Taeniopygia guttata), two polymorphic inversions are known cytogenetically and we set out to detect these two and potentially additional inversions using genomic tools and study their effects on embryo mortality and other fitness-related and morphological traits.Inversion polymorphisms constitute an evolutionary puzzle: they should increase embryo mortality in heterokaryotypic individuals but still they are widespread in some taxa. Some insect species have evolved mechanisms to reduce the cost of embryo mortality but humans have not. In birds, a detailed analysis is missing although intraspecific inversion polymorphisms are regarded as common. In Australian zebra finches  intraspecific inversion polymorphisms with allele frequencies close to 50 %. Using additional data from 5229 birds and 9764 eggs from wild and three captive zebra finch populations, we show that only the largest inversions increase embryo mortality in heterokaryotypic males, with surprisingly small effect sizes. We test for a heterozygote advantage on other fitness components but find no evidence for heterosis for any of the inversions. Yet, we find strong additive effects on several morphological traits.The mechanism that has carried the derived inversion haplotypes to such high allele frequencies remains elusive. It appears that selection has effectively minimized the costs associated with inversions in zebra finches. The highly skewed distribution of recombination events towards the chromosome ends in zebra finches and other estrildid species may function to minimize crossovers in the inverted regions.The online version of this article (doi:10.1186/s13059-016-1056-3) contains supplementary material, which is available to authorized users. Between-individual genetic variation is the substrate for selection. Genetic polymorphisms range in size from single nucleotides (SNPs) to large scale insertions, deletions, or rearrangements that span several millions of base pairs , 2. AmonDrosophila spp. or maize (Zea mays)] paracentric inversions often do not cause reduced fertility in females because the dicentric chromatid is preferentially passed into the second polar body  = 1.17 [1.01–1.36] for Tgu13, P = 0.040, and OR = 1.16 [0.99–1.36], P = 0.065 for TguZ).Neither the mother’s nor the father’s inversion genotype had an effect on embryo mortality that survived strict Bonferroni correction  and a dominance  predictor in the three captive populations . For females we included fecundity (number of eggs laid) and reproductive success (number of chicks that survived until an age of 35 days). For males we used siring success  and reproductive success . Sample sizes are given in Table Neither in females nor in males did any of the inversion polymorphisms exhibit additive or non-additive fitness effects  we tested whether the four inversion polymorphisms were transmitted to the next generation in a fair Mendelian way. None of them showed signs of segregation distortion  and the inversion genotype simultaneously as an additive and a dominance predictor  and body mass  and had a negative effect on tarsus length .The inversions on chromosomes None of the inversions exhibited significant dominance effects on any of the phenotypes  deviated from the random expectation, despite high power for detecting large effect sizes .The 40 empirical additive effect size estimates on morphology (5 comparisons between inversions × 8 phenotypes) clearly exceeded the random expectation (observed mean ± standard error (SE) = 0.0494 ± 0.0069, expected mean ± SE = 0.0163 ± 0.0002), suggesting that several of the associations which did not survive a strict Bonferroni correction were in fact real  in wild Australian zebra finches using molecular and population genetic tools. Two of them had been identified previously in cytogenetic screens because they shift the position of the centromere , 48–50. 2 to measure the strength of LD which can never be negative and never reach 0)  = 16.68–343.70 kb) on macrochromosomes (chromosomes P < 0.05/4553), or because their position in the zebra finch genome assembly was likely not correct, leaving 4401 SNPs.All 1059 “Fowlers Gap” individuals were genotyped for the 4553 SNPs at the IKMB at Kiel University. Quality control was done using the R package GWASTools (v1.6.2)  and deta2) as a standardized measure of LD between every two SNPs on a chromosome genotyped in the 948 individuals [2 and P values for loci with multiple alleles.Inversion polymorphisms lead to extensive LD across the inverted region, with the highest LD near the inversion breakpoints because recombination in these regions is almost completely suppressed in inversion heterozygotes –55. To sividuals , 100. Inividuals  to obtaiInversion polymorphisms appear as a localized population substructure within a genome because the two inversion haplotypes do not or only rarely recombine , 67; thiWe performed PCA on the quality-checked SNP set of the 948 individuals using the R package SNPRelate (v0.9.14) . On the In collinear parts of the genome composite LD >0.1 does not extend beyond 185 kb . For each inversion polymorphism we calculated standardized composite LD between the eigenvector of PC1 (and PC2 in case of three inversion types) and the SNPs on the respective chromosome as the squared Pearson’s correlation coefficient. Then, for each chromosome, we selected SNPs that tagged the inversion haplotypes uniquely. We tried to pick tag SNPs in both breakpoint regions of an inversion, spanning the largest physical distance possible , the inferred inversion genotypes from the tag SNPs correspond perfectly to the PCA results but leave some individuals uncalled  were included in three Sequenom genotyping assays (plexes), which in total consisted of 62 SNPs. All 5229 individuals were genotyped according to the manufacturer’s users guide on the Sequenom MassARRAY iPLEX platform [Tag SNPs  , the infTguZ was common  were run on both the Illumina and Sequenom genotyping platforms. Thus, we used the SNP loadings on PC1 and PC2 from the PCA of the Fowlers Gap birds on the population founders to calculate a PCA score for each individual  per individual such that phenotypic values and their measurement errors between the “Fowlers Gap” and the other populations are comparable . DescripEmbryo mortality and fitness measures were taken from the three captive populations held at the Max Planck Institute for Ornithology . Eggs were classified as infertile, naturally died embryo, hatched but died <35 days of age, and independent offspring (≥35 days of age) as described in Ihle et al. . Data weAll analyses were performed in R (v3.0.2) . Mixed-eWe fitted mixed-effects generalized linear models with embryo mortality as the binomial response variable  and the mother’s and the father’s inversion genotypes as two predictors . We included the pedigree-based inbreeding coefficient of the embryo (as a covariate) and the pair identity and the mother’s and father’s additive genetic relatedness matrices calculated from the pedigree as random effects. We also controlled for experimental setup (cage versus aviary breeding and cage versus aviary laying) by fitting it as a factor with four levels and the specific experiment (43 levels across 12 years and 3 populations) as an additional random effect.We used the Z-transformed morphological phenotypes as the response variable in univariate mixed-effects linear models and the individual’s inversion genotype simultaneously as an additive effect  and a dominance effect  as two predictors.In the wild “Fowlers Gap” population we included sex (factor with two levels), the individual’s estimated age (covariate for subadults), and season (factor with two levels referring to the catching seasons October–December 2010 and April–May 2011) as fixed effects and for body mass we also included time of day (covariate). We corrected for overall body size by fitting body mass as a covariate (when body mass was the independent variable we used tarsus length instead). We controlled for relatedness by fitting a genetic similarity matrix (GSM) as a random effect . Since we had neither pedigree nor genome-wide SNP data for these birds, we did not control for relatedness.In the three captive populations  we fitted the individual’s sex (factor), the observer of the measurement , the individual’s pedigree-based inbreeding coefficient (covariate), and its known exact age (covariate) as fixed effects. For body mass we included time of day (covariate) and in the “Seewiesen” population we included whether the bird was measured dead or live (factor) for the three beak morphology traits as fixed effects  as the dependent variable in the three captive populations and the inversion genotype of the individual coded as an additive  and dominance  effect as two predictors. We first square root-transformed the dependent variables to improve model fit and Z-transformed them prior to analysis. We also fitted Poisson models, which qualitatively gave the same results (not shown).As fixed effects we included the pedigree-based inbreeding coefficient of the individual (covariate) and for female fecundity, male siring success, and female and male reproductive success we added the number of days an individual spent in the respective experiment (covariate). We fitted an additive genetic relatedness matrix calculated from the pedigree as a random effect and since we had multiple measures per individual we also fitted a permanent environment random effect. We controlled for experimental setup (cage versus aviary breeding and cage versus aviary laying) by fitting it as a fixed effect (factor with four levels) and the specific experiment as an additional random effect.To obtain the expected distribution of effect sizes of inversion genotypes on morphological and fitness traits under randomness (null distribution), we permuted inversion genotypes 100 times within each sex, fitted the same mixed models for each inversion including the same fixed and random effects as for the empirical data, and extracted additive and dominance effect size estimates. We then calculated the same meta-analytic summary statistics as for the empirical data.We estimated the power to detect effects of different magnitude given our data using the following approach. First, we permuted inversion genotypes ten times within each sex and effect size category (10 permutations × 10 effect sizes = 100 simulations). For an additive effect, we then added or subtracted a predefined effect size from the phenotypic values of the two homozygous groups of individuals. For a dominance effect, we added a predefined effect size to the phenotypic values of the heterozygous individuals. We then fitted the same mixed models for each inversion including the same fixed and random effects as for the empirical data, extracted additive and dominance effect size estimates, and calculated the same meta-analytic summary statistics as for the empirical data.Tgu5, Tgu11, and Tgu13), the sum for heterokaryotypic individuals always equals 1 and the two homozygotes deviate equally from 1, unless the two alleles have an equal frequency (additive effect).To test for frequency-dependent selection we used the fitness data  measured in the aviary setting in two captive populations (“Seewiesen” and “Bielefeld”). For the “Seewiesen” population we had data from 72 aviaries (12 for reproductive success), each with 12–15 birds. For the “Bielefeld” population we had data from 23 aviaries with 10–12 individuals each. Allele frequency ranges are provided in Additional file We then used this sum as the predictor in univariate mixed-effects linear models using each of the four fitness parameters  as the dependent variable in the two captive populations. We first square root-transformed the dependent variables to improve model fit and Z-transformed them prior to analysis. As fixed and random effects we included the same variables as in the other fitness models (see above).TguZ we tested all two-way combinations of the three inversion types in heterokaryotypic males only. See [We tested whether the four inversion polymorphisms were transmitted to the next generation in a fair Mendelian way. For each heterokaryotypic parent we counted how many times it transmitted the major and minor allele to its offspring. We summed the number of transmissions across all families and populations and used the binomial test to assess fair Mendelian segregation of alleles. For the autosomal inversions we either included only heterokaryotypic females, only heterokaryotypic males, or both sexes combined. On chromosome nly. See  for meth


