Responses of alloplasmic (cytoplasm=Triticum timopheevii) and euplasmic wheats (Triticum aestivum) to photoperiod and vernalization

Summary Heritability estimated from sire family variance components, ignoring dams, pools conventional paternal and maternal half sib estimates, in a way which is biased upward, and sub-optimal for minimizing the sampling variance. Standard error of a sire family estimate will be smaller than that of the equivalent paternal half sib estimate, but not as small as that of an estimate obtained by optimal pooling of paternal and maternal half sib estimates. If only additive genetic variance components are significant, the bias may be removed by use of a computed average genetic relationship for sire families, in place of a nominal R = 0.25. Average genetic relationship may be computed from mean and variance of dam family size within sire families. If dominance, epistatic, or maternal components are significant, this simple correction is not appropriate. In situations likely to be encountered in large domestic species such as sheep and cattle (dam family size small and uniform) bias will be negligible. The method could be useful where cost of dam identification is a limiting factor.     

Estimating genetic correlations in natural populations in the absence of pedigree information: accuracy and precision of the Lynch method

Usually, genetic correlations are estimated from breeding designs in the laboratory or greenhouse. However, estimates of the genetic correlation for natural populations are lacking, mostly because pedigrees of wild individuals are rarely known. Recently Lynch (1999) proposed a formula to estimate the genetic correlation in the absence of data on pedigree. This method has been shown to be particularly accurate provided a large sample size and a minimum (20%) proportion of relatives. Lynch (1999) proposed the use of the bootstrap to estimate standard errors associated with genetic correlations, but did not test the reliability of such a method. We tested the bootstrap and showed the jackknife can provide valid estimates of the genetic correlation calculated with the Lynch formula. The occurrence of undefined estimates, combined with the high number of replicates involved in the bootstrap, means there is a high probability of obtaining a biased upward, incomplete bootstrap, even when there is a high fraction of related pairs in a sample. It is easier to obtain complete jackknife estimates for which all the pseudovalues have been defined. We therefore recommend the use of the jackknife to estimate the genetic correlation with the Lynch formula. Provided data can be collected for more than two individuals at each location, we propose a group sampling method that produces low standard errors associated with the jackknife, even when there is a low fraction of relatives in a sample.     

A Method of Screening for Genes of Major Effect

This paper describes a method for screening animal populations on an index of calculated probabilities of genotype status at an unknown single locus. Animals selected by such a method might then be candidates in test matings and genetic marker analyses for major gene detection. The method relies on phenotypic measures for a continuous trait plus identification of sire and dam. Some missing phenotypes and missing pedigree information are permitted. The method is an iterative two-step procedure, the first step estimates genotype probabilities and the second step estimates genotypic effects by regressing phenotypes on genotype probabilities, modeled as true genotype status plus error. Prior knowledge or choice of major locus-free heritability for the trait of interest is required, plus initial starting estimates of the effect on phenotype of carrying one and two copies of the unknown gene. Gene frequency can be estimated by this method, but it is demonstrated that the consequences of using an incorrect fixed prior for gene frequency are not particularly adverse where true frequency of the allele with major effect is low. Simulations involving deterministic sampling from the normal distribution lead to convergence for estimates of genotype effects at the true values, for a reasonable range of starting values, illustrating that estimation of major gene effects has a rational basis. In the absence of polygenic effects, stochastic simulations of 600 animals in five generations resulted in estimates of genotypic effects close to the true values. However, stochastic simulations involving generation and fitting of both major genotype and animal polygenic effects showed upward bias in estimates of major genotype effects. This can be partially overcome by not using information from relatives when calculating genotype probabilities-a result which suggests a route to a modified method which is unbiased and yet does use this information.     

