Bayesian analysis for nonlinear regression model under skewed errors,with application in growth curves

We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated measurements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew‐t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model.     

Detection of multiple QTL with epistatic effects under a mixed inheritance model in an outbred population

A quantitative trait depends on multiple quantitative trait loci (QTL) and on the interaction between two or more QTL, named epistasis. Several methods to detect multiple QTL in various types of design have been proposed, but most of these are based on the assumption that each QTL works independently and epistasis has not been explored sufficiently. The objective of the study was to propose an integrated method to detect multiple QTL with epistases using Bayesian inference via a Markov chain Monte Carlo (MCMC) algorithm. Since the mixed inheritance model is assumed and the deterministic algorithm to calculate the probabilities of QTL genotypes is incorporated in the method, this can be applied to an outbred population such as livestock. Additionally, we treated a pair of QTL as one variable in the Reversible jump Markov chain Monte Carlo (RJMCMC) algorithm so that two QTL were able to be simultaneously added into or deleted from a model. As a result, both of the QTL can be detected, not only in cases where either of the two QTL has main effects and they have epistatic effects between each other, but also in cases where neither of the two QTL has main effects but they have epistatic effects. The method will help ascertain the complicated structure of quantitative traits.     

Genomic prediction in CIMMYT maize and wheat breeding programs

Genomic selection (GS) has been implemented in animal and plant species, and is regarded as a useful tool for accelerating genetic gains. Varying levels of genomic prediction accuracy have been obtained in plants, depending on the prediction problem assessed and on several other factors, such as trait heritability, the relationship between the individuals to be predicted and those used to train the models for prediction, number of markers, sample size and genotype × environment interaction (GE). The main objective of this article is to describe the results of genomic prediction in International Maize and Wheat Improvement Center''s (CIMMYT''s) maize and wheat breeding programs, from the initial assessment of the predictive ability of different models using pedigree and marker information to the present, when methods for implementing GS in practical global maize and wheat breeding programs are being studied and investigated. Results show that pedigree (population structure) accounts for a sizeable proportion of the prediction accuracy when a global population is the prediction problem to be assessed. However, when the prediction uses unrelated populations to train the prediction equations, prediction accuracy becomes negligible. When genomic prediction includes modeling GE, an increase in prediction accuracy can be achieved by borrowing information from correlated environments. Several questions on how to incorporate GS into CIMMYT''s maize and wheat programs remain unanswered and subject to further investigation, for example, prediction within and between related bi-parental crosses. Further research on the quantification of breeding value components for GS in plant breeding populations is required.     

Fine mapping and single nucleotide polymorphism effects estimation on pig chromosomes 1, 4, 7, 8, 17 and X

Fine mapping of quantitative trait loci (QTL) from previous linkage studies was performed on pig chromosomes 1, 4, 7, 8, 17, and X which were known to harbor QTL. Traits were divided into: growth performance, carcass, internal organs, cut yields, and meat quality. Fifty families were used of a F2 population produced by crossing local Brazilian Piau boars with commercial sows. The linkage map consisted of 237 SNP and 37 microsatellite markers covering 866 centimorgans. QTL were identified by regression interval mapping using GridQTL. Individual marker effects were estimated by Bayesian LASSO regression using R. In total, 32 QTL affecting the evaluated traits were detected along the chromosomes studied. Seven of the QTL were known from previous studies using our F2 population, and 25 novel QTL resulted from the increased marker coverage. Six of the seven QTL that were significant at the 5% genome-wide level had SNPs within their confidence interval whose effects were among the 5% largest effects. The combined use of microsatellites along with SNP markers increased the saturation of the genome map and led to smaller confidence intervals of the QTL. The results showed that the tested models yield similar improvements in QTL mapping accuracy.     

Genomic signatures reveal selection of characteristics within and between Meishan pig populations

The Chinese Meishan pig breed is well known for its high prolificacy. Moreover, this breed can be divided into three types based on their body size: big Meishan, middle Meishan (MMS) and small Meishan (SMS) pigs. Few studies have reported on the genetic signatures of Meishan pigs, particularly on a genome‐wide scale. Exploring for genetic signatures could be quite valuable for revealing the genetic architecture of phenotypic variation. Thus, we performed research in two parts based on the genome reducing and sequencing data of 143 Meishan pigs (74 MMS pigs, 69 SMS pigs). First, we detected the selection signatures among all Meishan pigs studied using the relative extended haplotype homozygosity test. Second, we detected the selection signatures between MMS and SMS pigs using the cross‐population extended haplotype homozygosity and F_ST methods. A total of 111 398 SNPs were identified from the sequenced genomes. In the population analysis, the most significant genes were associated with the mental development (RGMA), reproduction (HDAC4, FOXL2) and lipid metabolism (ACACB). From the cross‐population analysis, we detected genes related to body weight (SPDEF, PACSIN1) in both methods. We suggest that rs341373351, located within the PACSIN1 gene, might be the causal variant. This study may have achieved consistency between selection signatures and characteristics within and between Meishan pig populations. These findings can provide insight into investigating the molecular background of high prolificacy and body size in pig.     