Demonstrating the impact that parents have on the fitness of their children is a crucial step towards understanding how parental investment has affected human evolution. Parents not only transfer genes to their children, they also influence their environments. By analyzing reproductive patterns within and between different categories of close relatives, this study provides insight into the genetic and environmental effects that parents have on the fitness of their offspring.h2) to further explore the genetic impact on lifetime reproductive success. Finally, we construct four simulations to model the expected contribution of genes and resources on reproductive success.We use data spanning over two centuries from an exceptionally accurate Icelandic genealogy, Íslendingabók, to analyze the relationship between the fertility rates of close relatives. Also, using genetic data, we determine narrow sense heritability estimates (r = 0.19) while the reproductive relationship between parents and offspring was often negative across many decades and undetectable overall (r = 0.00) (h2) of 0.00 for lifetime reproductive success. A resources model  revealed a similar trend: a negative relationship between parent and offspring reproduction (r =  − 0.35) but a positive relationship among full siblings (r = 0.28). The relationship between parent and offspring lifetime reproductive success (LRS) and full sibling LRS was strongly and positively correlated across time . Similarly, the LRS among full siblings was positively correlated with both the LRS among half siblings  and the relationship between the LRS of aunts and uncles with their nieces and nephews .The relationship between the reproduction of all full sibling pairs was significant and positive across all birth decades ( = 0.00) . MeanwhiWe show that an individual’s lifetime reproductive success is best predicted by the reproduction of their full and half siblings, but not their parents, grandparents or aunts and uncles. Because all siblings share at least one parent, we believe parental investment has had an important impact on fitness. Overall, these results indicate that direct parental investment, but not genes, is likely to have had an important and persistent impact on lifetime reproductive success across more than two centuries of Icelandic history. Parental investment (PI) is crucial for the success and survival of offspring in many species . Direct There are several ways to estimate heritability. The simplest method is to either compare parent and offspring traits (the mid-parent–offspring regression) or compare the similarity of traits between full siblings (full sibling’s correlation). Higher correlations between the traits of family members suggests higher heritability . These eIn the past, the most common technique for estimating heritability in humans has been the twin design  while thboth environmental and genetic effects  can help to partition the remaining environmental variance into various components. Therefore, the degree to which estimates between different categories of relatives are biased can be used to provide insight into which environmental factors  have the largest effects on a given phenotype. In sum, comparing traits between relatives who share a different degree of genetic relatedness and different types of environments can help partition these environmental effects.h2 ∼ 0.07) for both males and females, but these estimates did not consider the shared environmental effects of a common household or shared parents (The aim of this study was to determine the impact that parents have on the lifetime reproductive success (LRS) of their children. To date, a small number of studies have been able to use large genealogical databases to estimate the heritability of reproductive success. One study of a late 19th century population from Utah showed that increasing parental reproduction reduced the reproductive success of offspring  . High he parents . Finally parents .r = 0.5), full siblings also share parents. Furthermore, we predicted that if these relationships are strongly influenced by the environment that parents provide  they will respond to environmental volatility and should change over time. This study examined the effects that different categories of first (full siblings and parents) and second degree relatives  have had on an individual’s LRS across over two hundred years of Icelandic history.Using an exceptionally accurate and large database, spanning over two centuries, we examined the relationship between parental LRS and offspring LRS. Because parents and offspring share half their genes, we predicted that if genes have had an important effect on reproduction, then the LRS of ones’ parents will predict an individual’s LRS. Meanwhile, if parental investment PI; cf  and the We used an Icleandic genealogy, also known as Íslendingabók, to test our predictions. Íslendingabók has several important advantages over other genealogical databases. First, it is a population-based database that contains information about approximately 600,000 of the one million individuals estimated to have ever inhabited Iceland . A populThe first national census in Iceland was taken in 1703 , and theIndividual LRS was the primary dependent variable, but mean fertility rates fluctuated considerably across time. For example, average fertility rates for individuals born between 1810 and 1819 peak at 3.12 children but drop to 1.98 only thirty years later (1850–1859). Therefore, all LRS values for all individuals were first log transformed and standardized by the decade in which the individual was born . This transformation made the reproduction of individuals less dependent on changes in mean family size across birth decades, so that effective comparisons could be made across time .r) of 0.5 and are all first-degree relatives while half-siblings, aunts-uncle and nieces and nephews, and grandparents and their grandchildren are all second-degree relatives and share an average coefficient of relatedness (r) of 0.25. Comparing the degree to which different types of relatives with the same coefficients of relatedness share fitness outcomes may yield insights into the impacts that different environments have on reproduction.Although heritability estimates based on precise coefficients of relatedness among full siblings can be used to obtain accurate and unbiased estimates of the genetic impacts of parents, distinguishing the effect of parental investment (PI) from other environmental factors  is more difficult. One way to isolate the effects of PI on offspring LRS, however, is to compare the reproductive similarity of close relatives across varying degrees of social and genetic relatedness. Parents, children, and full siblings, for instance, all share a coefficient of relatedness (r = 1∕2) and half siblings (r = 1∕4)) may also produce insights. Therefore, comparing different types of relatives both between and within different categories of genetic and social relatedness may shed light on the effects of sharing different types of environments on an individual’s LRS. This is because heritability estimates based on correlations between relatives depend critically on the assumption that the environments shared between relatives with the same mean coefficients of relatedness are the same across all social categories and it is often unclear which relatives share a common environment. For example, do parent–offspring pairs have the same amount and type of environmental sharing as siblings?  for LRS were obtained from the historic genealogical data by correlating the traits of two types of first degree relatives : parents with their children and full siblings. Parent-offspring heritability was measured by correlating the mid-parent standardized reproduction or lifespan  with the standardized reproduction of their offspring. Full sibling heritability was measured by correlating an individual’s standardized LRS with the mean of the standardized LRS of all his or her full siblings. Correlations of the LRS of individuals with second degree relatives  were also obtained. All correlations between the LRS of relatives were calculated as the proband’s standardized LRS to the mean of the standardized LRS of all his or her relatives in the comparison group . All correlations were weighted by family size to provide equal weight to each group of relatives. For example, in determining the correlation amongst full siblings, individuals who had 4 full siblings were weighted 1/4 as much as those who had only one. Using SPSS, the ‘weight cases by’ command was used, the frequency of individuals for each type of relative was entered.In this study, broad sense heritability estimates  called ‘resources,’ and or a fixed  effect which we called ‘genes.’ These results were then compared with the actual results from the genealogical data to gain insight into which model best approximated the  data.Model 1, The Null Model: This model assumed neither genes nor resources played any role in the number of offspring an individual produced. Reproduction followed a random Poisson distribution and was based solely on certain fixed parameters, including the mean number of offspring per generation and the standard deviation of each generation’s size.Model 2, The Resources Model: Here, the number of children, and hence grandchildren, that an individual produced was tied to the number of resources that the F1 generation transmitted to their offspring.Model 3, The Genetic Model: This model was based on Mendelian inheritance, in which the number of children and grandchildren produced was determined by the alleles they inherited from each of their parents.Model 4, The Genes and Resources Model: A simulation was used to explore the impact of both genes and resources on an individual’s reproduction.y-axis are between mid-parent (mother and fathers LRS average) and offspring LRS and among full siblings  for each decade shown on the x-axis (1700–1919). Correlations were weighted by number .All reproductive values (LRS) were log transformed and standardized [/ standard deviation of decade)] by the individual’s birth decade. Pearson correlations on the Results of the resource model and the genetic model were based on 200 simulations . There wFamily size varied widely across and within decades and because individuals within a particular family were not independent, larger families were expected to inflate correlations. We addressed this problem by randomly choosing the reproduction of just two children . This method ensured larger families were not contributing more measurements in the regressions and within group correlations than smaller families. For the mid-parent (the average of the mother and fathers LRS) offspring correlations, we regressed the average number of children (F2 generation) from each set of parents on the average number of grandchildren of two randomly selected children (F3 generation). This process of randomly selecting two individuals and averaging their reproduction eliminated the erroneous inflation of both the full sibling and parent–offspring correlations from the results of the simulations. This same problem was solved for the genealogical data by standardizing LRS within everyone’s birth decade and statistically weighting the data by the number of individuals in each class of relatives .r = 0.42 while another pair is related at r = 0.58. These differences in relatedness between full siblings can be used to obtain unbiased narrow sense heritability estimates for any trait. We used a dummy variable , to estimate a ‘family effect.’ In other words, we could distinguish the effect of full siblings, due to their being members of the same family and living together , from the effects of genes that full siblings share identical by descent. Because heritability estimates can fluctuate considerably over time as the overall environmental impact on a given phenotype changes, these estimates only provided us with an accurate heritability estimate of LRS for contemporary Iceland.Genetic data for some individuals who were alive after 1996 were available from deCode genetics and were based on approximately 300,000 single nucleotide polymorphisms (SNP’s) for each genotyped individual. Therefore, accurate coefficients of relatedness were obtained for 8,456 pairs of full siblings and were entered into a restricted maximum likelihood (REML) model. The lifetime reproductive success of these individuals was standardized by sex, birth year and geographic region. This was only done for the genotyped individuals, however, because geographic region was not available for individuals in the historic dataset. Full siblings are related, on average, by a coefficient of relatedness of 1/2. Due to the process of meiosis, however, there are small but significant differences in coefficient of relatedness between them. For example, one pair of full siblings may be related at r = 0.63, p < 10−6). LRS was therefore considered to be a reasonable proxy for evolutionary ‘fitness.’Analysis of the genealogical data from Íslendingabók for all individuals born between 1700 and 1920 revealed that LRS was a strong predictor of the number of grandchildren an individual produced (r = 0.19 (p < 0.001) while there was no detectable relationship between the reproduction of parents and their offspring, r = 0.00, p = 0.08 .The overall relationship between the reproduction of all full sibling pairs, across all birth years (1700–1919) was significant and positive, p = 0.08 . Neverthr =  − 0.603, p < 0.001) and the correlation between parents and offspring . So as population wide reproductive rates increased, both full sibling and parent–offspring correlations declined. Population was also positively, but not significantly, correlated with the parent–offspring correlation . Finally, birth interval was weakly, but significantly, correlated with LRS (Pearson’s R = 0.041 (p < 0.001). In other words, full siblings who were closer in age had more similar fertility.There were major demographic changes that also interacted with these heritability estimates. Average reproduction per decade was negatively associated with the reproductive correlation among full siblings  of 0.137 with a standard error of (0.02). Adding a family effect  to the model and allowing it to compete with these coefficients of relatedness, however, revealed a family effect (f2) of 0.129 (0.03) and a genetic effect of 0.00 (0.05) This suggests that the heritability estimate (h2 = 0.137) was based solely on shared family effects among full siblings and was not due to shared genes. Furthermore, the intra-class correlation of LRS among the 8,456 pairs of full siblings was r = 0.076 (h2 = 0.152) reinforcing results from the REML model and indicating that the heritability estimate of LRS in modern Iceland may be lower than in previous centuries.A restricted maximum likelihood model (REML) entering the precise coefficients of relatedness for 8,456 pairs of full siblings yielded a narrow sense heritability estimate (h2) for LRS, but a significant shared family effect (f2) of parents on the reproduction of their children for the current population based on results from a restricted maximum likelihood model using precise IBD gene sharing (SNPs) amongst full sibling pairs. Finally, results of a model simulating the effects of genes and resources on LRS were most like the overall results from the genealogy  showed that an individual’s lifetime reproductive success (LRS) is strongly predicted by the reproduction of their full siblings but not their parents , Table 1Why do individuals reproduce like their siblings, but not their parents? Siblings bonds in humans are particularly strong, and brothers and sisters often maintain relationships throughout life . In hunth2 in the current population. Although most previous estimates of heritability’s using genealogies have shown a more moderate heritability (∼0.10) of LRS, these estimates have often been obtained using an animal model in which an entire pedigree is used and are therefore not able to parse specific intra-familial relationships. The low heritability estimates obtained in our study are consistent with Fishers fundamental theory of natural selection which states that additive genetic variance  for traits closely tied to fitness should be close to zero in natural populations at equilibrium   and the h2 decreases. This would also help to explain previous research revealing higher correlations between the LRS of parents and their offspring in resource rich environments  , is ofteronments .This study demonstrates that an individual’s LRS is best predicted by the reproduction of their full and half siblings. These correlations fluctuate over time which suggests that fertility rates and PI are sensitive to changes in the environment. Future studies can build on these methods and results, expanding both our understanding of the heritability of fitness and the impact of parents. For example, carefully examining the different environmental influences on LRS may help to distinguish between the effects of different types of relatives and common households from those of peer groups. In addition, expanding this analysis to other populations may enhance our understanding of the importance of sibling bonds, while also further teasing apart the root causes of sibling influence on fitness components. Overall, however, these results indicate that parental investment and or resources have had an important impact on the reproduction of offspring in Iceland.10.7717/peerj.2904/supp-1Supplemental Information 1Click here for additional data file.


Breeding value  at SRT was not efficient predicting which genotypes were more likely to reach the UYT stage. Number of families and progenies derived from a given progenitor were more efficient predicting the probabilities of the progeny from a given parent reaching the UYT stage. Large within-family genetic variation tends to mask the true breeding value of each progenitor. The use of partially inbred progenitors  would reduce the within-family genetic variation thus making the assessment of breeding value more accurate. Moreover, partial inbreeding of progenitors can improve the breeding value of the original (S0) parental material and sharply accelerate genetic gains. For instance, homozygous S1 genotypes for the dominant resistance to cassava mosaic disease (CMD) could be generated and selected. All gametes from these selected S1 genotypes would carry the desirable allele and 100% of their progenies would be resistant. Only half the gametes produced by the heterozygous S0 progenitor would carry the allele of interest. For other characteristics, progenies from the S1 genotypes should be, at worst, similar to those generated by the S0 progenitors.Breeding cassava relies on several selection stages . This study uses data from 14 years of evaluations. From more than 20,000 genotypes initially evaluated only 114 reached the last stage. The objective was to assess how the data at SRT could be used to predict the probabilities of genotypes reaching the UYT. Phenotypic data from each genotype at SRT was integrated into the selection index (SIN) used by the cassava breeding program. Average SIN from all the progenies derived from each progenitor was then obtained. Average SIN is an approximation of the breeding value of each progenitor. Data clearly suggested that some genotypes were better progenitors than others , suggesting important variation in breeding values of progenitors. However, regression of average SIN of each parental genotype on the number of their respective progenies reaching UYT resulted in a negligible coefficient of determination ( Most cassava breeding programs started in the 1970s or later. Ceballos et al.  proposedHowever, the impressive genetic progress achieved from 1975 to 1995 has slowed down considerably in the last two decades (1995–2015). Combined analyses of different reports from cassava breeding in Thailand indicate that gains from 1995 to 2015 are at best half of those observed in the previous two decades for FRY and DMC CIAT, . SimilarIt was expected that biotechnology tools, such as marker assisted selection, would help recover the rate of genetic gains. Molecular biology has been successful in diagnostics for cassava diseases and their genetic diversity  for cassava genetic enhancement based on promising results they had observed using phenotypic data  to estimate breeding values of progenitors of the more than 20,000 genotypes initially evaluated; (ii) assess the usefulness of these breeding values for predicting which genotypes eventually reach the most advanced stage of selection , grown in several locations and years, and (iii) attempt to identify factors that affect the probability of clone(s) from a given progenitor to reach the UYT stage.The current study consolidates phenotypic data from 14 years of successive trials in a sub-humid tropical environment of Colombia, from more than 20,000 genotypes initially evaluated in single row trials—SRT. The data consolidated, curated and organized for analysis can be accessed at Breeders apply a wide range of objectives in cassava in response to the diversity of production environments, management practices, and end uses. However, only a few are broadly accepted as common key traits for improvement: FRY; high and stable DMC; suitable plant architecture, and resistance to locally or regionally relevant pests and diseases. At CIAT, in addition to individual ratings, breeders integrate plant architecture and resistance to biotic/abiotic stresses into a single score indicating overall desirability of the above-ground plant appearance (plant type score or PTS) where 1 is very good and 5 is very poor. Because of the low heritability of FRY in early stages of selection, cassava breeders for many years have applied indirect selection for yield by using correlated traits with higher heritabilities, such as harvest index (HIN)  that integrates these four