A rapid method for computing the inverse of the gametic covariance matrix between relatives for a marked Quantitative Trait Locus

The inverse of the gametic covariance matrix between relatives, G^-1, for a marked quantitative trait locus (QTL) is required in best linear unbiased prediction (BLUP) of breeding values if marker data are available on a QTL. A rapid method for computing the inverse of a gametic relationship matrix for a marked QTL without building G itself is presented. The algorithm is particularly useful due to the approach taken in computing inbreeding coefficients by having to compute only few elements of G. Numerical techniques for determining, storing, and computing the required elements of G and the nonzero elements of the inverse are discussed. We show that the subset of G required for computing the inbreeding coefficients and hence the inverse is a tiny proportion of the whole matrix and can be easily stored in computer memory using sparse matrix storage techniques. We also introduce an algorithm to determine the maximum set of nonzero elements that can be found in G^-1 and a strategy to efficiently store and access them. Finally, we demonstrate that the inverse can be efficiently built using the present techniques for very large and inbred populations.     

Efficient computation of the inverse of gametic relationship matrix for a marked QTL

Best linear unbiased prediction of genetic merits for a marked quantitative trait locus (QTL) using mixed model methodology includes the inverse of conditional gametic relationship matrix (G^-1) for a marked QTL. When accounting for inbreeding, the conditional gametic relationships between two parents of individuals for a marked QTL are necessary to build G^-1 directly. Up to now, the tabular method and its adaptations have been used to compute these relationships. In the present paper, an indirect method was implemented at the gametic level to compute these few relationships. Simulation results showed that the indirect method can perform faster with significantly less storage requirements than adaptation of the tabular method. The efficiency of the indirect method was mainly due to the use of the sparseness of G^-1. The indirect method can also be applied to construct an approximate G^-1 for populations with incomplete marker data, providing approximate probabilities of descent for QTL alleles for individuals with incomplete marker data.     

Use of Multiple Genetic Markers in Prediction of Breeding Values

Genotypes at a marker locus give information on transmission of genes from parents to offspring and that information can be used in predicting the individuals' additive genetic value at a linked quantitative trait locus (MQTL). In this paper a recursive method is presented to build the gametic relationship matrix for an autosomal MQTL which requires knowledge on recombination rate between the marker locus and the MQTL linked to it. A method is also presented to obtain the inverse of the gametic relationship matrix. This information can be used in a mixed linear model for simultaneous evaluation of fixed effects, gametic effects at the MQTL and additive genetic effects due to quantitative trait loci unlinked to the marker locus (polygenes). An equivalent model can be written at the animal level using the numerator relationship matrix for the MQTL and a method for obtaining the inverse of this matrix is presented. Information on several unlinked marker loci, each of them linked to a different locus affecting the trait of interest, can be used by including an effect for each MQTL. The number of equations per animal in this case is 2m + 1 where m is the number of MQTL. A method is presented to reduce the number of equations per animal to one by combining information on all MQTL and polygenes into one numerator relationship matrix. It is illustrated how the method can accommodate individuals with partial or no marker information. Numerical examples are given to illustrate the methods presented. Opportunities to use the presented model in constructing genetic maps are discussed.     

Derivation of single-locus relationship coefficients conditional on marker information

The coefficient of relationship is defined as the correlation between the additive genetic values of two individuals. This coefficient can be defined specifically for a single quantitative trait locus (QTL) and may deviate considerably from the overall expectation if it is taken conditional on information from linked marker loci. Conditional halfsib correlations are derived under a simple genetic model with a biallelic QTL linked to a biallelic marker locus. The conditional relationship coefficients are shown to depend on the recombination rate between the marker and the QTL and the population frequency of the marker alleles, but not on parameters of the QTL, i.e. number and frequency of QTL alleles, degree of dominance etc., nor on the (usually unknown) QTL genotype of the sire. Extensions to less simplified cases (multiple alleles at the marker locus and the QTL, two marker loci flanking the QTL) are given. For arbitrary pedigrees, conditional relationship coefficients can also be derived from the conditional gametic covariance matrix suggested by Fernando and Grossman (1989). The connection of these two approaches is discussed. The conditional relationship coefficient can be used for marker-assisted genetic evaluation as well as for the detection of QTL and the estimation of their effects.     

