P-values method” (abbreviated as “conADA”), to analyze trios with/without unrelated controls. By first truncating the variants with larger P-values, we decrease the vulnerability of conADA to the inclusion of neutral variants. Moreover, because the test statistic is developed by conditioning on parental genotypes, conADA generates valid statistical inference in the presence of population stratification. With regard to statistical methods for next-generation sequencing data analyses, validity may be hampered by population stratification, whereas power may be affected by the inclusion of neutral variants. We recommend conADA for its robustness to these two factors .Detection of rare causal variants can help uncover the etiology of complex diseases. Recruiting case-parent trios is a popular study design in family-based studies. If researchers can obtain data from population controls, utilizing them in trio analyses can improve the power of methods. The transmission disequilibrium test (TDT) is a well-known method to analyze case-parent trio data. It has been extended to rare-variant association testing (abbreviated as “rvTDT”), with the flexibility to incorporate population controls. The rvTDT method is robust to population stratification. However, power loss may occur in the conditioning process. Here we propose a “conditioning adaptive combination of  Investigating rare causal variants [minor allele frequency (MAF) < 1%] can help uncover the etiology of complex diseases1235et al.The transmission disequilibrium test (TDT) is a well-known method used to analyze case-parent trios87et al. proposed a burden test (referred to as “Burden” hereafter) and a kernel test (referred to as “Kernel” hereafter) as analysis methods for pedigrees, in which population controls can be included in analysesIn addition to rvTDT, Schaid et al. fall into two categories: burden-based tests and kernel-based tests. However, in next-generation sequencing data analyses, many neutral variants may be included in a functional region. The power of the above-mentioned tests may be diluted because of the inclusion of neutral variants. In contrast to burden-based methods that test the genetic score after summing variant counts within a region, the “adaptive combination of P-values method” (abbreviated as “ADA”) combines P-values of more significant variants141516σ − MidP methodP-values according to Fisher’s combination of P-values formulaP-values from the combination formula, based on the “truncated product method for combining P-values”20P-value truncation threshold is not easy. ADA therefore considers variable P-value truncation thresholds during permutation, and adaptively finds the optimal threshold to truncate larger P-values that possibly arise from neutral variants. ADA has been extended to family data analysisDepending on how information from multiple variants is aggregated, the above-mentioned rvTDT and the approaches proposed by Schaid Depending on whether the test statistics are constructed by conditioning on parental genotypes, the above-mentioned methods can be categorized as conditioning approaches or unconditioning approaches. The rvTDT tests (including burden-based and kernel-based tests) and the family-based association testP-values method” (abbreviated as “conADA”). Because conADA adaptively finds the optimal threshold to truncate larger P-values that possibly arise from neutral variants, it is robust to the inclusion of neutral variants. This characteristic makes it more powerful than other conditioning approaches, such as the rvTDT testsTo develop a powerful method that is also robust to population stratification, we propose a “conditioning adaptive combination of We used the Cosi programWhen evaluating power, we considered two proportions of causal variants: “smaller” and “larger”. We specified 25% and 75% of rare variants (with pooled MAF ≤ 0.01) as causal variants, respectively.We considered two situations for causal variants: (I) all were deleterious, (II) 50% were randomly chosen as deleterious, and the other 50% were protective. The per-locus population attributable fraction (PAF) was assumed to be 0.01 and 0.02 for situations (I) and (II), respectively. The statistical power is generally low for all methods under situation (II). For a meaningful comparison, we assigned a larger per-locus PAF to situation (II).G, the probability of disease is G were 0, 1, or 2, representing the numbers of minor alleles. Following the simulation setting in the rvTDT paperβ0 was specified as β incorporates the effects of variants on disease, and its ith element is η and MAFi are the PAF and frequency of the ith variant, respectively. The setting of βi s was derived from the relationship between the relative risk of exposure and PAF , 50% of causal variants were protective, and their βi s were <0. A total of 500 case-parent trios and 500  unrelated controls were generated according to the above-mentioned model. The source populations for both trios and unrelated controls comprised 0:100 , 20:80, 50:50, 80:20, or 100:0  ratios of Europeans to Africans, respectively.The genotypes of a subject were formed by randomly selecting two haplotypes from the haplotype pool. For a subject with a genotype-score vector et al.Furthermore, we evaluated the performance of all methods given a substantial difference in the source populations of trios and controls. Following Jiang Considering the smaller proportion of causal variants, 25% of rare variants (with pooled MAF ≤ 0.01) were randomly specified as causal. Although 25% was not low, most of the causal variants were not observed in the sample of 500 trios and 500  unrelated controls. In the African samples, ~4 causal loci (with pooled MAF ≤ 0.01) were observed in the analysis marker set that contained ~87 loci (with pooled MAF ≤ 0.05), and the proportion of observed causal variants in the analysis marker set was approximately 4.6% Considering the larger proportion of causal variants, 75% of rare variants (with pooled MAF ≤ 0.01) were randomly specified as causal. Although 75% was a large percentage, most of the causal variants were not observed in the sample of 500 trios and 500  unrelated controls. In the African samples, ~12 causal loci (with pooled MAF ≤ 0.01) were observed in the analysis marker set that contained ~87 loci (with pooled MAF ≤ 0.05), and the proportion of causal variants in the analysis marker set was approximately 13.8% In the second part of our simulation study, we only analyzed the 500 trios, mimicking situations in which population controls cannot be obtained. The trio-parent population comprised 0:100 , 20:80, 50:50, 80:20, or 100:0  ratios of Europeans to Africans, respectively. Similarly, we considered the two situations for causal variants: (I) all were deleterious, (II) 50% were specified as deleterious, and the other 50% were protective. The per-locus PAF was assumed to be 0.01 and 0.02 for situations (I) and (II), respectively. The statistical power is generally low for all methods under situation (II). For a meaningful comparison, we assigned a larger per-locus PAF to situation (II).http://homepage.ntu.edu.tw/~linwy/ADA.r) were used to implement these statistical tests. The P-value of ADA was assessed with 1,000 permutations. The P-value of conADA was obtained with the above-mentioned sequential Monte Carlo permutation27jth genetic variant was Beta, where MAFj was the frequency of the jth variant. The P-values of SKAT and SKAT-O were obtained by the Davies methodWe let conADA(PC) be the conADA method for analyzing trios with population controls. In addition to conADA(PC), the tests under comparison included TLC(1), TLC(MAF), TLC(PC), TK(1), TK(MAF), TK(PC)P-value of conADA(MAF) was assessed with the above-mentioned sequential Monte Carlo permutation methodjth genetic variant was Beta, where MAFj was the frequency of the jth variant.We let conADA(MAF) be the conADA method for analyzing trios without population controls. When only trios were analyzed, TLC(PC) and TK(PC)By setting the PAF at exactly 0% for all variants, we assessed type-I error rates with 10,000 simulated data sets.P-value truncation thresholds, i.e., θ1 = 0.05, θ2 = 0.06, θ21 = 0.25. The results for 21 thresholds were similar to those for 11 thresholds .When the ethnicity compositions in trios and in population controls were the same: When the ethnicity compositions in trios and in unrelated controls were the same, all the 12 tests were valid; their type-I error rates matched the nominal significance levels . In thatWhen the ethnicity compositions in trios and in population controls were NOT similar: Given a substantial difference in the source populations of trios and controls, only seven conditioning approaches were valid and their type-I error rates were listed in When unrelated controls could not be obtained, P-value truncation thresholds, i.e., θ1 = 0.05, θ2 = 0.06, θ21 = 0.25. Its performance was very similar to conADA with 11 thresholds. Therefore, we only used 11 P-value truncation thresholds  for conADA hereafter.When the ethnicity compositions in trios and in population controls were the same: Given a larger proportion of causal variants: When the ethnicity compositions in trios and in unrelated controls were the same, With an increasing number of population controls, all tests had increasing power, except TLC(1), TLC(MAF), TK(1), and TK(MAF). These four tests did not utilize the information from population controls; therefore, their performance did not vary with the number of controls. Comparing the burden-based (or linear combination) tests  and the kernel-based tests  from the rvTDT packageAmong the six rvTDT tests, in general, TLC(MAF) had the highest power when all causal variants were deleterious  and TK(MAF)] was more powerful than unweighting [TLC(1) and TK(1)]. In reality, scientists have found that the majority of functional variants are very rare (MAF < 0.5%) and that rare variants are more likely to have larger predicted functional impacts than common variantsConsidering the seven conditioning tests, conADA(PC) given a larger number of PC had comparable power with TLC(MAF) when all causal variants were deleterious  as causal variants. Given the smaller proportion of causal variants, conADA(PC) became the most powerful test among the seven conditioning tests  because Among the six rvTDT testsP-values of conADA(PC) were obtained from 100–10,000 permutations, it was the most computationally intensive method. We also listed the average computation time for conADA(PC) based on 10–1000 permutations. When the nominal significance level was specified as 0.01 or 0.05, conADA(PC) with 10–1000 permutations was valid in the sense that its type-I error rates matched the nominal significance levels (results not shown). In this situation, using 10–1000 permutations for conADA(PC) would save a significant amount of time.When the ethnicity compositions in trios and in population controls were NOT similar: Given a larger proportion of causal variants: When the source populations of trios and controls were not identical, only the seven conditioning tests were valid; thus, only they were considered in power comparisons. Given a smaller proportion of causal variants: Comparing the burden-based tests {or “linear combination tests”, such as TLC(1), TLC(MAF)GAW 18 data sets contained 20 Mexican-American pedigrees that were selected from two San Antonio-based family studies: SAFHS33There were 21 case-parent trios and 90 unrelated controls extracted from the 20 pedigrees. Although these 90 unrelated controls were also drawn from the 20 Mexican-American pedigrees, they were genetically unrelated to each other or to the members of the 21 trios. Formal assessment of the relatedness was done with the function “pedigree.unrelated” in the R package “kinship2” (version 