A note on the sampling theory for infinite alleles and infinite sites models

This note considers sampling theory for a selectively neutral locus where it is supposed that the data provide nucleotide sequences for the genes sampled. It thus anticipates that technical advances will soon provide data of this form in volume approaching that currently obtained from electrophoresis. The assumption made on the nature of the data will require us to use, in the terminology ofKimura (Theor. Pop. Biol.2, 174–208 (1971)), the “infinite sites” model of Karlin and McGregor (Proc. Fifth Berkeley Symp. Math. Statist. Prob.4, 415–438 (1967)) rather that the “infinite alleles” model of Kimura and Crow (Genetics49, 174–738 (1964)). We emphasize that these two models refer not to two different real-world circumstances, but rather to two different assumptions concerning our capacity to investigate the real world. We compare our results where appropriate with corresponding sampling theory of Ewens (Theor. Pop. Biol.3, 87–112 (1972)) for the “infinite alleles” model. Note finally that some of our results depend on an assumption of independence of behavior at individual sites; a parallel paper byWatterson (submitted for publication (1974)) assumes no recombination between sites. Real-world behavior will lie between these two assumptions, closer to the situation assumed by Watterson than in this note. Our analysis provides upper bounds for increased efficiency in using complete nucleotide sequences.     

A Note on Maximum Likelihood Ratio Test of No Outliers in Regression Models

A derivation of the maximum likelihood ratio test for testing no outliers in regression models is given using the method of WETHERILL (1981, pp. 106–107) for estimating the regression parameters. This method is essentially similar to the one outlined in BARNETT and LEWIS (1978, p. 263), although by our detailed derivation it is easier to see that the maximum likelihood estimate of θ of model (3) under the hypothesis that the i^th observation in an outlier is the same as that obtained from model (1) when the i^th observation is removed.     

Analyses of the genetic relationships between lactose,somatic cell score,and growth traits in Simmental cattle

Lactose and somatic cell score (SCS) are major economic traits of milk. However, for many countries, they are typically not directly considered in the national genetic evaluation of Simmental cattle. This study aimed to estimate the genetic relationships between lactose, SCS, and growth traits of Simmental cattle to provide information for the national genetic evaluation of the selection of traits of this cattle population. The data of 1781 animals with 6519 records obtained over a period of 41 years (1975–2016) were collected from Xinjiang Hutubi Farm, China. The analyzed traits included 305 days of milk yield (305MY), milk fat percentage (MFP), milk protein percentage (MPP), milk lactose percentage (MLP), total solids (TS), SCS, body height (BH), body length (BL), chest girth (CG), abdominal circumference (AC), rump width (RW), rump length (RL), leg circumference (LC), and cannon circumference (CC). The multiple-trait repeatability model was adopted to estimate (co)variance components using the average information-restricted maximum likelihood method implemented using the DMU statistical package. The heritability estimates for milk components and growth traits ranged from 0.09 (SCS) to 0.51 (BH). Genetic correlations for milk components ranged from 0.03 ± 0.14 (MFP and MLP) to 0.81 ± 0.08 (MFP and MPP). Genetic correlation between MLP and SCS was moderate and negative (− 0.50 ± 0.15) compared with that among other traits. Genetic correlations between the milk components and growth traits ranged from 0.00 ± 0.07 (305MY and RW) to − 0.64 ± 0.15 (MLP and BL). Genetic correlations of BL, LC, RW, and RL with MLP were moderate to high and negative ranging from − 0.39 to − 0.64. Somatic cell score showed the highest correlation with BL (0.41) followed by LC (0.21). An increase in MLP would result in an increase in 305MY or TS and a decrease in BL, LC, RW, and RL. Additionally, a decrease in SCS would occur with the selection of increased MLP and reduced BL. We conclude that selection based on easily and inexpensively measured growth traits could improve the milk quality from Simmental cattle.     

