Approximating selection differentials and variances for correlated selection indices

Empirical formulae were derived to approximate selection differentials and variances of the selected estimated breeding values when the estimated breeding values of the candidates for directional selection are multinormally distributed and correlated in any manner. These formulae extended the well-known exact basic form for the equicorrelated case, taking into account selection pressure, average pairwise correlation coefficient and average standard deviation of pairwise correlation per observation, through polynomials fitted to simulated data. Simulations were carried out for different correlation structures (1, 2 or 3 different intra-class correlations per family, ranging from 0.3 to 0.99), for different numbers of independent families (1, 2, 5 or 10), for constant or variable family size and for selection pressures ranging from 0.5 to 50%. On average, 90% of the bias occurring when ignoring correlations between observations was removed by our prediction formula of selection differential or variance of selected observations. Comparisons with other correction methods, which assume special correlation structures, were also carried out.On propose des formules de calcul approché des différentielles de sélection et des variances d’index de sélection après sélection directionnelle quand les candidats à la sélection ont des index distribués normalement et corrélés de manière quelconque. Ces formules ont pour base celles établies en cas d’équicorrélation entre observations et font intervenir des polynômes des variables suivantes : taux de sélection, coefficient de corrélation moyen et écart type moyen de ce coefficient par observation. Les coefficients des polynômes sont calculés après ajustement à des données simulées. Les situations simulées font varier la structure des corrélations (1, 2 ou 3 coefficients de corrélation intra-classe, de valeurs 0,3 à 10,99), le nombre de familles (1, 2, 5 ou 10), la taille de famille (constante ou non) et le taux de sélection (de 0,5 à 50%). En moyenne, 90% du biais introduit en ignorant les corrélations entre observations est corrigé par nos formules de prédiction des différentielles de sélection et des variances des observations sélectionnées. Des comparaisons sont effectuées avec d’autres méthodes de correction proposées pour des structures de corrélation particulières

Considerations on measures of precision and connectedness in mixed linear models of genetic evaluation

Three criteria for the quality of a genetic evaluation are compared: the prediction error variance (PEV); the loss of precision due to the estimation of the fixed effects (degree of connectedness) (IC); and a criterion related to the information brought by the evaluation in terms of generalized coefficient and determination (CD) (precision). These criteria are introduced through simple examples based on an animal model. The main differences between them are the choice of the matrix studied (CD vs PEV, IC), the method used to account for the relationships (CD vs PEV), the use of a reference matrix or model (PEV vs CD, IC), and the data design (IC vs PEV, CD). IC is shown to favor designs with limited information provided by the data and another index is suggested, which minimizes this drawback. The behavior of IC and CD is studied in a hypothetical ’herd + sire’ model. The precision criteria set a balance between connectedness level and information provided by the data, whereas the connectedness criteria favor the model with minimum information and maximum connectedness level. Genetic relationships between animals decrease both PEV and genetic variability. PEV considers only the favorable effects on PEV; CD accounts for both effects. CD sets a balance between the design and the information brought by the data, the PEV and the genetic variability and is thus a method of choice for studying the quality of a genetic evaluation.Trois critères d’appréciation de la connexion et de la précision des évaluations génétiques sont étudiés et comparés. Le premier critère est la variance d’erreur de prédiction (PEV), le second mesure la diminution de la PEV quand les effets fixés sont connus (indice de connexion ou IC), et le troisième est un critère de précision de l’évaluation, exprimé par le coefficient de détermination généralisé (CD). Ces critères sont présentés à l’aide d’exemples simples basés sur un modèle animal. Ils se distinguent par le choix de la matrice étudiée (CD versus PEV, IC), la prisé en compte de la seule structure des données (IC versus PEV, CD), la présence d’une matrice ou d’un modèle de référence (PEV versus IC, CD), et la manière de prendre en compte les relations de parenté entre animaux (CD versus PEV). On montre comment IC favorise les situations où l’information apportée par les données est faible. Un nouvel indice de connexion, s’attachant également à la seule structure des données, est proposé, palliant cet inconvénient. L’intérêt d’IC et de CD est étudié sur un exemple de modèle « troupeau Père », où les troupeaux sont de taille fixée, les pères servent dans un seul troupeau, à l’exception d’un père de référence assurant les liaisons génétiques entre troupeaux. CD permet d’optimiser le plan d’expérience par un compromis entre connexion et information contenue dans les données, alors que l’utilisation d’IC aboutit au choix d’un plan où les pères utilisés dans un seul troupeau ont un seul veau par troupeau. Si CD et PEV sont équivalents pour des animaux non apparentés, PEV privilégie les forts apparentements, qui diminuent la variance d’erreur de prédiction. Mais les parentés diminuent également la variabilité génétique, ce que prend en compte CD. Ainsi, on montre, sur un modèle animal strictement aléatoire avec même apparentement entre animaux, comment PEV peut conduire au choix d’un plan minimisant le progrès génétique. On retrouve dans ce cas simple la formule classique du progrès génétique, où le CD généralisé joue le même rôle que le CD individuel d’un indice de sélection. CD, compromis entre structure et quantité de données, d’une part, et variance d’erreur de prédiction et variabilité génétique, d’autre part, est une méthode de choix pour l’analyse de la qualité d’une évaluation génétique

