Composite likelihood-based inferences on genetic data from dependent loci

The structure of dependence between neighboring genetic loci is intractable under some models that treat each locus as a single data-point. Composite likelihood-based methods present a simple approach under such models by treating the data as if they are independent. A maximum composite likelihood estimator (MCLE) is not easy to find numerically, as in most cases we do not have a way of knowing if a maximum is global. We study the local maxima of the composite likelihood (ECLE, the efficient composite likelihood estimators), which is straightforward to compute. We establish desirable properties of the ECLE and provide an estimator of the variance of MCLE and ECLE. We also modify two proper likelihood-based tests to be used with composite likelihood. We modify our methods to make them applicable to datasets where some loci are excluded.     

A maximum likelihood map of chromosome 1.

Thirteen loci are mapped on chromosome 1 from genetic evidence. The maximum likelihood map presented permits confirmation that Scianna (SC) and a fourteenth locus, phenylketonuria (PKU), are on chromosome 1, although the location of the latter on the PGM1-AMY segment is uncertain. Eight other controversial genetic assignments are rejected, providing a practical demonstration of the resolution which maximum likelihood theory brings to mapping.     

Effects of genotyping errors,missing values and segregation distortion in molecular marker data on the construction of linkage maps

A simulation study was performed to investigate the effects of missing values, typing errors and distorted segregation ratios in molecular marker data on the construction of genetic linkage maps, and to compare the performance of three locus-ordering criteria (weighted least squares, maximum likelihood and minimum sum of adjacent recombination fractions criteria) in the presence of such effects. The study was based upon three linkage groups of 10 loci at 2, 6, and 10 cM spacings simulated from a doubled-haploid population of size 150. Criteria performance were assessed using the number of replicates with correctly estimated orders, the mean rank correlation between the estimated and the true order and the mean total map length. Bootstrap samples from replicates in the maximum likelihood analysis produced a measure of confidence in the estimated locus order. The effects of missing values and/or typing errors in the data are to reduce the proportion of correctly ordered maps, and this problem worsens as the distances between loci decreases. The maximum likelihood criterion is most successful at ordering loci correctly, but gives estimated map lengths, which are substantially inflated when typing errors are present. The presence of missing values in the data produces shorter map lengths for more widely spaced markers, especially under the weighted least-squares criterion. Overall, the presence of segregation distortion has little effect on this population.     

两个位点主基因控制的质量—数量性状的遗传分析

应用极大似然法和EM算法提出了关于两个位点主基因控制的质量．数量性状的遗传分析方法,参照质量性状两位点互作在F_2代的分离比率建立了7种遗传假设及其似然比测验的程序,讨论了应用这一方法时应注意的几个问题．     

A Maximum Likelihood Method for Estimating Genome Length Using Genetic Linkage Data

The genetic length of a genome, in units of Morgans or centimorgans, is a fundamental characteristic of an organism. We propose a maximum likelihood method for estimating this quantity from counts of recombinants and nonrecombinants between marker locus pairs studied from a backcross linkage experiment, assuming no interference and equal chromosome lengths. This method allows the calculation of the standard deviation of the estimate and a confidence interval containing the estimate. Computer simulations have been performed to evaluate and compare the accuracy of the maximum likelihood method and a previously suggested method-of-moments estimator. Specifically, we have investigated the effects of the number of meioses, the number of marker loci, and variation in the genetic lengths of individual chromosomes on the estimate. The effect of missing data, obtained when the results of two separate linkage studies with a fraction of marker loci in common are pooled, is also investigated. The maximum likelihood estimator, in contrast to the method-of-moments estimator, is relatively insensitive to violation of the assumptions made during analysis and is the method of choice. The various methods are compared by application to partial linkage data from Xiphophorus.     

Stepwise mutation likelihood computation by sequential importance sampling in subdivided population models

An importance sampling algorithm for computing the likelihood of a sample of genes at loci under a stepwise mutation model in a subdivided population is developed. This allows maximum likelihood estimation of migration rates between subpopulations. The time to the most recent common ancestor of the sample can also be computed. The technique is illustrated by an analysis of a data set of Australian red fox populations.     

一个适于最大似然法估计物种分化年代的进化速率平滑近似方法

众所周知 ,物种分化年代的估计对分子钟 (进化速率恒定 )假定很敏感。另一方面 ,在远缘物种 (例如哺乳纲不同目的动物 )的比较中 ,分子钟几乎总是不成立的。这样在估计分化时间时考虑不同进化区系的速率差异至为重要。最大似然法可以很自然地考虑这种速率差异 ,并且可以同时分析多个基因位点的资料以及同时利用多重化石校正数据。以前提出的似然法需要研究者将进化树的树枝按速率分组 ,本文提出一个近似方法以使这个过程自动化。本方法综合了以前的似然法、贝斯法及近似速率平滑法的一些特征。此外 ,还对算法加以改进 ,以适应综合数据分析时某些基因在某些物种中缺乏资料的情形。应用新提出的方法来分析马达加斯加的倭狐猴的分化年代 ,并与以前的似然法及贝斯法的分析进行了比较     

Genetic linkage between the bovine plasma protease inhibitor 2 (Pi-2) and S blood group loci

A linkage relationship has been detected between the bovine plasma protease inhibitor 2 (Pi-2) and S blood group loci by linkage study within a single pedigree. Using the sequential lodscore test, the recombination fraction (theta) with maximum likelihood has been estimated at 0.200 +/- 0.043, with a maximum lodscore value of 3.466 at theta = 0.200.     