Estimation of the Number of Sex Alleles and Queen Matings from Diploid Male Frequencies in a Population of APIS MELLIFERA

The distribution of diploid males in a population of Apis mellifera was obtained by direct examination of the sexual phenotypes of the larvae. Using these data, estimates are derived for the number of sex alleles and the number of matings undergone by the queen. The number of sex alleles is estimated to be 18.9. The estimate is larger than previous ones, which have ranged between 10 and 12. However, the increase in the number of sex alleles can be explained by the large effective population number for our data. The best estimator of the number of matings by a queen is a maximum likelihood type that assumes a prior distribution on the number of matings. For the data presented here, this estimate is 17.3. This estimate is compared to others in the literature obtained by different approaches.     

Estimation in an Island Model Using Simulation

Estimation for an island model where mutation maintains ak-allele neutral polymorphism at a single locus on each island is considered. The likelihood of an observed sample type configuration is obtained by applying a computational algorithm analogous to Griffiths and Tavaré (Theor. Popul. Biol.46(1994), 131–159). This allows the computation of sampling distributions in an island model and investigation of their properties. Given a sample type configuration, the maximum likelihood estimate of the migration parameter is obtained by simulating independently the likelihood at a grid of points and, also, using a surface simulation method. The latter method generates the whole likelihood trajectory in a single application of the simulation program. An estimate of variance of the estimate of the migration parameter is obtained using the likelihood trajectory. A comparison of the maximum likelihood estimates of the gene flow between subpopulations is made with those obtained by using Wright'sF_STstatistic.     

Rare variant alleles in the light of the neutral theory

Based on the neutral theory of molecular evolution and polymorphism, and particularly assuming "the model of infinite alleles," a method is proposed which enables us to estimate the fraction of selectively neutral alleles (denoted by Pneut) among newly arisen mutations. It makes use of data on the distribution of rare variant alleles in large samples together with information on the average heterozygosity. The formula proposed is Pneut = [He/(1-He)] [loge(2nq)/n alpha (x less than q)], where n alpha(x less than q) is the average number of rare alleles per locus whose frequency, x, is less than q; n is the average sample size used to count rare alleles; He is the average heterozygosity per locus; and q is a small preassigned number such as q = 0.01. The method was applied to observations on enzyme and other protein loci in plaice, humans (European and Amerindian), Japanese monkeys, and fruit flies. Estimates obtained for them range from 0.064 to 0.21 with the mean and standard error Pneut = 0.14 +/- 0.06. It was pointed out that these estimates are consistent with the corresponding estimate Pneut(Hb) = 0.14 obtained independently based on the neutral theory and using data on the evolutionary rate of nucleotide substitutions in globin pseudogenes together with those in the normal globins.      

Estimates of Inbreeding in a Natural Population: A Comparison of Sampling Properties

The average inbreeding coefficient f of a population can be estimated in several different ways based solely on the genotypic frequencies at a single locus. The means and variances of four different estimates have been compared. While the four estimates are equivalent when there are two alleles, the best estimates when there are three or more alleles are based upon total heterozygosity (see PDF) where x and y are the expected and observed number of heterozygotes) and the proportion of alleles that are homozygous (see PDF) where k = the number of alleles, a_ii = the number of A_iA_i homozygotes, and 2a_ij = the number of A_iA_j heterozygotes). Both are minimally biased estimates of f and have identical sampling variances when all alleles are equally frequent. However, when alleles have different frequencies, the choice between these two estimates depends on the gene frequencies and the true inbreeding coefficient of a population; f₂ is the best estimate when the true average inbreeding coefficient is suspected to be low or f = 0, while f₁ is best in populations with large average inbreeding coefficients. Approximate sampling variances of these two estimates are given for any f and any number of alleles with arbitrary gene frequencies; these approximations are accurate for samples as small as n = 100. The chi-square and maximum likelihood estimates of f are not as good for realistic sample sizes.     

On the hypothesis that polymorphic enzyme alleles are selectively neutral. I. The evenness of allele frequency distribution

Using the theory developed by Ewens (1972, Theor. Pop. Biol.3, 87–112), some properties of the ratio of the observed to effective number of alleles are investigated. In particular the expected value of this ratio, as a function of the observed number of alleles, is seen to increase markedly under the neutral hypothesis. However, the corresponding values from field data for some drosophila species decrease as a function of the observed number of alleles.     

