A note on algorithms for genotype and allele elimination in complex pedigrees with incomplete genotype data

Elimination of genotypes or alleles for each individual or meiosis, which are inconsistent with observed genotypes, is a component of various genetic analyses of complex pedigrees. Computational efficiency of the elimination algorithm is critical in some applications such as genotype sampling via descent graph Markov chains. We present an allele elimination algorithm and two genotype elimination algorithms for complex pedigrees with incomplete genotype data. We modify all three algorithms to incorporate inheritance restrictions imposed by a complete or incomplete descent graph such that every inconsistent complete descent graph is detected in any pedigree, and every inconsistent incomplete descent graph is detected in any pedigree without loops with the genotype elimination algorithms. Allele elimination requires less CPU time and memory, but does not always eliminate all inconsistent alleles, even in pedigrees without loops. The first genotype algorithm produces genotype lists for each individual, which are identical to those obtained from the Lange-Goradia algorithm, but exploits the half-sib structure of some populations and reduces CPU time. The second genotype elimination algorithm deletes more inconsistent genotypes in pedigrees with loops and detects more illegal, incomplete descent graphs in such pedigrees.     

An optimal algorithm for automatic genotype elimination

In an effort to accelerate likelihood computations on pedigrees, Lange and Goradia defined a genotype-elimination algorithm that aims to identify those genotypes that need not be considered during the likelihood computation. For pedigrees without loops, they showed that their algorithm was optimal, in the sense that it identified all genotypes that lead to a Mendelian inconsistency. Their algorithm, however, is not optimal for pedigrees with loops, which continue to pose daunting computational challenges. We present here a simple extension of the Lange-Goradia algorithm that we prove is optimal on pedigrees with loops, and we give examples of how our new algorithm can be used to detect genotyping errors. We also introduce a more efficient and faster algorithm for carrying out the fundamental step in the Lange-Goradia algorithm-namely, genotype elimination within a nuclear family. Finally, we improve a common algorithm for computing the likelihood of a pedigree with multiple loops. This algorithm breaks each loop by duplicating a person in that loop and then carrying out a separate likelihood calculation for each vector of possible genotypes of the loop breakers. This algorithm, however, does unnecessary computations when the loop-breaker vector is inconsistent. In this paper we present a new recursive loop breaker-elimination algorithm that solves this problem and illustrate its effectiveness on a pedigree with six loops.     

Selective elimination of alleles in rice anther cultures

The nature of heterosis is discussed and selective elimination of alleles (introduced in the hybrid genotype by the parental forms) in anther culture is shown. This supports the possibility of removing viability-reducing alleles (lethal, semilethal, and less effective alleles) from the genotypes of heterotic hybrids in anther culture.     

The C1167T polymorphism of the catalase gene and polymorphic markers D11S907 and D11S2008 located in its vicinity are associated with diabetes mellitus type 2

To study the contribution of the catalase (CAT) gene in diabetes mellitus (DM) type 2, the allele and genotype frequencies of internal (polymorphism C1167T) and two neighboring (minisatellites D11S907 and D11S2008) polymorphic markers were studied in 132 healthy individuals and 154 patients from Moscow. Allele C and genotype CC of the C1167T polymorphism proved associated with a higher risk of DM type 2. Seven D11S907 alleles containing 14 to 20 dinucleotide repeats were found. The frequencies of alleles 15 and 16 and genotype 18/20 were significantly higher and those of allele 18 and genotypes 17/18 and 18/19 were lower in patients than in controls. Eight D11S2008 alleles containing 15 to 22 tetranucleotide repeats were found. The frequencies of alleles 17 and 18 and genotype 18/20 in patients were significantly higher than in controls. An association of the three polymorphic loci and DM type 2 was suggested.     

