with childhood obesity  and an obesity-risk-allele-score was calculated as the total number of ‘risk alleles’ possessed by each individual. To determine the statistical method that fits these data and has the ability to detect genetic differences in BMI growth profile, four methods were investigated: linear mixed effects model, linear mixed effects model with skew-Using statistical models appropriate to detect genetic variants, variations in adult obesity genes were associated with childhood growth. There were also differences between males and females. This study provides evidence of genetic effects that may identify individuals early in life that are more likely to rapidly increase their BMI through childhood, which provides some insight into the biology of childhood growth. Obesity is a major global public health problem. The World Health Organisation estimated in 2010 there were at least 42 million overweight children under the age of 5-years and one billion overweight adults globally 2 per allele) which translate into increased odds of obesity of 1.1–1.3 in adults An individual’s susceptibility to obesity is thought to result from a combination of their genetics, behaviours and environment. The heritability of obesity is estimated from family and twin studies to be between 40 and 80% Obesity develops over a period of time so investigating the genetic determinants underlying this developmental process may provide insights into mechanisms of the genetic associations. Sophisticated longitudinal analyses allow questions to be addressed that cannot be determined from cross-sectional analyses. These longitudinal models assess patterns and duration of genetic effect at baseline and over a time period and the differences in means and rates of change of a trait. It is therefore important to investigate the genetic component of BMI trajectory in order to better understand some of the underlying biology of growth. The analysis of longitudinal growth curves allows one to identify specific stages in which genes play a central role.A child’s growth rate profile often contains important information regarding their genetic make-up and environmental exposures; however, BMI trajectories are difficult to model statistically due to the various changes in growth rate over childhood. Children tend to have rapidly increasing BMI from birth to approximately 9 months of age where they reach their adiposity peak; BMI then decreases until around the age of 5–6 years at adiposity rebound and then steadily increases again until after puberty where it tends to plateau through adulthood. These patterns of growth tend to be different in males and females where females often reach each of the ‘landmarks’  at an earlier age than males. These changes over time within each individual, as well as the increasing variability over time of BMI between individuals, are often difficult to capture accurately in a statistical model. This is particularly the case when the aim is to detect modest genetic effects. The World Health Organization recently conducted research into statistical methods used to estimate growth curves over childhood and examined 30 previously published methods, of which only 7 could handle multiple measurements per child We aim to compare various modelling approaches to assess the genetic effects of BMI growth through infancy, childhood and adolescence. To investigate the sensitivity of these different modelling frameworks to detect genetic effects, we will use the previously published adult obesity and BMI associated SNPs that have been shown to be associated with childhood BMI and explore their associations with childhood growth.The Western Australian Pregnancy Cohort (Raine) Study 2>0.8]) were also presented by Elks et al −7, call rate >95% and minor allele frequency >1%). Individual level genotype data was extracted for those SNPs of interest that were directly genotyped by the chip and passed QC measures. Imputation of un-typed or missing genotypes was also performed using MACH v1.0.16 for the all 22 autosomes with the CEU samples from HapMap Phase2  used as a reference panel. Two variants in the BDNF gene were investigated as they have previously been shown to be independently associated with obesity 2 = 0.11). The 17 SNPs are described in We wanted to investigate markers that have an effect on childhood BMI, and more importantly, change in BMI over childhood so selected the 17 genetic variants published in den Hoed et al t Linear Mixed Effects Model (STLMM) 2 statistic for each method fit to these simulated datasets.Four popular methods were compared to assess the accuracy of estimation of BMI growth trajectories and the ability to detect genetic effects influencing these trajectories. These methods included: Linear Mixed Effects Model (LMM) 1,.,t, the time trend in the sample can be described by a (q-1)st-degree polynomial function, with q ≤ t. The growth curve LMM for the jth individual and tth time point and with the time scale measured by age is as follows:t time points in the sample (i.e. 8 years), βi are the parameter estimates for the fixed effects, ukj are the parameter estimates for the random effects