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Estimation of Genetic Parameters for Conformation Traits from Multiple Trait Models
L. R. Schaeffer and Hossein Yazdi
Centre for Genetic Improvement of Livestock,
Department of Animal and Poultry Science,
University of Guelph, Guelph, ON, Canada N1G 2W1
September 9, 2002

ABSTRACT

A multiple trait model for conformation traits in Holsteins was applied to 28 traits, including milking speed and temperament. The model included fixed round-classifier effects, random herd within round-classifier effects, age and stage effects at classification, random additive genetic effects, and residual effects. Herd by sire interaction effects were dropped from the model because the average number of animals in such subclasses averaged less than 2, and because inclusion of this factor in the model was thought to cause problems with the Gibbs sampler. Heritability estimates ranged from 0.11 to 0.61. Genetic correlation estimates went as high as 0.84 (size and body depth), and as low as -0.57 (set of rear legs and rear legs, side view). Heritability estimates were generally greater than single trait estimates. A multiple trait evaluation using the same model and all current data is planned.

1. General Comments About Conformation

Conformation traits consist of major scorecard traits (scored from 1 to 18) and general scorecard traits (scored from 1 to 9). All first lactation heifers in a herd are classified by the same classifier in one visit. The term 'round' is the period of time needed by classifiers to visit all herds in Canada, usually 7 to 9 months. A contemporary group is all cows classified in the herd on the same day by the same classifier.

From one round to another the breed improvement committees of the breed associations revise their classification standards and hold training sessions with classifiers to ensure that the same standards are used as much as possible. Few large changes are made during a round. The continually revised standards would be analogous to changing the amount of milk that comprises a 'kilogram' of milk every year. While continuous revision of the standards is desirable from a breed improvement standpoint, the consequence is that unbiased genetic comparisons of cows classified many years apart are impossible. Estimation of genetic trends for conformation are also impossible. A completely objective conformation assessment system is difficult to find, or too costly to apply. Unbiased predictions of breeding values for conformation traits seem impossible under these conditions. Tsuruta et al. (2002) have proposed a random regression model where genotypes are regressed on year of classification. Thus, the genetic correlations between years can be less than unity and all animals can be ranked fairly within each year (but these rankings could differ between years). Such an analysis is complicated by the fact that animals are only classified once. Even so, this model may be worthy of investigation.

Another aspect of subjectively measured conformation traits is the fact that a cow can not receive a higher score than the highest category allowed for the trait. Suppose cows were classified in intervals of 100 kg of milk above contemporaries from -1000 kg to +1000 kg, then if a cow produces +1500 kg of milk more than her contemporaries she will receive credit for +1000 kg because that is as high as the scale allows us to go. The effect of this limit would be to shrink the genetic variability that is actually present in the population. Breeders must work very hard over many years to get a herd of cows that will classify in the very highest categories. A herd that has cows that all classify 9 (for a 1 to 9 category trait) versus a herd of cows that all classify 5 are not different because of herd management only, because the cows that classify 5 will never be able to classify 9 even if they were in the first herd. The cows in a herd at a given point in time are the result of careful breeding and purchases over a number of years. With contemporary groups treated as fixed, the assumption is implicitly made that all differences between contemporary groups are due to management, and this is clearly not the case.

2. This Study

In September 2001 a report on estimates of genetic correlations between three groups of traits (Body, Legs, Mammary System) was given to the industry. The response from GEB was that all traits should be done simultaneously, and milking speed and temperament should be included. Thus, the main objective of this work was to re-estimate all genetic variances and covariances for all conformation traits in a multiple trait model.

There were 11,833 Holstein cows with records on all 28 traits (i.e. no missing traits). The pedigree file included 102,952 animals. There were 1,756 herd-round-classifier subclasses, 78 round-classifier subclasses, and 90 age-stage of classification groups.