Nonparametric confidence interval estimators for heritability and expected selection response

Statistical methods have not been described for comparing estimates of family-mean heritability (H) or expected selection response (R), nor have consistently valid methods been described for estimating R intervals. Nonparametric methods, e.g., delete-one jackknifing, may be used to estimate variances, intervals, and hypothesis test statistics in estimation problems where parametric methods are unsuitable, nonrobust, or undefinable. Our objective was to evaluate normal-approximation jackknife interval estimators for H and R using Monte Carlo simulation. Simulations were done using normally distributed within-family effects and normally, uniformly, and exponentially distributed between-family effects. Realized coverage probabilities for jackknife interval (2) and parametric interval (5) for H were not significantly different from stated probabilities when between-family effects were normally distributed. Coverages for jackknife intervals (3) and (4) for R were not significantly different from stated coverages when between-family effects were normally distributed. Coverages for interval (3) for R were occasionally significantly less than stated when between-family effects were uniformly or exponentially distributed. Coverages for interval (2) for H were occasionally significantly less than stated when between-family effects were exponentially distributed. Thus, intervals (3) and (4) for R and (2) for H were robust. Means of analysis of variance estimates of R were often significantly less than parametric values when the number of families evaluated was 60 or less. Means of analysis of variance estimates of H were consistently significantly less than parametric values. Means of jackknife estimates of H calculated from log transformed point estimates and R calculated from untransformed or log transformed point estimates were not significantly different from parametric values. Thus, jackknife estimators of H and R were unbiased. Delete-one jackknifing is a robust, versatile, and effective statistical method when applied to estimation problems involving variance functions. Jackknifing is especially valuable in hypothesis test estimation problems where the objective is comparing estimates from different populations.     

Precision of the genotypic correlation estimated from variety trials conducted in incomplete block designs

 Precise assessment of an association among traits of a crop plant is helpful in developing crop-improvement strategies. Two types of association, genotypic correlation and phenotypic correlation, may be used. An estimate of correlation is required along with a measure of precision in terms of standard error. Methods for the evaluation of the standard errors of genotypic and phenotypic correlations are not available in the literature, and when trials are conducted in incomplete blocks an algebraic evaluation of such correlation is cumbersome. Three methods – simulation, jackknife and bootstrap – have been used to evaluate bias and standard errors of genotypic, phenotypic and environmental correlations. We have evaluated their performance with data on grain yield, days-to-heading, and plant height, in barley genotypes in triple lattices. Simulation and jackknife techniques were found to be closer, compared to bootstrap, and can be recommended for assessing the precision of correlation estimates. Received: 9 December 1996 / Accepted: 2 May 1997     

ldne: a program for estimating effective population size from data on linkage disequilibrium

ldne is a program with a Visual Basic interface that implements a recently developed bias correction for estimates of effective population size (N(e) ) based on linkage disequilibrium data. The program reads genotypic data in standard formats and can accommodate an arbitrary number of samples, individuals, loci, and alleles, as well as two mating systems: random and lifetime monogamy. ldne calculates separate estimates using different criteria for excluding rare alleles, which facilitates evaluation of data for highly polymorphic markers such as microsatellites. The program also introduces a jackknife method for obtaining confidence intervals that appears to perform better than parametric methods currently in use.     

Comparing G matrices: a MANOVA approach

There is considerable interest in comparing genetic variance-covariances matrices (G matrix). However, present methods are difficult to implement and cannot readily be extended to incorporate effects of other variables such as habitat, sex, or location. In this paper I present a method based on MANOVA that can be done using only standard statistical packages (coding for the method using SPLUS is available from the author). The crux of the approach is to use the jackknife method to estimate the pseudovalues of the estimates; these estimates can then be used as datapoints in a MANOVA. I illustrate the method using two published datasets: (1) variation in G matrices resulting from differences in rearing condition, species, and sex in the crickets Gryllus firmus and G. pennsylvanicus; and (2) variation in G matrices associated with habitat and history in the amphipod Gammarus minus.     

Analysis of Allelic Association: Estimation of the Power of the TDT

Analysis of allelic associations is an increasingly more widely used approach to fine mapping of genes of various diseases. To interpret the results correctly, it is necessary to estimate the power of the statistical test used. The principle of the analysis of associations and testing of hypothesis are described, and analytically obtained estimates of the power of the transmission disequilibrium test (TDT), one of the most popular methods of analysis of allelic associations, are presented. These estimates are applicable to arbitrary models of inheritance formulated in terms of genotypic relative risk. The proposed method is illustrated by analysis of the associations of idiopathic scoliosis and aggrecan gene alleles.     

