Genetic analysis of growth curves using the SAEM algorithm

The analysis of nonlinear function-valued characters is very important in genetic studies, especially for growth traits of agricultural and laboratory species. Inference in nonlinear mixed effects models is, however, quite complex and is usually based on likelihood approximations or Bayesian methods. The aim of this paper was to present an efficient stochastic EM procedure, namely the SAEM algorithm, which is much faster to converge than the classical Monte Carlo EM algorithm and Bayesian estimation procedures, does not require specification of prior distributions and is quite robust to the choice of starting values. The key idea is to recycle the simulated values from one iteration to the next in the EM algorithm, which considerably accelerates the convergence. A simulation study is presented which confirms the advantages of this estimation procedure in the case of a genetic analysis. The SAEM algorithm was applied to real data sets on growth measurements in beef cattle and in chickens. The proposed estimation procedure, as the classical Monte Carlo EM algorithm, provides significance tests on the parameters and likelihood based model comparison criteria to compare the nonlinear models with other longitudinal methods.     

Simultaneous estimation of daily weight and feed intake curves for growing pigs by random regression

In this study, random regression models were used to estimate covariance functions between feed intake and BW in boars from the two breeds: the Norwegian Landrace and the Norwegian Duroc. In total, 1476 animals of the Norwegian Landrace breed and 1300 animals of the Norwegian Duroc breed had registrations on daily feed intake and growth from 54 to 180 days of age. Random regressions on the Legendre polynomials of age were used to describe genetic and permanent environmental curves in BW (up to the second order) and feed intake (up to the first order) for both the breeds. Heritabilities on BW increased over time for the Landrace (0.18 to 0.24), but were approximately constant for the Duroc (0.33 to 0.35). Average heritabilities for feed intake were approximately the same in both the breeds (0.09 to 0.11), and the estimates decreased over time, most pronounced in Duroc. On the basis of the current data, daily feed intake was seemingly controlled by the same genetic factors throughout the test period for Duroc; however, for Landrace, genetic correlations between test days decreased with increasing distance in time. For BW, the genetic correlations between test days were in general high, and did not go below 0.8 for any of the two breeds in this study. For both feed intake and BW, permanent environmental correlations between start and end of the test were reduced with increasing difference in days, most pronounced in Duroc. This study indicates that weight of the animal at the end of the test was more closely genetically correlated to feed intake of earlier periods compared with later periods of growth for both the breeds. This may be explained by the fact that BW is the cumulative growth of an individual, which is likely to be heavily affected by the feed intake during the most intense growth period.     

Detection and modelling of time-dependent QTL in animal populations

A longitudinal approach is proposed to map QTL affecting function-valued traits and to estimate their effect over time. The method is based on fitting mixed random regression models. The QTL allelic effects are modelled with random coefficient parametric curves and using a gametic relationship matrix. A simulation study was conducted in order to assess the ability of the approach to fit different patterns of QTL over time. It was found that this longitudinal approach was able to adequately fit the simulated variance functions and considerably improved the power of detection of time-varying QTL effects compared to the traditional univariate model. This was confirmed by an analysis of protein yield data in dairy cattle, where the model was able to detect QTL with high effect either at the beginning or the end of the lactation, that were not detected with a simple 305 day model.     

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.     

Postnatal growth in male Dunkin–Hartley guinea pigs (Cavia cutleri f. porcellus)

The aim of the present study was to describe postnatal organ and body weight growth in male Dunkin–Hartley guinea pigs from birth to 250 days of age. The modified JANOSCHEK growth curve was fitted to the age group means for each measurement by nonlinear regression and characteristics of the resulting growth curves were calculated. At birth, brain weight showed the highest percentage of its adult value (59%), followed by eye weight (37%). Lowest percentage birth weights were found for genital organs, adrenals and pancreas, the majority of organs showed values between 4% and 15%. Weights of body, heart, spleen, liver, genital organs, thyroids and adrenals followed a sigmoidal growth course. The remaining, as examined in this study, organs exhibited simple exponential growth without a postnatal point of inflection. Among internal organs, brain weight reaches adult size first (74 days of age). Genital organs with exception of prostate, duodenum, heart and spleen are fast-growing organs, too.     

