Sampling genotypes in large pedigrees with loops

Markov chain Monte Carlo (MCMC) methods have been proposed to overcome computational problems in linkage and segregation analyses. This approach involves sampling genotypes at the marker and trait loci. Scalar-Gibbs is easy to implement, and it is widely used in genetics. However, the Markov chain that corresponds to scalar-Gibbs may not be irreducible when the marker locus has more than two alleles, and even when the chain is irreducible, mixing has been observed to be slow. These problems do not arise if the genotypes are sampled jointly from the entire pedigree. This paper proposes a method to jointly sample genotypes. The method combines the Elston-Stewart algorithm and iterative peeling, and is called the ESIP sampler. For a hypothetical pedigree, genotype probabilities are estimated from samples obtained using ESIP and also scalar-Gibbs. Approximate probabilities were also obtained by iterative peeling. Comparisons of these with exact genotypic probabilities obtained by the Elston-Stewart algorithm showed that ESIP and iterative peeling yielded genotypic probabilities that were very close to the exact values. Nevertheless, estimated probabilities from scalar-Gibbs with a chain of length 235 000, including a burn-in of 200 000 steps, were less accurate than probabilities estimated using ESIP with a chain of length 10 000, with a burn-in of 5 000 steps. The effective chain size (ECS) was estimated from the last 25 000 elements of the chain of length 125 000. For one of the ESIP samplers, the ECS ranged from 21 579 to 22 741, while for the scalar-Gibbs sampler, the ECS ranged from 64 to 671. Genotype probabilities were also estimated for a large real pedigree consisting of 3 223 individuals. For this pedigree, it is not feasible to obtain exact genotype probabilities by the Elston-Stewart algorithm. ESIP and iterative peeling yielded very similar results. However, results from scalar-Gibbs were less accurate.     

Blocking Gibbs sampling for linkage analysis in large pedigrees with many loops.

We apply the method of "blocking Gibbs" sampling to a problem of great importance and complexity-linkage analysis. Blocking Gibbs sampling combines exact local computations with Gibbs sampling, in a way that complements the strengths of both. The method is able to handle problems with very high complexity, such as linkage analysis in large pedigrees with many loops, a task that no other known method is able to handle. New developments of the method are outlined, and it is applied to a highly complex linkage problem in a human pedigree.     

Improved techniques for sampling complex pedigrees with the Gibbs sampler

Markov chain Monte Carlo (MCMC) methods have been widely used to overcome computational problems in linkage and segregation analyses. Many variants of this approach exist and are practiced; among the most popular is the Gibbs sampler. The Gibbs sampler is simple to implement but has (in its simplest form) mixing and reducibility problems; furthermore in order to initiate a Gibbs sampling chain we need a starting genotypic or allelic configuration which is consistent with the marker data in the pedigree and which has suitable weight in the joint distribution. We outline a procedure for finding such a configuration in pedigrees which have too many loci to allow for exact peeling. We also explain how this technique could be used to implement a blocking Gibbs sampler.     

Comparison of an exact and a simulation method for calculating gene extinction probabilities in pedigrees

A comparison is made between a much used simulation method, commonly called gene dropping, and the exact computational technique of peeling. These methods are illustrated using the problem of finding the distribution of the number of distinct ancestral genes surviving at an autosomal locus. Each method is used on several real zoo pedigrees, of varying size and complexity, and the results are compared. Gene dropping is found to be a good approximation to peeling, but for all but the most complex pedigrees surveyed, peeling is preferable. The relationship between heterozygosity and allelic variability is investigated.     

Response of maize genotypes with different nitrogen use efficiency to low nitrogen stresses

Objectives

This paper aims to compare the property difference of spatial and temporal distribution of different nitrogen use efficiency maize genotypes and discuss the physiological mechanism of nitrogen efficiency of maize.