Estimating a Logistic Discrimination Functions When One of the Training Samples Is Subject to Misclassification: A Maximum Likelihood Approach

The problem of discrimination and classification is central to much of epidemiology. Here we consider the estimation of a logistic regression/discrimination function from training samples, when one of the training samples is subject to misclassification or mislabeling, e.g. diseased individuals are incorrectly classified/labeled as healthy controls. We show that this leads to zero-inflated binomial model with a defective logistic regression or discrimination function, whose parameters can be estimated using standard statistical methods such as maximum likelihood. These parameters can be used to estimate the probability of true group membership among those, possibly erroneously, classified as controls. Two examples are analyzed and discussed. A simulation study explores properties of the maximum likelihood parameter estimates and the estimates of the number of mislabeled observations.     

An analytical model for the estimation of chromosome substitution effects in the offspring of individuals heterozygous at a segregating marker locus

Summary Use of marker genes for quantitative traits has been suggested as a supplement to selection for livestock species. Linkage relationships can be estimated by using data from offspring of a heterozygous parent, if offspring can be positively assigned segregation of one or the other of the marker alleles. In field data, some data on offspring can be characterized and used to estimate the difference in chromosome substitution effects, but other matings result in uncertain transfer of the marker alleles. In this study, an alternative estimation procedure is proposed that would allow incorporation of data on all offspring of a heterozygous parent, even those where chromosome segregation is ambiguous. If the frequency of the marker alleles is known in the population of mates of a heterozygous individual, the mean and variance of the heterozygous offspring can be used in a generalized leastsquares model to estimate the chromosome substitution effect. When gene frequencies are not known, maximum likelihood estimates can be obtained from the data for use in a conditional estimate. Monte Carlo simulations of data following the assumed genetic model were analyzed as proposed, and parameter estimates were characterized. Estimates of chromosome substitution effects were reasonable approximations of input values. Distributions of t-statistics testing the null hypothesis of no difference between marked chromosome segments were unbiased, with only slightly larger variance than expected. Addition of data from heterozygous offspring improved the efficiency of detection of chromosome substitution effects by more than four times when marker gene frequencies were low.     

A maximum pseudo-likelihood approach for estimating species trees under the coalescent model

Background  

Several phylogenetic approaches have been developed to estimate species trees from collections of gene trees. However, maximum likelihood approaches for estimating species trees under the coalescent model are limited. Although the likelihood of a species tree under the multispecies coalescent model has already been derived by Rannala and Yang, it can be shown that the maximum likelihood estimate (MLE) of the species tree (topology, branch lengths, and population sizes) from gene trees under this formula does not exist. In this paper, we develop a pseudo-likelihood function of the species tree to obtain maximum pseudo-likelihood estimates (MPE) of species trees, with branch lengths of the species tree in coalescent units.     

Prediction of dry-cured ham weight loss and prospects of use in a pig breeding program

Large ham weight losses (WL) in dry-curing are undesired as they lead to a loss of marketable product and penalise the quality of the dry-cured ham. The availability of early predictions of WL may ease the adaptation of the dry-curing process to the characteristics of the thighs and increase the effectiveness of selective breeding in enhancing WL. Aims of this study were (i) to develop Bayesian and Random Forests (RFs) regression models for the prediction of ham WL during dry-curing using on-site infrared spectra of raw ham subcutaneous fat, carcass and raw ham traits as predictors and (ii) to estimate genetic parameters for WL and their predictions (P-WL). Visible-near infrared spectra were collected on the transversal section of the subcutaneous fat of raw hams. Carcass traits were carcass weight, carcass backfat depth, lean meat content and weight of raw hams. Raw ham traits included measures of ham subcutaneous fat depth and linear scores for round shape, subcutaneous fat thickness and marbling of the visible muscles of the thigh. Measures of WL were available for 1672 hams. The best prediction accuracies were those of a Bayesian regression model including the average spectrum, carcass and raw ham traits, with R² values in validation of 0.46, 0.55 and 0.62, for WL at end of salting (23 days), resting (90 days) and curing (12 months), respectively. When WL at salting was used as an additional predictor of total WL, the R² in validation was 0.67. Bayesian regressions were more accurate than RFs models in predicting all the investigated traits. Restricted maximum likelihood (REML) estimates of genetic parameters for WL and P-WL at the end of curing were estimated through a bivariate animal model including 1672 measures of WL and 8819 P-WL records. Results evidenced that the traits are heritable (h² ± SE was 0.27 ± 0.04 for WL and 0.39 ± 0.04 for P-WL), and the additive genetic correlation is positive and high (r_a = 0.88 ± 0.03). Prediction accuracy of ham WL is high enough to envisage a future use of prediction models in identifying batches of hams requiring an adaptation of the processing conditions to optimise results of the manufacturing process. The positive and high genetic correlation detected between WL and P-WL at the end of dry-curing, as well as the estimated heritability for P-WL, suggests that P-WL can be successfully used as an indicator trait of the measured WL in pig breeding programs.     