Comparison of family-based association tests in chromosome regions selected by linkage-based confidence intervals

We use the Genetic Analysis Workshop 14 simulated data to explore the effectiveness of a two-stage strategy for mapping complex disease loci consisting of an initial genome scan with confidence interval construction for gene location, followed by fine mapping with family-based tests of association on a dense set of single-nucleotide polymorphisms. We considered four types of intervals: the 1-LOD interval, a basic percentile bootstrap confidence interval based on the position of the maximum Zlr score, and asymptotic and bootstrap confidence intervals based on a generalized estimating equations method. For fine mapping we considered two family-based tests of association: a test based on a likelihood ratio statistic and a transmission-disequilibrium-type test implemented in the software FBAT. In two of the simulation replicates, we found that the bootstrap confidence intervals based on the peak Zlr and the 1-LOD support interval always contained the true disease loci and that the likelihood ratio test provided further strong confirmatory evidence of the presence of disease loci in these regions.     

Different filtering strategies of genotyping‐by‐sequencing data provide complementary resolutions of species boundaries and relationships in a clade of sexually deceptive orchids

Ongoing hybridization and retained ancestral polymorphism in rapidly radiating lineages could mask recent cladogenetic events. This presents a challenge for the application of molecular phylogenetic methods to resolve differences between closely related taxa. We reanalyzed published genotyping‐by‐sequencing (GBS) data to infer the phylogeny of four species within the Ophrys sphegodes complex, a recently radiated clade of orchids. We used different data filtering approaches to detect different signals contained in the dataset generated by GBS and estimated their effects on maximum likelihood trees, global F_ST and bootstrap support values. We obtained a maximum likelihood tree with high bootstrap support, separating the species by using a large dataset based on loci shared by at least 30% of accessions. Bootstrap and F_ST values progressively decreased when filtering for loci shared by a higher number of accessions. However, when filtering more stringently to retain homozygous and organellar loci, we identified two main clades. These clades group individuals independently from their a priori species assignment, but were associated with two organellar haplotype clusters. We infer that a less stringent filtering preferentially selects for rapidly evolving lineage‐specific loci, which might better delimit lineages. In contrast, when using homozygous/organellar DNA loci the signature of a putative hybridization event in the lineage prevails over the most recent phylogenetic signal. These results show that using differing filtering strategies on GBS data could dissect the organellar and nuclear DNA phylogenetic signal and yield novel insights into relationships between closely related species.     

Adaptive and Slightly Deleterious Evolution in a Conifer, <Emphasis Type="Italic">Cryptomeria japonica</Emphasis>

In order to evaluate effects of the population structure and natural selection on organisms having long generation times, we surveyed DNA polymorphisms at five loci encoding 9-cis-epoxycarotenoid dioxygenase (NCED), ammonium transporter, calmodulin, aquaporin, and the second major allergen with polymethylgalacturonase enzyme activity in the pollen (Cryj2) in a conifer, Cryptomeria japonica. The average nucleotide diversity at silent sites across 12 loci including the previously analyzed seven loci was 0.0044. The population recombination rate (4Nr, where N and r are the effective population size and recombination rate per base per generation, respectively) was estimated as 0.00046 and a slow reduction in the population size was indicated, according to the maximum likelihood method implemented in LAMARC. At NCED, the McDonald-Kreitman (MK) test revealed an excess of replacement polymorphisms, suggesting contributions of slightly deleterious mutations. In contrast, the MK test revealed an excess of replacement divergence at Cryj2 and a maximum likelihood approach using the PAML package revealed that certain amino acid sites had a nonsynonymous/synonymous substitution rate ratio (omega) > 4.0, indicating adaptive evolution at this locus. The overall analysis of the 12 loci suggested that adaptive, neutral, and slightly deleterious evolution played important roles in the evolution of C. japonica.     

远缘杂交中不育基因的位置和效应的最大似然估计

提出了一种统计方法,利用标记位点的异常分离,来估计远缘杂交中不育基因位点的位置和效应,在回交群体中,用最大似然法对不育基因与标记位点之间的生组值和配子存活率进行估计。将表现连续分布的育性指标转化为百连续变异的遗传标记的分离,可以避免对育性直接观测所带来的重组值估计结果的不稳定,还可以同时估计雌雄配子的存活率。     

Accuracy‐driven loci selection and assignment of individuals

We present two programs: gafs for optimal selection of loci for use in individual assignment tests, and mlc , a program for individual classification using maximum likelihood and k‐nearest neighbour decision rules. gafs software employs a genetic algorithm to heuristically search multilocus subsets with several objective functions to maximize predictive accuracy of the assignments.     

