Equivalence of multibreed animal models and hierarchical Bayes analysis for maternally influenced traits

Background

It has been argued that multibreed animal models should include a heterogeneous covariance structure. However, the estimation of the (co)variance components is not an easy task, because these parameters can not be factored out from the inverse of the additive genetic covariance matrix. An alternative model, based on the decomposition of the genetic covariance matrix by source of variability, provides a much simpler formulation. In this study, we formalize the equivalence between this alternative model and the one derived from the quantitative genetic theory. Further, we extend the model to include maternal effects and, in order to estimate the (co)variance components, we describe a hierarchical Bayes implementation. Finally, we implement the model to weaning weight data from an Angus × Hereford crossbred experiment.

Methods

Our argument is based on redefining the vectors of breeding values by breed origin such that they do not include individuals with null contributions. Next, we define matrices that retrieve the null-row and the null-column pattern and, by means of appropriate algebraic operations, we demonstrate the equivalence. The extension to include maternal effects and the estimation of the (co)variance components through the hierarchical Bayes analysis are then straightforward. A FORTRAN 90 Gibbs sampler was specifically programmed and executed to estimate the (co)variance components of the Angus × Hereford population.

Results

In general, genetic (co)variance components showed marginal posterior densities with a high degree of symmetry, except for the segregation components. Angus and Hereford breeds contributed with 50.26% and 41.73% of the total direct additive variance, and with 23.59% and 59.65% of the total maternal additive variance. In turn, the contribution of the segregation variance was not significant in either case, which suggests that the allelic frequencies in the two parental breeds were similar.

Conclusion

The multibreed maternal animal model introduced in this study simplifies the problem of estimating (co)variance components in the framework of a hierarchical Bayes analysis. Using this approach, we obtained for the first time estimates of the full set of genetic (co)variance components. It would be interesting to assess the performance of the procedure with field data, especially when interbreed information is limited.     

Phylogenetic analysis of the tenascin gene family: evidence of origin early in the chordate lineage

Background  

Tenascins are a family of glycoproteins found primarily in the extracellular matrix of embryos where they help to regulate cell proliferation, adhesion and migration. In order to learn more about their origins and relationships to each other, as well as to clarify the nomenclature used to describe them, the tenascin genes of the urochordate Ciona intestinalis, the pufferfish Tetraodon nigroviridis and Takifugu rubripes and the frog Xenopus tropicalis were identified and their gene organization and predicted protein products compared with the previously characterized tenascins of amniotes.     

Variation in Mentha arvensis L. (Labiatae). I. The North American populations

Most North American populations of Mentha arvensis differ from those in Europe in leaf and calyx characters, but the extremes of variation overlap. However the former have a diploid chromosome number of 96 and the latter 72. The North American populations are morphologically very variable and much of this variation is genotypic. However, none of it is discrete and, as it shows little geographic or ecological coherence, taxonomic recognition appears undesirable.
The following chemical races based on essential oil composition, occur in North America:
Type 1–high in pulegone, isomenthone and menthone.
Type 2–high in linalool, cfr-ocimene and trans-ocimene.
Type 3–high in cw-isopulegone and fnmi-isopulegone.
Type 4–high in cis- and trans-ocimene and in 1,8-cineol.
These four chemotypes are not correlated with any of the morphological variations. The recognition of chemical races is discussed and it is concluded that where possible they should be based on diagnostic components, rather than on quantitative differences or the mere presence or absence of given compounds. The literature relating to biosynthesis and essential oil composition in Mentha arvensis is reviewed.