relevant variables, assigning them best-judgment weight  established by the breeder's experience  were grown in Palmira, Valle del Cauca, Colombia (CIAT headquarters), which offers fertile soils, moderate temperatures and availability of irrigation—ideal for high cassava productivity. Selection and harvest of plants took place at 9–10 months after transplanting. The only selection criterion applied was the capacity of the plant to produce eight vegetative cuttings (20 cm stem pieces) for the following stage of selection. This step initiated the long process of phenotypic recurrent selection as described below  or open  crossing among outstanding progenitors . Seed was germinated, seedlings grown for about 2 months in a greenhouse, and then transplanted to the field. The seedling plants F were groThis is the first stage where selection for agronomic performance takes place in the sub-humid environment (Caribbean coast of Colombia). The region is characterized by moderate rainfall  and a long dry season (3–4 months), typical of many cassava-growing regions of the world. Trials usually include about 1000–2000 genotypes, each represented by six to eight plants in a single row (1–2 ha), in a single location. About 150–250 genotypes are selected for the next stage of evaluation. An important feature of SRTs is that, being the first stage of the selection process, information from all progenies (selected or not) is available, thus providing unbiased information about the progenitors used to generate them.Each genotype is represented in three repetitions with 10-plant plots (two rows of five plants). A randomized complete block design is used in all remaining type of trials. All plants in each plot (except the front plant in each row) are harvested. PYTs are planted in a single location.Plots consist of four (or five) rows and five plants per row, with, three replications. The six (or nine) central plants are harvested to generate the data used in the selection process. AYTs are usually planted in a single location.This is the final stage in the CIAT-managed evaluation and selection process. Plot size, number of repetitions and planting arrangement is the same as those for AYTs. UYTs are planted for 2 consecutive years in 5–10 locations. Typically UYTs will have 20–25 experimental clones and 5–8 local or commercial checks. Farmer and end user criteria are used during each step of selection, and they are invited to participate for more intensive input and interaction with breeders during the harvest of AYTs and UYTs. In addition, planting material of the most promising clones is shared with key farmers for semi-commercial evaluation. In general, varieties are released by national programs only after successful performance (according to the farmers' and end-users' criteria) in these semi-commercial evaluations (0.5–1.0 ha).Data from evaluation trials conducted from 2000 through 2013 were used. Target growing conditions included various sites within the sub-humid environment, the most important cassava growing region in Colombia and in most of the world.This large database was prepared for analysis with SAS . The firFrom the initial number of genotypes evaluated in SRT, 2652 were selected and evaluated in PYT, 567 in AYT and only 114 in UYT. This study concentrates on the data from the first and last stages of selection  and will not consider the intermediate stages.Data from all the individual genotypes belonging to a given full- or half-sib family was consolidated to obtain the respective averages and other statistical parameters for the key variables: FRY, DMC, PTS, HIN, and SIN. Since progenitors are used to generate more than one family, averages for each progenitor across all the families that it had generated were estimated. The phenotypic average of all the progenies (across different families) generated by a given progenitor will be considered as the breeding value of that progenitor. Phenotypic data from the 9108 full-sib genotypes was used twice: for the estimation of breeding values of the progenitor used as female, and for the breeding value when used as a male.Data from each progenitor was not balanced because of lack of a uniform number of progenies evaluated from each progenitor. The number of crosses  generated from each progenitor was also variable, as was the number of years in which progenies from a given progenitor were involved. It is acknowledged therefore that breeding value as estimated in this study is not as accurate as that obtained, for instance, from a diallel study. However, the estimated breeding values fully agree with the original concept in Falconer described earlier, and are based on actual data generated by an ongoing breeding process.Progenitors represented by fewer than 50 genotypes among the progeny, across all families in which they had been used, were discarded from the analysis. A sample size of <50 individuals was considered too small to properly represent the breeding value of the respective progenitor. The initial number of progenitors (297) was therefore reduced to 107.A large dataset was consolidated from the different trials conducted from 2000 to 2013. A total of 20,229 genotypes were evaluated in SRT. Table A total of 114 genotypes were evaluated in different UYTs in the sub-humid environment during the 2000–2013 period. A key objective of this study was to identify factors that influence the probability of clone(s) from a given progenitor to reach the UYT stage, taking into consideration that, in vegetatively propagated crops, breeding values can be measured across generations with the same genotypes. Progenitors of the 114 clones that reached UYTs were therefore identified. Only three progenitors  of clones in UYTs were not included in the study because they were represented by fewer than 50 progenies. The progenitors of clones reaching the UYTs that are analyzed in this study are listed in Table Selection from SRT, through PYT, AYT, and UYT is based on the SIN that integrates the information of four key variables . If the selection index is formulated well, average SIN for the progenies of each progenitor should be the parameter most closely associated with the true breeding value of each progenitor measurable at SRT. Table r2 = 0.05, indicating that breeding value  is not a good predictor of the probabilities of a clone from a given progenitor reaching the UYT.Figure In addition to the average SIN values, Table r2 value from the regression analysis of number of progenies from a progenitor reaching UYT on the total number of progenies per progenitor (0.48) was considerably better than the same parameter from a regression based on average SIN in Figure r2 = 0.40) than average SIN of the probability of its progeny reaching UYT.The plots presented in Figure n = 50. This number was a reasonable starting point  but, nonetheless it was arbitrary. Therefore, an exercise was made to analyze the relationship between average SIN at SRT and the probability of progenies reaching UYTs using different family sizes. Figure It is clear that family size, as expected, strongly influences the results of this study. The initial analysis arbitrarily set a minimum family size This study focuses on data from the extremes of the selection process—from the earliest (SRT) to the last stage (UYT). Between these two steps, however, are the PYT and AYT stages. It has been suggested that the phenotypic performance of individual genotypes may “evolve” through the different stages of selection. Epigenetic effects and the impact that biotic and abiotic factors have in the quality of planting material may affect differentially the performance of different genotypes through time  allows the selection of genotypes that have shown consistently outstanding performances. Data from SRT is of particular relevance because it offers unbiased information about the progenitors, i.e., data from all progenies, selected or not. Although SRT data is prone to large experimental errors , averages across many genotypes tend to provide more robust information.www.nextgencassava.org) will facilitate achieving a more balanced number of progenies from each progenitor.Selection of progenitors based on their general combining ability or breeding value in cassava, originally proposed by Ceballos et al.  is furth1 or S2 genotypes). This approach would reduce considerably the within-family genetic variation and in turn help breeders to more easily identify the true breeding value of these progenitors. Inbreeding depression is prevalent for FRY but not so much for traits such as plant height and traits related to above ground biomass  arises from the large within-family segregations that breeders observe in their nurseries, particularly for traits such as FRY. It is this large within-family variation, however, that weakens the usefulness of breeding value in cassava. It is the best clone(s) within each family that may eventually reach UYTs and it is the identification of that particular clone that is difficult and expensive. The use of homozygous progenitors in cassava would lead to a reduction of within-family genetic variation, in fact to zero unless there existed some residual heterozygosity . This concept is described on the left side of Figure 1 genotypes would be selected for agronomic performance as well. Similarly a “complementary” breeding population may be developed for increased levels of DMC . One population for example can be the source for defensive traits, while the other would provide desirable quality traits to the resulting hybrids.Partial inbreeding would not only contribute to identifying more clearly the breeding value of progenitors but it could also be the way to improve it  from the first step of selection in the two complementary populations presented in Figure 1 genotypes selected for resistance to CMD or high DMC are then crossed with the source of tolerance to herbicide. The resulting crosses will be heterozygous for the monogenic traits and intermediate for DMC. Self-pollination of the resulting crosses will allow the recovery of S1 genotypes that are homozygous for CMD and for tolerance to the herbicide  for tolerance to the herbicide. The initial products . For other traits the frequency of desirable alleles at worst should be (on average), similar in the S1 genotypes and in the S0 progenitors from which they were derived. More likely, however, for other traits the frequency of desirable alleles should be higher because deleterious factors  exposed in partially inbred genotypes would be eliminated. Crosses among the selected partially inbred lines, because of their enhanced breeding value, will generate (on average) better performing hybrids. A second and fundamental advantage of the proposed scheme is that it allows for the gradual, consistent, stepwise fixation of simply inherited traits in the partially inbred selected genotypes. Eventually, partially inbred lines from different heterotic groups (when identified or developed) would allow the implementation of conventional reciprocal recurrent selection schemes.The key principle here is that the gametes produced by the selected SThere are several traits in cassava that have relatively simple inheritance and would be easy to fix through  inbreeding. For root quality traits, carotenoids, and DMCs; amylose-free starch and small starch granules have been reported to have high heritabilities or to depend on single recessive genes. Resistance to pests and diseases  and plant architecture traits (erect vs. branching