Association between PrP genotypes and performance traits in a Welsh Mountain flock

The UK national scrapie plan (NSP) for sheep is based on selection for the resistant ARR/ARR genotype and elimination of susceptible types of the ovine prion protein (PrP) gene. The aim of this study was to estimate the possible association of the PrP genotype and performance traits by using data from the CAMDA Welsh Mountain flock. Four alleles (ARH, ARQ, ARR and VRQ) and 10 genotypes covering all five NSP risk groups were present in the CAMDA flock. Overall, the most common allele was ARR (35.2%), and VRQ was the least common (5.4%). The commonest genotypes were ARR/ARQ (23.7%) and ARR/AHQ (23.1%). The most resistant genotype, ARR/ARR, and the most susceptible genotype, VRQ/VRQ, were found in 10.2% and 0.3%, respectively, of the population tested. The associations of PrP genotypes with weight and ultrasonically scanned traits were investigated in three analyses, the first using genotypes, the second using risk categories and the third using number of alleles. These associations were evaluated by univariate analysis of each trait using an animal model with maternal effects where appropriate, and PrP was included as a fixed effect. Selection for scrapie resistance will not adversely affect progress in the traits considered and is consistent with improvements in muscle depth.     

GEL: a novel genotype calling algorithm using empirical likelihood

MOTIVATION: Preliminary results on the data produced using the Affymetrix large-scale genotyping platforms show that it is necessary to construct improved genotype calling algorithms. There is evidence that some of the existing algorithms lead to an increased error rate in heterozygous genotypes, and a disproportionately large rate of heterozygotes with missing genotypes. Non-random errors and missing data can lead to an increase in the number of false discoveries in genetic association studies. Therefore, the factors that need to be evaluated in assessing the performance of an algorithm are the missing data (call) and error rates, but also the heterozygous proportions in missing data and errors. RESULTS: We introduce a novel genotype calling algorithm (GEL) for the Affymetrix GeneChip arrays. The algorithm uses likelihood calculations that are based on distributions inferred from the observed data. A key ingredient in accurate genotype calling is weighting the information that comes from each probe quartet according to the quality/reliability of the data in the quartet, and prior information on the performance of the quartet. AVAILABILITY: The GEL software is implemented in R and is available by request from the corresponding author at nicolae@galton.uchicago.edu.     

PCR amplification of alleles at the DIS80 locus: comparison of a Finnish and a North American Caucasian population sample, and forensic casework evaluation.

Allele and genotype frequencies for the highly polymorphic D1S80 locus were determined in a Finnish population sample by using PCR followed by high-resolution PAGE and silver staining, a procedure called the amplified-fragment-length polymorphism (Amp-FLP) technique. In 140 unrelated Finnish individuals 15 alleles and 43 phenotypes were observed. The D1S80 locus demonstrated a heterozygosity of .77, and the power of discrimination was .92 in this sample representing a genetically isolated Finnish population. The distribution of observed genotypes conformed to Hardy-Weinberg expectations. In 36 mother-child pairs Mendelian inheritance for the alleles at the D1S80 locus could be demonstrated in all cases, and no mutations were observed. The usefulness of the D1S80 locus for forensic casework was assessed by using Amp-FLP analysis of the D1S80 locus in 36 forensic cases including 18 rapes, 14 homicides, and 4 other violent crimes. In most cases valuable information was obtained using the Amp-FLP technique, and in no case was there indication of either false-positive or false-negative results.     

荷斯坦牛Nramp1基因遗传多态性及其与乳房炎相关性的研究

利用PCR-SSCP技术检测了344头中国荷斯坦牛Nramp1基因exon 11的基因多态性, 并分析了其不同基因型与乳房炎及产奶量性状的关系。结果表明: 实验群体发现3种基因型AA、AB、BB, 其中A等位基因为优势等位基因, 等位基因频率为0.767, 而B等位基因频率则为0.233。经χ2适合性检验, 群体处于Hardy-Weinberg平衡状态(P>0.05)。测序结果显示: 扩增片段分别在200 bp(C/G)和254 bp(T/G)存在碱基突变, 并导致了氨基酸改变, 分别为丙氨酸替换为脯氨酸(Ala356Pro)、亮氨基酸替换为蛋氨酸(Leu374Met)。通过构建最小二乘线性模型, 进行Nramp1基因多态性与产奶量、体细胞评分(SCS)的相关性分析表明, AA型个体的SCS最小二乘均值显著低于BB﹑AB型(P<0.05), 而AA型﹑AB个体的产奶量最小二乘均值显著高于BB型(P<0.01, P<0.05), AA基因型可作为乳房炎抗性的优良基因型。因此, 可将Nramp1作为奶牛乳房炎候选基因应用于分子标记辅助选择育种。     

