Πραγματικά και προσομοιωμένα δεδομένα που ακολουθούσαν κανονική και διωνυμική κατανομή αναλύθηκαν χρησιμοποιώντας τη μέθοδο της υπό περιορισμό μέγιστης πιθανοφάνειας καθώς και δύο μεθόδους Bayes (MCMC και INLA). Τα αποτελέσματα της εργασίας δηλώνουν την χρησιμότητα της εφαρμογής των MCMC στη διερεύνηση συνδιακυμάνσεων μεταξύ τυχαίων επιδράσεων. Η μέθοδος INLA φαίνεται να αποτελεί μία εναλλακτική μέθοδο Bayes γρήγορη και χρήσιμη για ανάλυση δεδομένων που ακολουθούν κανονική κατανομή. Για την επιλογή του καταλληλότερου στατιστικού προτύπου ανάλυσης μία σειρά κριτηρίων έχει προταθεί. Εκτός από τα κριτήρια Akaike και BIC, στη συγκεκρίμενη μελέτη εφαρμόστηκε και το cAIC το οποίο λαμβάνει πιο αποτελεσματικά υπόψιν τους δραστικούς βαθμούς ελευθερίας και όπως προέκυψε από τις αναλύσεις είναι δυνατό να προτείνει διαφορετικά πρότυπο. Εξετάσθηκε η συνεισφορά των γενετικών επιδράσεων στο φαινόμενο του φυλετικού διμορφισμού του βάρους κρεοπαραγών ορνιθίων, χρησιμοποιώντας διμεταβλητά πρότυπα ανάλυσης αλλά και δευτερογενείς ιδιότητες που λάμβαναν υπόψη τη διαφορά και το λόγο των σωματικών βαρών αρσενικών και θηλυκών ατόμων. Για το σκοπό αυτό, χρησιμοποιήθηκε ένας μεγάλος αριθμός δεδομένων, αποτελούμενος από 203,323 ατομικές αποδόσεις σωματικών βαρών κρεοπαραγωγών ορνιθίων. Το καλύτερο πρότυπο περιελάμβανε προσθετικές γενετικές, μητρικές γενετικές και μητρικές περιβαλλοντικές επιδράσεις καθώς και τη συνδιακύμανση μεταξύ προσθετικών και μητρικών γενετικών επιδράσεων. Ο συντελεστής κληρονομικότητας δεν παρουσίασε διαφορές μεταξύ αρσενικών και θηλυκών (0.28 vs. 0.29). Μόνο ο συντελεστής συσχέτισης μεταξύ προσθετικών και μητρικών γενετικών επιδράσεων διέφερε ανάμεσα στα φύλα (-0.72 vs. -0.56 για αρσενικά και θηλυκά βάρη, αντίστοιχα), υποδεικύοντας έναν πιο έντονο ανταγωνισμό μεταξύ προσθετικών και μητρικών γενετικών επιδράσεων για τα αρσενικά. Τέλος, χρησιμοποιήθηκαν επιπλέον 35,595 αποδόσεις βαρών κρεοπαραγωγών ορνιθίων στις 35 ημέρες υπό δυσμενείς μικροβιακά συνθήκες για τη διερεύνηση της ύπαρξης αλληλεπίδρασης γονοτύπου περιβάλλοντος. Τα αποτελέσματα της μελέτης έδειξαν την ύπαρξη χαμηλού συντελεστή προσθετικής γενετικής συσχέτισης μεταξύ των δύο περιβαλλόντων, κυμαινόμενου μεταξύ 0,28 και 0,45 ανάλογα το πρότυπο, υποδηλώνοντας την ύπαρξη ισχυρής αλληλεπίδρασης γονοτύπου περιβάλλοντος για τη συγκεκριμένη ιδιότητα στον υπό εξέταση πληθυσμό.