types) have simple inheritance. Certainly another group of traits that would benefit from partial inbreeding are those arising from genetic transformation and gene editing . Future advances in our knowledge of plant biology (particularly from Arabidopsis) will foster the need and intensity of trait introgression as they are identified in cassava. The reduced within-family variation in progenies derived from partially inbred parents could also contribute toward improvement in more complex traits such as FRY.Results from this study highlight some key features of cassava breeding. There is a need to shift the current system based on crossing elite germplasm hoping to identify even better progenies, into a system based on the improvement of progenitors with enhanced breeding values, through partial or full inbreeding. This will improve the efficiency of cassava breeding and increase the likelihood of sustained and predictable genetic gains.HC implemented the changes in the breeding process that generated the phenotypic data analyzed in this article. He made the analyses and wrote the manuscript; JP was an associate to the breeding program and curated and stored data year after year; OJ conducted a 1-year internship at the program, retrieved the stored data and organized it for its analysis; JL conducted the trials at the sub-humid environment; NM coordinated the production of segregating progenies and the seedling nurseries from which the planting material for the SRT was generated; FC is a senior associate of the program that helped in the overall activities of the program; LP is an assistant in charge of data uploading and curation; CH is the coordinator of the program and also a senior cassava breeding. He reviewed and improved earlier versions of the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Much effort is put into identifying causative quantitative trait nucleotides (QTN) in animal breeding, empowered by the availability of dense single nucleotide polymorphism (SNP) information. Genomic selection using traditional SNP information is easily implemented for any number of genotyped individuals using single-step genomic best linear unbiased predictor (ssGBLUP) with the algorithm for proven and young (APY). Our aim was to investigate whether ssGBLUP is useful for genomic prediction when some or all QTN are known.Simulations included 180,000 animals across 11 generations. Phenotypes were available for all animals in generations 6 to 10. Genotypes for 60,000 SNPs across 10 chromosomes were available for 29,000 individuals. The genetic variance was fully accounted for by 100 or 1000 biallelic QTN. Raw genomic relationship matrices (GRM) were computed from (a) unweighted SNPs, (b) unweighted SNPs and causative QTN, (c) SNPs and causative QTN weighted with results obtained with genome-wide association studies, (d) unweighted SNPs and causative QTN with simulated weights, (e) only unweighted causative QTN, (f–h) as in (b–d) but using only the top 10% causative QTN, and (i) using only causative QTN with simulated weight. Predictions were computed by pedigree-based BLUP (PBLUP) and ssGBLUP. Raw GRM were blended with 1 or 5% of the numerator relationship matrix, or 1% of the identity matrix. Inverses of GRM were obtained directly or with APY.Accuracy of breeding values for 5000 genotyped animals in the last generation with PBLUP was 0.32, and for ssGBLUP it increased to 0.49 with an unweighted GRM, 0.53 after adding unweighted QTN, 0.63 when QTN weights were estimated, and 0.89 when QTN weights were based on true effects known from the simulation. When the GRM was constructed from causative QTN only, accuracy was 0.95 and 0.99 with blending at 5 and 1%, respectively. Accuracies simulating 1000 QTN were generally lower, with a similar trend. Accuracies using the APY inverse were equal or higher than those with a regular inverse.Single-step GBLUP can account for causative QTN via a weighted GRM. Accuracy gains are maximum when variances of causative QTN are known and blending is at 1%. Initially, genomic selection used a large set of single nucleotide polymorphisms (SNPs) for genetic evaluation without the explicit identification of quantitative trait loci (QTL) . SNP estThose Bayesian methods could not be implemented directly for commercial populations, for which only a fraction of animals are genotyped. The methods were incorporated indirectly by using pseudo-observations and combining results with pedigree structure , 3. SuchWhen the number of genotyped animals is small, the use of Bayesian regression was found to increase accuracy of genomic prediction for many traits , 8. HoweWhen the number of genotyped animals is very large, the computing costs of ssGBLUP, especially for inverting the GRM, could be prohibitive. Such costs could be reduced if the dimensionality of the genomic information is limited and exploited to reduce computations. VanRaden  found thn SNPs being retained, the dimensionality cannot be greater than n. Subsequently, a trait-specific GRM that is created via SNP selection or GWAS is likely to have lower dimensionality than a generic GRM. Subsequently, the ratio of trait-specific to generic dimensionality could be an indicator of complexity of the trait. In particular, a low value of this ratio for a trait-specific GRM that results in the highest accuracy of GEBV would indicate that relatively few genes control this trait.The concept of dimensionality of the genomic information, as described above, applies to generic GRM; however, it can also be applied to trait-specific or weighted GRM. If SNP selection for a specific trait results in only n QTN, the rank of the trait-specific genomic information (including GRM) is n, since only the QTN need to be used for the evaluation, and the accuracy of the genomic prediction reaches 100% if the dataset is large enough to estimate all QTN effects accurately. More realistically, if only a fraction of the causative QTN is identified, then both causative and non-causative SNPs must be used in the analyses. Some studies showed no improvement in accuracy of genetic evaluations when sequence data was included [Recent advances in sequencing methodologies have renewed the interest in finding genes or QTN. If a trait is influenced by included , 19, wheincluded –25. Brønincluded  reportedIf some causative QTN are identified, it would be useful to incorporate them in a simple analysis with increased gains in accuracy. The first goal of our study was to determine the properties of ssGBLUP when all or some QTN are identified and the second goal was to determine the dimensionality of genomic information when QTN are known and whether APY is applicable.SNP-BLUP and GBLUP are equivalent models . In partAssuming that the additive variance and gene frequencies are known, and under certain assumptions including Hardy–Weinberg and linkage equilibrium, the SNP variance is estimated as follows:entclass1pt{minimaAssume a priori unequal SNP variances:ariances  or, alteIn other words, pjqjσa2) , but thiUsing the software QMSim , we simuGenomic information was available only for animals in the last five generations. All animals with progenies were genotyped, i.e. 24,000 sires and dams. In addition, 5000 animals were randomly selected from the last generation to be genotyped. We simulated 10 chromosomes each 150 cM long and with evenly spaced 6000 SNPs, i.e. 60,000 SNPs in total. Each chromosome contained either 10 or 100 biallelic randomly located QTN , i.e. 100 or 1000 QTN in total that are not included on the 60,000-SNP array. QTN effects were sampled from a gamma distribution with a shape parameter of 0.4 and scaled internally for a genetic variance of 0.3, and explained 100% of the genetic variance of the trait.We used two methods for genetic evaluation: PBLUP and ssGBLUP. Both included 75,000 phenotypes in generations 6 to 10 and all pedigree information. The linear model was the same for all analyses and scenarios:The first method was PBLUP with a et al.  and its a et al. :\documenMatrix g et al. ; (d) as mentclass2pt{minimThen, a scaled breeding , and \doentclass1pt{minimar by APY . In the The quality of predictions was assessed for the 5000 genotyped animals in the last generation. The accuracy was measured as the Pearson correlation between the genomic EBV (GEBV) and the simulated true breeding value (TBV). All calculations were done by using the BLUPF90 program suite , preGSf92 between adjacent SNPs with a mean (standard deviation) of 0.63 (0.06) across all chromosomes and generations.We observed very little difference between the realized accuracies across the replicates ≤0.01), and standard errors were <0.005, thus only the results of one replicate are shown. Accuracies obtained with different options are in Figs. , and staThe accuracies obtained with PBLUP and ssGBLUP using only non-coding SNPs are in Fig. Figure Identifying all causative QTN and their weights is unrealistic, and Fig. To investigate how blending of the GRM affects the accuracy with causative QTN, we conducted analyses using GRM calculated from QTN assuming equal weights and different blending factors Fig. . While aWhen all causative QTN are known, blending with pedigree relationships only adds noise and is done for numerical stability. Blending at a 5% factor adds more noise than blending at 1%, and blending with the identity matrix may be slightly superior. The lower accuracy that is obtained with the 1000 QTN data can be explained by the use of an unweighted GRM. In SNP-BLUP, a large amount of data overwhelms the priors of variances when the number of SNPs is small (say 100) but less when it is larger (say 1000). Since SNP-BLUP and GBLUP are equivalent , 41, theAssigning zero as a weight for SNPs around causative variants increased the accuracy, until the weight of all non-causative SNPs was set to 0, which caused accuracies to reach the maximum of 0.99 for the 100-QTL scenario and 0.95 for the 1000-QTL scenario  and 77 times (100 QTN) with the 5% blending factor. While the extra dimensionality added noise, it made the matrix more stable to explicit inversion.The numbers of eigenvalues obtained with the 10% top QTN are in between those obtained with no causative SNPs and with only causative SNPs. In general, the dimensionality of unweighted GRM could be equal to the number of ICS or close to 4NeL and the dimensionality of GRM constructed with causative QTN only would be equal to the number of those QTN or smaller (if some causative QTN have very little effect or are in LD). With GRM uniformly weighted for SNPs  and with true variances for all or the top 10% causative QTN, intermediate numbers of eigenvalues will be obtained.Information on causative QTN can be included in single-step GBLUP via a weighted GRM. To obtain a high accuracy of prediction, the matrix has to be constructed using realistic weights for the causative QTN, by possibly eliminating non-coding SNPs that are located close to causative QTN, and with very little blending with pedigree information, i.e. the minimum required for stability. Use of the APY algorithm for inversion of GRM results in increased or similar accuracy as with the regular inverse but at much reduced cost, regardless of the inclusion of SNPs, QTN, or both. Finally, the dimensionality of the genomic information is roughly the number of independent chromosome segments for unweighted GRM, the number of causative QTN for GRM weighted with their exact weights, and in between with a fraction of causative QTN or with GRM using weights from GWAS.