HLA-DQα allele and genotype frequencies in various human populations determined by using enzymatic amplification and oligonucleotide probes

Allele and genotype frequencies at the HLA-DQ alpha locus have been determined by the use of polymerase chain reaction (PCR) amplification and nonradioactive oligonucleotide probes. The probes define six alleles and 21 genotypes in a dot-blot format. A total of over 1,400 individuals from 11 populations has been typed by two different laboratories using this method. In contrast to some variable-number-of-tandem-repeat markers that have been used for identity determination, DQ alpha genotype frequencies do not deviate significantly from Hardy-Weinberg equilibrium in all populations studied. The distribution of alleles varies significantly between most of these populations. In Caucasians, the allele frequencies range from 4.3% to 28.5%. In this population, the power of discrimination is .94, and, for paternity determination, the power of exclusion is .642. These population data will allow the use of the HLA-DQ alpha marker in paternity determination, the analysis of individual identity in forensic samples, and anthropological studies.     

Paraoxonase 1 gene polymorphism 192Q/R in old men and long-livers from Tatars ethnic group

Comparison in genotype and allele frequencies of people groups of younger (from 1 till 20 years), middle (21-55 years), elderly (56-74 years), senile (75-89 years) age and long-livers (90-109 years) have been performed (only 1116 person) with the purpose of analysis of molecular-genetic bases of ageing and longevity of the person. Allele variants of PON1 gene have been identified by polymerase chain reaction in a combination with restriction analysis. In the general sample of Tatars genotypes PON1*Q/*Q, PON1*Q/*R and PON1*R/*R are revealed with frequencies of 46.15, 44.35 and 9.5%, alleles PON1*Q and PON1*R are found with frequencies of 68.32 and 31.68% accordingly. Statistically significant distinctions on frequencies of genotypes and alleles between separate age groups are found. It has appeared, that frequency of PON1*R allele (28.46%) is lowered among old men in comparison with those among persons of younger age (37.42%, P = 0.009). However essentially above in group of long-livers, than in group of old men, frequencies allele PON1*R (P = 0.005) and genotype PON1*R/*R (P = 0.01).     

The use of the expectation-maximization (EM) algorithm for maximum likelihood estimation of gametic frequencies of multilocus polymorphic codominant systems based on sampled population data