Genetic diversity and association mapping of seed vigor in rice (Oryza sativa L.)

Key message

Twenty-seven QTLs were identified for rice seed vigor, in which 16 were novel QTLs. Fifteen elite parental combinations were designed for improving seed vigor in rice.

Abstract

Seed vigor is closely related to direct seeding in rice (Oryza sativa L.). Previous quantitative trait locus (QTL) studies for seed vigor were mainly derived from bi-parental segregating populations and no report from natural populations. In this study, association mapping for seed vigor was performed on a selected sample of 540 rice cultivars (419 from China and 121 from Vietnam). Population structure was estimated on the basis of 262 simple sequence repeat (SSR) markers. Seed vigor was evaluated by root length (RL), shoot length (SL) and shoot dry weight in 2011 and 2012. Abundant phenotypic and genetic diversities were found in the studied population. The population was divided into seven subpopulations, and the levels of linkage disequilibrium (LD) ranged from 10 to 80 cM. We identified 27 marker–trait associations involving 18 SSR markers for three traits. According to phenotypic effects for alleles of the detected QTLs, elite alleles were mined. These elite alleles could be used to design parental combinations and the expected results would be obtained by pyramiding or substituting the elite alleles per QTL (apart from possible epistatic effects). Our results demonstrate that association mapping can complement and enhance previous QTL information for marker-assisted selection and breeding by design.     

A Comparative Study of the Esterase-5 Locus in DROSOPHILA PSEUDOOBSCURA,D. PERSIMILIS and D. MIRANDA

Electrophoretic phenotypes of the esterase-5 locus were examined in the sibling species D. pseudoobscura, D. persimilis and D. miranda. D. persimilis alleles were found to have uniformly higher charge on monomers than corresponding alleles of either D. pseudoobscura or D. miranda. Consequently, D. persimilis shares no alleles in common with either D. pseudoobscura or D. miranda, while the latter two species share a number of alleles. It was discovered that by increasing the concentration of acrylamide gel and increasing the length of migration, more allelic differences could be distinguished. Also more alleles were discovered by examining monomer mobility in addition to dimer mobility. In D. persimilis and D. miranda it was found that the previously known high frequency allelic classes broke down into several allelic classes. A test of goodness-of-fit to the infinite alleles model was done and a rough agreement with the model was found.     

What phylogeny and gene genealogy analyses reveal about homoplasy in citrus microsatellite alleles

Sixty-five microsatellite alleles amplified from ancestral citrus accessions classified in three separate genera were evaluated for sequence polymorphism to establish the basis of inter- and intra-allelic genetic variation, evaluate the extent of size homoplasy, and determine an appropriate model (stepwise or infinite allele) for analysis of citrus microsatellite alleles. Sequences for each locus were aligned and subsequently used to determine relationships between alleles of different taxa via parsimony. Interallelic size variation at each SSR locus examined was due to changes in repeat copy number with one exception. Sequencing these alleles uncovered new distinct point mutations in the microsatellite region and the region flanking the microsatellite. Several of the point mutations were found to be genus, species, or allele specific, and some mutations were informative about the inferred evolutionary relationships among alleles. Overall, homoplasy was observed in alleles from all three loci, where the core microsatellite repeat was changed causing alleles of the same size class to be identical in state but not identical by descent. Because nearly all changes in allele size (with one exception) were due to expansion or contraction of the repeat motif, this suggests that a stepwise mutation model, which assumes homoplasy may occur, would be the most appropriate for analyzing Citrus SSR data. The collected data indicate that microsatellites can be a useful tool for evaluating Citrus species and two related genera since repeat motifs were reasonably well retained. However, this work also demonstrated that the number of microsatellite alleles is clearly an underestimate of the number of sequence variants present.     