1.6.4)http://www.ensembl.org). Totally, there were 38,091 genes or regions. Similar to our simulation study, the analysis marker set for each gene/region was formed by including all the variants with MAF ≤ 0.05.In the GAW18 data sets, only genotypes for odd numbered chromosomes were distributed. Following Feng and ZhuP-value of conADA(PC) was obtained with the sequential Monte Carlo permutation2 and 106, respectively. The 11 candidate P-value truncation thresholds were θ1 = 0.10, θ2 = 0.11, θ11 = 0.20. The R code to analyze the GAW 18 data set can be downloaded from http://homepage.ntu.edu.tw/~linwy/conADA.r.From our simulation study, we found that the seven conditioning tests [including the six rvTDT tests and conADA(PC)] were valid even when the ethnicity compositions in trios and in population controls were not similar. Therefore, we analyzed the GAW 18 data with these seven robust tests. The R package rvTDT-1.0P-values. We define singletons (doubletons) as alleles present only once (twice) in a data set. In conADA, after truncating variants with larger P-values, no singletons were left in any simulation data set, whereas ~6.2% of the remaining variants were doubletons. The conADA method removed all singletons from the analysis because of their larger P-values. Therefore, this method cannot detect causal variants that appear as singletons in a data set. In reality, it is difficult to distinguish these causal variants from random genetic variation, and accurate functional predictions of such variants are important to prioritize them as likely to be causalThe conADA method truncates variants with larger Case-parent association tests are robust to the bias introduced by population substructure. If unrelated controls (from the same source population of trios) can be obtained, utilizing them in rare-variant case-parent association studies can enhance the power of statistical methods, such as TK(PC) and TLC(PC) in the rvTDT packageP-values, which are more likely to be causal. The optimal P-value truncation threshold is searched through permutations, and therefore requires more computation time. The strength of conADA(PC) is its robustness to population stratification and the inclusion of neutral variants. However, the weakness is its longer computation time compared with other methods. Because analytical P-values cannot be obtained, it is time-consuming to perform conADA given a genome-wide significance level (The conADA(PC) method adaptively combines association signals of variants with smaller et al.As mentioned by Feng and Zhuet al.Although TLC(PC), TK(PC), and conADA(PC) used the population controls with a very different admixture proportion from that in trios, they maintained test sizes even in such an extreme admixture scenario . Let lth variant of the ith trio. Under the null hypothesis of no association between the lth variant and disease, the test statisticLet χ2 distribution with 1 degree of freedom.asymptotically follows L loci in the chromosomal region of interest. We calculate the statistic in P-values p1, p2, pL for the L loci, respectively. In conADA, we exclude markers with larger P-values, which are more likely to be neutral. The optimal P-value truncation threshold is determined by permutation. We consider 11 candidate P-value truncation thresholds, θ1 = 0.10, θ2 = 0.11, θ11 = 0.20. Using a wider range of P-value truncation thresholds, for example, θ1 = 0.05, θ2 = 0.06, θ21 = 0.25, will not contribute a noticeable power gain to conADA (shown in simulation results). Summarizing the markers with P-values smaller than θj (the jth truncation threshold), the significance score isConsider there are I [·] is an indicator variable coded as 1 or 0, and wl is the weight given to the lth marker.where lth marker is set at Beta , where MAFl is the variant frequency for the lth marker calculated from parental genotypes. The Beta density function with the two parameters 1 and 25 is the default weighting scheme of SKAT and SKAT-O27When population controls cannot be obtained, the weight given to the wls  in Eq. (2) are specified as:When population controls can be obtained, and the genotypes of the controls and the parents of trios are as summarized in This weighting scheme is based on the Armitage trend testP-values. Like most rare variant association tests, conADA is used to analyze a gene or a small chromosomal region. We therefore assume no recombination occurs within the region of interest. As mentioned by Zhang et al.et al.observed diplotype vs. the offspring has unobserved diplotype. The occurrence of observed diplotype means the offspring has the two haplotypes originally transmitted from the parents, one from the father and the other from the mother. The occurrence of unobserved diplotype means the offspring has the two originally non-transmitted haplotypes, one belonging to the father and the other belonging to the mother. Under the null hypothesis, the offspring has a probability of 1/2 to exhibit the observed diplotype or unobserved diplotype. For a set of n trios, there are 2n enumerations in totalobserved diplotype or unobserved diplotype to each child. If a child is selected to have the observed diplotype, his/her permuted genotype scores will remain the same as his/her unpermuted genotype scores. If he/she is selected to have the unobserved diplotype, his/her permuted genotype score at the lth variant will beThen we use the sequential Monte Carlo permutationwhere B permutations, we compare Sj  with P-value truncation threshold for the B permuted samples), and the P-value corresponding to Sj is P-value for the observed sample (MinP) is compared with the minimum P-values for the B permuted samples (MinP(1), MinP(2), MinPB), and the “adjusted P-value” is calculated as Bmin = 100 and Bmax = 10000, respectively. The permutation process will be terminated if B = Bmax, and it will not be terminated if B < Bmin. Following Besag and Cliffordc = 0.25, meaning that the standard error of Padjusted is approximately 25% of the P-value.If we perform How to cite this article: Lin, W.-Y. and Liang, Y.-C. Conditioning adaptive combination of P-values method to analyze case-parent trios with or without population controls. Sci. Rep.6, 28389; doi: 10.1038/srep28389 (2016).


Logistic regression is usually applied to investigate the association between inherited genetic variants and a binary disease phenotype. A limitation of standard methods used to estimate the parameters of logistic regression models is their strong dependence on a few observations deviating from the majority of the data.We used data from the Genetic Analysis Workshop 18 to explore the possible benefit of robust logistic regression to estimate the genetic risk of hypertension. The comparison between standard and robust methods relied on the influence of departing hypertension profiles (outliers) on the estimated odds ratios, areas under the receiver operating characteristic curves, and clinical net benefit.Our results confirmed that single outliers may substantially affect the estimated genotype relative risks. The ranking of variants by probability values was different in standard and in robust logistic regression. For cutoff probabilities between 0.2 and 0.6, the clinical net benefit estimated by leave-one-out cross-validation in the investigated sample was slightly larger under robust regression, but the overall area under the receiver operating characteristic curve was larger for standard logistic regression. The potential advantage of robust statistics in the context of genetic association studies should be investigated in future analyses based on real and simulated data. Hypertension is a common chronic medical condition characterized by elevated arterial blood pressure. High blood pressure is associated with an increased risk of stroke, heart attack, and other serious diseases. Age, gender, tobacco smoking, alcohol consumption, and high body mass index constitute established risk factors for hypertension . A genetThe relationship between inherited genetic polymorphisms and a binary response variable (with/without hypertension) can be investigated using logistic regression models that simultaneously consider the effects of multiple risk factors. Standard methods used to estimate the parameters of logistic regression models--for example, iteratively reweighted least squares--are limited by their dependence on a few observations departing from the majority of the data. This contrasts with the purpose of genetic risk models that aim to predict a particular health outcome that holds for the bulk of individuals, and to identify persons with a deviating high risk of disease. We use data from the Genetic Analysis Workshop (GAW18) to explore the possible benefit of robust parameter estimates in logistic regression models for the genetic prediction of hypertension risk.The analysed data  were derived from 142 unrelated individuals who participated in the San Antonio Family Heart or Family Diabetes/Gallbladder studies. Longitudinal information on hypertension, age, gender, and current tobacco smoking was measured up to 4 times per individual; the present analyses relied on the first available measurement. Further information is provided in several articles -12.The original data was filtered according to the following criteria: (a) at least 1 measurement with complete information on hypertension and age, (b) monomorphisms were excluded and each polymorphism had to be represented by at least 2 individuals, (c) individuals with more than 5% missing genotypes were excluded, and, finally, (d) variants with missing data in any individual were removed.2 tests. Covariates significantly associated at the 5% confidence level entered the intercept-only model to build the baseline model. Subsequently, standard logistic regression (iteratively reweighted least squares) was used to identify possible hypertension-associated single-nucleotide polymorphisms (SNPs) with minimal deviance, taking into account associated covariates. The deviance is defined as minus twice the logarithm of the likelihood. Genotypes were coded according to an additive penetrance model; that is, 0, 1, and 2. Departing observations (outliers) according to standard logistic regression were identified based on the Cook's distance in the baseline model. The Cook's distance for observation i is defined asThe relationship between hypertension and age, gender, and current tobacco smoking was first investigated by χq explanatory variables.where To investigate the possible benefit of robust parameter estimates in logistic regression, model coefficients were also estimated by solvingwhere th diagonal element of the matrix This estimator is based on a quasi-likelihood, asymptotically normally distributed and Fisher consistent . The objβ and where Our comparison of the performance of standard and robust logistic regression was based on different statistics. First, standard and robust estimates of age effects were used to exemplify the potential influence of departing observations. Because of a different handling of outliers, it was expected that different age-genotype models were selected under standard and robust logistic regression. Consequently, the areas under the receiver operating characteristic curves (AUCs) were subsequently compared in order to investigate the discriminative performance of the selected models. Comparisons were conducted for the complete data set and after exclusion of potential outliers.In addition, concordance, sensitivity, specificity, clinical net benefit, and AUCs were estimated for age-genotype models using a leave-one-out cross-validation approach . Concordc is the chosen threshold for allocating an individual to the cases based on the logistic regression probability estimate. Note that the net benefit depends on the hypertension prevalence in the study population. The standard and robust logistic regression models were also compared based on the integrated discrimination index (IDI) estimated by cross-validationwhere where controls . This incontrols .2 tests revealed no influence of gender (p = 0.95) and tobacco smoking (p = 1.00) on hypertension risk. Hence, only age was included in the logistic regression models as covariate. Filter criteria resulted in 130 individuals (43 cases and 87 controls) with complete genotype and phenotype information. The age of the individuals ranged between 20 and 95 years with a median age of 52 years. The total number of measured SNPs on chromosome 3 in the investigated GAW18 data set was 35,045.