Analyses of lambing dates in sheep breeds using von Mises distribution.

Regular changes in the environment and biological responses generate seasonal patterns in the reproduction in small ruminants. Breeding seasonality is a significant constraint impacting efficiency of lamb production. However, seasonality-related traits present a special peculiarity from a statistical point of view being circular data (day of year running 1:365). Recently, circular mixed models have been developed on the basis of the von Mises distribution and were applied to analyse lambing day distribution recorded from five major Canadian sheep breeds (Rideau Arcott, Romanov, Dorset, Suffolk and Polypay). In a simulation study, the linear model was not able to capture the variance components simulated under the circular paradigm; however, the von Mises model evidenced its ability to infer the variance components of simulated circular records. Using real data of sheep, mostly negligible variances were observed for additive genetic effect when using a linear model on circular data values. In contrast, when using the von Mises model, genetic variances were different across breeds, and it raises the possibility to delay the peak of reproduction and to change the seasonality of the ewes. However, a large variance was captured by flock-year effects emphasizing the strong influence of management in lambing seasons for Canadian sheep populations. Finally, the results suggest the potential of using the von Mises model to analyse circular data, and further research is needed for better understand the complexity of this trait and the von Mises models.

Competition model for international comparisons of livestock.

Interbull has been responsible for comparing dairy bulls across countries since the mid-1980s. The current methodology is called MACE (multiple across country evaluations) which has been in use since 1995. Now that genomic data are being utilized in many countries, this has led to two serious problems. The first is that of preselection of young bulls such that the young animals are no longer a random sample of progeny from a sire by dam mating pair. Secondly, some countries are becoming less willing to share genomic data with Interbull. Both issues raise concern over the future of Interbull and international comparisons. This paper suggests a competition model as a potential replacement for MACE. The competition model makes pairwise comparisons between all pairs of bulls within a country and combines these differences across countries through bulls that are used in more than one country. Pedigree information is ignored as are all genomic data because bulls are treated as fixed. The model produces one international ranking of bulls averaging out any genotype by environment interactions which may exist. The competition model is illustrated by a small example. The limitations and advantages of the competition model are discussed.