An approximate multitrait model for genetic evaluation in dairy cattle with a robust estimation of genetic trends (Open Access publication)

In a stochastic simulation study of a dairy cattle population three multitrait models for estimation of genetic parameters and prediction of breeding values were compared. The first model was an approximate multitrait model using a two-step procedure. The first step was a single trait model for all traits. The solutions for fixed effects from these analyses were subtracted from the phenotypes. A multitrait model only containing an overall mean, an additive genetic and a residual term was applied on these preadjusted data. The second model was similar to the first model, but the multitrait model also contained a year effect. The third model was a full multitrait model. Genetic trends for total merit and for the individual traits in the breeding goal were compared for the three scenarios to rank the models. The full multitrait model gave the highest genetic response, but was not significantly better than the approximate multitrait model including a year effect. The inclusion of a year effect into the second step of the approximate multitrait model significantly improved the genetic trend for total merit. In this study, estimation of genetic parameters for breeding value estimation using models corresponding to the ones used for prediction of breeding values increased the accuracy on the breeding values and thereby the genetic progress.     

Estimation of non-linear growth models by linearization: a simulation study using a Gompertz function

A method based on Taylor series expansion for estimation of location parameters and variance components of non-linear mixed effects models was considered. An attractive property of the method is the opportunity for an easily implemented algorithm. Estimation of non-linear mixed effects models can be done by common methods for linear mixed effects models, and thus existing programs can be used after small modifications. The applicability of this algorithm in animal breeding was studied with simulation using a Gompertz function growth model in pigs. Two growth data sets were analyzed: a full set containing observations from the entire growing period, and a truncated time trajectory set containing animals slaughtered prematurely, which is common in pig breeding. The results from the 50 simulation replicates with full data set indicate that the linearization approach was capable of estimating the original parameters satisfactorily. However, estimation of the parameters related to adult weight becomes unstable in the case of a truncated data set.     

Back to basics for Bayesian model building in genomic selection

Numerous Bayesian methods of phenotype prediction and genomic breeding value estimation based on multilocus association models have been proposed. Computationally the methods have been based either on Markov chain Monte Carlo or on faster maximum a posteriori estimation. The demand for more accurate and more efficient estimation has led to the rapid emergence of workable methods, unfortunately at the expense of well-defined principles for Bayesian model building. In this article we go back to the basics and build a Bayesian multilocus association model for quantitative and binary traits with carefully defined hierarchical parameterization of Student's t and Laplace priors. In this treatment we consider alternative model structures, using indicator variables and polygenic terms. We make the most of the conjugate analysis, enabled by the hierarchical formulation of the prior densities, by deriving the fully conditional posterior densities of the parameters and using the acquired known distributions in building fast generalized expectation-maximization estimation algorithms.     

利用混合模型分析地域对国内马尾松生物量的影响

开展全国森林生物量监测和评估,建立适合较大区域范围的通用性立木生物量模型是一项重要的基础工作,而分析森林生物量受不同地域的影响并保证不同尺度范围森林生物量估计值的可靠性,是必须面临的问题。以南方马尾松(Pinus massoniana)地上生物量数据为例,介绍了如何利用混合模型理论来分析地域对马尾松地上生物量的影响以及利用混合模型构建全国通用性立木生物量模型,为得到不同区域尺度范围内可靠的森林生物量评价和估计提供了有效途径。结果表明,混合模型不仅提高了模型的精度和通用性,并且模型中每个参数都有特定的数学含义,通过这些参数很容易分析出随机因子对生物量的影响程度。因此混合模型方法具有较大的灵活性和适应性,可推广到其它通用性模型(如材积方程)的建立。     

Estimation of quantitative genetic parameters

This paper gives a short review of the development of genetic parameter estimation over the last 40 years. The need to analyse genetic processes in both animal selection experiments and animal breeding improvement programmes motivated the majority of this work. The usage of animal model in conjunction with residual maximum likelihood (REML) techniques for mixed models has revolutionized the methods. These methods to estimate quantitative genetic parameters have recently been advocated for use in evolutionary studies of natural populations. Therefore, it is perhaps timely to discuss the development of REML methods and their application to the analysis of artificial selection experiments and breeding programmes in animals. This should give extra insight into the methods and hopefully lead to synergy between both the areas.     