Associations between marker genotypes, halothane reaction, CC activity and meat quality characters in a sample of German Landrace pigs

Routine blood typing of German Landrace pedigree populations and an earlier study revealed very low frequencies of the favourable alleles at the marker loci Phi, Pgd and H . The hypothesis was that in this population the whole linkage group of favourable alleles at the halothane and neighbouring marker loci may have been lost as a consequence of intense selection for leanness and type. The present study of 1050 German Landrace pigs at the Relliehausen experimental station, where some effort has been made to maintain a higher frequency of the favourable alleles Phi^A (0.48), H- (0.43) and Pgd^A (0.70) gave quite different results.
The frequency of halothane-positive pigs found by using a severe test was only 30 %. Only 5.4 %, 8.8 %, 13.4 % and 13.9 7% of animals with Phi^AIA, H^-I-, Pgd^A/A and Phi^A/B genotypes respectively were halothane-positive. Forty to sixty per cent of pigs with these marker genotypes could therefore be expected to be homozygous halothane-negative ( N/N ) animals. Creatine kinase activity and three selected meat quality characters showed highly significant differences between the A/A and the B/B genotypes for the marker loci Phi and Pgd , with the heterozygotes being intermediate. These differences are greater than those observed between halothane-negative and halothane-positive phenotypes. The only other consistently superior marker genotype in this population was the H blood group genotype H -^I- . In contrast to findings from Sweden and Switzerland, the postalbumin locus Po2 and the suppressor locus S for the A-O blood groups did not exhibit useful marker qualities.
It is concluded that in the German Landrace the marker loci Phi, Pgd and H could also be helpful in breeding homozygous halothane-negative pigs with distinctly better meat quality characteristics.     

Coordinated conditional simulation with SLINK and SUP of many markers linked or associated to a trait in large pedigrees

Simulation of genotypes in pedigrees is an important tool to evaluate the power of a linkage or an association study and to assess the empirical significance of results. SLINK is a widely-used package for pedigree simulations, but its implementation has not previously been described in a published paper. SLINK was initially derived from the LINKAGE programs. Over the 20 years since its release, SLINK has been modified to incorporate faster algorithms, notably from the linkage analysis package FASTLINK, also derived from LINKAGE. While SLINK can simulate genotypes on pedigrees of high complexity, one limitation of SLINK, as with most methods based on peeling algorithms to evaluate pedigree likelihoods, is the small number of linked markers that can be generated. The software package SUP includes an elegant wrapper for SLINK that circumvents the limitation on number of markers by using descent markers generated by SLINK to simulate a much larger number of markers on the same chromosome, linked and possibly associated with a trait locus. We have released new coordinated versions of SLINK (3.0; available from http://watson.hgen.pitt.edu) and SUP (v090804; available from http://mlemire.freeshell.org/software or http://watson.hgen.pitt.edu) that integrate the two software packages. Thereby, we have removed some of the previous limitations on the joint functionality of the programs, such as the number of founders in a pedigree. We review the history of SLINK and describe how SLINK and SUP are now coordinated to permit the simulation of large numbers of markers linked and possibly associated with a trait in large pedigrees.     

Identity-by-descent estimation and mapping of qualitative traits in large, complex pedigrees

Computing identity-by-descent sharing between individuals connected through a large, complex pedigree is a computationally demanding task that often cannot be done using exact methods. What I present here is a rapid computational method for estimating, in large complex pedigrees, the probability that pairs of alleles are IBD given the single-point genotype data at that marker for all individuals. The method can be used on pedigrees of essentially arbitrary size and complexity without the need to divide the individuals into separate subpedigrees. I apply the method to do qualitative trait linkage mapping using the nonparametric sharing statistic S(pairs). The validity of the method is demonstrated via simulation studies on a 13-generation 3028-person pedigree with 700 genotyped individuals. An analysis of an asthma data set of individuals in this pedigree finds four loci with P-values <10(-3) that were not detected in prior analyses. The mapping method is fast and can complete analyses of approximately 150 affected individuals within this pedigree for thousands of markers in a matter of hours.     

Associations between marker genotypes, halothane reaction, creatine kinase activity and meat quality characters in a sample of German Landrace pigs