χA plot of Cook's distances under the age-only standard logistic regression model revealed several observations Figure  that depULK4 gene as the variant that most improved the model fit. Robust logistic regression identified SNP rs11918360 in RP11-408H1.3 as the variant with the strongest association signal. Under both standard and robust regression, model selection clearly favored the 2 identified SNPs as represented in Figure 2 rbetween SNP rs3934103 and SNP rs11918360 was 0.003.Standard logistic regression identified SNP rs3934103 located in the Table Table Present results confirmed that single individuals (1/130 = 0.8% of the observations) with a departing risk of hypertension may substantially affect the overall risk estimates in the baseline model, causing up to an 11.2% change in the estimated excess risk of hypertension per year according to standard logistic regression in the present exercise.The identification of outliers is relatively straightforward using routine diagnostic plots, but outlier management is extremely challenging. For example, the specification of thresholds for outlier definition is often arbitrary. Robust statistics aim to generate estimates that hold for the majority of the population using complete data. The unequal weighting of outliers by standard and robust regression resulted in prediction models that included different genetic variants.Although robust estimates of age effects and AUCs for age-genotype models were less sensitive to outliers than standard estimates in the investigated sample, cross-validation AUCs based on standard and robust logistic regression, as well as IDI, were almost identical. The other investigated performance characteristics  were equal or better for robust logistic regression around the probability that reflects the case-control ratio.ULK4 gene. It was previously shown that variants in this gene are associated with hypertension [2 rvalues 0.83, 0.73, 0.83, and 0.83, respectively) with the associated SNP rs3934103.The standard logistic regression model selected 1 variant in the rtension . Among oPreliminary findings suggest some advantage of robust statistics in the context of genetic association studies. However, present results were limited to a given sample size, as well as to particular genetic effect sizes and proportions of outliers. Additional analyses based on both real data and more general simulated scenarios should be conducted to validate initial findings.The authors declare that they have no competing interests.MK analysed and interpreted the data, created figures and tables, searched literature, and drafted the manuscript. CL identified relevant literature, supported data analysis and interpretation, and reviewed the manuscript. BP and MKa supported data analysis and interpretation and reviewed the manuscript. CF and UH supported interpretation and reviewed the manuscript. JLB formulated study goals, supported data analysis and interpretation, and reviewed the manuscript. All authors read and approved the final version.


Genetic Analysis Workshop 18 provided a platform for evaluating genomic prediction power based on single-nucleotide polymorphisms from single-nucleotide polymorphism array data and sequencing data. Also, Genetic Analysis Workshop 18 provided a diverse pedigree structure to be explored in prediction. In this study, we attempted to combine pedigree information with single-nucleotide polymorphism data to predict systolic blood pressure. Our results suggested that the prediction power based on pedigree information only could be unsatisfactory. Using additional information such as single-nucleotide polymorphism genotypes would improve prediction accuracy. In particular, the improvement can be significant when there exist a few single-nucleotide polymorphisms with relatively larger effect sizes. We also compared the prediction performance based on genome-wide association study data  and sequencing data . The experimental result showed that inclusion of low frequency variants could not lead to improvement of prediction accuracy. Genomic prediction is an important problem in genetics. It aims at predicting a phenotype outcome based on information from genetic markers, population, pedigree structures, and other relevant covariates. Recent studies suggest that genomic prediction based on genome-wide case control data  has limited prediction accuracy . First, Genetic Analysis Workshop 18 (GAW18) provides both genotyping data and sequencing data of approximately 1000 samples from 20 pedigrees. This brings a good opportunity to evaluate genomic prediction from the following 2 perspectives:1. How do we integrate the pedigree structures and genome-wide dense markers for evaluating the power of genomic prediction?2. Can we improve prediction accuracy by including low-frequency variants?L1 estimation procedure has been proposed for LMM, named "LMMLasso" [Some pioneering studies suggested that integration of phenotype information from relatives and informative markers can improve prediction accuracy -7. LineaMMLasso" . Very reMMLasso" . Howevern be the sample size. We consider the following LMMLet β is the vector for regression coefficients of the covariates; α is the coefficient vector for p single-nucleotide polymorphisms (SNPs) (fixed effects); u is the random effect from e is the residual error with variance K is the genetic relatedness matrix that describes the pedigree structure among the individuals. The covariance matrix K can be constructed according to the known pedigree information or estimated from genome-wide SNP information.where d+p+2>n,ie, the number of parameters exceeds the number of samples . To overcome this difficulty, we use penalized LMM to perform model selection [α: t is some constant. First, we can write down the log-likelihood of LMM (1) by integrating out u and e asThere is a difficulty in applying the model when election ,9. Consiwhere To optimize the penalized log-likelihood function, we adopt an alternating strategy as follows:α, we can treat β, δ) using some recent algorithms proposed to efficiently solve the optimization, such as FastLMM [Step 1: For fixed  FastLMM  and GEMM FastLMM .β, δ), the problem (3) becomesStep 2: For fixed . As in Friedman et al [λ value such that all α equal to zero. We denote this λ as λ values such that k is the length of the λ sequence. Let k = 20, and choose the best λ value by cross-validation.Because the optimization problem (3) is not convex, a good initial point will help to find a better solution. We started at an et al , we usedFor the GAW18 data set, there are 959 samples from 20 pedigrees. In our study, we considered systolic blood pressure (SBP) as the quantitative trait of interest. Among all the samples, 849 individuals had at least one blood pressure measurement. We considered the first nonmissing measurement of SBP and used its log-transformed value as the response G, we focused on genetic markers on chromosome 3. The reason we chose chromosome 3 was that we identified a significant signal in the gene MAP4 by association tests on all 200 simulated SBPs. This signal was significantly stronger than the genetic background signal. We expected our method could automatically detect it and include it as a fixed effect.For the genotype data matrix r2 = 0.9, leaving 103,020 SNPs for chromosome 3 , which resulted in 33,248 SNPs for chromosome 3 . The reason was that the covariate "age" contributed more for the real phenotypes. If we did prediction for both the simulated and real phenotypes without "age," we could observe a slightly better performance for the simulated phenotype.Based on the estimated variance components , it seemed that we should do a better job for the simulated phenotype. From Figures R2 = 0.125 for MAP4 (the estimated effect size of rs11711953 is approximately −7.25 with the SE 1.46). For the real phenotype, although the performance was improved as a few genetic markers are included, the improvement was minor (R2 increases approximately 1%). By checking the association signals, we were unable to detect significant associations.Let us take a close look at the result using GWAS data. We used the correlation between the true value and predicted value to measure the accuracy. For the simulated phenotypes, the accuracy is around R2 = 0.285. Compared with the results of GWAS data, the prediction was not improved by using sequencing data.For prediction using sequencing data, the model performed almost the same as that of GWAS data based on the simulated phenotypes. For the real phenotypes, the best accuracy achieved was close to In this study, we show that our model can integrate information from pedigree structures and genetic markers. This model will work well when there are a few markers with relatively large effect, as suggested by the analysis of the simulated phenotype. The reason is that the information from the pedigree structure is a global average of signals from the genetic background and the shared environmental influence. When there are some large effects that are different from the genetic background, it is better to extract them and consider them as fixed effects. In this way, the markers with larger effects can be treated locally. If all markers have similar effect sizes, the proposed method can only have minor improvement, as suggested by the analysis of the real phenotype.In this study, we also compared the prediction performance based on GWAS data  and sequencing data . The experimental result showed that inclusion of low-frequency variants could not lead to improvement of prediction accuracy. To significantly improve the prediction accuracy, the difficulty caused by polygenicity of complex traits needs to be addressed; that is, many small effects should be estimated more accurately. This implies that a larger sample size is needed. Besides the recruitment of more samples, an economic way is to combine multiple GWAS data sets of correlated traits. The underlying assumption is that these correlated traits may share some genetic factors. By borrowing information from each other, it is expected that the prediction accuracy can be dramatically improved.Regarding the computational time, based on our current MATLAB implementation, we can finish a 10-fold cross-validation for the sequencing data in two hours.In this study, genetic prediction can be improved by combining pedigree structure and information from genetic markers. We use a penalized LMM for this purpose and we show that it is computationally feasible. The experiment result based on the GAW18 data suggests that the main prediction power comes from the pedigree information. The additional improvement could be substantial if the effect sizes of a few genetic markers are noticeable, otherwise, could be minor. Integration of multiple GWAS data sets for genomic prediction may be a promising direction.The authors declare that they have no competing interests.CY and HZ designed the overall study; CY, CL, MC, XC and LH conducted statistical analyses; and CY and HZ drafted the manuscript. All authors read and approved the final manuscript.