assumed multivariate normal and the εjt‘s are the error terms assumed normally distributed N, where Σ is the within-individual correlation matrix. Both age and the natural log transformation of age were considered as the time component to identify the optimal underlying scale. Both fixed (i) and random (k) effects up to polynomial of degree 3 were tested for significance. Several within-individual correlation structures were considered, including autoregressive, continuous autoregressive, exchangeable (compound symmetric) and unstructured.The LMM with a polynomial function is a common tool for growth curve analysis with continuous repeated measures. For a set of time points varying from Following the guidelines outlined in Cheng et al t distribution for the error terms, εjt‘s, and a multivariate skew-normal distribution for the random effects. The resulting model for the response over the t time points is multivariate skew-t with specific parameters that account for the asymmetry (skewness parameters) and long-tail (degree of freedom of the t distribution) of the response distribution The assumption of multivariate normal random effects and within-subject errors is often violated, particularly when modelling the childhood growth curve. This may lead to biased estimation of fixed effects and their SEs and thus to wrong statistical inference, in particular of the genetic association-related parameters. A common approach to achieve normality is to transform the response variable but generally there is not a unique transformation that could be used and the results of the analyses might depend on the transformation used. To avoid transforming the response and still obtain a valid inference under a non-normal distribution assumption for the response, we utilised an extension of the LMM model assuming a multivariate th individual and time-point t is as follows:Semi-parametric linear mixed models make use of smoothing splines, which yield a smoother growth curve estimate than the polynomial function in the LMM when fitting non-linear relationships. The basic model for the jWhere κk is the k-th knot and (t – κk)+ = 0 if t ≤ κk and (t – κk) if t>κk, which is known as the truncated power basis that ensures smooth continuity between the time windows.Various numbers and positions of knots and the degree of polynomial between knots were compared to find the best fit to the data. Knot points were initially estimated visually from both individual profiles and the population average curve in males and females separately. To optimise the number and placement of the knot points, we fit a series of models with the knot points placed at 6-month intervals around the estimated knot points and incorporated additional knot points to see if they improved the model fit. The model with the lowest Akaike Information Criterion (AIC) was selected as the final model. Finally, we investigated the degree of polynomial, up to the third degree, required for each spline, once again selecting the best model with the lowest AIC.The SITAR method The basic model for the growth curves is:ity = growth of subject i at age t.h(t) = natural cubic spline curve of growth vs. age.iα = random growth intercept that adjusts for differences in mean height (size).iβ = random growth intercept to adjust for difference in timing (tempo).iγ = random age scaling adjusting for the duration of the growth spurt (velocity).This model was fit with the three parameters  as random effects, size and velocity as fixed effects, and h(t) a natural cubic spline curve with 3 to 8 degrees of freedom (df) fitted as fixed effects. BMI and age were fitted both untransformed and natural log transformed, to identify the best fit to the data. Model fit to the data were compared using AIC, deviance and residual standard deviation. The estimates for the three parameters  were extracted for each individual and used for genetic analyses.R version 2.12.1 Given that growth curves differ greatly between males and females, particularly around puberty, and because different genes may influence the timing of growth spurts in males and females, sex stratified models were used for all analyses. Age was mean centred prior to analysis. Due to the possibility of population stratification in our sample given our sampling criteria of at least one parent of European descent, a sensitivity analysis was conducted adjusting the genetic analyses for the first five principal components generated in the EIGENSTRAT software Of the 1,506 children in the analysis, there are 773 males (51%) and 733 females. The optimal model for each method was defined before any cross-method comparisons were conducted. The selected models for each method are summarized in The optimal LMM model for both males and females was based on ln(BMI) and untransformed age, with cubic polynomial of age in the fixed effects, a quadratic polynomial of age in the random effects and a continuous autoregressive correlation structure of order one. Hence, the final model for both females and males wasThe LMM model defined previously was used for this method; however BMI was modelled on the untransformed scale as the method accounts for the skewness