A recursive procedure to compute the gametic relationship matrix and its inverse for marked QTL clusters

Recently, a variety of mixed linear models have been proposed for marker-assisted prediction of the effects of quantitative trait loci (QTLs) in outbred populations of animals. One of them addresses the effects of a cluster of linked QTLs, or those of a particular chromosomal segment, marked by DNA marker(s) and requires that the inverse of the corresponding gametic relationship matrix whose elements are the conditional expected values of the identity-by-descent (IBD) proportions between gametes for individuals be evaluated. Here, for a model of this type, utilizing the property of the IBD set and using the information on the joint gametogenesis processes at the flanking marker loci, we present a recursive method to systematically calculate the elements of the gametic relationship matrix and its inverse. A numerical example is given to illustrate the proposed computing procedure.     

Dynamic QTL Analysis and Candidate Gene Mapping for Waterlogging Tolerance at Maize Seedling Stage

Soil waterlogging is one of the major abiotic stresses adversely affecting maize growth and yield. To identify dynamic expression of genes or quantitative trait loci (QTL), QTL associated with plant height, root length, root dry weight, shoot dry weight and total dry weight were identified via conditional analysis in a mixed linear model and inclusive composite interval mapping method at three respective periods under waterlogging and control conditions. A total of 13, 19 and 23 QTL were detected at stages 3D|0D (the period during 0–3 d of waterlogging), 6D|3D and 9D|6D, respectively. The effects of each QTL were moderate and distributed over nine chromosomes, singly explaining 4.14–18.88% of the phenotypic variation. Six QTL (ph6-1, rl1-2, sdw4-1, sdw7-1, tdw4-1 and tdw7-1) were identified at two consistent stages of seedling development, which could reflect a continuous expression of genes; the remaining QTL were detected at only one stage. Thus, expression of most QTL was influenced by the developmental status. In order to provide additional evidence regarding the role of corresponding genes in waterlogging tolerance, mapping of Expressed Sequence Tags markers and microRNAs were conducted. Seven candidate genes were observed to co-localize with the identified QTL on chromosomes 1, 4, 6, 7 and 9, and may be important candidate genes for waterlogging tolerance. These results are a good starting point for understanding the genetic basis for selectively expressing of QTL in different stress periods and the common genetic control mechanism of the co-localized traits.     

Simple telomeres in a simple animal: absence of subtelomeric repeat regions in the placozoan Trichoplax adhaerens

Simple telomeres were identified in the genome assembly of the basal placozoan animal Trichoplax adhaerens. They have 1–2 kb of TTAGGG telomeric repeats, which are preceded by a subtelomeric region of 1.5–13 kb. Unlike subtelomeric regions in most animals examined, these subtelomeric regions are unique to each telomere.     

Analysis of complex allozyme polymorphisms in a barley population

Genotypes of 68,230 individuals taken from 10 generations (F₄–F₆, F₁₄–F₁₇, F₂₄–F₂₆) of an experimental population of barley were determined for four esterase loci. The results show that frequencies of gametic ditypes changed significantly over generations and that striking gametic phase disequilibrium developed within a few generations for each of the six pairwise combinations of loci which were monitored. The complex behavior of these four enzyme loci in the population is attributed to interactions between selection and restriction of recombination resulting from the effects of linkage and/or inbreeding.     

Identification of Quantitative Trait Loci Influencing Wood Specific Gravity in an Outbred Pedigree of Loblolly Pine