Equivalence of regression curves sharing common parameters

In clinical trials, the comparison of two different populations is a common problem. Nonlinear (parametric) regression models are commonly used to describe the relationship between covariates, such as concentration or dose, and a response variable in the two groups. In some situations, it is reasonable to assume some model parameters to be the same, for instance, the placebo effect or the maximum treatment effect. In this paper, we develop a (parametric) bootstrap test to establish the similarity of two regression curves sharing some common parameters. We show by theoretical arguments and by means of a simulation study that the new test controls its significance level and achieves a reasonable power. Moreover, it is demonstrated that under the assumption of common parameters, a considerably more powerful test can be constructed compared with the test that does not use this assumption. Finally, we illustrate the potential applications of the new methodology by a clinical trial example.     

On the efficiency of composite interval mapping in an outbred population

Composite interval mapping (CIM) has been successfully applied to the detection of QTL in experimental animals and plants. However, practical analyses based on CIM have been reported mainly for populations derived from cross between inbred lines. There are few studies on QTL analyses with CIM in outbred populations. To evaluate the applicability of CIM to outbred populations is prerequisite for the fine mapping of QTL in industrial animals such as pig and chicken. Some markers are usually not fully informative in outbred populations. In application of CIM to outbred populations, the influence of inclusion of such uninformative markers used as covariates on the efficiency of CIM should be investigated. In this paper a least-squares method for CIM was formalized in an F(2) population derived by crossing two outbred lines. The efficiencies of CIM were evaluated for outbred populations in comparison with simple interval mapping (SIM) for several cases of marker informativeness using simulations. By incorporating markers linked to a tested position as well as those unlinked, CIM showed a higher efficiency to separate two linked QTL over SIM. The efficiency of dissection was enhanced as the marker informativeness was increased. The power of CIM to detect an isolated QTL was improved by excluding markers linked to a tested position from covariates and higher than SIM regardless of marker informativeness. In conclusion, CIM is a useful procedure for the analysis of QTL in outbred populations even under low marker informativeness.     

QTL detection and allelic effects for growth and fat traits in outbred pig populations

Quantitative trait loci (QTL) for growth and fatness traits have previously been identified on chromosomes 4 and 7 in several experimental pig populations. The segregation of these QTL in commercial pigs was studied in a sample of 2713 animals from five different populations. Variance component analysis (VCA) using a marker-based identity by descent (IBD) matrix was applied. The IBD coefficient was estimated with simple deterministic (SMD) and Markov chain Monte Carlo (MCMC) methods. Data for two growth traits, average daily gain on test and whole life daily gain, and back fat thickness were analysed. With both methods, seven out of 26 combinations of population, chromosome and trait, were significant. Additionally, QTL genotypic and allelic effects were estimated when the QTL effect was significant. The range of QTL genotypic effects in a population varied from 4.8% to 10.9% of the phenotypic mean for growth traits and 7.9% to 19.5% for back fat trait. Heritabilities of the QTL genotypic values ranged from 8.6% to 18.2% for growth traits, and 14.5% to 19.2% for back fat. Very similar results were obtained with both SMD and MCMC. However, the MCMC method required a large number of iterations, and hence computation time, especially when the QTL test position was close to the marker.     

A Bayesian analysis of the effect of selection for growth rate on growth curves in rabbits

Gompertz growth curves were fitted to the data of 137 rabbits from control (C) and selected (S) lines. The animals came from a synthetic rabbit line selected for an increased growth rate. The embryos from generations 3 and 4 were frozen and thawed to be contemporary of rabbits born in generation 10. Group C was the offspring of generations 3 and 4, and group S was the contemporary offspring of generation 10. The animals were weighed individually twice a week during the first four weeks of life, and once a week thereafter, until 20 weeks of age. Subsequently, the males were weighed weekly until 40 weeks of age. The random samples of the posterior distributions of the growth curve parameters were drawn by using Markov Chain Monte Carlo (MCMC) methods. As a consequence of selection, the selected animals were heavier than the C animals throughout the entire growth curve. Adult body weight, estimated as a parameter of the Gompertz curve, was 7% higher in the selected line. The other parameters of the Gompertz curve were scarcely affected by selection. When selected and control growth curves are represented in a metabolic scale, all differences disappear.     

