Symbolic Formulae for Linear Mixed Models

A statistical model is a mathematical representation of an often simplified or idealised data-generating process. In this paper, we focus on a particular type of statistical model, called linear mixed models (LMMs), that is widely used in many disciplines e.g.~agriculture, ecology, econometrics, psychology. Mixed models, also commonly known as multi-level, nested, hierarchical or panel data models, incorporate a combination of fixed and random effects, with LMMs being a special case. The inclusion of random effects in particular gives LMMs considerable flexibility in accounting for many types of complex correlated structures often found in data. This flexibility, however, has given rise to a number of ways by which an end-user can specify the precise form of the LMM that they wish to fit in statistical software. In this paper, we review the software design for specification of the LMM (and its special case, the linear model), focusing in particular on the use of high-level symbolic model formulae and two popular but contrasting R-packages in lme4 and asreml

Performance evaluation of highly admixed Tanzanian smallholder dairy cattle using SNP derived kinship matrix

The main purpose of this study was to understand the type of dairy cattle that can be optimally used by smallholder farmers in various production environments such that they will maximize their yields without increasing the level of inputs. Anecdotal evidence and previous research suggests that the optimal level of taurine inheritance in crossbred animals lies between 50 and 75% when considering total productivity in tropical management clusters. We set out to assess the relationship between breed composition and productivity for various smallholder production systems in Tanzania. We surveyed 654 smallholder dairy households over a 1-year period and grouped them into production clusters. Based on supplementary feeding, milk productivity and sale as well as household wealth status four clusters were described: low-feed–low-output subsistence, medium-feed–low-output subsistence, maize germ intensive semi-commercial and feed intensive commercial management clusters. About 839 crossbred cows were genotyped at approximately 150,000 single nucleotide polymorphism (SNP) loci and their breed composition determined. Percentage dairyness (proportion of genes from international dairy breeds) was estimated through admixture analysis with Holstein, Friesian, Norwegian Red, Jersey, Guernsey, N’Dama, Gir, and Zebu as references. Four breed types were defined as RED–GUE (Norwegian Red/Friesian–Guernsey; Norwegian Red/Friesian–Jersey), RED–HOL (Norwegian Red/Friesian–Holstein), RED–Zebu (Norwegian Red/Friesian–Zebu), Zebu–RED (Zebu–Norwegian Red/Friesian) based on the combination of breeds that make up the top 76% breed composition. A fixed regression model using a genomic kinship matrix was used to analyze milk yield records. The fitted model accounted for year-month-test-date, parity, age, breed type and the production clusters as fixed effects in the model in addition to random effects of animal and permanent environment effect. Results suggested that RED–Zebu breed type with dairyness between 75 and 85% is the most appropriate for a majority of smallholder management clusters. Additionally, for farmers in the feed intensive management group, animals with a Holstein genetic background with at least 75% dairy composition were the best performing. These results indicate that matching breed type to production management group is central to maximizing productivity in smallholder systems. The findings from this study can serve as a basis to inform the development of the dairy sector in Tanzania and beyond.</p

Mapping quantitative trait loci in line cross with repeat records

<p>Abstract</p> <p>Background</p> <p>Phenotypes with repeat records from one individual or multiple individuals were often encountered in practices of mapping QTL in linecross. The current genetic mapping method for a trait with repeat records is adopted by simply replacing the phenotype by the average value of the repeat records. This simple treatment has not sufficiently utilized the information from the replication and ignored the impacts of the permanent environmental effects on the accuracy of the estimated QTL.</p> <p>Results</p> <p>We propose to map QTL by using the repeatability model to directly analyze the repeat records rather than simply analyze the mean phenotype, improving the efficiency of QTL detecting because of adequately utilizing the information from data and allowing for the permanent environmental effects. A maximum likelihood method implemented via the expectation-maximization (EM) algorithm is applied to perform the parameter estimation of the repeatability model. The superiority of the mapping method based on the repeatability model over simple analysis using the mean phenotype was demonstrated by a series of simulations.</p> <p>Conclusion</p> <p>Our results suggest that the proposed method can serve as a powerful alternative to existing methods. By mean of the repeatability model, utilizing the repeat records on individual may improve the efficiency of QTL detecting in line cross.</p

Genomic breeding value estimation using nonparametric additive regression models

Genomic selection refers to the use of genomewide dense markers for breeding value estimation and subsequently for selection. The main challenge of genomic breeding value estimation is the estimation of many effects from a limited number of observations. Bayesian methods have been proposed to successfully cope with these challenges. As an alternative class of models, non- and semiparametric models were recently introduced. The present study investigated the ability of nonparametric additive regression models to predict genomic breeding values. The genotypes were modelled for each marker or pair of flanking markers (i.e. the predictors) separately. The nonparametric functions for the predictors were estimated simultaneously using additive model theory, applying a binomial kernel. The optimal degree of smoothing was determined by bootstrapping. A mutation-drift-balance simulation was carried out. The breeding values of the last generation (genotyped) was predicted using data from the next last generation (genotyped and phenotyped). The results show moderate to high accuracies of the predicted breeding values. A determination of predictor specific degree of smoothing increased the accuracy

