Avoiding degeneracy in metric unfolding by penalizing the intercept.

It has long been thought that degeneracy in unfolding only concerned non-metric unfolding. Recently, Busing, Groenen, and Heiser have established that degeneracy occurs for all transformations that include estimation of an intercept and a slope. Consequently, degeneracy also plagues metric unfolding, since one member of the metric transformation family, the interval transformation, includes estimation of both an intercept and a slope. In this paper, a simple solution is proposed to the degeneracy problem for metric unfolding by penalizing for an undesirable intercept. An application of this approach will illustrate its potential.

Homogeneity of recombination rate within a conserved region on BTA3 that contains QTL.

The D3S20-D3S34-D3S3 region on BTA3 contains quantitative trait loci (QTL) controlling milk production traits. This region also displays extensive conservation of synteny among several species including cattle, humans, mice and sheep. In this study, we evaluated the adjacent intervals D3S20-D3S34 and D3S34-D3S3 for differences in recombination rate (theta) among bulls in order to assess the suitability of population-based estimates of theta for marker assisted selection and to explore the relationship between variation in theta and chromosome breakpoints associated with mammalian evolution. Using sperm typing, thetaD3S20-D3S34 and theta D3S34-D3S3 were estimated for six triply heterozygous bulls. Recombination frequency ranged from 6.2 to 12.5% and from 9.7 to 19.2% for the D3S20-D3S34 and D3S34-D3S3 intervals, respectively. However, significant variation in theta was not detected between bulls for either interval (D3S20-D3S34 chi(2)5 d.f.=2.59, P < 0.90; D3S34-D3S3 chi(2)5 d.f.=3.72, P < 0.75). The observed differences in theta were most readily attributed to differences in allele-specific amplification efficiencies among bulls. Our results suggest that the positions of QTL in this region can be reliably determined from population data and therefore accurate marker-assisted selection can be performed for desirable alleles without concern for variation in theta. Furthermore, when considered with results of earlier studies, these findings support a correlation between the existence of evolutionary breakpoints or chromosome rearrangements and variation in theta.

Fine-mapping of a region of variation in recombination rate on BTA23 to the D23S22-D23S23 interval using sperm typing and meiotic breakpoint analysis.

Meiotic recombination rate (theta) within chromosome segments of similar physical size is known to vary widely throughout the genome. This variation has a genetic component, occurring between the sexes and among individuals of the same sex. We reported previously the existence of variation in theta between males in the DYA-PRL interval on bovine chromosome 23 (BTA23). This region contains the bovine major histocompatibility complex and has been shown to contain recombination hotspots in humans and mice. The aim of this study was to map more finely the interval(s) on BTA23 where variation in theta occurs using sperm typing and meiotic breakpoint analysis. By adding a marker (DRB3) between DYA and PRL, the DYA-PRL interval was subdivided into two adjacent intervals, thus permitting evaluation and comparison of theta among five bulls. Significant variation in theta was found for both intervals; theta(DYA-DRB3) ranged from 13.2 to 28.1%, and theta(DRB3-PRL) ranged from 2.4 to 13.0%. The variation in theta was individual- and region-specific. A meiotic breakpoint strategy employing PCR amplification products from recombinant sperm was then used to refine the chromosomal location associated with variation in theta within the DYA-DRB3 interval. The subinterval D23S22-D23S23 exhibited the greatest degree of variation among bulls having high and low theta within the DYA-DRB3 interval. To confirm this result, theta(D23S22-D23S23) was directly evaluated in three additional randomly chosen bulls using sperm typing. The region showing variation in theta was narrowed to the D23S22-D23S23 subinterval, ranging from 4.6 to 9.2%. Identification of the molecular basis for variation in theta may be useful for map-dependent applications, such as marker-assisted selection and positional cloning of genes affecting physiologically important traits.