Prediction of haplotypes for ungenotyped animals and its effect on marker-assisted breeding value estimation

Background

In livestock populations, missing genotypes on a large proportion of animals are a major problem to implement the estimation of marker-assisted breeding values using haplotypes. The objective of this article is to develop a method to predict haplotypes of animals that are not genotyped using mixed model equations and to investigate the effect of using these predicted haplotypes on the accuracy of marker-assisted breeding value estimation.

Methods

For genotyped animals, haplotypes were determined and for each animal the number of haplotype copies (nhc) was counted, i.e. 0, 1 or 2 copies. In a mixed model framework, nhc for each haplotype were predicted for ungenotyped animals as well as for genotyped animals using the additive genetic relationship matrix. The heritability of nhc was assumed to be 0.99, allowing for minor genotyping and haplotyping errors. The predicted nhc were subsequently used in marker-assisted breeding value estimation by applying random regression on these covariables. To evaluate the method, a population was simulated with one additive QTL and an additive polygenic genetic effect. The QTL was located in the middle of a haplotype based on SNP-markers.

Results

The accuracy of predicted haplotype copies for ungenotyped animals ranged between 0.59 and 0.64 depending on haplotype length. Because powerful BLUP-software was used, the method was computationally very efficient. The accuracy of total EBV increased for genotyped animals when marker-assisted breeding value estimation was compared with conventional breeding value estimation, but for ungenotyped animals the increase was marginal unless the heritability was smaller than 0.1. Haplotypes based on four markers yielded the highest accuracies and when only the nearest left marker was used, it yielded the lowest accuracy. The accuracy increased with increasing marker density. Accuracy of the total EBV approached that of gene-assisted BLUP when 4-marker haplotypes were used with a distance of 0.1 cM between the markers.

Conclusions

The proposed method is computationally very efficient and suitable for marker-assisted breeding value estimation in large livestock populations including effects of a number of known QTL. Marker-assisted breeding value estimation using predicted haplotypes increases accuracy especially for traits with low heritability.     

Analysis of culling probability in dairy buffalo using survival models

In order to contribute to the genetic breeding programs of buffaloes, this study aimed to determine the influence of environmental effects on the stayability (ST) of dairy female Murrah buffalo in the herd. Data from 1016 buffaloes were used. ST was defined as the ability of the female to remain in the herd for 1, 2, 3, 4, 5 or 6 years after the first calving. Environmental effects were studied by survival analysis, adjusted to the fixed effects of farm, year and season of birth, class of first-lactation milk yield and age at first calving. The data were analyzed using the LIFEREG procedure of the SAS program that fits parametric models to failure time data (culling or ST = 0), and estimates parameters by maximum likelihood estimation. Breeding farm, year of birth and first-lactation milk yield significantly influenced (P < 0.0001) the ST to the specific ages (1 to 6 years after the first calving). Buffaloes that were older at first calving presented higher probabilities of being culled 1 year after the first calving, without any effect on culling at older ages. Buffaloes with a higher milk yield at first calving presented a lower culling probability and remained for a longer period of time in the herd. The effects of breeding farm, year of birth and first-lactation milk yield should be included in models used for the analysis of ST in buffaloes.     

Anaerobic digestion model No. 1-based distributed parameter model of an anaerobic reactor: II. Model validation

In this study, an ADM1-based distributed parameter model was validated using experimental results obtained in a laboratory-scale 10 L UASB reactor. Sensitivity analysis of the model parameters was used to select four parameters for estimation by a numerical procedure while other parameters were accepted from ADM1 benchmark simulations. The parameter estimation procedure used measurements of liquid phase components obtained at different sampling points in the reactor and under different operating conditions. Model verification used real time fluorescence-based measurements of chemical oxygen demand and volatile fatty acids at four sampling locations in the reactor. Overall, the distributed parameter model was able to describe the distribution of liquid phase components in the reactor and adequately simulated the effect of external recirculation on degradation efficiency. The model can be used in the design, analysis and optimization of UASB reactors.     

Principal component and factor analytic models in international sire evaluation

Background

Interbull is a non-profit organization that provides internationally comparable breeding values for globalized dairy cattle breeding programmes. Due to different trait definitions and models for genetic evaluation between countries, each biological trait is treated as a different trait in each of the participating countries. This yields a genetic covariance matrix of dimension equal to the number of countries which typically involves high genetic correlations between countries. This gives rise to several problems such as over-parameterized models and increased sampling variances, if genetic (co)variance matrices are considered to be unstructured.