Prediction of genetic growth curves in pigs

Genetic growth curves of boars in a test station were predicted on daily weight records collected by automated weighing scales. The data contained 121 865 observations from 1477 Norwegian Landrace boars and 108 589 observations from 1300 Norwegian Duroc boars. Random regression models using Legendre polynomials up to second order for weight at different ages were compared for best predicting ability and Bayesian information criterion (BIC) for both breeds. The model with second-order polynomials had best predictive ability and BIC. The heritability for weight, based on this model, was found to vary along the growth trajectory between 0.32-0.35 for Duroc and 0.17-0.25 for Landrace. By varying test length possibility to use shorter test time and pre-selection was tested. Test length was varied and compared with average termination at 100 kg, termination of the test at 90 kg gives, e.g. 2% reduction in accuracy of estimated breeding values (EBV) for both breeds and termination at 80 kg gives 5% reduction in accuracy of EBVs for Landrace and 3% for Duroc. A shorter test period can decrease test costs per boar, but also gives possibilities to increase selection intensity as there will be room for testing more boars.     

Genomic signatures of population bottleneck and recovery in Northwest Atlantic pinnipeds

Population increases over the past several decades provide natural settings in which to study the evolutionary processes that occur during bottleneck, growth, and spatial expansion. We used parallel natural experiments of historical decline and subsequent recovery in two sympatric pinniped species in the Northwest Atlantic, the gray seal (Halichoerus grypus atlantica) and harbor seal (Phoca vitulina vitulina), to study the impact of recent demographic change in genomic diversity. Using restriction site‐associated DNA sequencing, we assessed genomic diversity at over 8,700 polymorphic gray seal loci and 3,700 polymorphic harbor seal loci in samples from multiple cohorts collected throughout recovery over the past half‐century. Despite significant differences in the degree of genetic diversity assessed in the two species, we found signatures of historical bottlenecks in the contemporary genomes of both gray and harbor seals. We evaluated temporal trends in diversity across cohorts, as well as compared samples from sites at both the center and edge of a recent gray seal range expansion, but found no significant change in genomewide diversity following recovery. We did, however, find that the variance and degree of allele frequency change measured over the past several decades were significantly different from neutral expectations of drift under population growth. These two cases of well‐described demographic history provide opportunities for critical evaluation of current approaches to simulating and understanding the genetic effects of historical demographic change in natural populations.     

Bayesian versus frequentist analysis of multiple quantitative trait loci with an application to an outbred apple cross

Two methods, following different statistical paradigms for mapping multiple quantitative trait loci (QTLs), were compared: the first is a frequentist, the second a Bayesian approach. Both methods were applied to previously published experimental data from an outbred progeny of a single cross between two apple cultivars (Malus pumila Mill.). These approaches were compared with respect to (1) the models used, (2) the number of putative QTLs, (3) their estimated map positions and accuracies thereof and (4) the choice of cofactor markers. In general, the strongest evidence for QTLs, provided by both methods, was for the same linkage groups and for similar map positions. However, some differences were found with respect to evidence for QTLs on other linkage groups. The effect of using cofactor markers which were selected differently was also somewhat different. Received: 17 July 2000 / Accepted: 13 January 2001     

Genomic mating in outbred species: predicting cross usefulness with additive and total genetic covariance matrices

Diverse crops are both outbred and clonally propagated. Breeders typically use truncation selection of parents and invest significant time, land, and money evaluating the progeny of crosses to find exceptional genotypes. We developed and tested genomic mate selection criteria suitable for organisms of arbitrary homozygosity level where the full-sibling progeny are of direct interest as future parents and/or cultivars. We extended cross variance and covariance variance prediction to include dominance effects and predicted the multivariate selection index genetic variance of crosses based on haplotypes of proposed parents, marker effects, and recombination frequencies. We combined the predicted mean and variance into usefulness criteria for parent and variety development. We present an empirical study of cassava (Manihot esculenta), a staple tropical root crop. We assessed the potential to predict the multivariate genetic distribution (means, variances, and trait covariances) of 462 cassava families in terms of additive and total value using cross-validation. Most variance (89%) and covariance (70%) prediction accuracy estimates were greater than zero. The usefulness of crosses was accurately predicted with good correspondence between the predicted and the actual mean performance of family members breeders selected for advancement as new parents and candidate varieties. We also used a directional dominance model to quantify significant inbreeding depression for most traits. We predicted 47,083 possible crosses of 306 parents and contrasted them to those previously tested to show how mate selection can reveal the new potential within the germplasm. We enable breeders to consider the potential of crosses to produce future parents (progeny with top breeding values) and varieties (progeny with top own performance).     