We report the identification of quantitative trait loci (QTL) influencing wood specific gravity (WSG) in an outbred pedigree of loblolly pine (Pinus taeda L.). QTL mapping in an outcrossing species is complicated by the presence of multiple alleles (>2) at QTL and marker loci. Multiple alleles at QTL allow the examination of interaction among alleles at QTL (deviation from additive gene action). Restriction fragment length polymorphism (RFLP) marker genotypes and wood specific gravity phenotypes were determined for 177 progeny. Two RFLP linkage maps were constructed, representing maternal and paternal parent gamete segregations as inferred from diploid progeny RFLP genotypes. RFLP loci segregating for multiple alleles were vital for aligning the two maps. Each RFLP locus was assayed for cosegregation with WSG QTL using analysis of variance (ANOVA). Five regions of the genome contained one or more RFLP loci showing differences in mean WSG at or below the P = 0.05 level for progeny as grouped by RFLP genotype. One region contained a marker locus (S6a) whose QTL-associated effects were highly significant (P > 0.0002). Marker S6a segregated for multiple alleles, a prerequisite for determining the number of alleles segregating at the linked QTL and analyzing the interactions among QTL alleles. The QTL associated with marker S6a appeared to be segregating for multiple alleles which interacted with each other and with environments. No evidence for digenic epistasis was found among the five QTL.     

Postzygotic isolation involves strong mitochondrial and sex-specific effects in Tigriopus californicus,a species lacking heteromorphic sex chromosomes

Detailed studies of the genetics of speciation have focused on a few model systems, particularly Drosophila. The copepod Tigriopus californicus offers an alternative that differs from standard animal models in that it lacks heteromorphic chromosomes (instead, sex determination is polygenic) and has reduced opportunities for sexual conflict, because females mate only once. Quantitative trait loci (QTL) mapping was conducted on reciprocal F₂ hybrids between two strongly differentiated populations, using a saturated linkage map spanning all 12 autosomes and the mitochondrion. By comparing sexes, a possible sex ratio distorter was found but no sex chromosomes. Although studies of standard models often find an excess of hybrid male sterility factors, we found no QTL for sterility and multiple QTL for hybrid viability (indicated by non-Mendelian adult ratios) and other characters. Viability problems were found to be stronger in males, but the usual explanations for weaker hybrid males (sex chromosomes, sensitivity of spermatogenesis, sexual selection) cannot fully account for these male viability problems. Instead, higher metabolic rates may amplify deleterious effects in males. Although many studies of standard speciation models find the strongest genetic incompatibilities to be nuclear–nuclear (specifically X chromosome–autosome), we found the strongest deleterious interaction in this system was mito–nuclear. Consistent with the snowball theory of incompatibility accumulation, we found that trigenic interactions in this highly divergent cross were substantially more frequent (>6 × ) than digenic interactions. This alternative system thus allows important comparisons to studies of the genetics of reproductive isolation in more standard model systems.     

Nuclear DNA replicates during zygote development in Arabidopsis and Torenia fournieri

The progression of the cell cycle is continuous in most cells, but gametes (sperm and egg cells) exhibit an arrest of the cell cycle to await fertilization to form a zygote, which then continues through the subsequent phases to complete cell division. The phase in which gametes of flowering plants arrest has been a matter of debate, since different phases have been reported for the gametes of different species. In this study, we reassessed the phase of cell-cycle arrest in the gametes of two species, Arabidopsis (Arabidopsis thaliana) and Torenia fournieri. We first showed that 4’, 6-diamidino-2-phenylindole staining was not feasible to detect changes in gametic nuclear DNA in T. fournieri. Next, using 5-ethynyl-2’-deoxyuridine (EdU) staining that detects DNA replication by labeling the EdU absorbed by deoxyribonucleic acid, we found that the replication of nuclear DNA did not occur during gamete development but during zygote development, revealing that the gametes of these species have a haploid nuclear DNA content before fertilization. We thus propose that gametes in the G1 phase participate in the fertilization event in Arabidopsis and T. fournieri.

The replication of nuclear DNA does not occur during gamete development but during zygote development.     

Genetic Variation for Life History Sensitivity to Seasonal Warming in Arabidopsis thaliana

Climate change has altered life history events in many plant species; however, little is known about genetic variation underlying seasonal thermal response. In this study, we simulated current and three future warming climates and measured flowering time across a globally diverse set of Arabidopsis thaliana accessions. We found that increased diurnal and seasonal temperature (1°–3°) decreased flowering time in two fall cohorts. The early fall cohort was unique in that both rapid cycling and overwintering life history strategies were revealed; the proportion of rapid cycling plants increased by 3–7% for each 1° temperature increase. We performed genome-wide association studies (GWAS) to identify the underlying genetic basis of thermal sensitivity. GWAS identified five main-effect quantitative trait loci (QTL) controlling flowering time and another five QTL with thermal sensitivity. Candidate genes include known flowering loci; a cochaperone that interacts with heat-shock protein 90; and a flowering hormone, gibberellic acid, a biosynthetic enzyme. The identified genetic architecture allowed accurate prediction of flowering phenotypes (R² > 0.95) that has application for genomic selection of adaptive genotypes for future environments. This work may serve as a reference for breeding and conservation genetic studies under changing environments.     