Routine blood typing of German Landrace pedigree populations and an earlier study revealed very low frequencies of the favourable alleles at the marker loci Phi, Pgd and H. The hypothesis was that in this population the whole linkage group of favourable alleles at the halothane and neighbouring marker loci may have been lost as a consequence of intense selection for leanness and type. The present study of 1050 German Landrace pigs at the Relliehausen experimental station, where some effort has been made to maintain a higher frequency of the favourable alleles PhiA (0.48), H- (0.43) and PgdA (0.70) gave quite different results. The frequency of halothane-positive pigs found by using a severe test was only 30%. Only 5.4%, 8.8%, 13.4% and 13.9% of animals with PhiA/A, H-/-, PgdA/A and PhiA/B genotypes respecitively were halothane-positive. Forty to sixty per cent of pigs with these marker genotypes could therefore be expected to be homozygous halothane-negative (N/N) animals. Creatine kinase activity and three selected meat quality characters showed highly significant differences between the A/A and the B/B genotypes for the marker loci Phi and Pgd, with the heterozygotes being intermediate. These differences are greater than those observed between halothane-negative and halothane-positive phenotypes. The only other consistently superior marker genotype in this population was the H blood group genotype H-/-. In contrast to findings from Sweden and Switzerland, the postalbumin locus Po2 and the suppressor locus S for the A-O blood groups did not exhibit useful marker qualities.(ABSTRACT TRUNCATED AT 250 WORDS)     

不同硅吸收效率水稻品种根系对硅素水平的响应

为明确硅对水稻根系生长发育的影响,以4个硅吸收效率不同的水稻品种（高效吸收品种TN1、白香粳和低效吸收品种卷叶粳、一目惚）为材料,采用国际水稻研究所的营养液配方水培试验,设置0(T₁)、1.25 (T₂)和2 (T₃) mmol·L^-1 3个硅素水平,研究了不同硅素水平对不同基因型水稻根系和地上部干物质量、根条数、侧根数、根总长和根直径等的影响.结果表明：随硅素水平的提高,水稻各品种均表现为根系干物质量、根冠比、侧根数和根总长逐渐减少,地上部干物质量、根条数和根直径逐渐增大.较高的硅素水平有利于水稻不定根的分化发育,而不利于侧根的分化发育.在较低的硅素水平下,硅吸收效率高的基因型水稻TN1和白香粳的根干物质量和根冠比显著高于硅吸收效率低的品种卷叶粳和一目惚,其中白香粳的侧根数和根总长均显著高于卷叶粳和一目惚.可见,根总长和侧根数是引起水稻硅素吸收差异的主要原因.     

Modeling large regions in proteins: applications to loops, termini, and folding

Template-based methods for predicting protein structure provide models for a significant portion of the protein but often contain insertions or chain ends (InsEnds) of indeterminate conformation. The local structure prediction "problem" entails modeling the InsEnds onto the rest of the protein. A well-known limit involves predicting loops of ≤12 residues in crystal structures. However, InsEnds may contain as many as ~50 amino acids, and the template-based model of the protein itself may be imperfect. To address these challenges, we present a free modeling method for predicting the local structure of loops and large InsEnds in both crystal structures and template-based models. The approach uses single amino acid torsional angle "pivot" moves of the protein backbone with a C(β) level representation. Nevertheless, our accuracy for loops is comparable to existing methods. We also apply a more stringent test, the blind structure prediction and refinement categories of the CASP9 tournament, where we improve the quality of several homology based models by modeling InsEnds as long as 45 amino acids, sizes generally inaccessible to existing loop prediction methods. Our approach ranks as one of the best in the CASP9 refinement category that involves improving template-based models so that they can function as molecular replacement models to solve the phase problem for crystallographic structure determination.     

Nick-dependent and -independent processing of large DNA loops in human cells

DNA loop heterologies are products of normal DNA metabolism and can lead to severe genomic instability if unrepaired. To understand how human cells process DNA loop structures, a set of circular heteroduplexes containing a 30-nucleotide loop were constructed and tested for repair in vitro by human cell nuclear extracts. We demonstrate here that, in addition to the previously identified 5' nick-directed loop repair pathway (Littman, S. J., Fang, W. H., and Modrich, P. (1999) J. Biol. Chem. 274, 7474-7481), human cells can process large DNA loop heterologies in a loop-directed manner. The loop-directed repair specifically removes the loop structure and occurs only in the looped strand, and appears to require limited DNA synthesis. Like the nick-directed loop repair, the loop-directed repair is independent of many known DNA repair pathways, including DNA mismatch repair and nucleotide excision repair. In addition, our data also suggest that an aphidicolin-sensitive DNA polymerase is involved in the excision step of the nick-directed loop repair pathway.     