EM-REML estimation of covariance parameters in Gaussian mixed models for longitudinal data analysis

This paper presents procedures for implementing the EM algorithm to compute REML estimates of variance covariance components in Gaussian mixed models for longitudinal data analysis. The class of models considered includes random coefficient factors, stationary time processes and measurement errors. The EM algorithm allows separation of the computations pertaining to parameters involved in the random coefficient factors from those pertaining to the time processes and errors. The procedures are illustrated with Pothoff and Roy''s data example on growth measurements taken on 11 girls and 16 boys at four ages. Several variants and extensions are discussed.     

Estimation of genetic parameters for growth performance and carcass traits in Mukota pigs

The objective of the study was to determine genetic parameters for growth and carcass traits in Mukota pigs, maintained on a fibrous diet. Records (n = 1961) were obtained from a population housed at the University of Zimbabwe Farm (Harare, Zimbabwe) between January 1998 and August 2003. Backfat thickness was measured at 50 and 75 mm (K5 and K7.5), respectively. Carcass length (CL) was measured from the anterior edge of the first rib to the pubic bone using a measuring tape. Variance components were estimated using a model that accounted for direct, common environmental litter and maternal genetic effects, using average information restricted maximum likelihood. Heritability estimates for average daily gain from birth to weaning (ADGW) and average daily gain from weaning to 12 weeks (ADG1) were 0.15 and 0.27, respectively. Maternal genetic effects accounted for 2.6% of variation for ADG1. Heritability for average daily gain from 12 weeks to slaughter (ADG2) was 0.20. Common environmental litter effects accounted for 18% of phenotypic variance for cold dressed mass (CDM). Heritability estimates for CDM and CL were 0.32 and 0.62, respectively. Maternal genetic effects accounted for 10.5% of variance in CL. Heritability estimates for K5 and K7.5 were 0.64 and 0.40, respectively. The CDM was positively genetically correlated to K5, but negative to K7.5. The K5 and K7.5 had a high genetic correlation (0.88). Genetic correlations between ADGW and K5, K7.5 and CL were 0.30, 0.05 and 0.35, respectively. The existence of sufficient genetic variation makes genetic improvement for many growth and carcass traits in the Mukota breed possible through effective selection methods.     

Evaluation of the genetic variability of 13 microsatellite markers in native Indian pigs

We analysed polymorphism of 13 microsatellites in two Indian domesticated pig types (North Indian and Northeast Indian). Heterozygosity, polymorphism information content, and probability of identity of two random individuals were calculated for all microsatellites in both types. The number of alleles observed at a locus varied between five and 12. The evaluated microsatellites exhibited a very high heterozygosity and polymorphism information content. The probability of identity of two random individuals from different populations taking into account all the 13 microsatellites was as low as 3.51 × 10^-19. On the basis of these results, we propose that these microsatellite markers may be used with reliability for studying the genetic diversity and for identification of individuals in Indian pig types.     

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.     

Restriction fragment length polymorphisms at the growth hormone gene in pigs

Pigs from four Danish and two Swedish populations were examined for restriction fragment length polymorphism (RFLP) at the growth hormone (GH) gene. Polymorphism was detected with the restriction enzymes DraI and TaqI. A comparison of the Danish populations showed significant differences among their allelic frequencies.     

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.     

安徽省猪种特性与生态类型之关系的研究

对安徽省自然生态环境与猪种特性关系的研究表明,由北向南,旱地面积从５４．３％下降到１．９％,林地和草场分别由５．６％和３．０％上升到６２．４％和１５．８％;水田主要分布在江淮丘陵和沿江平原,水面主要分布在沿江平原;随着纬度的降低,气温和降雨量逐渐升高和加大,饲料条件由精料型逐渐变成青粗饲料型;猪的体型逐渐变小,仔猪１和２０日龄个体重分别由１．０２和３．４８ｋｇ下降到０．７３和２．１６ｋｇ,但皖南山区猪的有效乳头数多,产仔数偏高,其它类型变化不明显;猪的肥育期日增重和瘦肉率分别由５３５．９ｇ·ｄ－１和５５．３％下降到３６１．１ｇ·ｄ－１和３９．５％,但膘厚却由１９．９ｍｍ上升到３９．３ｍｍ;江淮丘陵、沿江平原和皖南山区猪的平均ＡｇＮＯＲ数分别为３．１７、３．６１和３．６８,３种类型猪之间遗传距离分别为０．１１７６、０．１４０４和０．０５６８．     