Trifolium subterraneum L.). In a bi-parental population the broadsense heritability in methanogenic potential was moderate (H2 = 0.4) and allelic variation in a region of Chr 8 accounted for 7.8% of phenotypic variation. In a genome-wide association study we identified four loci controlling methanogenic potential assessed by an in vitro fermentation system. Significantly, the discovery of a single nucleotide polymorphism (SNP) on Chr 5 in a defined haplotype block with an upstream putative candidate gene from a plant peroxidase-like superfamily (TSub_g18548) and a downstream lectin receptor protein kinase (TSub_g18549) provides valuable candidates for an assay for this complex trait. In this way haplotype variation can be tracked to breed pastures with reduced methanogenic potential. Of the quantitative trait loci candidates, the DNA-damage-repair/toleration DRT100-like protein (TSub_g26967), linked to avoid the severity of DNA damage induced by secondary metabolites, is considered central to enteric methane production, as are disease resistance  and ribonuclease proteins . These proteins are good pointers to elucidate the genetic basis of in vitro microbial fermentability and enteric methanogenic potential in subterranean clover. The genes identified allow the design of a suite of markers for marker-assisted selection to reduce rumen methane emission in selected pasture legumes. We demonstrate the feasibility of a plant breeding approach without compromising animal productivity to mitigate enteric methane emissions, which is one of the most significant challenges to global livestock production.Mitigating methane production by ruminants is a significant challenge to global livestock production. This research offers a new paradigm to reduce methane emissions from ruminants by breeding climate-clever clovers. We demonstrate wide genetic diversity for the trait methanogenic potential in Australia’s key pasture legume, subterranean clover ( Among heat-trapping gasses, methane is one of the most potent, about 25 times more than COcombined . As withcombined . Approxicombined .Methane is an unavoidable by product of the fermentation of feed in many animals, particularly ruminants . The worMethane production is influenced more by feed characteristics than animal genetic factors . The chein vitro microbial fermentability and methanogenic potential in the rumen ranged dramatically with the lowest methane-producing species, Biserrula pelecinus L., producing 90% less methane (4 mL CH4 g-1 dry matter incubated) than the highest methane-producing species, Trifolium spumosum L. (51 mL CH4 g-1 dry matter incubated) (Biserrula pelecinus L.) (Trifolium subterraneum L.)  , predominantly inbreeding, and has a well-assembled and annotated genome  and red clover (T. pratense L.). It also complements genomic studies in the model annual legume Medicago truncatula L. and the important perennial fodder legume, lucerne (M. sativa L.) (Variation between pasture species for cubated) . Furtherinus L.)  and subtneum L.)  and therneum L.) . Subterrninicum) , with ead genome . Elucidativa L.) .in vitro . These parents were initially chosen as they differ widely in a range of agronomic and morphological characters (P < 0.05) variability in the methanogenic potential amongst the two parents, ranging between 37.08 and 34.14 mL of CH4 per gram of DM supplied respectively .The Faracters . There wn design . In Phas3 lines, replicated twice; and (iii) the remaining 158 F3 lines, which were replicated once. In Phase II, a separate randomization was used for the IVFT test which extended over 3 days. To assess inter-day variability, 24 of the 158 single-pot plant samples of F3 lines were sub-divided for analysis on different days bringing the total of plant samples to 228. Each of these 228 biological samples was subdivided into triplicates for IVFT analysis for assay replication.In Phase I, the experimental units were pots, 204 in total, comprising: (i) the two parents, Daliak and Woogenellup, replicated three times; (ii) 20 random FT. subterraneum genotypes  was grown in the field at Shenton Park, Western Australia  and assayed in the laboratory. A panel of 124 Seeds of the 124 diversity panel lines were obtained from the ATGRC. All accessions were replicated twice in the field for biological replication and again in triplicate in the laboratory for assay replication. A row-column design with two-directional blocking was generated for the field and laboratory.All designs were generated using the experimental design software DiGGer  in R sofRhizobium inoculum, in the form of clustered clay granules (ALOSCA Technologies Pty Ltd.), was applied 7 days after sowing.Ten plants per line were grown in both experiments. Seeds for the 2009 experiment were sown into pots (22 cm diameter) in a phytotron maintained at 20/15°C day/night temperatures with 60% humidity. Group C Rhizobium inoculum  was sprinkled onto peat pots 7 days after sowing and watered in gently. Peat pots were watered daily, while soluble fertilizer  was watered on weekly at a rate of 5 g/10 L. Seedlings were transplanted to the field into a moist, weed-free seedbed, described as a loam-dressed sand (2) 6.5. The trial site was hand-weeded and irrigated by overhead sprinklers as required. Other site details and management are the same as described in Seeds for the 2011 experiment were sown into hydrated Jiffy-9 peat pots  in a glasshouse. Three seeds were sown per pot, which were randomly thinned to a single seedling per pot 20 days later. Group C sed sand , with pHin vitro fermentability testing. The material was then freeze-dried in a Bench-top Freeze Dryer  and ground  to pass through a 1.0 mm screen. Material was stored at room temperature in sealed containers for further analysis.The edible plant parts (leaves and stems less than 10 cm long) were harvested before flowering for in vitro batch fermentation system commonly used to examine plants and their extracts with rumen fluid (2:10% CO2:10% H2) to expel oxygen from the tubes. On the experimental day, rumen fluid was collected from two fistulated sheep fed a general maintenance diet consisting of lupins and oaten chaff  2 h after feeding. This study was approved by and the donor sheep were cared for in accordance with the guidelines The University of Western Australia (UWA) Animal Ethics Committee (AUP number RA/3/100/1171). An electric vacuum pump fitted with a plastic tube was used to collect rumen fluid and then transported to the laboratory where it was strained through cheesecloth to remove large particles. After straining, the rumen fluid was pooled, transferred into the anaerobic chamber, and buffered to pH 7.2 using McDougall’s buffer , and fixed effects were estimated using empirical best linear unbiased estimation (E-BLUE). The obtained prediction error variance matrix for the variety effects was used to calculate broad-sense heritability  for each1. The adjusted (predicted) mean values for methanogenic potential were used for quantitative trait loci (QTL) and genome-wide association study (GWAS) analyses.All statistical analyses were performed using ASREML-R  and R so2 as described in 3 (The high-density single nucleotide polymorphism (SNP) linkage map was constructed using MultiPoint 3.3bed in 3 . QTL witbed in 3 . MissingT. subterraneum. The core collection was formed by a two-step selection process using ecological data and stratified proportional strategy followed by combined datasets and a maximizing strategy to best represent the entire collection  was extracted from a single plant from each of the 97 accessions of the subterranean clover core collection and the 27 diverse Australian cultivars, and sequenced. High-quality whole-genome resequencing (WGRS) data were generated for all 124 accessions and cultivars using paired-end sequencing libraries with an insert size of approximately 550 bp sequenced on an Illumina HiSeq 2000 sequencer. A total of 13.89 billion paired-end resequencing reads were generated with 5.27 billion reads uniquely mapped to the advanced genome assembly (Tsub_Refv2.0)  using BWiew v4.2 .q-value  and the diversity panel of 124 core collection lines and cultivars was associated with specific regions in the advanced assembly (Tsub_Refv2.0)  using QT3 v2.3.7   and 2011  measurements. Furthermore, the broad-sense heritability (H2 = 0.4) reflected the complexity of the assayed trait.The methanogenic potential measured in the IVFT was assessed using a linear mixed model fitting procedure . High cotability  calculatP < 0.0002 at a threshold logarithm of odds (LODs) of threshold 2.5 defined by permutation tests] for methanogenic potential, Q_MP_LG8, was identified on Linkage Group 8 (LG8) with the phenotypic data available (Table 1). Q_MP_LG8 was identified as a significant QTL accounting for 7.8% of the variation in methanogenic potential. Within the bi-parental cross, the ‘Daliak’ alleles had a positive additive effect  (Table 1).The phenotyping information for methanogenic potential . The GWAS resulted in four markers, which reached suggestive P-values below 1e-5 on chromosomes 2, 5, 7, and 8 . The SNP located on Chr 5 was located in a haplotype block containing six other SNPs with a total length of 27.63 Kbp.WGRS data from the diversity panel were analyzed with phenotyping data collected from the GWAS method using TASSEL v5.2.30 for estimating MTAs , a suppressor-of-white-APricot splicing regulator (TSub_g26969), a transcription factor bHLH122-like protein, two disease resistance proteins , two ribonuclease proteins , a flowering time control FY-like protein (TSub_g26973) and a far1-related sequence 10-like protein (TSub_g26976) in addition to two uncharacterized proteins (TSub_g26968 and TSub_g26977) (Table 1).The Figure 2 and Table 2). Being in the haplotype block, these two genes are the most stable and promising candidates for designing molecular markers to track haplotype variation for this complex trait. The haplotype block containing the MTA SNP on Chr 5 with a total length of 27,629 bp was used to design PCR-ready markers for MAS for this complex trait . On Chr 8, we identified an upstream tubulin beta-1 chain (TSub_g27846) and a downstream transmembrane protein (TSub_g27847) at a distance of 12,050/3,060 bp respectively, from the suggestive SNP. The SNP located on Chr 5 was mapped in a haplotype block with TSub_g18548 (plant peroxidase-like superfamily) upstream at 22,314 bp and TSub_g18549 (lectin receptor protein kinase) downstream at 1,150 bp  and ssp. brachycalycinum (23.3 mL CH4/g DM), both collected from Italy , linked to modulating the severity of DNA damage induced by the production of secondary metabolites considered important in enteric methane production. A plant having more of this or a variant of this that minimizes DNA damage by secondary compounds may be able to ‘handle’ more of the secondary compounds which ultimately then influences the rumen microbial organisms. Also implicated are three disease resistance genes , a suppressor-of-white-APricot splicing regulator (TSub_g26969), a transcription factor bHLH122-like protein and ribonuclease proteins . These genes are good indicators for elucidating the genetics in subterranean clover of in vitro microbial fermentability and enteric methanogenic potential.Given the imperative to reduce the methanogenic potential of ruminant feed and the likely sizeable environmental effect on its phenotypic expression, this study was designed to assess the heritability of methanogenic potential and to study the feasibility of a marker-assisted approach to its selection. The intermediate/low broadsense heritability of C. roseus  upstream gene and a TSub_g18549 (lectin receptor protein kinase) downstream gene. The plant peroxidase-like superfamily performs a variety of biosynthetic and degradative functions. Among the sub-families, Class I includes intracellular peroxidases present in fungi, plants, archaea and bacteria, called catalase-peroxidases, that can exhibit both catalase and broad-spectrum peroxidase activities, depending on the steady-state concentration of hydrogen peroxide. Class II includes ligninase and other extracellular fungal peroxidases, while Class III comprises classic extracellular plant peroxidases, such as horseradish peroxidase . Class I. roseus . The sigN-acetylgalactosamine, fructose, chitobiose, and other complex sugars (in vitro studies using the rumen simulation technique (RUSITEC) to better mimic what may be occuring in vivo are recommended for phenotyping this complex trait while functionally