Synthesis,X-ray molecular structure analysis,and study on ligand scrambling reactions of new thiolatogold(I) complexes with various phosphines

Treatment of Au(PPh₃)Cl, (AuCl)₂(trans-dpen) and (AuCl)₂(dppfe) with Sn(SPh)(n-Bu)₃ and/or PhSH/KOH affords Au(PPh₃)(SPh) (1), (AuSPh)₂(μ-trans-dpen) (2), (AuSPh)2(μ-dppfe) (3), (AuSPh)(μ-trans-dpen)(AuCl) (4), and (AuSPh)(μ-dppfe)(AuCl) (5) in good yields. All these thiophenolates are characterized by single crystal X-ray analysis, ¹H and ³¹P NMR spectroscopy. 1 forms tetramer through Au⋯Au interaction and π–π interaction between the phenyl group in SPh and one of the phenyl groups in PPh₃ in the solid state. An infinite chain structure is formed for 2 through intermolecular aurophilicity and these chains are connected by partial overlap (π–π interaction) of neighboring phenyl groups in SPh to give two-dimensional networks in the solid state. Similar infinite chains are formed through aurophilicity, but two-dimensional networks are not formed for 4 in the solid state. No multidimensional structure is formed for 3 and 5 in the solid state. ¹H and ³¹P NMR spectroscopy of CDC1₃ solutions of 2, 3, 4, and 5 has revealed that rapid ligand scrambling takes place for 4 and 5.     

Association of functional markers with flowering time in lentil

In the present study, a diverse panel of 96 accessions of lentil germplasm was used to study flowering time over environments and to identify simple sequence repeat markers associated with flowering time through association mapping. The study showed high broad sense heritability estimate (h ² bs=0.93) for flowering time in lentil. Screening of 534 SSR markers resulted in an identification of 75 SSR polymorphic markers (13.9%) across studied genotypes. These markers amplified 266 loci and generated 697 alleles ranging from two to 16 alleles per locus. Model-based cluster analysis used for the determination of population structure resulted in the identification of two distinct subpopulations. Distribution of flowering time was ranged from 40 to 70 days in subpopulation I and from 54 to 69 days in subpopulation II and did not skew either late or early flowering time within a subpopulation. No admixture was observed within the subpopulations. Use of the most accepted maximum likelihood model (P3D mixed linear model with optimum compression) of MTA analysis showed significant association of 26 SSR markers with flowering time at <0.05 probability. The percent of phenotypic explained by each associated marker with flowering time ranged from 2.1 to 21.8% and identified QTLs for flowering time explaining high phenotypic variation across the environments (10.7-21.8%) or in a particular environment (10.2-21.4%). In the present study, 13 EST-SSR showed significant association with flowering time and explained large phenotypic variation (2.3-21.8%) compared to genomic SSR markers (2.1-10.2%). Hence, these markers can be used as functional markers in the lentil breeding program to develop short duration cultivars.     

Investigating molecular dynamics-guided lead optimization of EGFR inhibitors

The epidermal growth factor receptor (EGFR) is part of an extended family of proteins that together control aspects of cell growth and development, and thus a validated target for drug discovery. We explore in this work the suitability of a molecular dynamics-based end-point binding free energy protocol to estimate the relative affinities of a virtual combinatorial library designed around the EGFR model inhibitor 6{1} as a tool to guide chemical synthesis toward the most promising compounds. To investigate the validity of this approach, selected analogs including some with better and worse predicted affinities relative to 6{1} were synthesized, and their biological activity determined. To understand the binding determinants of the different analogs, hydrogen bonding and van der Waals contributions, and water molecule bridging in the EGFR–analog complexes were analyzed. The experimental validation was in good qualitative agreement with our theoretical calculations, while also a 6-dibromophenyl-substituted compound with enhanced inhibitory effect on EGFR compared to the reference ligand was obtained.