Estimation of gametic frequencies in multilocus polymorphic systems based on the numerical distribution of multilocus genotypes in a population sample ("analysis without pedigrees") is difficult because some gametes are not recognized in the data obtained. Even in the case of codominant systems, where all alleles can be recognized by genotypes, so that direct estimation of the frequencies of genes (alleles) is possible ("complete data"), estimation of the frequencies of multilocus gametes based on the data on multilocus genotypes is sometimes impossible, whether population data or even family data are used for studying genotypic segregation or analysis of linkage ("incomplete data"). Such "incomplete data" are analyzed based on the corresponding genetic models using the expectation-maximization (EM) algorithm. In this study, the EM algorithm based on the random-marriage model for a nonsubdivided population was used to estimate gametic frequencies. The EM algorithm used in the study does not set any limitations on the number of loci and the number of alleles of each locus. Locus and alleles are identified by numeration making possible to arrange loops. In each combination of alleles for a given combination of m out of L loci (L is the total number of loci studied), all alleles are assigned value 1, and the remaining alleles are assigned value 0. The sum of zeros and unities for each gamete is its gametic value (h), and the sum of the gametic values of the gametes that form a given genotype is the genotypic value (g) of this genotype. Then, gametes with the same h are united into a single class, which reduces the number of the estimated parameters. In a general case of m loci, this procedure yields m + 1 classes of gametes and 2m + 1 classes of genotypes with genotypic values g = 0, 1, 2, ..., 2m. The unknown frequencies of the m + 1 classes of gametes can be represented as functions of the gametic frequencies whose maximum likelihood estimations (MLEs) have been obtained in all previous EM procedures and the only unknown frequency (Pm(m)) that is to be estimated in the given EM procedure. At the expectation step, the expected frequencies (Fm(g) of the genotypes with genotypic values g are expressed in terms of the products of the frequencies of m + 1 classes of gametes. The data on genotypes are the numbers (ng) of individuals with genotypic values g = 0, 1, 2, 3, ..., 2m. The maximization step is the maximization of the logarithm of the likelihood function (LLF) for ng values. Thus, the EM algorithm is reduced, in each case, to solution of only one equation with one unknown parameter with the use of the ng values, i.e., the numbers of individuals after the corresponding regrouping of the data on the individuals' genotypes. Treatment of the data obtained by Kurbatova on the MNSs and Rhesus systems with alleles C, Cw, c, D, d, E, e with the use of Weir's EM algorithm and the EM algorithm suggested in this study yielded similar results. However, the MLEs of the parameters obtained with the use of either algorithm often converged to a wrong solution: the sum of the frequencies of all gametes (4 and 12 gametes for MNSs and Rhesus, respectively) was not equal to 1.0 even if the global maximum of LLF was reached for each of them (as it was for MNSs with the use of Weir's EM algorithm), with each parameter falling within admissible limits (e.g., [0, min(PN,Ps)] for PNs). The chi 2 function is suggested to be used as a goodness-of-fit function for the distribution of genotypes in a sample in order to select acceptable solutions. However, the minimum of this function only guarantee the acceptability of solutions if all limitations on the parameters are met: the sum of estimations of gametic frequencies is 1.0, each frequency falls within the admissible limits, and the "gametic algebra" is complied with (none of the frequencies is negative).     

On adaptive accuracy and precision in natural populations

Adaptation is usually conceived as the fit of a population mean to a fitness optimum. Natural selection, however, does not act only to optimize the population mean. Rather, selection normally acts on the fitness of individual organisms in the population. Furthermore, individual genotypes do not produce invariant phenotypes, and their fitness depends on how precisely they are able to realize their target phenotypes. For these reasons we suggest that it is better to conceptualize adaptation as accuracy rather than as optimality. The adaptive inaccuracy of a genotype can be measured as a function of the expected distance of its associated phenotype from a fitness optimum. The less the distance, the more accurate is the adaptation. Adaptive accuracy has two components: the deviance of the genotypically set target phenotype from the optimum and the precision with which this target phenotype can be realized. The second component, the adaptive precision, has rarely been quantified as such. We survey the literature to quantify how much of the phenotypic variation in wild populations is due to imprecise development. We find that this component is often substantial and highly variable across traits. We suggest that selection for improved precision may be important for many traits.     

The use of microsatellites for detecting DNA polymorphism, genotype identification and genetic diversity in wheat

A set of 20 wheat microsatellite markers was used with 55 elite wheat genotypes to examine their utility (1) in detecting DNA polymorphism, (2)in the identifying genotypes and (3) in estimating genetic diversity among wheat genotypes. The 55 elite genotypes of wheat used in this study originated in 29 countries representing six continents. A total of 155 alleles were detected at 21 loci using the above microsatellite primer pairs (only 1 primer amplified 2 loci; all other primers amplified 1 locus each). Of the 20 primers amplifying 21 loci, 17 primers and their corresponding 18 loci were assigned to 13 different chromosomes (6 chromosomes of the A genome, 5 chromosomes of the B genome and 2 chromosomes of the D genome). The number of alleles per locus ranged from 1 to 13, with an average of 7.4 alleles per locus. The values of average polymorphic information content (PIC) and the marker index (MI) for these markers were estimated to be 0.71 and 0.70, respectively. The (GT)_n microsatellites were found to be the most polymorphic. The genetic similarity (GS) coefficient for all possible 1485 pairs of genotypes ranged from 0.05 to 0.88 with an average of 0.23. The dendrogram, prepared on the basis of similarity matrix using the UPGMA algorithm, delineated the above genotypes into two major clusters (I and II), each with two subclusters (Ia, Ib and IIa, IIb). One of these subclusters (Ib) consisted of a solitary genotype (E3111) from Portugal, so that it was unique and diverse with respect to all other genotypes belonging to cluster I and placed in subcluster Ia. Using a set of only 12 primer pairs, we were able to distinguish a maximum of 48 of the above 55 wheat genotypes. The results demonstrate the utility of microsatellite markers for detecting polymorphism leading to genotype identification and for estimating genetic diversity. Received: 15 May 1999 / Accepted: 27 July 1999     