Analysis of allelic association: estimation of the criteria power of the TDT

Analysis of allelic associations is an increasingly more widely used approach to fine mapping of genes of various diseases. To interpret the results correctly, it is necessary to estimate the power of the statistical test used. The principle of the analysis of associations and testing of hypothesis are described, and analytically obtained estimates of the power of the transmission disequilibrium test (TDT), one of the most popular methods of analysis of allelic associations, are presented. These estimates are applicable to arbitrary models of inheritance formulated in terms of relative genotypic risk. The proposed method is illustrated by analysis of the associations of idiopathic scoliosis and aggrecan gene alleles.     

利用单元内方差分析法估计遗传参数的探讨

在遗传力的估计过程中,需将多种非遗传因素的影响从公畜间方差或者母畜间方差中剔除。在我国常使用的是盛志廉教授提出的单元内同胞相关法。本文对该法从理论上进行了更详细的证明,并将其推广到两层分类方差分析时的情况。同时还给出了当公母畜彼此间有亲缘关系时,利用单元内方差分析估计遗传力的方法。这些方法既可使遗传力的估计简便,又具有多因方差分析的功用。     

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.     

Progeny testing for recessive genes: procedures and interpretations

Summary Methods for calculating the probability of detecting a carrier of a recessive gene by utilizing matings among related individuals are presented for single and litter bearing species. The confidence level for detection of heterozygosity depends upon: (1) the genetic relationship between mates, (2) the number of mates per male and the number of offspring per mate, (3) whether an estimate of recessive gene frequency before selection is available and (4) the magnitude of that frequency. Methods of computing probability of heterozygosity vs homozygosity utilizing Bayes theorem also are presented. In the conventional progeny test method, a sire initially is assumed heterozygous before calculations are made, but no prior information concerning his probable genotype is utilized. In the method using Bayes theorem, prior sources of information from relatives or from estimates of population allele frequency are utilized. This method gives the exact probability that a sire is not a carrier, given prior information and that he produces all normal offspring. These methods could be used in any sexually reproducing species to identify not only detrimental genes but beneficial genes as well.     

Simple test statistics for major gene detection: a numerical comparison

Summary We compare 22 simple tests for the detection of major gene segregation in livestock populations. These tests belong to two groups: methods based on the comparison of within-family distribution and methods based on the comparison of parents' and offspring performances. The power of the 22 tests and the robustness of the two more powerful of these 22 are evaluated by simulation. Thirteen types of major loci, differing in the within-genotype means, variances or alleles frequencies, are studied. Thirty hierarchically balanced populations defined by the number of sire families (5–20), dams per sire (1–20) and progenies per dam (1–20) are simulated. The quantiles are estimated from 2000 samples, the power from 1000 samples and the robustness from 100 samples. The more powerful tests are the within family-variance heterogenity test (Bartlett test) and the within-family mean-variance regression (Fain 1978). Their robustness may be very low, in particular when the trait distribution is skewed.     

Estimating variance components and predicting breeding values for eventing disciplines and grades in sport horses