Genetic properties of feed efficiency parameters in meat-type chickens

<p>Abstract</p> <p>Background</p> <p>Feed cost constitutes about 70% of the cost of raising broilers, but the efficiency of feed utilization has not kept up the growth potential of today's broilers. Improvement in feed efficiency would reduce the amount of feed required for growth, the production cost and the amount of nitrogenous waste. We studied residual feed intake (RFI) and feed conversion ratio (FCR) over two age periods to delineate their genetic inter-relationships.</p> <p>Methods</p> <p>We used an animal model combined with Gibb sampling to estimate genetic parameters in a pedigreed random mating broiler control population.</p> <p>Results</p> <p>Heritability of RFI and FCR was 0.42-0.45. Thus selection on RFI was expected to improve feed efficiency and subsequently reduce feed intake (FI). Whereas the genetic correlation between RFI and body weight gain (BWG) at days 28-35 was moderately positive, it was negligible at days 35-42. Therefore, the timing of selection for RFI will influence the expected response. Selection for improved RFI at days 28-35 will reduce FI, but also increase growth rate. However, selection for improved RFI at days 35-42 will reduce FI without any significant change in growth rate. The nature of the pleiotropic relationship between RFI and FCR may be dependent on age, and consequently the molecular factors that govern RFI and FCR may also depend on stage of development, or on the nature of resource allocation of FI above maintenance directed towards protein accretion and fat deposition. The insignificant genetic correlation between RFI and BWG at days 35-42 demonstrates the independence of RFI on the level of production, thereby making it possible to study the molecular, physiological and nutrient digestibility mechanisms underlying RFI without the confounding effects of growth. The heritability estimate of FCR was 0.49 and 0.41 for days 28-35 and days 35-42, respectively.</p> <p>Conclusion</p> <p>Selection for FCR will improve efficiency of feed utilization but because of the genetic dependence of FCR and its components, selection based on FCR will reduce FI and increase growth rate. However, the correlated responses in both FI and BWG cannot be predicted accurately because of the inherent problem of FCR being a ratio trait.</p

Genetic parameters for somatic cell score according to udder infection status in Valle del Belice dairy sheep and impact of imperfect diagnosis of infection

<p>Abstract</p> <p>Background</p> <p>Somatic cell score (SCS) has been promoted as a selection criterion to improve mastitis resistance. However, SCS from healthy and infected animals may be considered as separate traits. Moreover, imperfect sensitivity and specificity could influence animals' classification and impact on estimated variance components. This study was aimed at: (1) estimating the heritability of bacteria negative SCS, bacteria positive SCS, and infection status, (2) estimating phenotypic and genetic correlations between bacteria negative and bacteria positive SCS, and the genetic correlation between bacteria negative SCS and infection status, and (3) evaluating the impact of imperfect diagnosis of infection on variance component estimates.</p> <p>Methods</p> <p>Data on SCS and udder infection status for 1,120 ewes were collected from four Valle del Belice flocks. The pedigree file included 1,603 animals. The SCS dataset was split according to whether animals were infected or not at the time of sampling. A repeatability test-day animal model was used to estimate genetic parameters for SCS traits and the heritability of infection status. The genetic correlation between bacteria negative SCS and infection status was estimated using an MCMC threshold model, implemented by Gibbs Sampling.</p> <p>Results</p> <p>The heritability was 0.10 for bacteria negative SCS, 0.03 for bacteria positive SCS, and 0.09 for infection status, on the liability scale. The genetic correlation between bacteria negative and bacteria positive SCS was 0.62, suggesting that they may be genetically different traits. The genetic correlation between bacteria negative SCS and infection status was 0.51. We demonstrate that imperfect diagnosis of infection leads to underestimation of differences between bacteria negative and bacteria positive SCS, and we derive formulae to predict impacts on estimated genetic parameters.</p> <p>Conclusions</p> <p>The results suggest that bacteria negative and bacteria positive SCS are genetically different traits. A positive genetic correlation between bacteria negative SCS and liability to infection was found, suggesting that the approach of selecting animals for decreased SCS should help to reduce mastitis prevalence. However, the results show that imperfect diagnosis of infection has an impact on estimated genetic parameters, which may reduce the efficiency of selection strategies aiming at distinguishing between bacteria negative and bacteria positive SCS.</p