Fitness-related traits of allozyme genotypes in Bromus hordeaceus L. (Poaceae) associated with field habitat and experimental flooding

Genetic variation at alcohol dehydrogenase and phosphoglucose isomerase loci in Bromus hordeaceus has in an earlier study been found to show substantial microgeographic spatial structuring. The present study reports differences in fitness related characters between the enzyme genotypes, both from a field study and a greenhouse experiment. The field study showed overall differences in seed set between allozyme genotypes and also that Pgi-1b genotypes differed in number of seeds set at different levels of herb cover in their habitat. In the greenhouse, dry, normal or flooded conditions were applied. Seeds from individuals with the Adh-1b-11 genotype matured faster in the dry and slower in the flooded treatments than did seeds from individuals with the Adh-1b-22 genotype. Individuals containing Pgi-1b-1f1f alleles and Adh-1b-11 alleles are more plastic than individuals with other allele combinations, meaning that allozyme variation could partly explain what could be seen as adaptive phenotypic plasticity. Mean seed weight was different between dry and flooding treatments for Pgi-1b genotypes. There were also direct effects of allozyme genotype on the probability of survival, total plant weight, weight of reproductive parts, seed weight, days to seed maturation and the percentage of reproductive parts out of the total plant weight.     

Genetic and environmental factors affecting mating type frequency in natural isolates of Tetrahymena thermophila

In Tetrahymena thermophila mating type alleles specify temperature sensitive frequency distributions of multiple mating types. A-like alleles specify mating types I, II, III, V and VI, whereas B-like alleles specify mating types II through VII. We have characterized the mating type distributions specified by several A- and B-like genotypes segregated by genomic exclusion from cells isolated from a pond in northwestern Pennsylvania. The B-like genotypes are alike in specifying very low frequencies of mating type III, but differ with respect to the frequencies of other mating types, particularly II and VII. An A-like genotype specifies a high frequency of mating type III and is unstable in successive generations for the expression of mating type II, suggesting a possible modifier. Inter se crosses performed at 18 degrees C, 28 degrees C and 34 degrees C showed that each genotype specifies a frequency distribution that is uniquely affected by temperature. No mating type was affected the same way by temperature in all genotypes. In A/B heterozygotes, the B-like genotype exhibited partial dominance. The genotypes described here differ significantly from previously described genotypes from the same pond, indicating that there are numerous mating type alleles. For frequency-dependent selection to equalize mating type frequencies, it must act not only on complex multiple alleles but also on the response of mating type alleles to temperature.     

新疆4个民族STR基因座遗传多态性研究

对新疆维吾尔放族,锡伯族,乌孜别克族,柯尔克孜族4个民族的400份样本和40个家系进行STR基因扫描,基因分型和遗传结构分析。获得了4个民族STR遗传特征及遗传方式等的科学数据。结果为9个STR基因座上维吾尔族有66种STR等位基因,148种基因型;锡伯族有72种STR等位基因,163种基因型;乌孜别克族有65种TSR等位基因,168种基因型;柯尔克孜族有71种STR等位基因,191种基因型,用新疆4个民族的数据和汉族人群,美国高加索人群,美国黑人相比较发现,中国民族遗传特征数据之间差异不显著,而和国外民族相比差异显著,进一步证明中华民族是一个不可分割的大家庭。     

MHC class IIB alleles contribute to both additive and nonadditive genetic effects on survival in Chinook salmon