Methods for multiple-marker mapping of quantitative trait loci in half-sib populations

In this paper we consider the detection of individual loci controlling quantitative traits of interest (quantitative trait loci or QTLs) in the large half-sib family structure found in some species. Two simple approaches using multiple markers are proposed, one using least squares and the other maximum likelihood. These methods are intended to provide a relatively fast screening of the entire genome to pinpoint regions of interest for further investigation. They are compared with a more traditional single-marker least-squares approach. The use of multiple markers is shown to increase power and has the advantage of providing an estimate for the location of the QTL. The maximum-likelihood and the least-squares approaches using multiple markers give similar power and estimates for the QTL location, although the likelihood approach also provides estimates of the QTL effect and sire heterozygote frequency. A number of assumptions have been made in order to make the likelihood calculations feasible, however, and computationally it is still more demanding than the least-squares approach. The least-squares approach using multiple markers provides a fast method that can easily be extended to include additional effects.     

Correcting for bias in estimation of quantitative trait loci effects

Estimates of quantitative trait loci (QTL) effects derived from complete genome scans are biased, if no assumptions are made about the distribution of QTL effects. Bias should be reduced if estimates are derived by maximum likelihood, with the QTL effects sampled from a known distribution. The parameters of the distributions of QTL effects for nine economic traits in dairy cattle were estimated from a daughter design analysis of the Israeli Holstein population including 490 marker-by-sire contrasts. A separate gamma distribution was derived for each trait. Estimates for both the α and β parameters and their SE decreased as a function of heritability. The maximum likelihood estimates derived for the individual QTL effects using the gamma distributions for each trait were regressed relative to the least squares estimates, but the regression factor decreased as a function of the least squares estimate. On simulated data, the mean of least squares estimates for effects with nominal 1% significance was more than twice the simulated values, while the mean of the maximum likelihood estimates was slightly lower than the mean of the simulated values. The coefficient of determination for the maximum likelihood estimates was five-fold the corresponding value for the least squares estimates.     

ACCURACY OF PHYLOGENETIC-ESTIMATION METHODS UNDER UNEQUAL EVOLUTIONARY RATES

A comparative study of the accuracy of three different approaches to phylogenetic estimation was made on simulated data with differing rates of change in different lineages. The three approaches were maximum likelihood, maximum parsimony, and phenetic clustering. The data were generated by simulating genetic drift with different population sizes over a simple four-species tree topology. Although the accuracy of all three approaches was found to be dependent on the number of loci (characters), maximum likelihood was found to perform considerably and consistently better than maximum parsimony or phenetic clustering.     

A comparison between methods for linkage disequilibrium fine mapping of quantitative trait loci

We present a maximum likelihood method for mapping quantitative trait loci that uses linkage disequilibrium information from single and multiple markers. We made paired comparisons between analyses using a single marker, two markers and six markers. We also compared the method to single marker regression analysis under several scenarios using simulated data. In general, our method outperformed regression (smaller mean square error and confidence intervals of location estimate) for quantitative trait loci with dominance effects. In addition, the method provides estimates of the frequency and additive and dominance effects of the quantitative trait locus.     

Estimating divergence times

A statistical method of estimating population splitting times is developed in this paper. We consider three populations, with an assumed known tree topology for their phylogenetic tree. From simulation studies, we find that the method of moments performs very well, in particular for both large number of loci and divergence times, in estimating genetic divergence times. The bias decreases as the number of loci increases. The maximum likelihood method proves to be a good method for constructing an unknown phylogenetic tree, in particular for large divergence times.     

A pairwise relatedness estimator for polyploids

Studies in genetics and ecology often require estimates of relatedness coefficients based on genetic marker data. Many diploid estimators have been developed using either method‐of‐moments or maximum‐likelihood estimates. However, there are no relatedness estimators for polyploids. The development of a moment estimator for polyploids with polysomic inheritance, which simultaneously incorporates the two‐gene relatedness coefficient and various ‘higher‐order’ coefficients, is described here. The performance of the estimator is compared to other estimators under a variety of conditions. When using a small number of loci, the estimator is biased because of an increase in ill‐conditioned matrices. However, the estimator becomes asymptotically unbiased with large numbers of loci. The ambiguity of polyploid heterozygotes (when balanced heterozygotes cannot be distinguished from unbalanced heterozygotes) is also considered; as with low numbers of loci, genotype ambiguity leads to bias. A software, PolyRelatedness , implementing this method and supporting a maximum ploidy of 8 is provided.     

A centromere-based linkage group on the long arm of human chromosome 17

A genetic linkage group on the long arm of chromosome 17 is reported. A maximum likelihood of theta = 0.20 between the centromere-based locus D17Z1 and COL1A1 has been found, as well as a theta = 0.10 between COL1A1 and GH1. The most likely order of the three loci is D17Z1-COL1A1-GH1.