3. The Model

The final model for conformation traits used in this study was

y_ijkmn = (RC)_i+(RC:H)_ij+ (Age,Stage)_m + a_n + e_ijkmn,

where (RC)_i is a fixed effect of round by classifier subclasses, (RC:H)_ij is a random effect of herd by round by classifier subclass and identifies all cows classified in that herd by one classifier in one particular herd visit, (Age,Stage)_m are fixed subclasses of age at classification within stage of lactation (by month) groups, a_n is the animal additive genetic effect, e_ijkmn is a random residual effect, and y_ijkmnis a first lactation, first classification of an animal. In matrix notation,

$${\bf y} = {\bf Xb} + {\bf Wc} + {\bf a} + {\bf e},$$

where ${\bf b}$ includes round-classifier effects and the age-stage subclasses, ${\bf c}$ includes random (RC:H) effects, ${\bf a}$ is the vector of random animal additive genetic effects, ${\bf e}$ is the vector of random residual effects, and ${\bf X}$ and ${\bf W}$are incidence matrices. Also,

$$E \left( \begin{array}{c} {\bf c} \\ {\bf a} \\ {\bf e} \end... ...egin{array}{c} {\bf0} \\ {\bf0} \\ {\bf0} \end{array} \right),$$

and

$$Var \left( \begin{array}{c} {\bf c} \\ {\bf a} \\ {\bf e} \e... ... {\bf0} & {\bf0} & {\bf I}\sigma^{2}_{e} \end{array} \right).$$

Inbreeding was ignored in the construction of ${\bf A}$ and its inverse. Bayesian estimation methods using Gibbs sampling were applied to the data. A number of computational problems arose during the analyses which prolonged the study.

4. Computing Problems

In the previous work, the three groups of traits had, at most, 10 traits in a group. Computation time for Gibbs sampling is related to the cube of the number of traits. Hence the time to get estimates for 36 or more traits would take a long time. Several attempts were made, but the Gibbs sampling estimation program would falter around 2500 rounds and all estimates of parameters would be zero from that point onwards.

Firstly, there were some very high correlations among some of the 36 traits, and this was thought to be the cause of program failures. Therefore, the major scorecard traits (1 to 18 categories) were removed from the analyses as all of the general descriptive traits were sub-units of the major traits. The remaining 28 traits had scores of 1 to 9 only, except for milking speed and temperament which had scores from 1 to 5. This action did not eliminate the problem with the Gibbs sampling program.

The next step was to remove the Herd by Sire interaction effects from the model. On average there were less than 2 cows per herd by sire subclass, which did not allow for proper estimation of a herd by sire interaction variance. The program still failed at the same point in sampling.

Next a Cholesky decomposition was applied to the inverse of the phenotypic (co)variance matrix. This was used to transform all observations such that the phenotypic correlations among the transformed traits were zero. The transformed traits were put into the Gibbs sampling program. Afterwards the estimates were converted back to the original scale by pre and post multiplying the estimated covariance matrices by the inverse of the Cholesky decomposition transformation matrix. Still the Gibbs sampling program failed.

Finally the cause of the problem was discovered. The random (RC:H)(co)variance matrix had some very small diagonal elements which when divided into the corresponding residual diagonal element gave a very large number, which continued to get larger in the next sample, and eventually gave a zero variance estimate. A zero variance estimate gave a matrix that was not positive definite and subsequently all of the elements became zero because the inversion routines would not invert the matrix. A ratio of the residual variance to contemporary group variance should not be greater than 14 (from the single trait studies of last year). Thus, the program was modified so that if the ratios of residual to genetic, or residual to contemporary group variances were greater than 25, then the 'new' genetic or herd variance was set to the residual variance divided by 25. All 28 diagonals were checked after the generation of new (co)variance matrices. If any values were changed, then this resulted in a new variance that was always greater than the 'sampled' value, and therefore, did not cause any problems with positive definiteness. The herd or genetic variances were prevented from going to zero, and the Gibbs sampling process was kept going.

Each attempt took about one week to test. The final program did 16,000 samples of which the first 2000 were discarded, and only every seventh sample was saved. Thus, estimates were based on the means of 2000 samples (16,000 minus 2000 divided by 7). Two months were needed to run the 16,000 samples.

5. Results and Discussion

5.1 Estimates of Heritability

The heritability estimates from the current multitrait model and the three multiple trait models from September 2001 are shown in Table 1. The trait with the highest or next highest correlation to each trait is also shown. Estimates of heritability ranged from 0.09 for milking speed to 0.61 for udder depth.

In general, all of the heritability estimates were greater than in the 2001 study. This could be due to removing all of the major scorecard traits from the analyses, or to removing herd-sire interactions from the model. The higher estimates may also be due to collectively considering the genetic and environmental correlations between traits simultaneously, especially if some of those correlations were negative.