For this reason, we conducted an analysis of rare variants informed by tests of single-marker association at loci with common variants. We identified highly significant common variants within chromosome 3, as well as rare variants around these locations. Based on a predetermined window size, we then analyzed these rare variants with the C-alpha test to determine significant associations with hypertension. We found significant rare variants around common variants; however, the C-alpha test was sensitive to the specified window size. When comparing markers in genes to markers not in genes, we found that markers not in genes had more significant C-alpha test  Whole genome sequencing provides geneticists and statisticians with the genome data necessary to attribute genetic variants with specific phenotypes such as high cholesterol, cancer, and diabetes. Many genome-wide association studies (GWAS) link phenotypes to genetic variants through logistic regression analyses. These single-marker association tests perform well for common variants (CVs). However, for rare variants (RVs), defined here as having minor allele frequencies (MAFs) of less than 0.05, single-marker association tests lack the power to detect significant associations .Complex phenotypes have been found to be poorly explained by CVs. A hypothesis has emerged that RVs may contribute more significantly to disease heritability than CVs . Howevero: i p= 0pHa: i pfollows a mixture distribution, with some variants detrimental (i p>0p), some neutral, and some protective (i p<0p)Hi pis the proportion of the rare allele at the ith RV occurring in cases versus controls. 0 Pis equal to the proportion of cases among all subjects, where a similar proportion of the rare alleles at the RVs is expected to occur at random in the cases and the controls. A small p value indicates that the distribution of the rare alleles is not random.where A combination of protective, harmful, and neutral variants is likely associated with hypertension. Longitudinal hypertension data and whole genome sequence data were provided to the authors as part of the Genetic Analysis Workshop 18 (GAW18). The data set is from the Type 2 Diabetes Genetic Exploration by Next-generation sequencing in Ethnic Samples (T2D-GENES) Project 2, which was designed to identify RVs associated with hypertension and provided an opportunity to test a novel method for RV analysis.The hypothesis of interest was to see whether significant RV associations occurred near CVs, and whether or not these associations were affected by the CVs occurring in genes versus not in genes. The RV analysis thus was related to and based off of single-marker association tests. Highly significant CVs were identified within chromosome 3, as were RVs around these locations. Based on a predetermined window size, these RVs were then analyzed with the C-alpha test to determine significant associations with hypertension. Markers in genes were compared to markers not in genes.Based on the hypothesis of interest, the analysis consisted of the following steps: data clean-up, single-marker association tests, and the RV analysis. The following sections provide details for each of these methods.n = 103). The real data rather than the simulated GAW18 data was used in order to not bias the results toward more significance in genes versus not in genes.From the original GAW18 sequenced chromosome 3 file, only columns with the single-nucleotide polymorphism (SNP) IDs and genotype information for each subject were retained. Base-pair locations that appeared to have 3 or more alleles were excluded from further analyses. Only fully sequenced data from unrelated individuals was included in this analysis (p <0.01) were excluded from the analysis.If a subject had hypertension listed for one or more of the four doctor visits, the subject was coded as 2 for affected. Otherwise, a subject was coded as 1 for unaffected. The covariates of interest were gender (M/F), age at first visit, smoking (Yes/No), and blood pressure medication (Yes/No). Similarly to how hypertension was coded, smoking was coded as 2 if the subject was listed as smoking for any of the 4 doctor visits, and subjects were coded as 2 if the subject was listed as using blood pressure medication during any of the 4 visits. Markers that did not satisfy the Hardy-Weinberg equilibrium  of the gene. Gene locations were based on information from GeneCruiser .p values that accounted for population stratification in permutations of case and/or control status [r2 ≤0.01 and no missing alleles was obtained. A total of 94 subjects were included in the reduced set of SNPs, of which 60 were cases and 34 were controls. The first 5 eigenvectors from a principal components analysis, along with the same covariates from above, were used to generate 1000 biased urn samples based on Fisher's noncentral hypergeometric distribution [Window sizes of 1 kilobase (kb), 5 kb, and 25 kb were examined around these CVs for RVs. RVs were defined as having a MAF <0.05. These RVs were then extracted and a C-alpha test was calculated for each window size to determine the sensitivity of arbitrary window sizes. Singletons were removed from the analysis. The biased urn method was used to obtain C-alpha test l status . From thribution .Data analyses were performed with PLINK version 1.07 and the R packages AssotesteR and Epstein et al's modified BiasedUrn package . All datp value for association test <0.05), and approximately 1% were located in genes. Table p values for both the association test and the C-alpha test for the top 5 markers in genes and the top 5 markers not in genes. The C-alpha test is sensitive to the specified window size, and for some markers an increase in window size corresponded to an increase in p values. For marker rs34366649, the opposite effect was seen, where the p value decreased as window size increased.A total of 408,343 CVs were analyzed; 13,017 were nominally significant .On average, markers not in genes were more significant than markers in genes. Fisher's exact tests comparing significance for the 1-kb, 5-kb and 25-kb windows were not significant , and this may have biased the results. In addition, the p values from the single-marker association tests were underpowered . However, the p values from the single-marker association tests were comparable in magnitude in genes versus not in genes. Also, among the top 10 most significant SNPs, 5 were located in genes and 5 were located not in genes, which minimized bias in the results. Future research can investigate in more depth whether RVs occur more in genes versus not in genes.When comparing markers in genes to markers not in genes, we found that markers not in genes had more significant C-alpha test The authors declare that they have no competing interests.AF, AW, and LS designed the overall study. AF conducted statistical analyses and drafted the manuscript. AP and LS conducted data cleaning. All authors read and approved the final manuscript.


We analyzed the genetic effects and heterosis of yield and yield components in the F1 hybrids and parents in four environments via the additive-dominance genetic model. Yield and yield components of the CSSLs were controlled by combined additive and dominance effects, and lint percentage was mainly controlled by additive effects, but boll weight, boll number, seedcotton yield and lint yield were mainly controlled by dominance effects. We detected significant interaction effects between genetics and the environment for all yields traits. Similar interactions were detected between two CSSL populations (Pop CCRI 36 and Pop CCRI 45). Significant positive mid-parent heterosis was detected for all yield traits in both populations, and significant positive better-parent heterosis was also detected for all yield traits except lint percentage. The differences among parents were relatively small, but significant heterosis was detected for yield and yield components. Therefore, the relationship between heterosis and genetic distance for yield traits is complicated and requires further study. These CSSLs represent useful tools for improving yield and yield components in cotton.We hybridized 10 chromosome segment substitution lines (CSSLs) each from two CSSL populations and produced 50 F Gossypium spp.) is one of the most important cash crops and the leading fiber resource for the textile industry worldwide. Most global cotton production involves two cultivated species, G. hirsutum and G. barbadense. G. hirsutum, also known as Upland cotton, represents 95% of global cotton fiber production [G. barbadense, another important tetraploid cultivated species, has excellent fiber quality and disease resistance compared to Upland cotton, which exhibits high yield but only moderate fiber quality [Cotton  and Pop CCRI 45 (CCRI45 × Hai1 BC4F3:5). We randomly selected 10 CSSLs that each line has at least 3 chromosome segments, the segements of Hai1 are anchored. Each of these populations as parents for hybridization and produced 50 F1 hybrids according to North Carolina Design II. We measured and analyzed the genetic effects and heterosis of yield and yield component traits via the additive-dominance genetic model. The objectives of this study were to determine the genetic mechanism underlying yield and yield components of the CSSLs. The results of this study will facilitate the utilization of CSSLs in future cotton breeding programs.In this study, we developed two sets of CSSLs, Pop CCRI 36 (CCRI36 × Hai1 BC5F3:5): The F1 population was generated by a cross using early-maturing variety CCRI36  as the recipient and Hai1 (Gossypium barbadense) as the donor parent. The cross was performed in the summer of 2003 at the experimental station of the Institute of Cotton Research of CAAS, Anyang, Henan Province, China. The development scheme for the CSSLs was as described [1 (CCRI36 × Hai1) progeny were backcrossed to CCRI36 to produce BC1 in the winter of 2003 in Sanya, Hainan province. The BC1 