Photosynthetic efficiency and nitrogen distribution under different nitrogen management and relationship with physiological N-use efficiency in three rice genotypes

Nitrogen fertilization strategies were widely adopted to enhance grain production and improve nitrogen utilization in rice all over the world. For fertilization timing strategy, ear fertilization was usually employed in recent years. For fertilization amount strategy, nitrogen fertilization would continually increase to meet the demands of increasing people for food. However, under heavy ear fertilization as well as great nitrogen amount (NA), physiological N-use efficiency (PE, defined as grain production per unit nitrogen uptake by plants) decreased. Under three NA and two ratios of fertilization given during ear development period to total NA (ear fertilization distribution ratio, EFDR), net photosynthetic rate (Pn), Pn to nitrogen content per unit area (photosynthetic N-use efficiency, Pn/N), nitrogen accumulation in plant tissues and PE of three rice (Oryza sativaL.) genotypes, Jinyou 253, Liangyoupeijiu and Baguixiang were screened in the first and second seasons in 2002 so as to understand the fluctuation patterns of Pn/N and nitrogen distribution in leaf blades under great NA & EFDR and relationship with PE in rice. Results showed that under greater NA & EFDR, Pn in flag leaves at heading and plant nitrogen accumulation at maturity always increased and PE & Pn/N always decreased in spite of increased grain production. Rice distributed more nitrogen in leaf blade under greater NA and EFDR. PE indicated significantly (P<0.05) positive relationship with Pn/N and negative relationship with nitrogen distribution ratio in leaf blades at heading and maturity, and no association with Pn in two growing seasons. Results suggested that low PE in rice under great NA and heavy ear fertilization is associated to more nitrogen distribution in leaf blades and decreases in photosynthetic efficiency.     

Linkage analysis of the GAW14 simulated dataset with microsatellite and single-nucleotide polymorphism markers in large pedigrees

Recent studies have suggested that a high-density single nucleotide polymorphism (SNP) marker set could provide equivalent or even superior information compared with currently used microsatellite (STR) marker sets for gene mapping by linkage. The focus of this study was to compare results obtained from linkage analyses involving extended pedigrees with STR and single-nucleotide polymorphism (SNP) marker sets. We also wanted to compare the performance of current linkage programs in the presence of high marker density and extended pedigree structures. One replicate of the Genetic Analysis Workshop 14 (GAW14) simulated extended pedigrees (n = 50) from New York City was analyzed to identify the major gene D2. Four marker sets with varying information content and density on chromosome 3 (STR [7.5 cM]; SNP [3 cM, 1 cM, 0.3 cM]) were analyzed to detect two traits, the original affection status, and a redefined trait more closely correlated with D2. Multipoint parametric and nonparametric linkage analyses (NPL) were performed using programs GENEHUNTER, MERLIN, SIMWALK2, and S.A.G.E. SIBPAL. Our results suggested that the densest SNP map (0.3 cM) had the greatest power to detect linkage for the original trait (genetic heterogeneity), with the highest LOD score/NPL score and mapping precision. However, no significant improvement in linkage signals was observed with the densest SNP map compared with STR or SNP-1 cM maps for the redefined affection status (genetic homogeneity), possibly due to the extremely high information contents for all maps. Finally, our results suggested that each linkage program had limitations in handling the large, complex pedigrees as well as a high-density SNP marker set.     

Crops and genotypes differ in efficiency of potassium uptake and use

Cultivars with increased efficiency of uptake and utilization of soil nutrients are likely to have positive environmental effects through reduced usage of chemicals in agriculture. This review assesses the available literature on differential uptake and utilization efficiency of K in farming systems. Large areas of agricultural land in the world are deficient in K (e.g. 3/4 of paddy soils in China, 2/3 of the wheatbelt in Southern Australia), with export in agricultural produce (especially hay) and leaching (especially in sandy soils) contributing to lowering of K content in the soil. The capacity of a genotype to grow and yield well in soils low in available K is K efficiency. Genotypic differences in efficiency of K uptake and utilization have been reported for all major economically important plants. The K-efficient phenotype is a complex one comprising a mixture of uptake and utilization efficiency mechanisms. Differential exudation of organic compounds to facilitate release of non-exchangeable K is one of the mechanisms of differential K uptake efficiency. Genotypes efficient in K uptake may have a larger surface area of contact between roots and soil and increased uptake at the root–soil interface to maintain a larger diffusive gradient towards roots. Better translocation of K into different organs, greater capacity to maintain cytosolic K⁺ concentration within optimal ranges and increased capacity to substitute Na⁺ for K⁺ are the main mechanisms underlying K utilization efficiency. Further breeding for increased K efficiency will be dependent on identification of suitable markers and compounding of efficiency mechanisms into locally adapted germplasm.     