5.2 Estimates of Correlations

Estimates of genetic correlations are shown in Tables 2a, 2b, 2c, and 2d. Estimates of correlations due to herd effects within round-classifier subclasses are given in Tables 3a to 3d, and estimates of correlations due to residual effects are given in Tables 4a to 4d.

Some of the high genetic correlations were between pairs of unexpected traits, such as 0.35 between rump angle and milking speed; -0.32 between milking speed and temperament; 0.45 between temperament and set of rear legs; and 0.33 between front end and fore teat attachment. However, most of the high correlations were as expected, such as 0.86 between size and chest width; 0.75 between heel depth and foot angle; 0.72 between udder depth and fore teat attachment; 0.81 between udder texture and median suspensory; and 0.73 between median suspensory and rear teat placement.

There were a total of 378 genetic correlations estimated in this analysis. Thirty-one (8%) were greater than 0.50; 142 (38%) were between 0.10 and 0.50; 138 (37%) were between -0.10 and +0.10; and 67 (18%) were below -0.10; and only one was below -0.50. The majority were therefore between -0.10 and +0.50.

The correlations among traits for the herd component followed a similar pattern to the genetic correlations. Twenty-one (5.5%) were greater than 0.50; 166 (44%) between 0.10 and 0.50; 133 between -0.10 and +0.10; and 58 below -0.10. Thus, these correlations were more tightly compressed between -0.10 and +0.50.

The residual correlations among traits were generally much smaller and closer to zero. In fact, 69% of the residual correlations were between -0.10 and +0.10. While there were 74 correlations above 0.10, most of these were in the 0.10 to 0.20 range. Only 2 correlations were above 0.50. Similarly, correlations below -0.10 were also not very large.

6. Conclusions

Because of the increased heritabilities and the fairly strong positive genetic correlations, genetic evaluations for these conformation traits would be expected to have a wider range (on the original scale) than current evaluations. Also, the agreement between EBVs of different traits on the same animal should better reflect the picture of conformation on that animal. EBVs for the major scorecard traits will have to be constructed through regression equations on the 28 traits that are actually evaluated. The regression equations can either be estimated or simply constructed by committee to combine the 28 trait EBVs into EBVs for Mammary System, Fore Udder, Rear Udder, Rump, Feet and Legs, Capacity, and Overall Conformation.

A multiple trait genetic evaluation is planned to use all of the data that are currently utilized in genetic evaluations for conformation, plus all milking speed and temperament data. Comparisons to the single trait evaluations will be made. The relationships among the single trait evaluations for the same 28 traits will be computed, and the relationships of the 28 traits to the major scorecard traits could be used to derive the appropriate regression equations for predicting the major scorecard trait EBVs. Derivation of the appropriate prediction error variance for Overall Conformation EBVs will also have to be determined from the multiple trait model.

Acknowledgements

Financial support from the Ontario Ministry of Agriculture and Food, DairyGen, and the Natural Sciences and Engineering Research Council are gratefully acknowledged.

Table 1.
Estimates of Heritability

	Sept	Multiple	Largest
	2001	Trait	Correlation	with
Size	.37	.41	.86	Chst wi
Stature	.51	.58	.67	Chst wi
Frt end	.23	.37	.33	Fore at
Chst wi	.24	.29	.58	Pin wid
Body de		.33	.55	Size
Loin st	.26	.55	.49	Rump an
Pin wid	.32	.57	.57	Size
Pin set	.10	.21	.41	Rump an
Rump an	.37	.39	.35	M speed
Bone qu	.26	.40	.57	Uddr tx
Foot an	.08	.20	.75	Heel de
Heel de	.04	.17	.48	Setrear
Setrear	.09	.17	-.62	Rleg sv
Rleg sv	.21	.59	.48	Bone qu
Rleg rv	.05	.21	.58	Claw un
Uddr de		.61	.72	Fore at
Uddr tx	.15	.42	.81	Med sus
Med sus	.16	.29	.73	Rear pl
Fore at	.24	.43	.58	Rear he
Fore pl	.26	.46	.66	Rear pl
Fore le		.44	-.45	Rear pl
Rear he	.22	.34	.65	Rear wi
Rear wi		.28	.56	Fore at
Rear pl	.23	.49	.73	Uddr tx
Dy form		.53	.66	Uddr tx
Claw un		.18	.58	Rleg rv
M speed		.09	-.32	Tempera
Tempera		.14	.45	Setrear