Methods

Principal component (PC) and factor analytic (FA) models allow highly parsimonious representations of the (co)variance matrix compared to the standard multi-trait model and have, therefore, attracted considerable interest for their potential to ease the burden of the estimation process for multiple-trait across country evaluation (MACE). This study evaluated the utility of PC and FA models to estimate variance components and to predict breeding values for MACE for protein yield. This was tested using a dataset comprising Holstein bull evaluations obtained in 2007 from 25 countries.

Results

In total, 19 principal components or nine factors were needed to explain the genetic variation in the test dataset. Estimates of the genetic parameters under the optimal fit were almost identical for the two approaches. Furthermore, the results were in a good agreement with those obtained from the full rank model and with those provided by Interbull. The estimation time was shortest for models fitting the optimal number of parameters and prolonged when under- or over-parameterized models were applied. Correlations between estimated breeding values (EBV) from the PC19 and PC25 were unity. With few exceptions, correlations between EBV obtained using FA and PC approaches under the optimal fit were ≥ 0.99. For both approaches, EBV correlations decreased when the optimal model and models fitting too few parameters were compared.

Conclusions

Genetic parameters from the PC and FA approaches were very similar when the optimal number of principal components or factors was fitted. Over-fitting increased estimation time and standard errors of the estimates but did not affect the estimates of genetic correlations or the predictions of breeding values, whereas fitting too few parameters affected bull rankings in different countries.     

Spatial modelling of the barn owl Tyto alba habitat using landscape characteristics derived from SPOT data

Landscape parameters extracted from classified SPOT satellite imagery are used as independent variables for predicting potential habitat areas of the barn owl Tyto alba in a landscape north-east of Brussels, Belgium Field data on the nest sites, recorded during 9 yr, are used as the dependent variable A canonical correlation analysis of the landscape characteristics of 'successful breeding and non-breeding sites' selects a set of most significant parameters contributing to the distinction between suitable and unsuitable breeding habitat parameters measuring the spatial configuration and fragmentation of landscape elements, such as deciduous woods and grasslands, in combination with some visual characteristics of the open spaces in the landscape The selected set of parameters formed the basis for the calculation of a habitat model, whereby potential breeding sites could be located throughout the complete study area, at specific levels of confidence The results showed the relevance of this method for landscape ecological research and nature conservation planning     

非等试验设计胚乳品质性状的遗传分析方法

根据朱军(1996)提出的包括基因型×环境互作的胚乳品质性状三倍体遗传模型,运用蒙特卡罗模拟证明,以混合线性模型统计分析的MINQUE法,对非等试验设计获得的实验数据进行数量遗传分析是可行的.蒙特卡罗模拟结果表明在样本群体大小基本一致的条件下,采用相等试验设计或非等试验设计所估算的遗传参数的偏差(Blas)和功效值(Power)没有明显差异,表明以非等试验设计获得的非平衡数据也可用来进行遗传分析,估算上述遗传模型中的各项遗传方差分量和协方差分量,并且可以采用朱军(1993)提出的AUP法来预测遗传模型中的各项遗传效应值.     

A mixed-effects regression model for longitudinal multivariate ordinal data

A mixed-effects item response theory model that allows for three-level multivariate ordinal outcomes and accommodates multiple random subject effects is proposed for analysis of multivariate ordinal outcomes in longitudinal studies. This model allows for the estimation of different item factor loadings (item discrimination parameters) for the multiple outcomes. The covariates in the model do not have to follow the proportional odds assumption and can be at any level. Assuming either a probit or logistic response function, maximum marginal likelihood estimation is proposed utilizing multidimensional Gauss-Hermite quadrature for integration of the random effects. An iterative Fisher scoring solution, which provides standard errors for all model parameters, is used. An analysis of a longitudinal substance use data set, where four items of substance use behavior (cigarette use, alcohol use, marijuana use, and getting drunk or high) are repeatedly measured over time, is used to illustrate application of the proposed model.     