progeny were backcrossed to CCRI36 to produce BC2 in the summer of 2004 in Anyang , and advanced backcross generations up to BC5 were similarly obtained. A total of 133 BC5 family lines were selfed and individually planted to produce BC5F2 in the summer of 2007 in Anyang . BC5F2 progeny were selfed and individually planted to generate BC5F3 in the summer of 2008 in Anyang . A total of 2,660 plants from 133 BC5F3 families were planted in the summer of 2009, and DNA samples were extracted from each plant to initiate MAS screening of G. barbadense introgressed chromosome segments. Phenotypic traits of 658 BC5F3:4 lines related to fiber yield and quality were evaluated in the summer of 2010 in Anyang . Ten CCRI36 × Hai1 BC5F3:5 lines with good fiber quality and stable performance of yield traits were selected from PopCCRI36 and planted in the summer of 2011 in Anyang  .PopCCRI36 (CCRI36 × Hai1 BCescribed . The F1 34.27″E) . Five li4F3:5): The F1 population was generated by a cross using mid-maturing variety CCRI45  as the recipient and Hai1 as the donor parent in the summer of 2003 at the experimental station of the Institute of Cotton Research of CAAS, Anyang, Henan Province, China . The development scheme for CSSLs was as described [1 progeny of CCRI45 × Hai1 were backcrossed to CCRI45 to produce BC1 in the winter of 2003 in Sanya, Hainan province . The BC1 progeny were backcrossed to CCRI45 to produce BC2 in the summer of 2004 in Anyang , and advanced backcross generations up to BC4 were similarly obtained. A total of 116 BC4 family lines were selfed and individually planted to produce the BC4F2 population in the summer of 2007 in Anyang . BC4F2 plants were selfed and individually planted to generate the BC4F3 population in the summer of 2008 in Anyang . A total of 2,328 plants from 116 BC4F3 families were planted in the summer of 2009, and DNA samples were extracted from each plant to initiate MAS screening of G. barbadense introgressed chromosome segments. Phenotypic traits of 332 BC4F3:4 lines related to fiber yield and quality were evaluated in the summer of 2010 in Anyang . Ten CCRI45 × Hai1 BC4F3:5 lines with good fiber quality and stable performance of yield traits were randomly selected and planted in the summer of 2011 in Anyang  .PopCCRI45 (CCRI45 × Hai1 BCescribed . The F1 34.27″E) . Five li1 hybrids were grown in one location  in 2012 and in three locations  in 2013. All experiments were conducted in a randomized complete block design with two replications. Each plot contained two rows with the following layout: 5 m long and 0.8 m apart with 20 plants per row in Anyang, 36°05′5.78″N, 114°30′34.27″E; 5 m long and 1.0 m apart with 11 plants per row in Changde; 3 m long and 0.55 m apart with 15 plants per row in Liaoyang. Standard agronomic practices were employed during the growing season for all environments.The recipient parent (CCRI36), the donor parent (Hai1), 10 parents of CSSLs from PopCCRI36 and 25 F1 hybrids were grown in two locations  in 2012 and in two locations  in 2013. All experiments were conducted in a randomized complete block design with two replications. Each plot contained two rows with the following layout: 5 m long and 0.8 m apart with 20 plants per row in Anyang, 36°05′5.78″N, 114°30′34.27″E; 5 m long and 1.0 m apart with 11 plants per row at Changde, 29°02′17.64″N, 111°37′39.89″E; 5 m long and 0.85 m apart with 20 plants per row in Zhoukou, 33°38′40.39″N, 114°40′42.35″E. Standard agronomic practices were employed during the growing season for all environments.The recipient parent (CCRI45), the donor parent (Hai1), 10 parental lines of CSSLs from PopCCRI45 and 25 FThirty normal, open bolls from each plot were randomly sampled by hand, weighed and ginned on a laboratory ginning machine to determine boll weight (BW) and lint percentage (LP). The plots were harvested by hand, and the seedcotton was weighed and used to calculate seedcotton yields (SCY). Boll number (BN) per hectare was calculated by dividing SCY by boll weight , 15. Lin1 hybrids and parents . An additive-dominance (AD) genetic model with genotype and environment interaction effects was employed for data analysis [1) = (F1-MP)/μ; Hpb (F1) = (F1-BP)/μ, where, F1 denotes F1 genotypic value; MP denotes the mid-parent value of both parents; BP is the genotypic value of the better parent; and μ denotes the average value of all parents and F1 combinations using North Carolina Design II. The length of substituted chromosome segments in CSSLs was estimated based on Graphical genotypes 32 [The LSD (Least-Significant Difference) method was used for mean comparisons among Fanalysis . A mixedanalysis . Jackknianalysis : Hpm , donor parents, CSSLs parents and F1 had higher values for all yield traits, but the differences were not significant. Compared to F1, the values of the parents were lower on average for all yield traits, with significant differences for BW, SCY and LY. These results indicate that heterosis was detected for all yield traits, especially BW, SCY and LY.Compared to CCRI45, Hai1 had lower values for all yield traits, and significant differences were detected for all traits except LP. The values of parents selected from the CSSLs were lower on average than those of CCRI45 for all yield traits, but the differences were not significant. Compared to CCRI45, F1 hybrids exhibited heterosis for all yield traits for both populations (PopCCRI36and PopCCRI45), especially SCY and LY.The results indicate that significant differences existed for all yield traits between the recipient parent (CCRI36 or CCRI45) and donor parent (Hai1), but the differences were relatively small on average between the recipient parent and CSSLs. In addition, the FWe estimated variance components for yield and yield components; the estimated ratios of variance components to phenotypic variance are shown in In PopCCRI45, additive effects were significant for all yield traits except SCY and LY. Significant dominance effects were detected for all yield traits except LP. Additive-by-environment and dominance-by-environment interaction effects were significant for all yield traits. Dominance effects played a major role in genetic variation for BW, BN, SCY and LY. Additive genetic variance contributed 52.0% of phenotypic variance for LP. In addition, the results indicate that genotypic variances (A and D) were more important than genetic-by-environment variances (AE and DE) for all yield traits.In general, the yield traits of CSSLs from both PopCCRI36 and PopCCRI45 were controlled by both additive and dominance effects, and significant genetic-by-environment interaction effects were detected. In addition, LP was mainly controlled by additive effects, but BW, BN, SCY and LY were mainly controlled by dominance effects. Therefore, selection for LP should be effective in early generations. We detected a similar genetic mechanism for all yield traits of CSSLs in two populations (PopCCRI36 and PopCCRI45) with different genetic backgrounds, although the proportions of genetic variance components were slightly different.Determining additive effects is important for identifying desirable general combiners to improve traits of interest . The predicted additive effects for yield and yield components are shown in In PopCCRI45, the number of parents with significant positive additive effects were as follows: three for BW , four for LP  and four for BN . These results indicate that these lines can be used as general combiners to improve BW, LP and BN, respectively. In addition, MBI7346 had significant positive additive effects for BW and BN, indicating that this line could be used as a combiner to improve seedcotton yield and lint yield.2, respectively. In PopCCRI45, significant positive heterozygous dominance effects for SCY and LY were detected in 10 and 10 hybrids, respectively . Selecting high-yielding lines or hybrids depends on the ability to dissect the genetic effects of yield and its component traits [Boll weight, lint percentage and boll number are three important components of lint yield in Upland cotton , with a few chromosome substitution segments from G. barbadense present in each CSSL (data not shown). Significant positive MP heterosis was detected for all yield traits in both PopCCRI36 and PopCCRI45, and significant positive HP heterosis was also detected for all yield traits except LP. These results are in good agreement with those of Li et al. [The relationship between parental genetic distance and heterosis in cotton has been intensively investigated. Within a restricted range, greater genetic distance is associated with greater heterosis but over this range, heterosis decreases while genetic distance increases . Yang eti et al. , Liu et i et al.  and Luani et al. . The obvG. barbadense into a G. hirsutum background is a useful approach for developing CSSLs [Genetic diversity is considered to be a critical issue in cotton breeding programs , 15. Intng CSSLs , 3, 10. Yield and yield component of the CSSLs were controlled by combined additive and dominance effects, and LP was mainly controlled by additive effects, but BW, BN, SCY and LY were mainly controlled by dominance effects. Meanwhile, significant interaction effects between genetics and the environment were detected for all yields traits in the CSSLs. A similar genetic mechanism contributed to yield traits in two CSSL populations (PopCCRI36 and PopCCRI45) with different genetic backgrounds. Significant positive MP heterosis was detected for all yield traits in both PopCCRI36 and PopCCRI45, and significant positive HP heterosis was also detected for all yield traits except LP. The difference among parent lines selected from the CSSLs was relatively small, but widespread, significant heterosis was detected for yield and yield components. Therefore, CSSLs are useful genetic materials for improving yield and yield components in cotton breeding programs.S1 Excel(XLS)Click here for additional data file.S2 Excel(XLSX)Click here for additional data file.