Large-effect pleiotropic or closely linked QTL segregate within and across ten US cattle breeds

Background

The availability of high-density SNP assays including the BovineSNP50 (50 K) enables the identification of novel quantitative trait loci (QTL) and improvement of the resolution of the locations of previously mapped QTL. We performed a series of genome-wide association studies (GWAS) using 50 K genotypes scored in 18,274 animals from 10 US beef cattle breeds with observations for twelve body weights, calving ease and carcass traits.

Results

A total of 159 large-effects QTL (defined as 1-Mb genome windows explaining more than 1% of additive genetic variance) were identified. In general, more QTL were identified in analyses with bigger sample sizes. Four large-effect pleiotropic or closely linked QTLs located on BTA6 at 37–42 Mb (primarily at 38 Mb), on BTA7 at 93 Mb, on BTA14 at 23–26 Mb (primarily at 25 Mb) and on BTA20 at 4 Mb were identified in more than one breed. Several breed-specific large-effect pleiotropic or closely linked QTL were also identified. Some identified QTL regions harbor genes known to have large effects on a variety of traits in cattle such as PLAG1 and MSTN and others harbor promising candidate genes including NCAPG, ARRDC3, ERGIC1, SH3PXD2B, HMGA2, MSRB3, LEMD3, TIGAR, SEPT7, and KIRREL3. Gene ontology analysis revealed that genes involved in ossification and in adipose tissue development were over-represented in the identified pleiotropic QTL. Also, the MAPK signaling pathway was identified as a common pathway affected by the genes located near the pleiotropic QTL.

Conclusions

This largest GWAS ever performed in beef cattle, led us to discover several novel across-breed and breed-specific large-effect pleiotropic QTL that cumulatively account for a significant percentage of additive genetic variance (e.g. more than a third of additive genetic variance of birth and mature weights; and calving ease direct in Hereford). These results will improve our understanding of the biology of growth and body composition in cattle.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2164-15-442) contains supplementary material, which is available to authorized users.     

Mapping a Large Number of QTL for Durable Resistance to Stripe Rust in Winter Wheat Druchamp Using SSR and SNP Markers

Winter wheat Druchamp has both high-temperature adult-plant (HTAP) resistance and all-stage resistance to stripe rust caused by Puccinia striiformis f. sp. tritici (Pst). The HTAP resistance in Druchamp is durable as the variety has been resistant in adult-plant stage since it was introduced from France to the United States in late 1940s. To map the quantitative trait loci (QTL) for stripe rust resistance, an F₈ recombinant inbred line (RIL) population from cross Druchamp × Michigan Amber was phenotyped for stripe rust response in multiple years in fields under natural infection and with selected Pst races under controlled greenhouse conditions, and genotyped with simple sequence repeat (SSR) and single nucleotide polymorphism (SNP) markers. Composite interval mapping (CIM) identified eight HTAP resistance QTL and three all-stage resistance QTL. Among the eight HTAP resistance QTL, QYrdr.wgp-1BL.2 (explaining 2.36-31.04% variation), QYrdr.wgp-2BL (2.81–15.65%), QYrdr.wgp-5AL (2.27–17.22%) and QYrdr.wgp-5BL.2 (2.42–15.13%) were significant in all tests; and QYrdr.wgp-1BL.1 (1.94–10.19%), QYrdr.wgp-1DS (2.04–27.24%), QYrdr.wgp-3AL (1.78–13.85%) and QYrdr.wgp-6BL.2 (1.69–33.71%) were significant in some of the tests. The three all-stage resistance QTL, QYrdr.wgp-5BL.1 (5.47–36.04%), QYrdr.wgp-5DL (9.27–11.94%) and QYrdr.wgp-6BL.1 (13.07-20.36%), were detected based on reactions in the seedlings tested with certain Pst races. Among the eleven QTL detected in Druchamp, at least three (QYrdr.wgp-5DL for race-specific all-stage resistance and QYrdr.wgp-3AL and QYrdr.wgp-6BL.2 for race non-specific HTAP resistance) are new. All these QTL, especially those for durable HTAP resistance, and their closely linked molecular markers could be useful for developing wheat cultivars with durable resistance to stripe rust.     