The genes of the major histocompatibility complex (MHC) are found in all vertebrates and are an important component of individual fitness through their role in disease and pathogen resistance. These genes are among the most polymorphic in genomes and the mechanism that maintains the diversity has been actively debated with arguments for natural selection centering on either additive or nonadditive genetic effects. Here, we use a quantitative genetics breeding design to examine the genetic effects of MHC class IIB alleles on offspring survivorship in Chinook salmon (Oncorhynchus tshawytscha). We develop a novel genetic algorithm that can be used to assign values to specific alleles or genotypes. We use this genetic algorithm to show simultaneous additive and nonadditive effects of specific MHC class IIB alleles and genotypes on offspring survivorship. The additive effect supports the rare-allele hypothesis as a potential mechanism for maintaining genetic diversity at the MHC. However, contrary to the overdominance hypothesis, the nonadditive effect led to underdominance at one heterozygous genotype, which could instead reduce variability at the MHC. Our algorithm is an advancement over traditional animal models that only partition variance in fitness to additive and nonadditive genetic effects, but do not allocate these effects to specific alleles and genotypes. Additionally, we found evidence of nonrandom segregation during meiosis in females that promotes an MHC allele that is associated with higher survivorship. Such nonrandom segregation could further reduce variability at the MHC and may explain why Chinook salmon has one of the lowest levels of MHC diversity of all vertebrates.     

Family-based association tests for genomewide association scans

With millions of single-nucleotide polymorphisms (SNPs) identified and characterized, genomewide association studies have begun to identify susceptibility genes for complex traits and diseases. These studies involve the characterization and analysis of very-high-resolution SNP genotype data for hundreds or thousands of individuals. We describe a computationally efficient approach to testing association between SNPs and quantitative phenotypes, which can be applied to whole-genome association scans. In addition to observed genotypes, our approach allows estimation of missing genotypes, resulting in substantial increases in power when genotyping resources are limited. We estimate missing genotypes probabilistically using the Lander-Green or Elston-Stewart algorithms and combine high-resolution SNP genotypes for a subset of individuals in each pedigree with sparser marker data for the remaining individuals. We show that power is increased whenever phenotype information for ungenotyped individuals is included in analyses and that high-density genotyping of just three carefully selected individuals in a nuclear family can recover >90% of the information available if every individual were genotyped, for a fraction of the cost and experimental effort. To aid in study design, we evaluate the power of strategies that genotype different subsets of individuals in each pedigree and make recommendations about which individuals should be genotyped at a high density. To illustrate our method, we performed genomewide association analysis for 27 gene-expression phenotypes in 3-generation families (Centre d'Etude du Polymorphisme Humain pedigrees), in which genotypes for ~860,000 SNPs in 90 grandparents and parents are complemented by genotypes for ~6,700 SNPs in a total of 168 individuals. In addition to increasing the evidence of association at 15 previously identified cis-acting associated alleles, our genotype-inference algorithm allowed us to identify associated alleles at 4 cis-acting loci that were missed when analysis was restricted to individuals with the high-density SNP data. Our genotype-inference algorithm and the proposed association tests are implemented in software that is available for free.     

Short tandem repeat polymorphism of the D2S1242 locus in a Japanese population

Allele frequencies and sequence characteristics of the D2S1242 short tandem repeat (STR) locus were studied in a Japanese population sample. A total of 10 D2S1242 alleles and 34 genotypes were identified in 273 unrelated Japanese individuals. The five most common alleles detected had frequencies of over 10%. No deviations from Hardy-Weinberg equilibrium were found when the expected allele values were compared with the observed values. Sequence analysis of each allele showed a tetranucleotide polymorphism. Alleles 9 to 14 had different sequence structures than alleles 15 to 19. Allele 18 had a different sequence in the Japanese sample compared to an Austrian sample. The power of discrimination was 0.95. The present results demonstrate that the D2S1242 STR locus is a useful genetic marker in the Japanese population.     

An algorithm for automatic genotype elimination.

Automatic genotype elimination algorithms for a single locus play a central role in making likelihood computations on human pedigree data feasible. We present a simple algorithm that is fully efficient in pedigrees without loops. This algorithm can be easily coded and has been instrumental in greatly reducing computing times for pedigree analysis. A contrived counter-example demonstrates that some superfluous genotypes cannot be excluded for inbred pedigrees.