Conflict over parental investment between parent and offspring is predicted to lead to selection on genes expressed in offspring for traits influencing maternal investment, and on parentally expressed genes affecting offspring behaviour. However, the specific genetic variants that indirectly modify maternal or offspring behaviour remain largely unknown. Using a cross-fostered population of mice, we map maternal behaviour in genetically uniform mothers as a function of genetic variation in offspring and identify loci on offspring chromosomes 5 and 7 that modify maternal behaviour. Conversely, we found that genetic variation among mothers influences offspring development, independent of offspring genotype. Offspring solicitation and maternal behaviour show signs of coadaptation as they are negatively correlated between mothers and their biological offspring, which may be linked to costs of increased solicitation on growth found in our study. Overall, our results show levels of parental provisioning and offspring solicitation are unique to specific genotypes.DOI:http://dx.doi.org/10.7554/eLife.11814.001 Genes encode instructions that can influence the behaviour and physical traits of the individual that carries them. Individuals of the same species can carry different versions (or variants) of the same gene, leading to a variety of traits in the population. However, a gene expressed in one individual can also alter the traits of another individual. This is known as an indirect genetic effect. For example, a gene in a mother that affects her ability to provide care may influence how her offspring develop.Researchers have predicted that offspring should be able to manipulate their mothers to try and gain more care than the mothers are willing to give. Furthermore, the offspring born to mothers who respond to this begging are predicted to save energy and beg less. However, few gene variants that indirectly modify the behaviour of mothers or offspring have so far been identified.Ashbrook et al. used mice to test the idea that genetic variation in particular locations in the offspring’s genome can affect maternal behaviour, and vice versa. In the first experiment, mother mice with different gene variants fostered litters of mouse pups that were all genetically identical. In the other experiment, genetically identical mothers fostered litters of mouse pups with different gene variants. Ashbrook et al. identified several locations in the offspring’s genome that modified the behaviour of their foster mothers. Furthermore, the experiments also show that genetic variation among the mothers influenced the development of their offspring, independent of the genes carried by the offspring.The next steps are to identify the specific genes underlying the changes in behaviour, and the molecular and genetic pathways by which they impact indirectly on the traits of other individuals.DOI:http://dx.doi.org/10.7554/eLife.11814.002 The close interaction between mother and offspring in mammals is fundamental to offspring development and fitness. However, parent and offspring are in conflict over how much parents should invest in their young where offspring typically demand more than is optimal for the parent , and theTo investigate the genetics of parent-offspring interactions we conducted a cross-fostering experiment between genetically variable and genetically uniform mice, using the largest genetic reference panel in mammals, the BXD mouse population. We generated families of genetically variable mothers and genetically uniform offspring by cross-fostering C57BL/6J (B6) litters, in which no genetic variation occurs between animals of this strain, to mothers of a given BXD strain. Conversely, a BXD female’s litter was cross-fostered to B6 mothers . Thus, wMat or Osp, followed by whether it is an indirect effect (Ige) or a direct effect locus (Dge). We provide a summary of all loci in OspIge7.1, modifying maternal nestbuidling on day 6 (OspIge5.1) that affects maternal behaviour on day 14, around the time we expect the weaning conflict to be highest , where the B6 allele increases the trait value in both cases. We also detected a locus for offspring solicitation behaviour on chromosome 5 (OspDge5.1) with the D2 allele increasing the level of solicitation shown. Its location is at the opposite end on chromosome 5 from where OspIge5.1 is located.We first investigated whether there is evidence for indirect genetic effects in offspring influencing maternal behaviour, keeping maternal genotype constant. To find out if maternal behaviour is modified by genes expressed in offspring, we mapped variation in maternal behaviour as a function of their adoptive BXD offspring genotype. We found that variation in offspring genotype affects maternal behaviour, which in turn influences offspring development and fitness. Throughout, we denote loci as either maternal or offspring, on day 6 . At thison day 6 . We dete highest . Here, mit value . In addiF1,103 = 17.62, P < 0.001 and F2,103 = 14.22, P < 0.001, respectively; day 6: Pearsons’r = 0.56, P = 0.003; day 10: r = 0.63, P = 0.001, and day 14: r = 0.55, P = 0.008; F1,118 = 6.33, P = 0.013, and F2,118 = 6.33, P < 0.001; Overall, our results show that IGEs, as well as DGEs, can be linked to specific loci that affect parent-offspring interaction, and it is thus possible that selection may occur on genes with indirect and direct effects on parental behaviour. Importantly, our result that variation in maternal behaviour is affected by genes expressed in offspring is also clearly borne out at the phenotypic level: offspring solicitation behaviour in genetically variable BXD pups is positively correlated with the level of maternal behaviour in their genetically uniform B6 adoptive mothers on all three days we measured behaviour with significant effects of maternal behaviour and day on offspring solicitation 2 / S2QTL / S2Res). Zα and Zβ are Z values for a given α and β; S2QTL is the phenotypic variance due to a QTL and S2Res is the residual variance. With power (1-β) of 80%, α of 0.05 we estimated that with 45 lines we can detect QTL at genome-wide significance explaining ~ 16% of trait variance, which is sufficient mapping power given effect sizes of prior work. We have modelled the relationship between power and number of replicates using qtlDesign (http://www.genenetwork.org) and further information combined from QTLminer (http://www.ncbi.nlm.nih.gov/gene) and Mouse Genome Informatics  were obtained from Professor Robert W. Williams at the University of Tennessee Health Science Centre, Memphis, TN. C57BL/6J (B6) mice were obtained from Charles River, UK. Three within-line repeats plus the corresponding 42 B6 families with three within-line repeats were set up for the experiment . Sample eds four . We haveeds four : n =  and 12h white light.Mice were maintained under standard laboratory conditions in the same room, exclusively used for the experiment in individually ventilated cages (IVC Tecniplast Green line), and given chow and water Cross-fostering of entire litters took place within 24h of birth of corresponding B6 and BXD females and analyses used trait values per pup to adjust for differences in adoptive litter size, which is a significant covariate for provisioning and solicitation as of course a mother nursing a large litter will overall provide more than a mother nursing a small litter. Both mothers and litters were weighed at birth and once weekly, for three weeks until weaning, i.e. at the end of week 1, week 2 and week 3, respectively, to enable the calculation of growth during these periods. In addition, we recorded maternal and offspring behaviour on postnatal days 6, 10 and 14 when we simulated maternal departure to standardize observation conditions , 2005. A review process). Similarly, the author response typically shows only responses to the major concerns raised by the reviewers.eLife posts the editorial decision letter and author response on a selection of the published articles . An edited version of the letter sent to the authors after peer review is shown, indicating the substantive concerns or comments; minor concerns are not usually shown. Reviewers have the opportunity to discuss the decision before the letter is sent  and three reviewers, one of whom is a member of our Board of Reviewing Editors.The reviewers have discussed the reviews with one another and the Reviewing editor has drafted this decision to help you prepare a revised submission.Summary:This paper demonstrates that indirect genetic effects can be identified and genetically mapped. The authors adopt a cross-fostering design so that in families either the mothers or the offspring are genetically variable (from the BXD recombinant inbred panel) while the corresponding offspring or mothers show no genetic variation (i.e. are from the B6 inbred strain). The authors identify three indirect genetic effects, and three direct genetic effects. Overall this study represents a substantial and well-designed effort to address an important question.Essential revisions:1) Design limitations need to be acknowledged and discussed. In their design the in-utero maternal effects are perfectly confounded with offspring genotypes. This means that the results of part 1 could be interpreted as "Variation in BXD mothers genotypes causes variation in in-utero environment, which causes variation in BXD offspring behaviour later in early life, which causes variation in B6 adoptive mothers provisioning". This would effectively be IGE from BXD mothers on B6 mothers.The results of part 2 could be interpreted as "Variation in BXD mothers genotypes causes variation in in-utero environment, which causes variation in BxD offspring weight gain and solicitation in early life" and Variation in BXD mothers genotypes independently causes variation in BXD biological mothers provisioning, in which case there would not be coadaptation between BXD offspring phenotypes and BXD maternal behaviour.This caveat is sufficiently important that its implications should be discussed in the Discussion. As the authors note in the Discussion however, overcoming this limitation would be extremely challenging.2) The results are only just significant. Given that they have tested multiple behaviors, and both direct and indirect effects, the chances are that a proportion of the loci are likely false positives. The authors should assess a false discovery rate and provide results corrected for the total number of tests carried out.3) The mapping approach is relatively un-sophisticated and in particular environmental effects receive scant attention. Cage effects should be accounted for in all the analyses. In addition there may be unacknowledged environmental effects, which might be captured if they included the time when the experiment was carried out as a covariate. The fact that results for the genetic effects only just achieve significance means that there is a concern that even slight contributions from covariates may be giving rise to false positives.4) It wasn't clear why they used per pup values. Why not fit litter size should be fitted as a covariate? They should repeat the analyses with litter fitted as a covariate.5) The phenotypic correlation observed between BXD offspring solicitation and B6 maternal behaviour could arise from environmental effects only as BXD offspring and B6 mothers share a cage. It is not strong evidence that BXD genotypes affect B6 maternal behaviour, and can only weakly be linked to the QTLs identified as no overlap was found between DGE QTLs for offspring solicitation and IGE QTLs for maternal behaviour. Genetic correlation should be computed from the individual measurements.eLife. Your revised article has been favorably evaluated by Diethard Tautz (Senior editor) and three reviewers, one of whom is a member of our Board of Reviewing Editors. The manuscript has been improved but there are some remaining issues that need to be addressed