Genes located on a SSC17 meat quality QTL region are associated with growth in outbred pig populations

The objective of this study was to evaluate the effect of markers developed in eight genes, located in a previously detected meat quality QTL region on SSC17, on growth, fat and meat quality traits collected in commercial pig populations of different genetic backgrounds. The genes had been previously mapped to SSC17 as part of a fine-mapping effort. Association analyses were conducted between each marker and the available phenotypic traits. Results showed that three genes ( CTSZ , CSTF1 and C20orf43 ) were significantly associated with the growth traits. In addition, CTSZ also impacted on meat colour, with the less favourable genotype for growth being associated with darker meat. The differences observed between genotypes were substantial and may be of economic importance to pig producers. These markers may be useful for selecting for faster growth or improved meat quality.     

An empirical assessment of individual-based population genetic statistical techniques: application to British pig breeds

Recently developed Bayesian genotypic clustering methods for analysing genetic data offer a powerful tool to evaluate the genetic structure of domestic farm animal breeds. The unit of study with these approaches is the individual instead of the population. We aimed to empirically evaluate various individual-based population genetic statistical methods for characterization of genetic diversity and structure of livestock breeds. Eighteen British pig populations, comprising 819 individuals, were genotyped at 46 microsatellite markers. Three Bayesian genotypic clustering approaches, principle component analysis (PCA) and phylogenetic reconstruction were applied to individual multilocus genotypes to infer the genetic structure and diversity of the British pig breeds. Comparisons of the three Bayesian genotypic clustering methods (, and ) revealed some broad similarities but also some notable differences. Overall, the methods agreed that majority of the British pig breeds are independent genetic units with little evidence of admixture. The three Bayesian genotypic clustering methods provided complementary, biologically credible clustering solutions but at different levels of resolution. detected finer genetic differentiation and in some cases, populations within breeds. Consequently, it estimated a greater number of underlying genetic populations (K, in the notation of Bayesian clustering methods). Two of the Bayesian methods ( and ) and phylogenetic reconstruction provided similar success in assignment of individuals, supporting the use of these methods for breed assignment.     

Varying coefficient model with unknown within-subject covariance for analysis of tumor growth curves

SUMMARY: In this article we develop a nonparametric estimation procedure for the varying coefficient model when the within-subject covariance is unknown. Extending the idea of iterative reweighted least squares to the functional setting, we iterate between estimating the coefficients conditional on the covariance and estimating the functional covariance conditional on the coefficients. Smoothing splines for correlated errors are used to estimate the functional coefficients with smoothing parameters selected via the generalized maximum likelihood. The covariance is nonparametrically estimated using a penalized estimator with smoothing parameters chosen via a Kullback-Leibler criterion. Empirical properties of the proposed method are demonstrated in simulations and the method is applied to the data collected from an ovarian tumor study in mice to analyze the effects of different chemotherapy treatments on the volumes of two classes of tumors.     

Evaluation of the paraoxonase-1 kinetic parameters of the lactonase activity by nonlinear fit of progress curves

Abstract

Although paraoxonase-1 (PON1) activity has been demonstrated to be a reliable biomarker of various diseases, clinical studies have been based only on relative comparison of specific enzyme activities, which capture differences mainly due to (usually unknown) PON1 concentration. Hence, the aim of this report is to present for the first time the simple evaluation method for determining autonomous kinetic parameter of PON1 that could be also associated with polymorphic forms and diseases; i.e. the Michaelis constant which is enzyme concentration independent quantity. This alternative approach significantly reduces the number of experiments needed, and it yields the results with great accuracy.     

Power of two and three-generation QTL mapping experiments in an outbred population containing full-sib or half-sib families

QTL mapping experiments involve many animals to be genotyped and performance tested. Consequently, experimental designs need to be optimized to minimize the costs of data collection and genotyping. The present study has analyzed the power and efficiency of experiments with two or three-generation family structures containing full-sib families, half-sib families, or both. The focus was on data from one outbred population because the main interest is to locate genes that can be used for within-line selection. For a two generation experiment more animals had to be typed for marker loci to obtain a certain power than for a three generation experiment. Fewer trait values, however, had to be obtained for a two-generation experiment than for a three-generation experiment. A two or three-generation family structure with full-sib offspring was more efficient than a two or three-generation family structure with half-sib offspring. A family structure with full-sib grand-offspring, however, was less efficient than a family structure with half-sib grand-offspring. For the most efficient family structure each pair of parents had full-sib offspring that were genotyped for the marker. For the most-efficient family structure each full-sib offspring had half-sib grand-offspring for which trait values were obtained. For equal power with a heritability of 0.1 and 100 grand-offspring per full-sib offspring, 30-times less marker typings were required for this most efficient family structure than for a two-generation half-sib structure in which marker genotypes and trait values were obtained for half-sib offspring. The effect of heritability and the type of analysis (single marker or interval analysis) on the efficiency of a family structure is described. The results of this study should help to design QTL mapping experiments in an outbred population.