Using quantile regression methodology to evaluate changes in the shape of growth curves in pigs selected for increased feed efficiency based on residual feed intake

Growth rate is a major component of feed efficiency when estimating residual feed intake (RFI). Quantile regression (QR) methodology can be used to identify animals with different growth trajectories. The objective of this study was to evaluate the use of QR to identify phenotypic and genetic differences in pigs selected for low RFI. Using performance data on 750 Yorkshire pigs selected for low RFI, individual average daily gain (ADG), average daily feed intake (ADFI), RFI and Gompertz growth curve parameters (asymptotic weight (a), inflection point (b) and decay parameter (c)) were estimated for each pig. Using QR methodology, three Gompertz growth curves were estimated for the whole population for three quantiles (0.1, 0.5 and 0.9) of the BW data. Each animal was classified into one of the quantile regression groups (QRG) based on their overall Euclidian distance between each observed and estimated BW from the quantile growth curves. These three curves were also estimated using only part of the data (generations −1 to 3, and −1 to 4) in order to evaluate the agreement classification rate of animals from later generations into QRGs. We evaluated the effect of QRG on growth parameters and performance traits. Genetic parameters were estimated for these traits, as well as for QRG. In addition, genetic trends for each QRG were estimated. Three distinct growth curves were observed for animals classified into either quantiles 0.1 (QRG_0.1), 0.5 (QRG_0.5) or 0.9 (QRG_0.9). When only part of the data was used to estimate quantile growth curves, all animals from QRG_0.1 were correctly classified in their group. Animals in QRG_0.1 had significantly lower ADFI, ADG and RFI, and greater a, b and c than animals in the other groups. Quantile regression groups analysed as a trait was highly heritable (0.41) and had high (0.8) and moderate (0.46) genetic correlations with ADG and RFI, respectively. Selection for reduced RFI increased the number of animals classified as QRG_0.1 in the population. Overall, downward genetic trends were observed for all traits as a function of selection for reduced RFI. However, QRG_0.1 was the only group that had a positive genetic trend for ADG. Altogether, these results indicate that selection for reduced RFI changes the shape of growth curves in Yorkshire in pigs, and that QR methodology was able to identify animals having different genetic potential for feed efficiency, bringing a new opportunity to improve selection for reduced RFI.     

Use of the score test as a goodness-of-fit measure of the covariance structure in genetic analysis of longitudinal data

Model selection is an essential issue in longitudinal data analysis since many different models have been proposed to fit the covariance structure. The likelihood criterion is commonly used and allows to compare the fit of alternative models. Its value does not reflect, however, the potential improvement that can still be reached in fitting the data unless a reference model with the actual covariance structure is available. The score test approach does not require the knowledge of a reference model, and the score statistic has a meaningful interpretation in itself as a goodness-of-fit measure. The aim of this paper was to show how the score statistic may be separated into the genetic and environmental parts, which is difficult with the likelihood criterion, and how it can be used to check parametric assumptions made on variance and correlation parameters. Selection of models for genetic analysis was applied to a dairy cattle example for milk production.     