before acceptance, as outlined below:Thank you for resubmitting your work entitled "Genetic variation in offspring indirectly influences the quality of maternal behaviour in mice" for further consideration at You state that you have "used the correct litter size to calculate per pup measures, namely adoptive litter size." That a litter size effect exists does not imply that per pup values are appropriate, i.e., it does not prove that per pup values are independent of litter size. This would only be correct if you could prove that total provisioning is exactly linear in litter size; the mere significance of a (linear) litter size effect is no proof thereof.Intuitively, one would expect that provisioning per pup decreases with litter size, simply because there is some sort of limit to total provisioning that is feasible. If you can fit a litter size effect on total provisioning using linear models, then you can also do this on provisioning defined per pup.While this may not be feasible in the Genenetwork software that you used for the mapping, it could be investigated in a prior analysis using simple linear models. Then the results should be reported in the manuscript, and if the litter size effect on per pup provisioning is significant in the prior analysis, then you should acknowledge in the manuscript that ideally a covariate for litter size would have been included in the mapping.The correlation/covariance that may exist between direct and indirect environmental effects (IDE and IEE) should be modelled when calculating the correlation between mother and offspring phenotypes as it may increase or decrease the correlation reported in the manuscript.Example of such a correlation between IDE and IEE: differences in noise across cages may lead to B6 mothers in noisy cages showing reduced maternal behaviour and BXD offspring in those same cages soliciting less (or more).To account for this covariance, you would need to focus on the genetic component of the correlation and use the replicate structure of the data (3 replicates per genotype) to calculate something analogous to a genetic correlation but where phenotypes are measured in B6 mothers and BXD offspring  and the genotypes would be those of the BXD offspring.Although a sentence was added in the Discussion with regard to in-utero effects, you still need to put the results of part 1 in perspective and address interpretation of the results of part 2 (co-adaptation). Essential revisions:1) Design limitations need to be acknowledged and discussed. In their design the in-utero maternal effects are perfectly confounded with offspring genotypes. This means that the results of part 1 could be interpreted as "Variation in BXD mothers genotypes causes variation in in-utero environment, which causes variation in BXD offspring behaviour later in early life, which causes variation in B6 adoptive mothers provisioning". This would effectively be IGE from BXD mothers on B6 mothers.The results of part 2 could be interpreted as "Variation in BXD mothers genotypes causes variation in in-utero environment, which causes variation in BxD offspring weight gain and solicitation in early life" and Variation in BXD mothers genotypes independently causes variation in BXD biological mothers provisioning, in which case there would not be coadaptation between BXD offspring phenotypes and BXD maternal behaviour.This caveat is sufficiently important that its implications should be discussed in the Discussion. As the authors note in the Discussion however, overcoming this limitation would be extremely challenging.We agree, and have thus expanded the first paragraph of the Discussion following this suggestion though we note coadaptation may well be manifest in utero .2) The results are only just significant. Given that they have tested multiple behaviors, and both direct and indirect effects, the chances are that a proportion of the loci are likely false positives. The authors should assess a false discovery rate and provide results corrected for the total number of tests carried out.The experiment was designed to test the hypothesis that genetic variation in BXD offspring can affect trait variation in B6 maternal behaviour and vice versa in the context of family interactions. While we need protection against many false discoveries we need, at the same time, assurance we are not neglecting truly interesting locations (see e.g. Chen and Storey 2005 Genetics 173: 2371–2381). Traditionally, LOD scores above 3.3 are considered in interval mapping studies and we follow the convention of previous studies on maternal behaviour  and other multiple complex traits  in reporting significance both at the genome-wide and suggestive level, which we exceed with five offspring and maternal traits for all loci .In addition, our result that variation in maternal behaviour is affected by our identified (IGE) in offspring is further supported by the phenotypic correlation: “offspring solicitation behaviour in […] BXD pups is positively correlated with the level of maternal behaviour […] in B6 adoptive mothers on all three days we measured behaviour with significant effects of maternal behaviour and day on offspring solicitation[…]” , notwithstanding the caveat added in the Discussion about in-utero effects.3) The mapping approach is relatively un-sophisticated and in particular environmental effects receive scant attention. Cage effects should be accounted for in all the analyses. In addition there may be unacknowledged environmental effects, which might be captured if they included the time when the experiment was carried out as a covariate. The fact that results for the genetic effects only just achieve significance means that there is a concern that even slight contributions from covariates may be giving rise to false positives.Please see next point.4) It wasn't clear why they used per pup values. Why not fit litter size should be fitted as a covariate? They should repeat the analyses with litter fitted as a covariate.In reply to points 3 and 4: First, we need to clarify the per pup measure used as it appears that this will answer several points raised. We did not record individual pup behaviour (where cage effects may appear) but rather for the entire litter and the per pup measure divides the score by litter size. This is because mothers may differ e.g. in their provisioning not because they have different genotypes but simply because they nurse litters of different sizes. Using linear models we found significant litter size effects. Thus, using a per pup measure is fully justified and appropriate, as well as supported by statistics, and we have used the correct litter size to calculate per pup measures, namely adoptive litter size. We have clarified this in the Methods section now. All our analyses are conduced within Genenetwork, the analytical tool kit for the BXD population (www.genenetwork.org) used in over 1000 papers, which at present does not allow running models with covariates but we understand this will be implemented in future.While we unfortunately do not have the time of each recording we have experimentally ensured as much as possible to standardize motivation in mothers and offspring. This is a technique we have employed and developed over years  for the following reasons: consider the scenario of measuring nursing behaviour. Prior to the experiment on the day we have no information about whether mothers have just been nursing their pups or whether the last bout of nursing was several hours ago. Thus, we might see a difference in the pups’ motivation to suck, and in the mothers to nurse, not because of differences in genotypes but because of differences in the times that elapsed between the last feed. Therefore, we standardize the time prior to us measuring nursing.5) The phenotypic correlation observed between BXD offspring solicitation and B6 maternal behaviour (part 1.2) could arise from environmental effects only as BXD offspring and B6 mothers share a cage. It is not strong evidence that BXD genotypes affect B6 maternal behaviour, and can only weakly be linked to the QTLs identified as no overlap was found between DGE QTLs for offspring solicitation and IGE QTLs for maternal behaviour. Genetic correlation should be computed from the individual measurements.Cage effects may arise by a shared environment among multiple offspring that have been individually phenotyped but this is not how offspring traits were measured (see previous comment). Given that one family (i.e. one BXD genotype plus B6) occupied one cage we do not think that this effect applies here, and we have published correlations using the same protocol multiply before . Further, our result that variation in maternal behaviour is affected by genes expressed in offspring is supported by phenotypic results: offspring solicitation behaviour in genetically variable BXD pups is positively correlated with the level of maternal behaviour in their genetically uniform B6 adoptive mothers on all three days we measured behaviour with significant effects of maternal behaviour and day on offspring solicitation. We appreciate the point the reviewer is making regarding an overlap of DGE QTL and IGE QTL, but no direct support is provided and we have no reason to assume that DGE QTL and IGE QTL have to overlap to support this argument.Intuitively, one would expect that provisioning per pup decreases with litter size, simply because there is some sort of limit to total provisioning that is feasible. If you can fit a litter size effect on total provisioning using linear models, then you can also do this on provisioning defined per pup. While this may not be feasible in the Genenetwork software that you used for the mapping, it could be investigated in a prior analysis using simple linear models. Then the results should be reported in the manuscript, and if the litter size effect on per pup provisioning is significant in the prior analysis, then you should acknowledge in the manuscript that ideally a covariate for litter size would have been included in the mapping. We have run linear models as suggested and can confirm that litter size is a non-significant predictor for all our per pup provisioning traits.The correlation/covariance that may exist between direct and indirect environmental effects (IDE and IEE) should be modelled when calculating the correlation between mother and offspring phenotypes as it may increase or decrease the correlation reported in the manuscript.Example of such a correlation between IDE and IEE: differences in noise across cages may lead to B6 mothers in noisy cages showing reduced maternal behaviour and BXD offspring in those same cages soliciting less (or more). To account for this covariance, you would need to focus on the genetic component of the correlation and use the replicate structure of the data (3 replicates per genotype) to calculate something analogous to a genetic correlation but where phenotypes are measured in B6 mothers and BXD offspring  and the genotypes would be those of the BXD offspring.The example given that a correlation between B6 maternal behaviour and BXD offspring solicitation could arise because all B6 shared the same environment (e.g. noise) is a very unlikely scenario as all animals are kept in the same small room (exclusively used by us), which is sound proofed, and in IVC cages, each with the same conditions. We note that the conditions experienced by B6 females are identical except the genotypes of the adoptive BXD litters, and that correlations are calculated per maternal genotype, not cage; and have added some additional information about housing to the Methods.Although a sentence was added in the Discussion with regard to in-utero effects, you still need to put the results of part 1 in perspective and address interpretation of the results of part 2 (co-adaptation).Yes, agreed. We have added potential implications of in-utero effects to that section in the Discussion.