and kurtosis of the BMI distribution. The model would not converge with both linear and quadratic age components in the random effects so this was reduced to only linear age. This was the most computationally intensive method to fit as it uses an expectation-maximization (EM) algorithm for parameter estimation, and hence took the longest time to converge.For females, the optimal model had three knot points placed at two, eight and 12 years with a cubic slope for each spline. The males displayed a similar curve to the females, also with three knots at two, eight and 12 years and a cubic slope between each knot.The optimal model for females had a natural cubic spline curve with three degrees of freedom and both BMI and age on the natural log transformed scale. Similarly, the optimal model for males was with BMI and age on the natural log transformed scale but with four degrees of freedom for the natural cubic spline curve.2, R2 from 1,000 simulated datasets, observed-fitted values, number of SNPs detected and computational time. The R2, in conjunction with interquartile range of variation of R2 estimated through simulations, clearly favour the SPLMM as the best model fit for the females. The R2 estimates from the simulations indicate that although the STLMM method has higher R2 for both females and males, the interquartile range is much larger for STLMM method, indicating the model fit is more data dependent than the other methods, which is not desirable for generalization to other cohorts. The conclusion for the males is not as simplistic as the R2 is largest for the STLMM, however with the considerably longer computational time and the larger deviation the fitted values are from the observed values indicates that this model might not be appropriate for large scale genetic studies. t for the STLMM). Several within-subject outliers (at the tails of the distribution) were not captured in all methods. However, the NLMM in particular had additional outliers not present with the other methods. The LMM and SPLMM methods both have some deviation from the normal distribution at the top end of the curve signifying that they under estimate the high BMI values. In contrast, there were an excess of extreme residual values at both ends when using the NLMM method indicating a poor fit for the data. It over estimates low BMI values and under estimates high values, thus under estimating within-individual variability and potentially leading to conservative inference about genetic associations. The male residuals displayed a similar pattern to females, although there were fewer obvious outliers. In addition, as there was less skewness in the males, the STLMM method deviated from the expected t distribution but in the opposite direction to that of the females, whereby the low values of BMI are underestimated. Based on model fit, all four methods were adequate in modelling childhood growth curves; however, the SPLMM was slightly better than the other methods at accounting for outliers and had the best model fit.Of the 17 SNPs, a likelihood ratio test indicated the LMM method detected one significant association in the females and three in males at the 5% level of significance, the STLMM method detected three in females and four in males, the SPLMM detected three in females and four in males and finally the NLMM method detected no significant SNPs in either females or males for the size parameter but 2 significant SNPs for the velocity parameter in males. Results of all 17 SNPs can be found in The obesity-risk allele score based on the genotypes at each of the 17 loci was normally distributed and showed an approximately linear association with BMI across childhood, based on the mean BMI  for each score at each age . When inth, 50th and 75th percentile) obesity-risk alleles. The growth curves in each of the genders show different patterns; females begin their trajectory smaller than males, they have an earlier rebound, and by the age of 18 years they are beginning to plateau at their potential adult BMI. In contrast, males go through puberty at a slightly later age resulting in their BMI continuing to increase at the age of 18 years. It is apparent that the genetic effect begins later for females, around seven and a half years (P = 0.03), than males at four years (P = 0.02).The current study has shown that of the four statistical methods evaluated, the semi-parametric linear mixed model (SPLMM) method was the most efficient for modelling childhood growth to detect modest genetic effects in the longitudinal pregnancy cohort study investigated. In addition, we have shown that there are potentially different genetic pathways leading to increased growth rate in males and females and that the obesity-risk-allele score increases both average BMI and rate of growth throughout childhood.There are several different statistical methods that can be used to model childhood growth. We selected four methods that would allow for adjustment of potential confounders, appropriately account for the correlation between the repeated measures, allow for incomplete data, and were computationally feasible in the context of candidate gene studies