Table 2a.
GENETIC CORRELATIONS

	Size	Stature	Frt end	Chst wi	Body de	Loin st	Pin wid
Size	.41	.83	.28	.86	.55	.19	.57
Stature	.83	.58	.33	.67	.21	.16	.55
Frt end	.28	.33	.37	.16	.04	-.16	.08
Chst wi	.86	.67	.16	.29	.54	.07	.58
Body de	.55	.21	.04	.54	.33	.16	.27
Loin st	.19	.16	-.16	.07	.16	.55	.11
Pin wid	.57	.55	.08	.58	.27	.11	.57
Pin set	.01	.05	.06	.11	-.17	-.07	-.01
Rump an	.12	.17	-.12	.02	-.10	.49	-.10
Bone qu	-.20	-.02	.22	-.38	-.03	.27	-.28
Foot an	.06	.02	-.14	.11	.20	.20	.00
Heel de	.07	-.04	-.29	.18	.30	.13	.06
Setrear	.09	-.06	-.32	.23	.20	.20	.10
Rleg sv	-.25	-.11	.32	-.43	-.24	.09	-.33
Rleg rv	.10	-.01	.02	.22	.25	-.44	.02
Uddr de	.26	.45	.30	.34	-.02	.00	.32
Uddr tx	.14	.19	-.02	.05	.36	.25	.06
Med sus	.03	.10	-.02	-.03	.26	.15	-.03
Fore at	.36	.38	.33	.45	.31	-.08	.25
Fore pl	.00	.07	.08	-.02	.25	-.13	-.14
Fore le	.08	.10	.18	.02	-.18	-.08	.00
Rear he	.12	.21	.28	.21	.20	-.01	.07
Rear wi	.44	.37	.08	.43	.45	.21	.42
Rear pl	.00	-.02	-.17	-.05	.31	.18	.04
Dy form	.18	.21	.07	.04	.42	.04	.03
Claw un	.04	-.05	-.01	.07	.14	-.29	-.11
M speed	.19	.21	.13	.09	.02	.16	-.08
Tempera	.01	-.16	-.29	.12	.25	-.02	.12

Table 2b.
GENETIC CORRELATIONS

	Pin set	Rump an	Bone qu	Foot an	Heel de	Setrear	Rleg sv
Size	.01	.12	-.20	.06	.07	.09	-.25
Stature	.05	.17	-.02	.02	-.04	-.06	-.11
Frt end	.06	-.12	.22	-.14	-.29	-.32	.32
Chst wi	.11	.02	-.38	.11	.18	.23	-.43
Body de	-.17	-.10	-.03	.20	.30	.20	-.24
Loin st	-.07	.49	.27	.20	.13	.20	.09
Pin wid	-.01	-.10	-.28	.00	.06	.10	-.33
Pin set	.21	.41	-.19	-.23	-.07	-.03	-.16
Rump an	.41	.39	.13	-.02	-.04	-.06	.04
Bone qu	-.19	.13	.40	-.03	-.17	-.14	.48
Foot an	-.23	-.02	-.03	.20	.75	.47	-.34
Heel de	-.07	-.04	-.17	.75	.17	.48	-.42
Setrear	-.03	-.06	-.14	.47	.48	.16	-.62
Rleg sv	-.16	.04	.48	-.34	-.42	-.62	.59
Rleg rv	.15	-.18	-.15	.18	.26	.20	-.42
Uddr de	.09	.04	.15	-.08	-.13	-.14	.01
Uddr tx	-.36	-.06	.57	.22	.25	.03	.01
Med sus	-.23	-.07	.53	.10	.24	-.02	.11
Fore at	.11	-.10	.11	.04	.12	-.06	-.08
Fore pl	-.05	-.13	.40	.04	.13	-.09	.09
Fore le	.04	.02	-.11	-.06	-.13	-.14	.18
Rear he	.06	-.04	.34	.14	.18	.09	.00
Rear wi	-.15	-.02	.21	.15	.23	.14	-.10
Rear pl	-.30	-.09	.33	.02	.21	.02	-.04
Dy form	-.24	-.08	.44	.14	.21	-.05	.09
Claw un	.25	-.08	-.16	.08	.20	.17	-.18
M speed	.02	.35	.14	-.04	-.12	-.06	.31
Tempera	-.02	-.11	-.19	.29	.33	.45	-.39