Genetic parameters and responses of performance and body composition traits in pigs selected for high and low growth rate on a fixed ration over a set time

Two lines of Large White pigs of common genetic origin were divergently selected over four years for high and low growth rate during a 6 week post-weaning test period in which all pigs were fed the same total amount of food (80% of estimated ad libitum intake). Genetic parameters and direct and correlated responses in performance and carcass traits were estimated on 2884 pigs with pedigrees comprising a total of 5324 animals, with restricted maximum likelihood and best linear unbiased prediction methods applied to a multi-trait animal model. Estimates of heritability (± SE) were 0.19 ± 0.04 for lifetime daily gain (LDG), 0.16 ± 0.03 for test daily gain (TDG), 0.25 ± 0.04 for ultrasound P2 backfat (UBF) and 0.16 ± 0.03 for food conversion ratio during test (TFC), and 0.15 ± 0.04 for daily carcass weight gain (CDG), 0.43 ± 0.06 for carcass backfat (CFT) and 0.40 ± 0.06 for carcass lean percentage (LEAN). Common litter effects for TDG, UBF and TFC were less than 5% and for LDG, 17% of total phenotypic variance. Genetic correlations between performance and carcass traits were moderately to highly favourable. After four years of divergent selection for growth rate, the selection responses in estimated breeding value (EBV) for TDG were 40.14 and -41.11 g (SED 2.95) for the high and low growth lines, respectively. The regressions of EBV on year of birth, indicate that the annual genetic trend for TDG, was 8.73 g/yr in the high and -8.48 g/yr in the low lines (P < 0.001). Correlated genetic responses in the high and low lines respectively were 5.28 g and -12.40 g (SED 2.09) in LDG, -0.35 mm and 0.56 mm (SED 0.009) in UBF, -0.145 units and 0.185 units (SED 0.012) in TFC, 3.17 g and -10.97 g (SED 1.53) in CDG, -1.13 mm and 1.01 mm (SED 0.155) in CFT and 1.24% and -1.27% (SED 0.150) in LEAN. It was concluded that selection for increased post-weaning daily gain on a ration of fixed amount reduces the age at slaughter and the level of backfat and increases the efficiency of food utilisation, weight and leanness of pig carcasses.     

Quantitative genetics of continuous reaction norms: thermal sensitivity of caterpillar growth rates

A continuous reaction norm or performance curve represents a phenotypic trait of an individual or genotype in which the trait value may vary with some continuous environmental variable. We explore patterns of genetic variation in thermal performance curves of short-term caterpillar growth rate in a population of Pieris rapae. We compare multivariate methods, which treat performance at each test temperature as a distinct trait, with function-valued methods that treat a performance curve as a continuous function. Mean growth rate increased with increasing temperatures from 8 to 35 degrees C, was highest at 35 degrees C, and declined at 40 degrees C. There was substantial and significant variation among full-sib families in their thermal performance curves. Estimates of broad-sense genetic variances and covariances showed that genetic variance in growth rate increased more than 30-fold from low (8-11 degrees C) to high (35-40 degrees C) temperatures, even after differences in mean growth rate across temperatures were removed. Growth rate at 35 and 40 degrees C was negatively correlated genetically, suggesting a genetic trade-off in growth rate at these temperatures; this trade-off may represent either a generalist-specialist trade-off and/or variation in the optimal temperature for growth. The estimated genetic variance-covariance function (G function), the function-valued analog of the variance-covariance matrix (G matrix), was quite bumpy compared with the estimated G matrix; and results of principal component analyses of the G function were difficult to interpret. The use of orthogonal polynomials as the basis functions in current function-valued estimation methods may generate artifacts when the true G function has prominent local features, such as strong negative covariances at nearby temperatures (e.g. at 35 and 40 degrees C); this may be a particular issue for thermal performance curves and other highly nonlinear reaction norms.     

Random effects modeling approaches for estimating ROC curves from repeated ordinal tests without a gold standard

Estimating diagnostic accuracy without a gold standard is an important problem in medical testing. Although there is a fairly large literature on this problem for the case of repeated binary tests, there is substantially less work for the case of ordinal tests. A noted exception is the work by Zhou, Castelluccio, and Zhou (2005, Biometrics 61, 600-609), which proposed a methodology for estimating receiver operating characteristic (ROC) curves without a gold standard from multiple ordinal tests. A key assumption in their work was that the test results are independent conditional on the true test result. I propose random effects modeling approaches that incorporate dependence between the ordinal tests, and I show through asymptotic results and simulations the importance of correctly accounting for the dependence between tests. These modeling approaches, along with the importance of accounting for the dependence between tests, are illustrated by analyzing the uterine cancer pathology data analyzed by Zhou et al. (2005).     