and GWAS. The evidence suggested that the SPLMM method does a better job at accounting for the variation in BMI growth than the LMM as it had a smaller residual standard deviation. The SPLMM and NLMM methods produce similar differences between observed and fitted values. The LME and STLMM methods have a larger range which indicates the prediction of BMI for each individual over time is worst using both of these methods, introducing bias whereby they over estimate low BMI values and under estimate high BMI values. As seen in the residual plots, there are a small number of outliers in this dataset, which are highly influential for both the LMM and STLMM and will effect there ability for accurate prediction. Furthermore, the estimates of skewness from the STLMM model were relatively large , which could be influenced by outliers and result in inaccurate predictions. Although residual plots indicate the STLMM method has the best fit to the data, it does not produce the most accurate predictions. Based on model fit, all four methods are adequate in modelling childhood growth curves; however the SPLMM produces the most accurate fitted values and can account for outliers.Of the 17 genetic variants associated with adult BMI and obesity risk that we investigated, the SPLMM method was able to detect a higher proportion of associations with childhood growth in both males and females than the other methods. The NLMM method performed poorly in both males (five significant tests of 51) and females (two significant tests of 51) consistent with it being more conservative than the other three methods. The STLMM method detected a number of genetic effects, however it was a more computationally intensive method, which would prove difficult in larger scale genetic studies such as genome-wide association studies. Moreover, it is not as flexible as the other methods in terms of extensions to evaluate gene-environment or gene-gene interactions. The current study provides evidence that the SPLMM method is the most effective method to detect genetic associations and allows the flexibility for extensions into large scale and more complex genetic analyses.post hoc power calculation using 1,000 non-parametric bootstrap simulations based on the Raine data indicated that this study had 97% power to detect the FTO loci rs1121980 with MAF = 0.41, which has one of the larger effect sizes on BMI, but still had 83% power to detect a more realistic smaller effect size like the BDNF SNP rs1488830 association in females with MAF = 0.21. In contrast, the power to detect the allele score, combining all risk alleles, was 95% in both males and females separately. The current study is the first to investigate, separately in males and females, an association between 17 published obesity-risk loci as an allele score and BMI trajectory throughout childhood and adolescence. Hoed et al Single genetic loci typically have small effects on complex diseases or explain only a small proportion of the variability in a quantitative trait; therefore, major increases in disease risk are expected from simultaneous exposure to multiple genetic risk variants. A A recent longitudinal study investigating the life-course effects of variants in the FTO gene and near the MC4R gene demonstrated that the effects strengthen throughout childhood and peak at age 20 before weakening during adulthood 2; NEGR1 0.011 kg/m2), while assuming a multiplicative model for the interaction. However, the power decreases rapidly with the minor allele frequency (FTO*MC4R) and effect size  to 4.6%. We therefore believe that our study was not appropriately designed to detect gene-gene or gene-environment interactions but instead think that meta-analyses of multiple cohorts might be a better way to tackle this problem.Further studies are now required to assess the validity of these findings and also extend them to perhaps focus on interactions between genes and the environment. Interactions, both gene-gene and gene-environment, are an important area of research that is critical for understanding the mechanisms underlying obesity. We performed a small simulation study using re-sampling techniques based on 1,000 non-parametric bootstrap data sets with replacement from the Raine data and calculating the power to detect a gene-gene interaction. Two SNP combinations were investigated to gather an understanding of the range of power in our study; these included the two most commonly reported BMI associated loci, FTO rs1121980 (MAF = 0.41) by MC4R rs17782313 (MAF = 0.23) as well as two loci with large minor allele frequency, FTO rs1121980 by NEGR1 rs2815752 (MAF = 0.38). Based on these simulations, our study had 58.0% power to detect an interaction between two SNPs with larger minor allele frequencies (FTO*NEGR1) and effect sizes Click here for additional data file.Table S2Results of genetic association analysis in females for all 17 SNPs in each of the four statistical methods.(XLSX)Click here for additional data file.Table S3Results of genetic association analysis in males for all 17 SNPs in each of the four statistical methods.(XLSX)Click here for additional data file.