Detection and modelling of time-dependent QTL in animal populations

A longitudinal approach is proposed to map QTL affecting function-valued traits and to estimate their effect over time. The method is based on fitting mixed random regression models. The QTL allelic effects are modelled with random coefficient parametric curves and using a gametic relationship matrix. A simulation study was conducted in order to assess the ability of the approach to fit different patterns of QTL over time. It was found that this longitudinal approach was able to adequately fit the simulated variance functions and considerably improved the power of detection of time-varying QTL effects compared to the traditional univariate model. This was confirmed by an analysis of protein yield data in dairy cattle, where the model was able to detect QTL with high effect either at the beginning or the end of the lactation, that were not detected with a simple 305 day model.     

Conditional QTL mapping of oil content in rapeseed with respect to protein content and traits related to plant development and grain yield

Oil content in rapeseed (Brassica napus L.) is generally regarded as a character with high heritability that is negatively correlated with protein content and influenced by plant developmental and yield related traits. To evaluate possible genetic interrelationships between these traits and oil content, QTL for oil content were mapped using data on oil content and on oil content conditioned on the putatively interrelated traits. Phenotypic data were evaluated in a segregating doubled haploid population of 282 lines derived from the F₁ of a cross between the old German cultivar Sollux and the Chinese cultivar Gaoyou. The material was tested at four locations, two each in Germany and in China. QTLMapper version 1.0 was used for mapping unconditional and conditional QTL with additive (a) and locus pairs with additive × additive epistatic (aa) effects. Clear evidence was found for a strong genetic relationship between oil and protein content. Six QTL and nine epistatic locus pairs were found, which had pleiotropic effects on both traits. Nevertheless, two QTL were also identified, which control oil content independent from protein content and which could be used in practical breeding programs to increase oil content without affecting seed protein content. In addition, six additional QTL with small effects were only identified in the conditional mapping. Some evidence was apparent for a genetic interrelationship between oil content and the number of seeds per silique but no evidence was found for a genetic relationship between oil content and flowering time, grain filling period or single seed weight. The results indicate that for closely correlated traits conditional QTL mapping can be used to dissect the genetic interrelationship between two traits at the level of individual QTL. Furthermore, conditional QTL mapping can reveal additional QTL with small effects that are undetectable in unconditional mapping.     

Riboflavin status modifies the effects of methylenetetrahydrofolate reductase (MTHFR) and methionine synthase reductase (MTRR) polymorphisms on homocysteine

Methylenetetrahydrofolate reductase (MTHFR) and methionine synthase reductase (MTRR), riboflavin-dependent enzymes, participate in homocysteine metabolism. Reported effects of riboflavin status on the association between the MTHFR 677C>T polymorphism and homocysteine vary, and the effects of the MTRR 66A>G or MTRR 524C>T polymorphisms on homocysteine are unclear. We tested the hypothesis that the effects of the MTHFR 677C>T, MTRR 66A>G and MTRR 524C>T polymorphisms on fasting plasma total homocysteine (tHcy) depend on riboflavin status (erythrocyte glutathionine reductase activation coefficient, optimum: <1.2; marginally deficient: 1.2–1.4; deficient: ≥1.4) in 771 adults aged 18–75 years. MTHFR 677T allele carriers with middle or low tertile plasma folate (<14.7 nmol/L) had 8.2 % higher tHcy compared to the 677CC genotype (p < 0.01). This effect was eliminated when riboflavin status was optimal (p for interaction: 0.048). In the lowest cobalamin quartile (≤273 pmol/L), riboflavin status modifies the relationship between the MTRR 66 A>G polymorphism and tHcy (p for interaction: 0.034). tHcy was 6.6 % higher in MTRR 66G allele carriers compared to the 66AA genotype with marginally deficient or optimal riboflavin status, but there was no difference when riboflavin status was deficient (p for interaction: 0.059). tHcy was 13.7 % higher in MTRR 524T allele carriers compared to the 524CC genotype when cobalamin status was low (p < 0.01), but no difference was observed when we stratified by riboflavin status. The effect of the MTHFR 677C>T polymorphism on tHcy depends on riboflavin status, that of the MTRR 66A>G polymorphism on cobalamin and riboflavin status and that of the MTRR 524C>T polymorphism on cobalamin status.     