Table 2c.
GENETIC CORRELATIONS

	Rleg rv	Uddr de	Uddr tx	Med sus	Fore at	Fore pl	Fore le
Size	.10	.26	.14	.03	.36	.00	.08
Stature	-.01	.45	.19	.10	.38	.07	.10
Frt end	.02	.30	-.02	-.02	.33	.08	.18
Chst wi	.22	.34	.05	-.03	.45	-.02	.02
Body de	.25	-.02	.36	.26	.31	.25	-.18
Loin st	-.44	.00	.25	.15	-.08	-.13	-.08
Pin wid	.02	.32	.06	-.03	.25	-.14	.00
Pin set	.15	.09	-.36	-.23	.11	-.05	.04
Rump an	-.18	.04	-.06	-.07	-.10	-.13	.02
Bone qu	-.15	.15	.57	.53	.11	.40	-.11
Foot an	.18	-.08	.22	.10	.04	.04	-.06
Heel de	.26	-.13	.25	.24	.12	.13	-.13
Setrear	.20	-.14	.03	-.02	-.06	-.09	-.14
Rleg sv	-.42	.01	.01	.11	-.08	.09	.18
Rleg rv	.21	-.05	.05	.10	.33	.46	-.24
Uddr de	-.05	.61	.31	.23	.72	.21	-.05
Uddr tx	.05	.31	.42	.81	.43	.54	-.33
Med sus	.10	.23	.81	.29	.39	.64	-.15
Fore at	.33	.72	.43	.39	.43	.55	-.16
Fore pl	.46	.21	.54	.64	.55	.46	-.33
Fore le	-.24	-.05	-.33	-.15	-.16	-.33	.44
Rear he	.26	.40	.51	.52	.58	.45	-.07
Rear wi	.19	.31	.56	.53	.56	.40	-.13
Rear pl	.14	.16	.73	.73	.33	.66	-.45
Dy form	.33	-.13	.66	.62	.28	.59	-.18
Claw un	.58	-.25	-.26	-.03	.02	.21	.21
M speed	-.13	.16	-.08	.01	-.04	.00	.26
Tempera	.41	-.36	.01	.04	-.05	.14	-.06

Table 2d.
GENETIC CORRELATIONS

	Rear he	Rear wi	Rear pl	Dy form	Claw un	M speed	Tempera
Size	.12	.44	.00	.18	.04	.19	.01
Stature	.21	.37	-.02	.21	-.05	.21	-.16
Frt end	.28	.08	-.17	.07	-.01	.13	-.29
Chst wi	.21	.43	-.05	.04	.07	.09	.12
Body de	.20	.45	.31	.42	.14	.02	.25
Loin st	-.01	.21	.18	.04	-.29	.16	-.02
Pin wid	.07	.42	.04	.03	-.11	-.08	.12
Pin set	.06	-.15	-.30	-.24	.25	.02	-.02
Rump an	-.04	-.02	-.09	-.08	-.08	.35	-.11
Bone qu	.34	.21	.33	.44	-.16	.14	-.19
Foot an	.14	.15	.02	.14	.08	-.04	.29
Heel de	.18	.23	.21	.21	.20	-.12	.33
Setrear	.09	.14	.02	-.05	.17	-.06	.45
Rleg sv	.00	-.10	-.04	.09	-.18	.31	-.39
Rleg rv	.26	.19	.14	.33	.58	-.13	.41
Uddr de	.40	.31	.16	-.13	-.25	.16	-.36
Uddr tx	.51	.56	.73	.66	-.26	-.08	.01
Med sus	.52	.53	.73	.62	-.03	.01	.04
Fore at	.58	.56	.33	.28	.02	-.04	-.05
Fore pl	.45	.40	.66	.59	.21	.00	.14
Fore le	-.07	-.13	-.45	-.18	.21	.26	-.06
Rear he	.34	.65	.34	.50	-.02	.10	-.02
Rear wi	.65	.28	.53	.52	-.12	.09	.13
Rear pl	.34	.53	.49	.48	-.17	-.10	.06
Dy form	.50	.52	.48	.53	.06	-.07	.27
Claw un	-.02	-.12	-.17	.06	.18	.04	.35
M speed	.10	.09	-.10	-.07	.04	.09	-.32
Tempera	-.02	.13	.06	.27	.35	-.32	.14