MC1R variants modulate MITF transcription factor signaling, which in turn affects tumor cell proliferation, apoptosis, and DNA repair. The aim of this BioGenoMEL collaborative study in 10 melanoma cohorts was to test the hypothesis that inherited variants thereby moderate survival expectation. A survival analysis in the largest cohort (Leeds) was carried out adjusting for factors known to impact on survival. The results were then compared with data from nine smaller cohorts. The absence of any consensus MC1R alleles was associated with a significantly lower risk of death in the Leeds set  and overall in the 10 data sets  with some support from the nine smaller data sets considered together . The data are suggestive of a survival benefit for inherited MC1R variants in melanoma patients.Inherited  MC1R variants in survival.AJCC staging is of strong prognostic value for melanoma patients but only explains a proportion of the variance in survival. In some patients, there is evidence of a host immune response to the tumor both histologically and in the clinical manifestation of vitiligo, so that host/tumor interaction is postulated to be an additional factor which modifies prognosis. It is also likely that interaction between stromal tissues and cancer cells is important, genetically determined, and potentially modifiable. The new consortium BioGenoMEL seeks to bring together distinct patient cohorts to identify genes impacting on host/tumor interaction and therefore outcome, thereby improving our understanding of key biological pathways. This article is the first generated by BioGenoMEL as a consortium pooling data across multiple cohorts and provides evidence for a role for inherited MC1R) (ASIP)   and the ) (ASIP) . The MC1) (ASIP) , and sigMC1R variants are thought to increase melanoma risk as a result of consequent relative lack of eumelanin, but it is postulated that there are additional non-pigmentary effects (APEX1)  (BCL2) (DIA1) (APEX1), is important in DNA repair responses to reactive oxygen species (ROS) and oxidative DNA base damage -mediated DNA repair. The same group had earlier shown that MC1R activation mediated reduced oxidative DNA damage in melanocytes when exposed to UV radiation (Inherited  effects . The MIT (APEX1) , the celA, CDK2) , apoptos) (BCL2) , and inv) (DIA1) . The DNAe damage . Kadekaradiation .MC1R variants on DNA repair and apoptosis may contribute to susceptibility but our hypothesis is that there may be additional effects on survival. There are published data to support this view. Overexpression of DNA repair pathways in melanoma has already been reported to be associated with metastasis and poor patient survival (APEX1) on apoptosis may be relevant to melanoma: APEX1 using antisense resulted in apoptosis of melanoma cells in culture . BioGenoMEL has been created to collaboratively identify small, inherited effects on survival, which potentially have profound biological significance.We tested this hypothesis by looking at Breslow thickness and overall survival (OS) in 10 melanoma cohorts in relation to MC1R status and hair color (Table S2) as expected  in cases whose tumor was thicker than 0.75 mm over all 10 cohorts, adjusted for center. This association was weaker, and not statistically significant, when the model was also adjusted for site of primary thickness .There was a small but significant inverse association between The Kaplan–Meier curve looking at the relationship between hair color and survival in the Leeds cohort (in the 1397 cases in the cohort who had hair color and were eligible) is shown in MC1R score, and agouti (ASIP) status in the Leeds data set are shown in MC1R status was significantly associated with survival if considered as MC1R score , no consensus MC1R alleles versus one or more consensus alleles , and if MC1R score and ASIP were included together in a multivariable model .Results from the proportional hazards analysis of hair color, MC1R variants was associated with improved outcome . This result attained statistical significance with the addition of the Leeds data .MC1R alleles versus one or more consensus alleles) and in all 10 cohorts combined . This suggests that adjustment for Breslow thickness has only a small overall effect on the association of MC1R with outcome. To test this, we compared the results of the same analysis under a univariable model with one adjusted for Breslow thickness only. We found little difference in the estimated hazard ratio under both models (data not shown).In the analyses adjusted additionally for site of primary and Breslow thickness, we see similar patterns of association in the smaller nine cohorts , suggesting that adjusting for Breslow thickness may be obscuring the true relationship between MC1R and outcome in the Philadelphia data set even though in the overall analysis it does not.Individually, little change was observed in the magnitude and direction of hazard ratios for most of the cohorts with adjustment for site and thickness. However, in the Philadelphia cohort, the direction of effect was protective in the model adjusted for sex and age only  but deleterious in the model adjusted for sex, age, site of primary and Breslow