Eventing competitions in Great Britain (GB) comprise three disciplines, each split into four grades, yielding 12 discipline-grade traits. As there is a demand for tools to estimate (co)variance matrices with a large number of traits, the aim of this work was to investigate different methods to produce large (co)variance matrices using GB eventing data. Data from 1999 to 2008 were used and penalty points were converted to normal scores. A sire model was utilised to estimate fixed effects of gender, age and class, and random effects of sire, horse and rider. Three methods were used to estimate (co)variance matrices. Method 1 used a method based on Gibbs sampling and data augmentation and imputation. Methods 2a and 2b combined sub-matrices from bivariate analyses; one took samples from a multivariate Normal distribution defined by the covariance matrix from each bivariate analysis, then analysed these data in a 12-trait multivariate analysis; the other replaced negative eigenvalues in the matrix with positive values to obtain a positive definite (co)variance matrix. A formal comparison of models could not be conducted; however, estimates from all methods, particularly Methods 2a/2b, were in reasonable agreement. The computational requirements of Method 1 were much less compared with Methods 2a or 2b. Method 2a heritability estimates were as follows: for dressage 7.2% to 9.0%, for show jumping 8.9% to 16.2% and for cross-country 1.3% to 1.4%. Method 1 heritability estimates were higher for the advanced grades, particularly for dressage (17.1%) and show jumping (22.6%). Irrespective of the model, genetic correlations between grades, for dressage and show jumping, were positive, high and significant, ranging from 0.59 to 0.99 for Method 2a and 0.78 to 0.95 for Method 1. For cross-country, using Method 2a, genetic correlations were only significant between novice and pre-novice (0.75); however, using Method 1 estimates were all significant and low to moderate (0.36 to 0.70). Between-discipline correlations were all low and of mixed sign. All methods produced positive definite 12 × 12 (co)variance matrices, suitable for the prediction of breeding values. Method 1 benefits from much reduced computational requirements, and by performing a true multivariate analysis.     

Growth of Octopus maya (Mollusca: Cephalopoda) of the Yucatan coast, Mexico: a long-term analysis]

Growth of the octopus (Octopus maya) off Yucatan (Mexico) was estimated from a long-term study (seven years) by the length-based methods ELEFAN, PROJMAT and SLCA. Some 19,251 octopuses with a range of mantle length between 50 and 240 mm were sampled from commercial landings in 1983-1987, 1989 and 1992. The jackknife technique was applied to deal with uncertainty in growth estimates resulting from chance variations in sampling design. The growth index phi' was used for comparative purposes. Results differed markedly among methods: ELEFAN produced parameter estimates within the range reported in the literature, whereas PROJMAT and SLCA showed problems to converge in an optimum combination of parameters, and tended to underestimate them. Jackknife analysis revealed very low intraannual variability in phi' but high variability among years, especially when applying PROJMAT. No significant differences were found in precision parameters--percent error and coefficient of variation--among methods. Estimates of phi' derived by ELEFAN varied between 4.19 and 5.23 and agreed with those reported in the literature (between 4.25 and 4.91), whereas PROJMAT and SLCA estimates were significantly lower. We suggest the use of ELEFAN, together with jackknife, to estimate growth parameters of Octopus maya.     

Estimation of Additive Genetic Variance Components in Aquaculture Populations Selectively Pedigreed by DNA Fingerprinting

A method to estimate genetic variance components in populations partially pedigreed by DNA fingerprinting is presented. The focus is on aquaculture, where breeding procedures may produce thousands of individuals. In aquaculture populations the individuals available for measurement will often be selected, i.e. will come from the upper tail of a size‐at‐age distribution, or the lower tail of an age‐at‐maturity distribution etc. Selection typically occurs by size grading during grow‐out and/or choice of superior fish as broodstock. The method presented in this paper enables us to estimate genetic variance components when only a small proportion of individuals, those with extreme phenotypes, have been identified by DNA fingerprinting. We replace the usual normal density by appropriate robust least favourable densities to ensure the robustness of our estimates. Standard analysis of variance or maximum likelihood estimation cannot be used when only the extreme progeny have been pedigreed because of the biased nature of the estimates. In our model‐based procedure a full robust likelihood function is defined, in which the missing information about non‐extreme progeny has been taken into account. This robust likelihood function is transformed into a computable function which is maximized to get the estimates. The estimates of sire and dam additive variance components are significantly and uniformly more accurate than those obtained by any of the standard methods when tested on simulated population data and have desirable robustness properties.     