Evolutionary ecologists commonly use reaction norms, which show the range of phenotypes produced by a set of genotypes exposed to different environments, to quantify the degree of phenotypic variance and the magnitude of plasticity of morphometric and life-history traits. Significant differences among the values of the slopes of the reaction norms are interpreted as significant differences in phenotypic plasticity, whereas significant differences among phenotypic variances (variance or coefficient of variation) are interpreted as differences in the degree of developmental instability or canalization. We highlight some potential problems with this approach to quantifying phenotypic variance and suggest a novel and more informative way to plot reaction norms: namely “a plot of log (variance) on the y-axis versus log (mean) on the x-axis, with a reference line added”. This approach gives an immediate impression of how the degree of phenotypic variance varies across an environmental gradient, taking into account the consequences of the scaling effect of the variance with the mean. The evolutionary implications of the variation in the degree of phenotypic variance, which we call a “phenotypic variance gradient”, are discussed together with its potential interactions with variation in the degree of phenotypic plasticity and canalization. Recent studies suggest that phenotypic variability can allow rapid adaptation to new conditions  on log σ2 and where w Taylor , which mutsunori .Both log transformation of the variance  = 2rσp(A)σp(B), and r is the correlation coefficient between trait A and trait B. Hence, if traits A and B are negatively correlated, X) will be deflated by this correlation and where 2cov, originating from five populations in Queensland, Australia, spanning an 800 km transect. The progeny of these five populations was reared at three different temperatures  at controlled densities  of wild-caught flies , the distal length of the third longitudinal vein (L3d) and wing width 1 (W1) of 840 flies  were measures with negligible measurement error  , between sexes (within population) and in the same trait (between populations). This analysis compared the slopes of the reaction norms for the log-transformed values of ) Taylor .Z-test within a locality . Where the slope is negative, the degree of phenotypic variance decreases across environments. The extent to which the degree of phenotypic variance changes across environments will be called the “phenotypic variance gradient”, which can be measured as the difference in regression coefficients. Our data set was tested for differences between the slopes measured for a trait in the interval (between 20°C and 25°C and between 25°C and 30°C) by comparing the values of the slopes of the regressions by means of a lity Zar . FurtherF-test, and the ratios of the F-tests, which result to be significant, were plotted versus the sample size.In order to get an idea on the effect of the standard error of the variance, we conducted a simulation by generating two groups of values of normally distributed points with the same means and different variance. The normal distributions were simulated with different number of points  and for every simulation, 100 replications were made. The variances of the simulated distributions were then tested for differences with an All the statistical analyses and graphic plotting were performed using the softwares PAST  from this expected relationship, with β values ranging from −38.2 to 95.75  and 34 values of β > 0. Table β values vary significantly (P < 0.05) between traits (with only five exceptions), when compared between the two temperature intervals. The β values of a given trait also vary between sexes and between populations collected in the five localities .The β values when measuring the same trait in the same sex in the different populations can still be used for comparative analysis. The reaction norms presented by Loeschcke et al. , then we commit both a qualitative and a quantitative error. In fact, will still conclude that the degree of canalization is smaller at the temperature in which the trait is largest compared to the temperature where the trait is smaller. However, this is not true because after a correction of the slope by subtracting the value of 2, the slope will become negative, which means that the degree of phenotypic variance is in reality higher at the temperature where the trait is largest compared to the temperature where the trait is smaller. And the correct value of the negative slope can be estimated again by subtracting the value of 2.If the slope of the trait is negative, then the error will not be qualitative but quantitative as the interpretation that the degree of phenotypic variance for the trait is higher at the temperature in which the trait is largest compared to the degree of canalization at the temperature in which the trait is smaller, is not wrong. However, the degree at which phenotypic variance has increased when moving from one temperature to the other has been underestimated as the slope has to be corrected with a subtraction of the value of 2, making the slope even more negative.The degree of phenotypic variance of a trait is often represented in a reaction norm with a vertical bar (symmetric around the The heterogeneity of the slope values observed for the different traits in Figs


CBM) which included non-genetic covariates only. CBM was extended by adding the first two marker-derived principal components and 65 SNPs identified by a recent GWAS consortium for T2D (M-65SNPs). Subsequently, it was further extended by adding 249,798 genome-wide SNPs from a high-density array. The Bayesian models used to incorporate genome-wide marker information as predictors were: Bayes A, Bayes Cπ, Bayesian LASSO (BL), and the Genomic Best Linear Unbiased Prediction (G-BLUP). Results included estimates of the genetic variance and heritability, genetic scores for T2D, and predictive ability evaluated in a 10-fold cross-validation. The predictive AUC estimates for CBM and M-65SNPs were: 0.668 and 0.684, respectively. We found evidence of contribution of genetic effects in T2D, as reflected in the genomic heritability estimates (0.492±0.066). The highest predictive AUC among the genome-wide marker Bayesian models was 0.681 for the Bayesian LASSO. Overall, the improvement in predictive ability was moderate and did not differ greatly among models that included genetic information. Approximately 58% of the total number of genetic variants was found to contribute to the overall genetic variation, indicating a complex genetic architecture for T2D. Our results suggest that the Bayes Cπ and the G-BLUP models with a large set of genome-wide markers could be used for predicting risk to T2D, as an alternative to using high-density arrays when selected markers from large consortiums for a given complex trait or disease are unavailable.Lifestyle and genetic factors play a large role in the development of Type 2 Diabetes (T2D). Despite the important role of genetic factors, genetic information is not incorporated into the clinical assessment of T2D risk. We assessed and compared Whole Genome Regression methods to predict the T2D status of 5,245 subjects from the Framingham Heart Study. For evaluating each method we constructed the following set of regression models: A clinical baseline model ( WGR), all the heritability in family-based data  and the γ = {γi}’s are marker effects. When absent in the platform, these SNPs were imputed with IMPUTE2 with 1,092 subjects from the 1,000 Genomes data as reported previously [orted by . This moeviously –38.ui) modeled with whole-genome markers. These were comprised of a high density array of p = 249,798 SNPs and were regressed on a function of the phenotype evaluated in this study. SNP effects were included in the models using either Bayes A, Bayes Cπ, Bayesian LASSO (BL), and G-BLUP. The linear predictor for these models could be written in general as,Subsequently, we evaluated several WGRs using the CBM as the base and included the genomic effects  ∝ 1. This yields estimates of effects comparable to those obtained with maximum likelihood. The genomic effect term ui is different in every one of the Bayesian models evaluated. The definition of ui and its prior probability completes the Bayesian model. We describe them below for each Bayesian model evaluated.In addition to the joint conditional probability of the data, given the unknown coefficients, the prior density of the unknowns was flat for Bayes A (BA). In Bayes A models [T, , which could be re-expressed as jth position; see [βj is normal with mean 0 and variance A models , ui=∑j=1ion; see . Thus, tgiven in  and implBayes C π (BC). In Bayes C models [Beta  (see). We assBayesian LASSO (B-LASSO). In the Bayesian LASSO [λ2 is a gamma distribution, G, with the hyper-parameter rate set to 0.0001 and shape 0.55; .G-BLUP. In this model [u = {ui} is a random effect in the regression which distribution is G = {Gii′} is an n × n matrix of relationships based on the p SNP genotypes such that,qj is the estimated jth allele frequency; and is model , u = {ulsewhere .The parameters of the above-described model were estimated in a Bayesian framework using the BGLR package,44 in R In the models described above, narrow sense heritability in the liability scale is defined as the ratio of the genetic variance to the total variance. The residual variance is fixed at one, thus the narrow sense heritability is ry traits,47. The glm function) from the R base package [ith observation or any relative of the ith observation. AUC was computed using the pairs of points that included the presence/absence of diabetes and the risk score was predicted using cross validation yi) is a binary response (0/1), it is more appropriate to report results in terms of false positive rate and Area Under the Receiver Operating Characteristic Curve . We estAUC, see .Participants in the two cohorts that were included in this study were born between 1890 and 1968, and the age at either last contact or death was 74±12 (mean ± standard deviation). The total number of T2D cases was 939 out of the 5,245 subjects; since FHS is an ongoing study, many study participants do not have diabetes yet. The incidence of diabetes in participants with last contact at age <65 was 8%, while it was 26% for participants with last contact at age > 83 years. The 939 cases showed a first record of diabetes at 63±24 years of age . The proThe effects estimated in CBM are on a liability scale. The estimated effect of sex  was -0.26± 0.04 , with an odds ratio of 0.77, implying a decreased risk of developing diabetes in females, relative to males. The estimated effect of the Offspring cohort was -0.40±0.06 , with an odds ratio of 0.68, implying a lower risk of diabetes for subjects on the Offspring cohort relative to subjects of the Original cohort. This estimate is probably affected by the shorter observational period of the members of the Offspring cohort, even though the age at the last contact was included in the study to correct for different censoring times. The estimated effect for the age at the last contact was 0.016±0.002  with an odds ratio of 1.02, implying that there is a slightly higher risk of observing diabetes per year of exposure. Finally, PCs 1 and 2 were non-significant with odds ratios of 1.25±1.89  and 1.18±2.06 , respectively. However, in order to correct for population stratification, we retained the principal components in the model.Odds ratio for the 65 SNPs obtained with the M-65SNP model and odds previously reported in the literature  have a cThe estimated proportion of SNPs with a genetic signal (1- π) was quite large at 0.579± 0.114. Thus, this result suggests that more than 50% of the total number of SNPs contributed to the overall genetic variation, although the individual contribution of most of these SNPs is likely to be a miniscule proportion of the total genetic variation.The G-BLUP model results in an estimate of genetic variance associated with common SNPs in the full training sample of 0.92 ± 0.26. Considering that the residual variance was fixed at 1, the estimate of genomic heritability for Type 2 Diabetes was 0.492±0.066. Previous studies demonstrated that in family datasets genomic heritability from G-BLUP yielded similar results ,21.Models were also evaluated for their predictive ability using a 10-fold cross-validation. We randomized families and assigned entire families to folds. The number of families per fold and the size of the families can be seen in Diabetes increases morbidity and mortality significantly, even when the condition is treated . DiabeteThe predictive ability of the WGR models was moderately improved in comparison to the model based only on clinical covariates. It is known that prediction accuracy will greatly depend on the genetic distance between training and testing sets –57. SeveIn our study, most models evaluated did not differ in the shrinkage of the SNP estimates or in the prediction accuracy. In agreement with our results in humans, Daetwyler and coauthors in a review paper report that there are not major differences in the predictive ability of WGR methods in several animal and plant studies . Most trπ and the G-BLUP. In the case of diabetes, BMI, height, and several other complex traits or diseases, mega consortiums are pulling thousands of genotyped subjects and their phenotypes to find the SNPs highly associated with the phenotype. However, for several phenotypes these resources are not available, and will probably never be , and significant SNP markers are unknown. Hence it is worth using the G-BLUP or Bayes Cπ, both of which achieved the same performance relative to the model using information of the well-established SNPs without using any prior information from large GWAS consortiums.Nevertheless, the AUC and performance achieved with 65 known markers was the same as the one achieved with Bayes CIn summary, we found evidence of genetic effects in T2D, which reflects in the heritability estimates; additionally, existing genetic variation can be captured by high-density markers. Results from different WGR methods did not differ. We can find similar reports in the animal science literature; the improvement in AUC using cross validation was positive, albeit poor. Finally, the AUC from 65 well-known variants affecting diabetes was similar to that obtained from including all variants. However, these 65 SNPs were found in a large consortium study. Most complex traits and diseases do not have large consortiums data available, and in rare diseases, it is possible that there will never be large amounts of phenotypic and genomic data. WGRs could be important for diseases where no large consortium is available. Bayes LASSO and G-BLUP models are alternative methodologies using dense arrays of markers.S1 Fig(TIFF)Click here for additional data file.S2 Fig(TIFF)Click here for additional data file.S1 Table(DOCX)Click here for additional data file.