thickness . There is a significant association between log Breslow thickness and MC1R score (Cochran’s Q test for heterogeneity P = 0.2) or the model comparing no consensus MC1R alleles versus one or more consensus alleles (Cochran’s Q test for heterogeneity P = 0.8). However, the clearest support for our hypothesis is seen in the second biggest study , and there was also some suggestion of a stronger effect in the Mediterranean countries compared with others.There is no evidence of significant study heterogeneity between the 10 cohorts in either the model using the MC1R variants on the association of MC1R score with outcome and found that this had little effect on our overall conclusions. Details can be found in Supporting information.We tested the effect of ignoring the rare MC1R gene on OS. We sought to validate these findings in nine additional cohorts within the melanoma genetics consortium BioGenoMEL (http://www.biogenomel.eu).This study reports a survival analysis of a large cohort of melanoma patients from the UK, which identified an effect of hair color and inherited variants in the R’MC1R variants in the 10 cohorts also shows significant differences among them. This was expected given the known variation in MC1R allele frequencies across Europe. The highest proportion with ‘R’ variants was seen in UK melanoma patients. High frequencies were also seen in the melanoma patients from Germany and Sweden. The proportion of ‘R’ variants in some studies was so low however, these had little individual power to test the hypothesis. Because we could only identify individuals with metastatic disease in a few of our cohorts, we could not comprehensively investigate the effect on the data of excluding individuals who presented with metastatic disease. We are not certain that omitting metastatic cases should be standard in survival analyses that use OS as an end point, given that it is known that there is considerable variation in the survival outcome of cases with stage III disease . In collaborative studies of this type, there will always be genetic variation between the populations, which is difficult to correct for; this study was therefore of particular interest because some of that genetic variation was evident as a difference in phenotype. While the main purpose of the study was to investigate MC1R. The survival analyses provided strong supportive evidence that increased numbers of MC1R‘R’ or ‘r’ variants have a protective effect on outcome, consistent with the hypothesis. Although the analysis based upon the number of variant ‘R’ or ‘r’ alleles is persuasive, there also appeared to be a deleterious effect of inheritance of one or more consensus MC1R alleles. Thus, these data suggest that in the presence of physiological signaling via the melanocortin receptor, biological processes downstream of MITF may result in poorer prognosis for melanoma patients. This is putatively through reduced apoptosis mediated by APEX1, greater double-strand break DNA repair, and/or increased cellular proliferation.The analysis of the data from the largest cohort benefitted from its size, but also SNP typing for the agouti locus as well as MC1R variants, and thinner tumors is also supportive of the view that reduced proliferative effects may be seen in the presence of variant MC1R. We considered the possibility that differences in thickness may also reflect differences in ease of clinical diagnosis for patients with different skin type but published data suggest rather that diagnosis may be more readily missed in the very fair skinned  and the Patient Information Advisory Group  approved the study. Population-ascertained incident melanoma cases were recruited to a case–control study in a geographically defined area of the UK (Yorkshire and the Northern region south of the River Tyne) (67% participation rate); 960 cases (aged 18–76 yrs) were recruited in the period from September 2000 to December 2005, as described previously . RecruitMC1R gene was sequenced, and in one center (Sweden), the most common variants were genotyped (see below).In nine centers, the whole MC1R gene, plus the surrounding untranslated regions, either as a single large amplicon or in smaller overlapping amplicons. Purified PCR products were sequenced using sequencing primers spanning the MC1R gene. Sequencing reactions were performed using the BigDye Terminator v1.1 Cycle Sequencing Kit  using standard sequencing conditions. The sequencing reaction products were run on an ABI prism 3130XL Genetic Analyzer (Applied Biosystems).For the Leeds samples, standard PCR techniques were used to amplify the entire 954-nucleotide coding region of the single-exon MC1R polymorphisms were identified by comparison with the MC1R consensus sequence (NCBI accession no. NM_002386). Primer sequences for PCR and sequencing are available on request. There was no centralized sequencing between groups, most groups had previously sequenced MC1R for other analyses addressed to understanding genetic susceptibility to melanoma  or CodonCode Aligner software . Compiled sequence data were double scored and checked by a second analyst. melanoma . DetailsIn the Leeds samples, one of 