Progress on breeding for best-hybridized crossing of meat rabbits

Best-hybridized crossing should ideally result in optimal exploitation of heterosis of lines and capitalize on expressed heterosis. Rabbit breeding is heading in the direction of breeding for best-hybridized crossing of meat rabbits. Most special sire lines are selected for post-weaning average daily gain and marketing weight. Post-weaning growth has a negative and favorable genetic correlation with the feed conversion ratio, which is used in indirect selection for feed conversion ratio. The most common selection criteria for special maternal lines are related to litter size at birth or at weaning. Since the heritability of most reproductive traits is low, we must collect as many individual and relative records as possible in the genetic evaluation of rabbits. The BLUP procedure under an animal repeatability model is the most common procedure used for evaluation of animals in selection programs for special lines of meat rabbits. Direct selection for litter size is less efficient than selection for post-weaning growth, but the estimation of heterosis is generally higher for litter size than that for the post-weaning growth. Evaluation of heterosis could be performed by estimating crossbreeding parameters in the cross or comparing contemporary productivity among purebreds and crossbreds. Here, we reviewed breeding of special lines, exploitation of heterosis of crossbreds, and establishment of crossbreeding system of hybrid meat rabbits and summarized the methodologies of breeding special lines, criteria in selection programs, and the result of heterosis estimates.     

肉兔配套系的选育研究进展

配套系在动物育种中能最大程度地利用品系的杂种优势,以获得最大的经济效益,配套系的选育是今后肉兔遗传改良的发展趋势。肉兔父系以选择平均日增重和上市体重为主,断奶后生长性状一般与料肉比呈有利的负遗传相关,可作为料肉比的间接选择标准。而母系以选择断奶数和产仔数为主。大多数繁殖性状的遗传力较低,在进行遗传评估时应当尽可能全面地收集个体和相关亲缘关系个体的记录。重复观测值动物模型下的BLUP估计是进行肉兔专门化品系选育的主要方法。虽然窝内个体数性状的直接选择效率低于生长性状,但其杂种优势一般高于生长性状。通过计算杂交参数和比较同代杂种与纯种间的生产性能可以进行杂种优势的估计。文章对肉兔专门化品系的选育、杂种优势的利用和良种繁育体系的建立进行了综述,总结了肉兔专门化品系的培育方法,性状选择的标准以及杂种优势的估计结果。     

Breeding durations as estimators of adult sex ratios and population size

Adult sex ratios (ASRs) and population size are two of the most fundamental parameters in population biology, as they are the main determinants of genetic and demographic viability, and vulnerability of a population to stochastic events. Underpinning the application of population viability analysis for predicting the extinction risk of populations is the need to accurately estimate parameters that determine the viability of populations (i.e. the ASR and population size). Here we demonstrate that a lack of temporal information can confound estimation of both parameters. Using acoustic telemetry, we compared differences in breeding durations of both sexes for a giant Australian cuttlefish Sepia apama breeding aggregation to the strongly male-biased operational sex ratio (4:1), in order to estimate the population ASR. The ratio of breeding durations between sexes was equal to the operational sex ratio, suggesting that the ASR is not strongly male-biased, but balanced. Furthermore, the short residence times of individuals at the breeding aggregation suggests that previous density-based abundance estimates have significantly underestimated population size. With the current wide application of population viability analysis for predicting the extinction risk of populations, tools to improve the accuracy of such predictions are vital. Here we provide a new approach to estimating the fundamental ASR parameter, and call for temporal considerations when estimating population size.     

Analysis and implementation of a neural extended Kalman filter for target tracking

Having a better motion model in the state estimator is one way to improve target tracking performance. Since the motion model of the target is not known a priori, either robust modeling techniques or adaptive modeling techniques are required. The neural extended Kalman filter is a technique that learns unmodeled dynamics while performing state estimation in the feedback loop of a control system. This coupled system performs the standard estimation of the states of the plant while estimating a function to approximate the difference between the given state-coupling function model and the behavior of the true plant dynamics. At each sample step, this new model is added to the existing model to improve the state estimate. The neural extended Kalman filter has also been investigated as a target tracking estimation routine. Implementation issues for this adaptive modeling technique, including neural network training parameters, were investigated and an analysis was made of the quality of performance that the technique can have for tracking maneuvering targets.     