validating the candidates identified in the present study.The lectin receptor protein kinases contain legume lectin motifs originally found in the seeds of leguminous plants . Legume x sugars . It is wx sugars  and feedx sugars . Thus, ix sugars . The canThe origin of the assessed germplasm spans the Mediterranean basin from Morocco and the Iberian Peninsula in the west to Turkey and Israel in the east and an altitudinal range from 3 to 1300 m asl. Some traits, such as flowering time, are strongly associated with climatic and other environmental variables over this broad range of ecological conditions indicating their adaptive nature . Other tTrifolium and other legumes. The genomic and molecular data from the present study can now be exploited for analysis of genetic diversity and trait-dissection, as well as gene tagging for MAS. Phenotyping for methanogenic potential is costly and uses fistulated sheep. The availability of diagnostic markers based on the suite of genes identified will minimize the need for animals in the screening process. A similar approach in the development of diagnostic markers for MAS in subterranean clover and related species can be applied to other economic traits, such as phosphate-use efficiency and oestrogenic isoflavone content , or the rumen microbial population responsible for generating the methane through the use of feed additives . Our wor content .Our results contribute significantly to meeting the global challenge for ruminant livestock industries to improve productivity and production efficiency while also reducing their environmental footprint. The suite of genes identified through GWAS (7) and QTL analyses (11) form the basis of a resource for use in breeding to modify plant feed composition and influence the amount of methane generated from fermentation by ruminal microbes, while also improving feed efficiency. The analyses demonstrate the feasibility of selection for haplotypes of alleles within identified genes to move the genetic constitution of pastures toward lower enteric methane production.PK performed the research under the guidance of RA and WE and wrote the manuscript with contributions from PB, SI, HH, GK-G, JW, KaS, PV, KeS, ZD, PN, DE and CR, PK, WE, PV, ZD, PN and KeS designed the IVFT experiments, and PK performed the experiments. KeS provided the statistical expertise and conducted the analyses for the IVFT methanogenic potential data. PK, RA, SI and WE designed the sequencing experiments, and PK, SI and KaS performed the experiments. PB HH and GK-G did the bioinformatics analysis. JW provided the support and expertise on the QTL IciMapping software used to develop the next-generation linkage map and QTL analyses for the study. All authors read the manuscript and approved the content.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Although gene‐environment (G× E) interactions play an important role in many biological systems, detecting these interactions within genome‐wide data can be challenging due to the loss in statistical power incurred by multiple hypothesis correction. To address the challenge of poor power and the limitations of existing multistage methods, we recently developed a screening‐testing approach for G× E interaction detection that combines elastic net penalized regression with joint estimation to support a single omnibus test for the presence of G× E interactions. In our original work on this technique, however, we did not assess type I error control or power and evaluated the method using just a single, small bladder cancer data set. In this paper, we extend the original method in two important directions and provide a more rigorous performance evaluation. First, we introduce a hierarchical false discovery rate approach to formally assess the significance of individual G× E interactions. Second, to support the analysis of truly genome‐wide data sets, we incorporate a score statistic‐based prescreening step to reduce the number of single nucleotide polymorphisms prior to fitting the first stage penalized regression model. To assess the statistical properties of our method, we compare the type I error rate and statistical power of our approach with competing techniques using both simple simulation designs as well as designs based on real disease architectures. Finally, we demonstrate the ability of our approach to identify biologically plausible SNP‐education interactions relative to Alzheimer's disease status using genome‐wide association study data from the Alzheimer's Disease Neuroimaging Initiative (ADNI). To control either the family‐wise error rate (FWER) or FDR, the interaction P‐values generated via LR or Wald tests must to be adjusted using the desired MHC approach for the family of p separate hypothesis tests. Variations of this approach exist that also perform a separate hypothesis test for each genetic marker. These include the case‐only gene‐environment association test, the test of marginal association  and the combined marginal and interaction test . Selection of the elastic net penalty parameter λ can be done based on cross‐validation or to generate a specific number of nonzero coefficients. Note that if marginal terms for additional covariates are included in either model The workflow for the original SPUR method, as described in Frost et al. , is illuThe test stage model for SPUR is an unpenalized multiple logistic regression model with marginal and interaction terms for all genetic markers that had nonzero coefficients in the penalized screening stage mode l :P‐values for the two test stage models. Although standard G× E approaches failed to detect any statistically significant interactions in this data set, this SPUR‐based analysis successfully identified statistically significant associations between SNPs and smoking status relative to bladder cancer status that were biologically plausible based on prior research findings.In the bladder cancer example included in Frost et al. , the mar2.5The version of the SPUR method described in Frost et al.  had two The original SPUR method required all genetic markers in the data set to be fit by a single penalized multiple logistic regression model in the screening stage. Because it is computationally impractical to fit models with more than several tens of thousands of predictors with current penalized logistic regression implementations , this requirement meant that the original SPUR method could not be used with truly genome‐wide data sets measuring hundreds of thousands to millions of genetic markers.H0:∑i=1qβGiE=0. Although a Wald or LR test was performed for individual G× E interactions in significant test stage models, with a correction for the total number of interactions in the model, these adjusted interaction P‐values failed to account for the prior global test and could therefore only used as an informal guide to help researchers identify promising interactions for follow‐on investigations.In the original SPUR method, statistical significance was only formally assessed for the global test of the null hypothesis that none of the G× E interactions in the test stage model were significant, i.e., 33.1To address the limitations of the original SPUR method, as outlined in Section 3.1.11.aj for each of the p genetic markers in the input data set. Using the notation from Section Compute a score statistic 2.k genetic markers with the largest aj. They suggest setting k=10q, where q represents the desired number of markers selected from the penalized regression model.Select the 3.q predictors.Fit the penalized regression model and select the LASSO penalty λ to achieve exactly 4.q selected markers and the k−q omitted markers satisfy the expected Karush‐Kahn‐Tucker (KKT) conditions specified by equations Check that both the 5.k by a factor of 2 and repeat starting at step 2.If one of the omitted markers fails to satisfy the expected KKT condition, increase To support the analysis of large GWAS data sets, i.e., data sets with hundreds of thousands to over one million markers, we have extended the SPUR method to include a prescreening step that uses a score statistic to reduce the set of measured genetic markers to a size feasible for penalized regression. This technique is motivated by the work of Wu et al.  in whichk to be at least 20q  and skip the explicit check of the KKT conditions and potential iterative refinement of k. This simplification is motivated by the observation in Wu et al.  usually suffices to satisfy the KKT conditions. The score statistic‐based prescreening step included in SPUR also differs from the Wu et al.  under H0 given rejection of the parent hypothesis.To address the lack of a formal significance test for specific G× E interactions, we have extended the SPUR method to use the hierarchical FDR technique of Yekutieli  to test q within each level of the hierarchy will provide level‐specific FDR control of approximately:δ* is approximately 1, d is the number of discoveries made within the level , and f is the number of families tested. For the bladder cancer example presented in Frost et al.  and d=4 for the four SNP‐smoking interactions that had significant Wald tests at a level‐specific FDR of q=0.1. Therefore, if hierarchical FDR been employed in this case with q=0.1, approximate FDR control for the interaction‐specific Wald test results would have been achieved at a level of 0.1(2+4)/(4+1)=0.12.As detailed in Yekutieli , hierarct et al. , f=2 . Thus, the SPUR method can provide FDR control on just a single level of postfiltering hypotheses using standard FDR methods .2.SPUR using just the gene‐environment correlation filter. An omnibus test is also skipped in this case with significance of G× E interactions again assessed using FDR‐adjusted Wald tests.3.SPUR using hierarchical FDR, as detailed in Section 4.q‐value computed for the omnibus test. The FDR adjustment is based on the family of two omnibus test P‐values, one for the marginal association filter and one for the gene‐environment correlation filter. To support the comparison of this approach with the other methods, the number of markers to retain in the test stage model was set equal to the number with a real G× E interaction.SPUR based on just the omnibus test for interactions considering both the marginal association filter and the gene‐environment correlation filter in parallel. Specifically, each of the G× E terms included in the test stage model is assigned the FDR and four variations of the extended SPUR method:k=20q, where q is set to be the same for all SPUR methods and for the two screening‐testing benchmark approaches. The SPUR method and all benchmark approaches were implemented in R =,log(1.5)) for i=1,...,10, i.e., a marginal association was simulated for the first 10 SNPs. Score statistic‐based prescreening was configured to remove 1,950 of the 2,000 SNPs. The λ parameter used with the elastic net penalty for the screening stage models was set so that the number of nonzero coefficients in the estimated model, q, was 25. The number of markers retained after screening for the standard screening‐testing method was also set to 25 to support a comparative evaluation. The type I error rate was computed at an α=0.05 level for all benchmark method and SPUR using either the marginal association filter or the gene‐environment correlation filter, i.e., all methods that generate unadjusted P‐values for individual G× E interactions.A simple simulation design, based on the study in Dai et al. , was usei et al. , the othβGiE=log(3) with all other interaction coefficients set to 0. For both models the SNP‐SNP correlation was set to 0.1 and the SNP‐exposure correlation was set to 0.3. For model 1, the other coefficients were simulated as simulated as =,log(1.5)) for i=1,...,5 and the SNP‐exposure correlation was 0 except for the second five SNPs, i.e., only SNPs with a true G× E interaction had a marginal association and none of the SNPs correlated with the exposure had a true interaction. For model 2, the other coefficients were simulated as simulated as =,log(3)) for i=6,...,10 and the SNP‐exposure correlation was 0 except for the first five SNPs, i.e., only SNPs with a true interaction were correlated with the exposure and none of the SNPs with a marginal association had a true interaction. Score statistic‐based prescreening was configured to remove 1,900 of the 2,000 SNPs. The λ parameter used with the elastic net penalty for the screening stage models was set so that the number of nonzero coefficients in the estimated model, q, was 5. Standard screening‐testing