Variability of traits associated with phosphorus efficiency in wild and cultivated genotypes of common bean

Genetic variation in plant growth under limited phosphorus (P) supply is necessary to obtain more productive cultivars on low P-available soils. Two pot experiments were conducted to evaluate the variability of some traits associated with efficiency of P absorption and utilization in wild and cultivated genotypes of common bean (Phaseolus vulgaris L.) under biological N2 fixation. At two P levels (20 and 80 mg P kg-1 soil, P1 and P2, respectively), 20 wild and 6 cultivated genotypes were grown in Experiment 1, and 4 wild and 27 cultivated genotypes were grown in Experiment 2. Plants were harvested at flowering, but in Experiment 1 wild accessions that did not flower were harvested at the beginning of leaf senescence. In Experiment 1, part of the genotypic variability of wild accessions was attributed to a less homogeneous ontogenetic stage at harvest, whereas in Experiment 2 some variation in biomass production was due to distinct phenologies of cultivated genotypes. Wild lines did not seem more tolerant to low P conditions, but the genotypic variation observed suggests these materials as a source of genetic diversity. Part of the variation in the root area and root efficiency ratio (total P content:root area) was compensatory, resulting in narrow genotypic differences in the total P content. The total P content and root efficiency ratio presented a wider amplitude of variation at P2 than at P1, and P uptake was more influenced by P supply than root production. Since the genotype × P level interaction was not significant for shoot biomass and shoot P concentration in Experiment 2, P utilization efficiency may be a useful selection criterion for cultivars between limited and adequate P supply. Within the sample of genetic diversity evaluated herein, there was large genotypic variability for traits related to P efficiency among wild and cultivated genotypes of common bean.     

Biomass accumulation and energy conversion efficiency in aromatic rice genotypes

A field experiment was conducted to evaluate photosynthetic efficiency along with different growth parameters of aromatic rice genotypes. Forty genotypes including three non-aromatic checks exhibited enormous variations for leaf area index (LAI), crop growth rate (CGR), relative growth rate (RGR), net assimilation rate (NAR), grain yield, total dry matter, harvest index and photosynthetic efficiency or energy use efficiency (Eμ) at panicle initiation and heading stages. Minimum LAI-value was 0.52 in Khazar at PI stage and maximum was 4.91 in Sakkor khora at heading stage. The CGR-value was in the range of 4.80−24.11 g m⁻² per day. The best yielder BR39 produced grain of 4.21 t ha⁻¹ and the worst yielder Khazar gave 1.42 t ha⁻¹. Total dry matter (TDM) yield varied from 4.04 to 12.26 t ha⁻¹ where genotypes proved their energy use efficiency a range between 0.58 to 1.65%. Eμ showed a significant positive relation with TDM (r = 0.80^**), CGR (r = 0.72^**) and grain yield (r = 0.66^**). A negative correlation was established between TDM and harvest index and LAI and RGR. Path analysis result showed that NAR at heading stage exerted highest positive direct effect (0.70) on Eμ.     

Prediction of sample size to maintain genetic variation in doubled-haploid populations following marker selection

Marker selection (MS) and doubled-haploid (DH) technologies have the potential to reduce the time taken to breed new cereal cultivars. However, a limiting factor is the potential increased genetic drift. The aim of this study was to design and test a genetic model for predicting the sample sizes needed to maintain genetic variation among DH plants following marker selection. The model estimates the amount of the genome that is fixed during the production of DH populations of a given size using a given number of markers. To test the model, doubled-haploids were produced from wheat plants selected for three PCR-based markers. When the genetic variation of the DH population (108 plants), produced from 15 selected F₂ plants homozygous at three loci, was compared to the genetic variation of an unselected F₃ population (200 plants), five of the six measured quantitative traits were identical and normally distributed. This model should prove to be a valid breeding tool, allowing a breeder to apply MS to a breeding programme and estimate the minimum DH population sizes required for minimal loss of genetic variation through genetic drift. Received: 16 October 2000 / Accepted: 20 March 2001