31 plates was genotyped in both Leeds and Leiden to test for errors in the genotyping process. There was 100% concordance between calls for these samples.MC1R variants in European populations  method, specific to 21 of the most common ulations .MC1R variants are numerous and are thought to have a variable impact on signaling through MITF, the analytic approach was considered carefully. We based the analysis upon a published and widely adopted classification system using the ‘r’, ‘R’ nomenclature first described by As r’ and 2 to ‘R’ variants. Thus, individuals with two copies of the consensus sequence (−/−) scored 0, and individuals with two ‘R’ variants (R/R) scored 4. It has been suggested previously that red hair color alleles may act in a recessive manner and that one fully functional copy of MC1R may be sufficient to provide normal function  with those who have one or more consensus alleles .The classification was turned into a numerical score in the range 0–4 by summing across the two alleles, giving a value of 1 to ‘function . TherefoMC1R variants have thinner tumors, a linear regression analysis was conducted, regressing the natural logarithm of Breslow thickness on the MC1R score, adjusting for center, using the ‘lm’ routine in r 2.10.1 .To test the hypothesis that individuals with MC1R status in the Leeds cohort, using the ‘survfit’ routine in the ‘survival’ package in r. To test for a significant different in outcome between the three hair color groups in the Leeds cohort, a log rank test was performed using the ‘survdiff’ routine in the ‘survival’ package in r.We defined survival time as the period between the date of surgical excision of the primary and date of death or last date of follow-up (at which point records were censored). Kaplan–Meier curves were drawn to investigate differences in OS with respect to hair color  and r. Hazard ratio estimates were calculated for the effect of hair color and MC1R on OS adjusted for Breslow thickness, sex, site of melanoma , and age of diagnosis. We also report models adjusted only for age of diagnosis and sex for the MC1R analyses. We did not adjust for tumor ulceration because of incomplete data for this variable across all the cohorts. We could not adjust for AJCC staging for the same reason. We tested the effect of adding stage in three cohorts for which we had data and we found that including stage did not change the association of MC1R with outcome. To test for study heterogeneity, we performed Cochran’s Q test. To do this, we first took relevant point estimates and standard errors for each study from the fitted Cox’s proportional hazards models. These data were then used to construct a meta-analysis assuming fixed effects using the ‘metaan’ function in Stata version 10, which reports the result of Cochran’s Q test.Multivariate survival analyses were performed using Cox’s proportional hazards model. Models were fitted using the ‘coxph’ routine in the ‘survival’ package in CDKN2A mutation carrier status in the 10 melanoma cohorts, but we expect that because the cohorts were not ascertained on the basis of family history that these would be rare and account for 2% of the cases (based on our own unpublished data). A modest number of cases with nodal or metastatic disease were included in the analysis; nodal primaries were assigned a Breslow thickness of 4 mm. We also excluded individuals with multiple primary melanomas and prevalent cases that were recruited in a proportion of the studies. It has been shown that introducing cases into a study a long time after diagnosis (left truncated data) can introduce bias into survival analysis . It is important that the proportional hazards assumption holds when including prevalent cases in this way (We excluded cases with thin tumors (0.75 mm or less) from all analyses on the basis that these cases have an excellent prognosis and add little information to the estimation of the effect of predictors of survival. We did not test for analysis . Each cethis way  so we diMC1R variants might be associated with survival was first tested by evaluating hair color and survival. Hair color is determined by a number of pigment genes, but red hair is predominantly (but not exclusively) determined by MC1R. Support for the hypothesis was seen, in that those with red hair had better survival  is a competitive agonist of melanocyte-stimulating hormone (MSH) which binds to the melanocortin receptor, so that inheritance of the risk allele at ASIP results in reversion to the null (pheomelanin) phenotype. Hence, it is postulated that inheritance of risk alleles at ASIP has a similar effect to variant MC1R on MITF signaling. Therefore, in the Leeds data set, where we had both MC1R sequence data and ASIP SNP genotyping (for the single nucleotide polymorphism rs4911442), we included the ASIP and MC1R data together in a separate model to investigate the combined effect of the two on survival.The agouti signaling protein  estimates across studies; HR estimates for The relationship between the age variable and the log hazard for survival was suspected to be nonlinear. Details of how we tested this are provided in Supporting information.