methods were also configured to retain five SNPs after the first stage. Statistical power for all SPUR variations and benchmark methods was computed as the proportion of the q SNPs with G× E interactions that were identified as significant according to an FDR q‐value of 0.1.To assess statistical power, data were simulated according to two different models. Model 1 was designed to work well with the marginal association filter and model 2 was designed to favor the gene‐environment correlation filter. For each of these models, a collection of data sets was simulated using a similar approach to that described for the type I error control assessment above. For these simulated data sets, 2,000 SNPs were generated with true G× E interactions for the first five markers. Coefficient values for these interactions were set as 3.2.3U and no association with the outcome. No correlation was simulated between markers, between exposures, or between markers and exposures. The binary outcome variable, reflecting disease case‐control status, was simulated according to the model represented by equation γl,m in the Aschard model set to ±log(1.5) )=0.95), SPUR prescreening was set to remove 1,900 SNPs and a total of five SNPs were retained in the final test stage models. All five interactions were generated using a fixed environmental exposure for each disease. For breast cancer this was the number of previous biopsies, physical activity was used for type 2 diabetes, and breast feeding was used for rheumatoid arthritis.To understand the relative performance of the SPUR method in a more realistic scenario, we also assessed type I error control and power on data sets simulated according to the genetic architectures of breast cancer, type 2 diabetes, and rheumatoid arthritis. This disease‐based simulation design was based on the approach of Aschard et al. (2012a) for evaluating the impact of gene‐gene and gene‐environment interactions on disease risk predication. Specifically, we customized Aschard's original simulation code to support disease‐based simulation scenarios for the comparative evaluation of G× E detection methods. For each of the three disease architectures, type I error control and power were assessed using separate simulation designs. In both cases, 1,000 data sets were generated for each disease with each data set containing 1,000 subjects with measurements for the set of known risk SNPs and known environmental risk factors, as detailed for each disease in the supplementary material for Aschard et al. (2012a), and a set of additional SNPs with a MAF drawn from 3.2.4www.adni‐info.org. For the evaluation of the extended SPUR method, we used clinical and genotyping data from the first phase of ADNI. For this analysis, subjects with either mild cognitive impairment or AD were considered cases and controls were cognitively normal subjects. QC and preprocessing was carried out using PLINK 1.9  and 398,230 SNPs, specified using additive coding, remained in the data set.The ADNI .Table q‐values are computed via the FDR adjustment of the two LR tests comparing the unpenalized test stage logistic regression models without interaction terms to the models with interaction terms. The SNP‐specific interaction FDR values are computed according to the hierarchical FDR procedure outlined in Section q‐value of 0.1 after hierarchical FDR adjustment. If identified in dbSNP  are marked in bold in the table. TOMM40 is located near the APOE locus and has a well‐known association with both AD and Parkinson's disease (Gottschalk et al., Table 5Biologically meaningful gene‐environment interactions exist for many common human diseases and other clinically relevant phenotypes (Buil et al., In an attempt to improve G× E interaction detection power, researchers developed a number of two‐stage or screening‐testing approaches (Dai et al., To address the shortcomings of early screening‐testing methods, we recently created a new screening‐testing approach for G× E interaction detection ( SPUR, reviewed in Section In this paper, we have described an extended and generalized version of our SPUR method that corrects the methodological limitations of the original technique. To support the analysis of data sets with hundreds of thousands to millions of genetic markers, we added a score statistic‐based prescreening step, detailed in Section This paper also contains a much more thorough evaluation of the SPUR method using simulation studies to assess type I error control and power and a large GWAS data set to assess practical utility. Both the simple simulation design and the simulations based on the genetic architectures of breast cancer, type 2 diabetes, and rheumatoid arthritis demonstrate that the extended SPUR method has acceptable type I error control and superior power to detect known G× E interactions relative to competing approaches. The two models used with the simple simulation design also highlighted the dramatic impact that the filter statistic can have on overall performance of screening‐testing methods. This fact makes the hierarchical FDR support in the extended SPUR method especially useful because it allows both filters to be evaluated in parallel with only a small loss in power. Analysis of the ADNI GWAS data shows that the extended SPUR method can be used to analyze truly genome‐scale data sets. Importantly, the extended SPUR method was able to identify statistically significant, biologically plausible, and previously unreported education‐SNP interactions despite the relatively small sample size of the ADNI data.In future work, we plan to use the SPUR method to search for G× E interactions in a wider range of GWAS data sets and explore methodological enhancements such as support for higher order interactions and the concurrent evaluation of different marker codings and interaction scales.


Statistical association tests for rare variants can be classified as the burden approach and the sequence kernel association test (SKAT) approach. The burden and SKAT approaches, originally developed for case–control analysis, have also been extended to family-based tests. In the presence of both case–control and family data for a study, joint analysis for the combined data set can increase the statistical power. We extended the Combined Association in the Presence of Linkage (CAPL) test, using both case–control and family data for testing common variants, to rare variant association analysis. The burden and SKAT algorithms were applied to the CAPL test. We used simulations to verify that the CAPL tests incorporating the burden and SKAT algorithms have correct type I error rates. Power studies suggested that both tests have adequate power to identify rare variants associated with the disease. We applied the tests to the Genetic Analysis Workshop 19 data set using the combined family and case–control data for hypertension. The analysis identified several candidate genes for hypertension. Rare variants may contribute to a large portion of disease risks . Rare vahttp://snp.gs.washington.edu/SeattleSeqAnnotation138/). We performed gene-based tests by testing the association of all variants in exons within a gene with the disease.The GAW19 data set consists of 20 large Mexican American families with a total of 959 individuals and 1944 unrelated individuals. The family data include 464 individuals for whom whole genome sequencing data are available, while the sequences for other family members were imputed based on the sequenced individuals. Admixture analysis for the family data suggested that most of the family ancestry is European and Native American, where the proportions of the two ancestries in each individual are different [p-values less than 10−4 in the merged data were removed. As we focused on analyzing rare variants, variants with minor allele frequencies (MAFs) greater than 5 % were removed.We used the PLINK  PI_HAT si, let Xi be the number of a specific allele in affected siblings, Gi be the siblings’ genotypes, A be the siblings’ affection status, GPj be the parental mating type, Nij be the number of alleles in GPj, and ψ be the set of all possible parental mating types conditional on Gi. The CAPL test statistic Ti is calculated asWe first review the CAPL test statistic, which is the fundamental statistic in the proposed test. For a nuclear family ψ is the observed genotype. A case or a control is treated as a single offspring with two missing parents and Ti can be calculated. Assuming there are m populations in the data, P in equation   2) involnce of T . The CAPN nuclear families and M variants, the CAPL-burden test statistic is defined as B = ∑k = 1MwkTk, where wk is the weight for variant k and Tk is the CAPL statistic at variant k. Following Madsen and Browning [wk is n is the number of unrelated individuals and qk is the estimated MAF based on the unrelated individuals for variant k. The CAPL-SKAT statistic is defined as S = ∑k = 1Muk2Tk2. Following Wu et al. [Beta, the beta density function with parameters of , as the weight function for uk. We used the bootstrap statistics to evaluate the significance for B and S. Assuming L bootstraps are performed, the bootstrap CAPL statistics under the null hypothesis at variant k is j, where Tk at bootstrap replicate j and j. The p-values for B and S are calculated as (number of Bj* ≥ B)/L and (number of Sj* ≥ S)/L, respectively. In our analysis, L was set as 10,000.We applied the burden approach based on the weighted-sum method  and SKATBrowning , the weiu et al. , we usedMAP4) gene based on the 1000 Genomes project sequence data for the CEU (Utah residents with Northern and Western European ancestry) and MXL  populations, where each set consists of 10,000 haplotypes. SeqSIMLA [i was calculated as ORi = 1 + (0.01/(0.99 × MAFi)), where MAFi is the MAF for i. We also simulated the scenario where 50 % of the disease loci were protective. The OR for protective variant i was specified as 1/ORi. The power was calculated based on 1000 replicates of the simulated data.As the simulated trait data for unrelated individuals were not available when we attempted to evaluate the statistical properties of the proposed tests, we used computer simulations to evaluate the type I error rates and power for the CAPL-burden and CAPL-SKAT. HAPGEN2  was usedSeqSIMLA  was usedSeqSIMLA  for the SeqSIMLA , where lTable Because the CAPL can only analyze nuclear families, we split the extended pedigrees to non-overlapping nuclear families. A total of 863 individuals in the 1944 unrelated samples were removed because of their cryptic relatedness based on the PI_HAT statistics. In the combined data, there were 1509 individuals, including 948 unrelated controls and 305 unrelated cases, and 256 individuals in 47 nuclear families. There were 2,649,583 variants after quality control. A total of 12,340 genes were analyzed. In the CAPL, we specified the number of populations as 2 for the clustering algorithm, where the family data and unrelated data were clustered in two populations, to account for the batch effect for the 2 data sets.− 6), some genes, which are underlined in Table Table UBE2Q2), has been identified to have association with chronic kidney disease [ELMO1), is a susceptible gene in diabetic nephropathy [Another underlined gene, ubiquitin-conjugating enzyme E2Q family member 2 . The results suggest that the CAPL-SKAT had slight power loss with the increase of the MAF thresholds, whereas the power for the CAPL-burden decreased to 0.36 when the proportion of causal variants in the variants being tested decreased to 7 % at the MAF threshold of 40 %. Consequently, in practice, the CAPL-SKAT should be performed if common variants are included in the analysis.P in equation (The CAPL uses a clustering algorithm, which assumes family members have the same genetic background across the genome, to identify subpopulations. Our simulation results showed that the CAPL test maintained correct type I error rates for the admixed population, where the assumption of homogeneous genetic background across the genome in all family members is violated. It is possible to extend the CAPL test to account for population admixture by calculating equation  based onIt is possible to combine the CAPL-burden and CAPL-SKAT into a test, using algorithms such as SKAT-O, which can reduce the number of tests. Moreover, the CAPL-burden and CAPL-SKAT currently focus on analyzing rare variants. It is possible to extend the tests to accommodate both common and rare variants, using algorithms such as those found in Chung et al.  and Saad