Phenotypic and genetic relationships between growth and feed intake curves and feed efficiency and amino acid requirements in the growing pig

Improvement of feed efficiency in pigs has been achieved essentially by increasing lean growth rate, which resulted in lower feed intake (FI). The objective was to evaluate the impact of strategies for improving feed efficiency on the dynamics of FI and growth in growing pigs to revisit nutrient recommendations and strategies for feed efficiency improvement. In 2010, three BWs, at 35±2, 63±9 and 107±7 kg, and daily FI during this period were recorded in three French test stations on 379 Large White and 327 French Landrace from maternal pig populations and 215 Large White from a sire population. Individual growth and FI model parameters were obtained with the InraPorc^R software and individual nutrient requirements were computed. The model parameters were explored according to feed efficiency as measured by residual feed intake (RFI) or feed conversion ratio (FCR). Animals were separated in groups of better feed efficiency (RFI⁻ or FCR⁻), medium feed efficiency and poor feed efficiency. Second, genetic relationships between feed efficiency and model parameters were estimated. Despite similar average daily gains (ADG) during the test for all RFI groups, RFI⁻ pigs had a lower initial growth rate and a higher final growth rate compared with other pigs. The same initial growth rate was found for all FCR groups, but FCR⁻ pigs had significantly higher final growth rates than other pigs, resulting in significantly different ADG. Dynamic of FI also differed between RFI or FCR groups. The calculated digestible lysine requirements, expressed in g/MJ net energy (NE), showed the same trends for RFI or FCR groups: the average requirements for the 25% most efficient animals were 13% higher than that of the 25% least efficient animals during the whole test, reaching 0.90 to 0.95 g/MJ NE at the beginning of the test, which is slightly greater than usual feed recommendations for growing pigs. Model parameters were moderately heritable (0.30±0.13 to 0.56±0.13), except for the precocity of growth (0.06±0.08). The parameter representing the quantity of feed at 50 kg BW showed a relatively high genetic correlation with RFI (0.49±0.14), and average protein deposition between 35 and 110 kg had the highest correlation with FCR (−0.76±0.08). Thus, growth and FI dynamics may be envisaged as breeding tools to improve feed efficiency. Furthermore, improvement of feed efficiency should be envisaged jointly with new feeding strategies.     

Detection of quantitative trait loci for growth and fatness in pigs

A quantitative trait locus (QTL) analysis of growth and fatness data from a three-generation experimental cross between Meishan (MS) and Large White (LW) pig breeds is presented. Six boars and 23 F1 sows, the progeny of six LW boars and six MS sows, produced 530 F2 males and 573 F2 females. Nine growth traits, i.e. body weight at birth and at 3, 10, 13, 17 and 22 weeks of age, average daily gain from birth to 3 weeks, from 3 to 10 weeks and from 10 to 22 weeks of age, as well as backfat thickness at 13, 17 and 22 weeks of age and at 40 and 60 kg live weight were analysed. Animals were typed for a total of 137 markers covering the entire porcine genome. Analyses were performed using two interval mapping methods: a line-cross (LC) regression method where founder lines were assumed to be fixed for different QTL alleles and a half-/full-sib (HFS) maximum likelihood method where allele substitution effects were estimated within each half-/full-sib family. Both methods revealed highly significant gene effects for growth on chromosomes 1, 4 and 7 and for backfat thickness on chromosomes 1, 4, 5, 7 and X, and significant gene effects on chromosome 6 for growth and backfat thickness. Suggestive QTLs were also revealed by both methods on chromosomes 2 and 3 for growth and 2 for backfat thickness. Significant gene effects were detected for growth on chromosomes 11, 13, 14, 16 and 18 and for backfat thickness on chromosome 8, 10, 13 and 14. LW alleles were associated with high growth rate and low backfat thickness, except for those of chromosome 7 and to a lesser extent early-growth alleles on chromosomes 1 and 2 and backfat thickness alleles on chromosome 6.