Verification of QTL for Grain Starch Content and Its Genetic Correlation with Oil Content Using Two Connected RIL Populations in High-Oil Maize

Grain oil content is negatively correlated with starch content in maize in general. In this study, 282 and 263 recombinant inbred lines (RIL) developed from two crosses between one high-oil maize inbred and two normal dent maize inbreds were evaluated for grain starch content and its correlation with oil content under four environments. Single-trait QTL for starch content in single-population and joint-population analysis, and multiple-trait QTL for both starch and oil content were detected, and compared with the result obtained in the two related F_2∶3 populations. Totally, 20 single-population QTL for grain starch content were detected. No QTL was simultaneously detected across all ten cases. QTL at bins 5.03 and 9.03 were all detected in both populations and in 4 and 5 cases, respectively. Only 2 of the 16 joint-population QTL had significant effects in both populations. Three single-population QTL and 8 joint-population QTL at bins 1.03, 1.04–1.05, 3.05, 8.04–8.05, 9.03, and 9.05 could be considered as fine-mapped. Common QTL across F_2∶3 and RIL generations were observed at bins 5.04, 8.04 and 8.05 in population 1 (Pop.1), and at bin 5.03 in population 2 (Pop.2). QTL at bins 3.02–3.03, 3.05, 8.04–8.05 and 9.03 should be focused in high-starch maize breeding. In multiple-trait QTL analysis, 17 starch-oil QTL were detected, 10 in Pop.1 and 7 in Pop.2. And 22 single-trait QTL failed to show significance in multiple-trait analysis, 13 QTL for starch content and 9 QTL for oil content. However, QTL at bins 1.03, 6.03–6.04 and 8.03–8.04 might increase grain starch content and/or grain oil content without reduction in another trait. Further research should be conducted to validate the effect of these QTL in the simultaneous improvement of grain starch and oil content in maize.     

Precipitation Increases the Occurrence of Sporadic Legionnaires’ Disease in Taiwan

Legionnaires’ disease (LD) is an acute form of pneumonia, and changing weather is considered a plausible risk factor. Yet, the relationship between weather and LD has rarely been investigated, especially using long-term daily data. In this study, daily data was used to evaluate the impacts of precipitation, temperature, and relative humidity on LD occurrence in Taiwan from 1995–2011. A time-stratified 2:1 matched-period case-crossover design was used to compare each case with self-controlled data using a conditional logistic regression analysis, and odds ratios (ORs) for LD occurrence was estimated. The city, gender and age were defined as a stratum for each matched set to modify the effects. For lag day- 0 to 15, the precipitation at lag day-11 significantly affected LD occurrence (p<0.05), and a 2.5% (95% CIs = 0.3–4.7%) increased risk of LD occurrence was associated with every 5-mm increase in precipitation. In addition, stratified analyses further showed that positive associations of precipitation with LD incidence were only significant in male and elderly groups and during the warm season ORs = 1.023–1.029). However, such an effect was not completely linear. Only precipitations at 21–40 (OR = 1.643 (95% CIs = 1.074–2.513)) and 61–80 mm (OR = 2.572 (1.106–5.978)) significantly increased the risk of LD occurrence. Moreover, a negative correlation between mean temperature at an 11-day lag and LD occurrence was also found (OR = 0.975 (0.953–0.996)). No significant association between relative humidity and LD occurrence was identified (p>0.05). In conclusion, in warm, humid regions, an increase of daily precipitation is likely to be a critical weather factor triggering LD occurrence where the risk is found particularly significant at an 11-day lag. Additionally, precipitation at 21–40 and 61–80 mm might make LD occurrence more likely.