Comparison of confidence intervals for adjusted attributable risk estimates under multinomial sampling

The epidemiologic concept of the adjusted attributable risk is a useful approach to quantitatively describe the importance of risk factors on the population level. It measures the proportional reduction in disease probability when a risk factor is eliminated from the population, accounting for effects of confounding and effect-modification by nuisance variables. The computation of asymptotic variance estimates for estimates of the adjusted attributable risk is often done by applying the delta method. Investigations on the delta method have shown, however, that the delta method generally tends to underestimate the standard error, leading to biased confidence intervals. We compare confidence intervals for the adjusted attributable risk derived by applying computer intensive methods like the bootstrap or jackknife to confidence intervals based on asymptotic variance estimates using an extensive Monte Carlo simulation and within a real data example from a cohort study in cardiovascular disease epidemiology. Our results show that confidence intervals based on bootstrap and jackknife methods outperform intervals based on asymptotic theory. Best variants of computer intensive confidence intervals are indicated for different situations.     

Probability of Obtaning Negative Estimates of Heritability from Full-Sib Analysis under a General Model of Gene Action

Formulae are derived for the probability of obtaining negative estimates of heritability (h²) in full-sib analysis under the additive-dominance-epistasis model of gene action. Evaluation of the probabilities was undertaken for several combinations of sire/dam number, h² and proportions of dominance and additive X additive epistatic variances, assuming two full-sibs per mating and that the dominance related epistasis is absent. In the light of the results, minimum sample sizes for obtaining admissible estimates from sire, dam components and their combination have been prescribed.     

Evaluation of three methods to estimate density and detectability from roadside point counts

Roadside point counts are often used to estimate trends of bird populations. The use of aural counts of birds without adjustment for detection probability, however, can lead to incorrect population trend estimates. We compared precision of estimates of density and detectability of whistling northern bobwhites (Colinus virginianus) using distance sampling, independent double-observer, and removal methods from roadside surveys. Two observers independently recorded each whistling bird heard, distance from the observer, and time of first detection at 362 call-count stops in Ohio. We examined models that included covariates for year and observer effects for each method and distance from observer effects for the double-observer and removal methods using Akaike's Information Criterion (AIC). The best model of detectability from distance sampling included observer and year effects. The best models from the removal and double-observer techniques included observer and distance effects. All 3 methods provided precise estimates of detection probability (CV = 2.4–4.4%) with a range of detectability of 0.44–0.95 for a 6-min survey. Density estimates from double-observer surveys had the lowest coefficient of variation (2005 = 3.2%, 2006 = 1.7%), but the removal method also provided precise estimates of density (2005 CV = 3.4%, 2006 CV = 4.8%), and density estimates from distance sampling were less precise (2005 CV = 9.6%, 2006 CV = 7.9%). Assumptions of distance sampling were violated in our study because probability of detecting bobwhites near the observer was <1 or the roadside survey points were not randomly distributed with respect to the birds. Distances also were not consistently recorded by individual members of observer pairs. Although double-observer surveys provided more precise estimates, we recommend using the removal method to estimate detectability and abundance of bobwhites. The removal method provided precise estimates of density and detection probability and requires half the personnel time as double-observer surveys. Furthermore, the likelihood of meeting model assumptions is higher for the removal survey than with independent double-observers. © 2011 The Wildlife Society.     

Screening for possible human carcinogens and mutagens. False positives, false negatives: statistical implications

A screening method aimed at identifying potential human carcinogens using either animal cancer bioassays or short-term genotoxic assays has 4 possible results: true positive, true negative, false positive and false negative. Such a categorisation is superficially similar to the results of hypothesis testing in a statistical analysis. In this latter case the false positive rate is determined by the significance level of the test and the false negative rate by the statistical power of the test. Although the two types of categorisation appear somewhat similar, different statistical issues are involved in their interpretation. Statistical methods appropriate for the analysis of the results of a series of assays include the use of Bayes' theorem and multivariate methods such as clustering techniques for the selection of batteries of short-term test capable of a better prediction of potential carcinogens. The conclusions drawn from such studies are dependent upon the estimates of values of sensitivity and specificity used, the choice of statistical method and the nature of the data set. The statistical issues resulting from the analysis of specific genotoxicity experiments involve the choice of suitable experimental designs and appropriate analyses together with the relationship of statistical significance to biological importance. The purpose of statistical analysis should increasingly be to estimate and explore effects rather than for formal hypothesis testing.