Review: Towards the agroecological management of ruminants, pigs and poultry through the development of sustainable breeding programmes. II. Breeding strategies

Agroecology uses ecological processes and local resources rather than chemical inputs to develop productive and resilient livestock and crop production systems. In this context, breeding innovations are necessary to obtain animals that are both productive and adapted to a broad range of local contexts and diversity of systems. Breeding strategies to promote agroecological systems are similar for different animal species. However, current practices differ regarding the breeding of ruminants, pigs and poultry. Ruminant breeding is still an open system where farmers continue to choose their own breeds and strategies. Conversely, pig and poultry breeding is more or less the exclusive domain of international breeding companies which supply farmers with hybrid animals. Innovations in breeding strategies must therefore be adapted to the different species. In developed countries, reorienting current breeding programmes seems to be more effective than developing programmes dedicated to agroecological systems that will struggle to be really effective because of the small size of the populations currently concerned by such systems. Particular attention needs to be paid to determining the respective usefulness of cross-breeding v. straight breeding strategies of well-adapted local breeds. While cross-breeding may offer some immediate benefits in terms of improving certain traits that enable the animals to adapt well to local environmental conditions, it may be difficult to sustain these benefits in the longer term and could also induce an important loss of genetic diversity if the initial pure-bred populations are no longer produced. As well as supporting the value of within-breed diversity, we must preserve between-breed diversity in order to maintain numerous options for adaptation to a variety of production environments and contexts. This may involve specific public policies to maintain and characterize local breeds (in terms of both phenotypes and genotypes), which could be used more effectively if they benefited from the scientific and technical resources currently available for more common breeds. Last but not least, public policies need to enable improved information concerning the genetic resources and breeding tools available for the agroecological management of livestock production systems, and facilitate its assimilation by farmers and farm technicians

Breeding beef cattle for an extended productive life: Evaluation of selection criteria in the Retinta breed

We characterized genetically the longevity and the productive life of beef cows considering three different traits: length of true life (LTL), the length of productive life (LPL) and a number of calvings (NC), in the Retinta breed. Data considered in the analysis were collected in 30 Spanish herds and consisted of 3187 cows born between 1993 and 2013: 1802 cows had complete information while 1385 cows had censored information. Pedigree information accounted for 7359 individuals and the genetic evaluation was performed under an animal model using the Weibull proportional hazard model for survival analysis. Results indicated that cow effects (age at first calving, herd, season-year of cow birth), as well as some calf effects (breed group, season-year of birth), were significant (P<0.05) for all traits; however, sex of calves did not affect the traits. The low heritabilities obtained for LTL and LPL (0.14±0.01 and 0.14±0.01 respectively) and modest heritability for NC (0.30±0.01), suggest that a higher response to selection can be expected for NC than for LTL and LPL.Instituto de Genética Veterinari

Connectedness among herds of beef cattle bred under natural service

Background: A procedure to measure connectedness among herds was applied to a beef cattle population bred by natural service. It consists of two steps: (a) computing coefficients of determination (CDs) of comparisons among herds; and (b) building sets of connected herds. Methods: The CDs of comparisons among herds were calculated using a sampling-based method that estimates empirical variances of true and predicted breeding values from a simulated n-sample. Once the CD matrix was estimated, a clustering method that can handle a large number of comparisons was applied to build compact clusters of connected herds of the Bruna dels Pirineus beef cattle. Since in this breed, natural service is predominant and there are almost no links with reference sires, to estimate CDs, an animal model was used taking into consideration all pedigree information and, especially, the connections with dams. A sensitivity analysis was performed to contrast single-trait sire and animal model evaluations with different heritabilities, multiple-trait animal model evaluations with different degrees of genetic correlations and models with maternal effects. Results: Using a sire model, the percentage of connected herds was very low even for highly heritable traits whereas with an animal model, most of the herds of the breed were well connected and high CD values were obtained among them, especially for highly heritable traits (the mean of average CD per herd was 0.535 for a simulated heritability of 0.40). For the lowly heritable traits, the average CD increased from 0.310 in the single-trait evaluation to 0.319 and 0.354 in the multi-trait evaluation with moderate and high genetic correlations, respectively. In models with maternal effects, the average CD per herd for the direct effects was similar to that from single-trait evaluations. For the maternal effects, the average CD per herd increased if the maternal effects had a high genetic correlation with the direct effects, but the percentage of connected herds for maternal effects was very low, less than 12%. Conclusions: The degree of connectedness in a bovine population bred by natural service mating, such as Bruna del Pirineus beef cattle, measured as the CD of comparisons among herds, is high. It is possible to define a pool of animals for which estimated breeding values can be compared after an across-herds genetic evaluation, especially for highly heritable traits