25. Threshold Characters
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since 17 October 1995 
As found by Jim Fry (University of Rochester),
Table 25.1 contains numerous (minor) numerical errors.
pdf copy of the corrected table.
Updated Notes
Dealing simultaneously with multiple thresholds
( Posted 20 September 2000)
The following comments are from Gary Snowder
(Animal Geneticist, USDA, ARS, U.S. Sheep Experiment Station, Dubois, ID 83423).
The topic of multiple thresholds only considers the approaches of Reich
et al. 1972. While there is nothing incorrect with this approach there
are other approaches that allow one to consider all thresholds without
having to combine classification groups.

W. E. Vinsen, J. M. White and R. H. Kliewer. 1976. Overall
classification as a selection criterion for improving categorically
scored components of type in Holsteins. J. Dairy Sci. 59:21042114.
Buried in this manuscript is a simple formula for correcting a
heritability estimate of any polychotomous trait to the underlying
continuous scale. See pg 2106, equation 3.
I have used this method for subjective traits with 3 and 4 levels to
obtain reasonable adjustments. For example, with sheep data I have
estimated that the heritability of a subjective milk score (low,
average, high) for range ewes at the observed level is .10. After
correcting to the underlying scale, the estimate increases to .26. This
latter estimate agrees with heritability estimates for the quantitative
trait of milk production in milking sheep.
Anyway, it provides a useful and simple procedure for a qualitative
trait whose distribution is greater than binomial.
 D. Gianola. 1979. Heritability of polychotomous characters. Genetics 93:
10511055.
See equations 10, 11 and 12 for his adjustments from the binomial
distribution to the underlying scale. He proves Robertson's approach
and infers that it can be expanded to include classifications greater
than binomial.
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Created 12 May 1995, last updated 14 May 2001
Bruce Walsh. jbwalsh@u.arizona.edu .
Comments welcome.