Accounting for competition in genetic analysis, with particular emphasis on forest genetic trials

Available experimental evidence suggests that there are genetic differences in the abilities of trees to compete for resources, in addition to non-genetic differences due to micro-site variation. The use of indirect genetic effects within the framework of linear mixed model methodology has been proposed for estimating genetic parameters and responses to selection in the presence of genetic competition. In this context, an individual’s total breeding value reflects the effects of its direct breeding value on its own phenotype and its competitive breeding value on the phenotype of its neighbours. The present study used simulated data to investigate the relevance of accounting for competitive effects at the genetic and non-genetic levels in terms of the estimation of (co)variance components and selection response. Different experimental designs that resulted in different genetic relatedness levels within a neighbourhood and survival were other key issues examined. Variances estimated for additive genetic and residual effects tended to be biased under models that ignored genetic competition. Models that fitted competition at the genetic level only also resulted in biased (co)variance estimates for direct additive, competitive additive and residual effects. The ability to detect the correct model was reduced when relatedness within a neighbourhood was very low and survival decreased. Selection responses changed considerably between selecting on breeding value estimates from a model ignoring genetic competition and total breeding estimates using the correct model. Our results suggest that considering a genetic basis to competitive ability will be important to optimise selection programmes for genetic improvement of tree species.     

The effect of missing marker genotypes on the accuracy of gene-assisted breeding value estimation: a comparison of methods

In livestock populations, missing genotypes on a large proportion of the animals is a major problem when implementing gene-assisted breeding value estimation for genes with known effect. The objective of this study was to compare different methods to deal with missing genotypes on accuracy of gene-assisted breeding value estimation for identified bi-allelic genes using Monte Carlo simulation. A nested full-sib half-sib structure was simulated with a mixed inheritance model with one bi-allelic quantitative trait loci (QTL) and a polygenic effect due to infinite number of polygenes. The effect of the QTL was included in gene-assisted BLUP either by random regression on predicted gene content, i.e. the number of positive alleles, or including haplotype effects in the model with an inverse IBD matrix to account for identity-by-descent relationships between haplotypes using linkage analysis information (IBD-LA). The inverse IBD matrix was constructed using segregation indicator probabilities obtained from multiple marker iterative peeling. Gene contents for unknown genotypes were predicted using either multiple marker iterative peeling or mixed model methodology. For both methods, gene-assisted breeding value estimation increased accuracies of total estimated breeding value (EBV) with 0% to 22% for genotyped animals in comparison to conventional breeding value estimation. For animals that were not genotyped, the increase in accuracy was much lower (0% to 5%), but still substantial when the heritability was 0.1 and when the QTL explained at least 15% of the genetic variance. Regression on predicted gene content yielded higher accuracies than IBD-LA. Allele substitution effects were, however, overestimated, especially when only sires and males in the last generation were genotyped. For juveniles without phenotypic records and traits measured only on females, the superiority of regression on gene content over IBD-LA was larger than when all animals had phenotypes. Missing gene contents were predicted with higher accuracy using multiple-marker iterative peeling than with using mixed model methodology, but the difference in accuracy of total EBV was negligible and mixed model methodology was computationally much faster than multiple iterative peeling. For large livestock populations it can be concluded that gene-assisted breeding value estimation can be practically best performed by regression on gene contents, using mixed model methodology to predict missing marker genotypes, combining phenotypic information of genotyped and ungenotyped animals in one evaluation. This technique would be, in principle, also feasible for genomic selection. It is expected that genomic selection for ungenotyped animals using predicted single nucleotide polymorphism gene contents might be beneficial especially for low heritable traits.     

远交群体动态性状基因定位的似然分析Ⅰ.理论方法

受动物遗传育种中用来估计动态性状育种值的随机回归测定日模型思想的启发 ,将关于时间 (测定日期 )的Legendre多项式镶嵌在遗传模型的每个遗传效应中 ,以刻画QTL对动态性状变化过程的作用 ,从而建立起动态性状基因定位的数学模型。利用远交设计群体 ,阐述了动态性状基因定位的似然分析原理 ,推导了定位参数似然估计的EM法两步求解过程。结合动态性状遗传分析的特点和普通数量性状基因定位研究进展 ,还提出了有关动态性状基因定位进一步研究的设想     

A Study of Log-Logistic Model in Survival Analysis

In survival analysis when the mortality reaches a peak after some finite period and then slowly declines, it is appropriate to use a model which has a nonmonotonic failure rate. In this paper we study the log-logistic model whose failure rate exhibits the above behavior and its mean residual life behaves in the reverse fashion. The maximum likelihood estimation of the parameters is examined and it is proved analytically that unique maximum likelihood estimates exist for the parameters. A lung cancer data set is analyzed. Confidence intervals for the parameters as well as for the critical points of the failure rate and mean residual life functions are obtained for the high performance status (PS) and low PS subgroups, where the term performance status is a measure of general medical status.