Bayesian analysis of the linear reaction norm model with unknown covariate

The reaction norm model is becoming a popular approach for the analysis of G x E interactions. In a classical reaction norm model, the expression of a genotype in different environments is described as a linear function (a reaction norm) of an environmental gradient or value. A common environmental value is defined as the mean performance of all genotypes in the environment, which is typically unknown. One approximation is to estimate the mean phenotypic performance in each environment, and then treat these estimates as known covariates in the model. However, a more satisfactory alternative is to infer environmental values simultaneously with the other parameters of the model. This study describes a method and its Bayesian MCMC implementation that makes this possible. Frequentist properties of the proposed method are tested in a simulation study. Estimates of parameters of interest agree well with the true values. Further, inferences about genetic parameters from the proposed method are similar to those derived from a reaction norm model using true environmental values. On the other hand, using phenotypic means as proxies for environmental values results in poor inferences

Relationships between mastitis and functional longevity in Danish Black and White dairy cattle estimated using survival analysis

The relationship between mastitis and functional longevity was assessed with survival analysis on data of Danish Black and White dairy cows. Different methods of including the effect of mastitis treatment on the culling decision by a farmer in the model were compared. The model in which mastitis treatment was assumed to have an effect on functional longevity until the end of the lactation had the highest likelihood, and the model in which mastitis treatment had an effect for only a short period had the lowest likelihood. A cow with mastitis had 1.69 times greater risk of being culled than did a healthy herdmate with all other effects being the same. A model without mastitis treatment was used to predict transmitting abilities of bulls for risk of being culled, based on longevity records of their daughters, and was expressed in terms of risk of being culled. The correlation between the risk of being culled and the national evaluations of the bulls for mastitis resistance was approximately -0.4, indicating that resistance against mastitis was genetically correlated with a lower risk of being culled and, thus, a longer functional length of productive life

Electrical Conductivity of milk: ability to predict mastitis status

Electrical conductivity (EC) of milk has been introduced as an indicator trait for mastitis over the last decade, and it may be considered as a potential trait in a breeding program where selection for improved udder health is included. In this study, various EC traits were investigated for their association with udder health. In total, 322 cows with 549 lactations were included in the study. Cows were classified as healthy or clinically or subclinically infected, and EC was measured repeatedly during milking on each quarter. Four EC traits were defined; the inter-quarter ratio (IQR) between the highest and lowest quarter EC values, the maximum EC level for a cow, IQR between the highest and lowest quarter EC variation, and the maximum EC variation for a cow. Values for the traits were calculated for every milking throughout the entire lactation. All EC traits increased significantly (