REML has become the standard method of variance components estimation in animal breeding. Inference in Bayesian animal models is typically based upon Markov Chain Monte Carlo (MCMC) methods which are generally flexible but time consuming. Recently, a new Bayesian computational method, Integrated Nested Laplace Approximation (INLA), has been introduced for making fast non-sampling-based Bayesian inference for hierarchical Gaussian Markov models. This paper is concerned with the application and comparison of estimates provided by the three methods (REML, MCMC and INLA) using three representative programs (ASREML, WinBUGS and the R-package AnimalINLA) to the methods. A dataset comprising of 2,319 body weight records of a commercial line of broiler chicken was used. Both, a normally distributed trait i.e. body weight at 35 days of age (BW) and a binary response trait (after transformation of the Gaussian trait, assuming a 20% value as the threshold value), were explored. All model evaluation criteria suggested a purely additive animal model, in which the heritability estimates ranged from 0.31 to 0.34, for the Gaussian trait, and from 0.19 to 0.36 for the binary trait, depending on the software. WinBUGS revealed the existence of a small negative correlation between the additive genetic and maternal environmental effects (-0.20) that is usually neglected during REML-based analyses and may have an effect on parameter estimation. A simulation study was conducted based upon the results of the real dataset (Gaussian case), exploiting two scenarios of correlation between direct genetic and maternal environmental effects. Results suggest that while WinBUGS appeared to successfully accommodate more complicated structures between the various random effects, REML remains a fast and accurate procedure with general applicability. Although in need for further development, AnimalINLA seems a fast program for Bayesian Animal modelling, particularly suitable for inference of Gaussian traits. The availability of powerful computing and advances in algorithmic efficiency allow for the consideration of increasingly complex models. Consequently, the development and application of appropriate statistical procedures for model evaluation is becoming increasingly important. This paper is concerned with the application of an alternative model determination criterion (conditional Akaike Information Criterion, cAIC) in a large dataset comprising 203,323 body weights of broilers, pertaining to 7 (BW7) and 35 (BW35) days of age. Seven univariate and seven bivariate models were applied. Direct genetic, maternal genetic and c2 effects were estimated via REML. The model evaluation criteria included conditional Akaike Information Criterion (cAIC), Bayesian Information Criterion (BIC) and the standard Akaike Information Criterion (henceforth marginal; mAIC). According to cAIC the best-fitting model included direct genetic, maternal genetic and c2 effects. Maternal heritabilities were low (0.10 and 0.03) compared to the direct heritabilities (0.17 and 0.21), while c2 was 0.05 and 0.04 for BW7 and BW35, respectively. BIC and mAIC favoured a model that additionally included a direct-maternal genetic covariance, resulting in highly negative direct-maternal genetic correlations (-0.47 and -0.64 for BW7 and BW35, respectively) and higher direct heritabilities (0.25 and 0.28 for BW7 and BW35, respectively). Results suggest that cAIC can select different animal models than mAIC and BIC, having potential implications on selection decisions.Variation in sexual dimorphism (SD) is particularly marked in meat type chickens. This paper investigates the genetic basis of SD in an important economic trait such as body weight at the 35 days of age (BW) in broilers by applying quantitative genetic analysis. A large dataset comprising 203,323 BW records of a commercial line of broiler chicken was used. First, a bivariate approach was employed treating BW as a sex-specific trait. During this approach, seven bivariate models were applied and variances due to direct additive genetic, maternal genetic and maternal environmental effects were estimated via Restricted Maximum Likelihood. The best-fitting model included direct additive genetic, maternal genetic and maternal environmental effects with a direct-maternal genetic covariance. Differences between male and female direct heritabilities were non-significant (0.28 vs. 0.29, males and females, respectively) implying no need for sex-specific selection strategies. The direct-maternal genetic correlation was more strongly negative in males than in females (-0.72 vs. -0.56), implying a more profound antagonism between direct additive and maternal genetic effects in this particular gender. The direct genetic correlation of BW between the two sexes was as high as 0.91 i.e. only slightly lower than unity. Second, variance components and genetic parameters of two measures of SD i.e. the weight difference (Δ) and the weight ratio (R) between the genders were estimated. Direct heritabilities for both measures were significantly different than 0 but of low magnitude (0.04). Apart from the additive-maternal covariance no other random effects were found to be of importance for Δ and R. Results of the present study suggest that only minimal selection responses due to selection of Δ and/or R and a small capacity for amplifying or reducing the BW differences between the sexes are to be expected, in this specific population. Furthermore, selection pressure on BW is expected to amplify sexual dimorphism.A study was conducted to evaluate the effect of genotype by environment interaction (GEI) on body weight (BW) at 35 days of age for commercial broilers. A large dataset was used, consisting of 203,323 and 35,595 records obtained in high (H) and low (L) hygiene conditions, respectively. Bi- and quadra-variate analyses of environmental and sex-environmental specific traits were employed in an attempt to estimate genetic parameters. BW in the two different environments was treated as two distinct traits (BWH, BWL) in the bi-variate analyses, while it was analyzed separately for each sex in each environment (BWH♂, BWH♀, BWL♂ and BWL♀) via quadra-variate analyses. Variance components due to direct additive genetic, maternal genetic and maternal environmental effects were estimated via Restricted Maximum Likelihood. Model fit was assessed by the conditional Akaike Information Criterion (cAIC), the Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC). The best fitting models that successfully converged always included the direct genetic and the maternal environmental effects. During bivariate analysis, the direct heritability of BW was significantly higher in the L environment when contrasted to H (0.27 vs. 0.14), while the maternal environmental variance accounted for 0.05 of the total phenotypic variance in both environments. During the quadravariate approach, the direct heritabilities were estimated as high as 0.14, 0.19, 0.26 and 0.30 for BWH♂, BWH♀ BWL♂ and BWL♀, respectively, whence the maternal environmental variance accounted for 0.06-0.08 of the total phenotypic variance of the trait(s). The direct genetic correlations between the two environments ranged from 0.28 to 0.45, indicating the presence of strong GEI. The direct genetic correlations between the two sexes within the same environment (BWH♂-BWH♀ and BWL♂-BWL♀) were of high magnitude (0.81). Based on the current findings, no sex-specific selection policies are to be pursued while GEI should be appropriately accounted for during genetic evaluation.