Table 3a.
HRC CORRELATIONS

	Size	Stature	Frt end	Chst wi	Body de	Loin st	Pin wid
Size	.12	.71	.20	.87	.29	.33	.53
Stature	.71	.12	.13	.64	.16	.35	.59
Frt end	.20	.13	.10	.12	.26	.11	.03
Chst wi	.87	.64	.12	.08	.12	.25	.44
Body de	.29	.16	.26	.12	.07	.19	.14
Loin st	.33	.35	.11	.25	.19	.07	.36
Pin wid	.53	.59	.03	.44	.14	.36	.06
Pin set	.11	.30	-.17	.12	.01	.42	.35
Rump an	.05	.10	-.25	.05	-.37	.22	.50
Bone qu	.10	.04	.30	.16	.28	.45	.12
Foot an	.14	.12	.12	.14	.13	-.02	.12
Heel de	.15	.12	.13	.06	.21	-.05	.04
Setrear	.19	.27	-.04	.19	.14	.22	.21
Rleg sv	-.13	-.32	.24	-.22	.29	-.36	-.17
Rleg rv	.30	.35	.07	.37	-.22	.17	.22
Uddr de	-.46	-.13	.16	-.57	.10	.17	-.17
Uddr tx	.17	.34	.17	.15	.16	.40	.20
Med sus	.24	.26	.08	.25	.16	.38	.22
Fore at	.16	.20	.00	.15	.15	.30	.07
Fore pl	.05	.16	-.29	.13	-.20	.09	.14
Fore le	.18	.18	-.17	.12	-.16	.30	.11
Rear he	-.15	-.02	-.02	-.17	.00	.42	-.03
Rear wi	.58	.38	-.10	.56	-.09	.21	.46
Rear pl	-.09	-.04	-.19	-.06	.19	.01	.08
Dy form	.48	.30	.16	.47	.48	.42	.32
Claw un	.21	.22	.09	.12	-.04	.12	.22
M speed	.00	-.05	.00	.00	-.05	-.03	-.10
Tempera	.06	-.02	.01	.08	-.06	.00	-.07

Table 3b.
HRC CORRELATIONS

	Pin set	Rump an	Bone qu	Foot an	Heel de	Setrear	Rleg sv
Size	.11	.05	.10	.14	.15	.19	-.13
Stature	.30	.10	.04	.12	.12	.27	-.32
Frt end	-.17	-.25	.30	.12	.13	-.04	.24
Chst wi	.12	.05	.16	.14	.06	.19	-.22
Body de	.01	-.37	.28	.13	.21	.14	.29
Loin st	.42	.22	.45	-.02	-.05	.22	-.36
Pin wid	.35	.50	.12	.12	.04	.21	-.17
Pin set	.03	.44	.19	.10	-.06	.24	-.34
Rump an	.44	.04	-.14	-.17	-.14	-.17	-.32
Bone qu	.19	-.14	.08	.10	.11	.35	-.19
Foot an	.10	-.17	.10	.13	.78	.22	.01
Heel de	-.06	-.14	.11	.78	.14	.06	.03
Setrear	.24	-.17	.35	.22	.06	.05	-.33
Rleg sv	-.34	-.32	-.19	.01	.03	-.33	.10
Rleg rv	.14	.00	.60	.03	.05	.58	-.48
Uddr de	.06	-.13	.19	-.10	-.12	.10	.05
Uddr tx	.23	.04	.44	-.06	-.08	.11	-.28
Med sus	.13	-.03	.41	.00	.07	.09	-.23
Fore at	.19	-.11	.52	.03	-.07	.30	-.29
Fore pl	.12	.30	-.26	-.38	-.39	-.07	-.24
Fore le	.11	.24	.06	.00	.06	.07	-.22
Rear he	.18	-.09	.48	-.04	-.08	.18	-.31
Rear wi	.08	.14	.13	.09	.10	.09	-.37
Rear pl	-.06	-.02	-.10	-.21	-.15	-.30	.17
Dy form	.16	-.11	.54	.19	.17	.26	-.11
Claw un	.19	-.01	.46	.46	.45	.35	-.14
M speed	.05	-.03	.05	-.14	-.06	-.06	.01
Tempera	-.13	-.05	-.06	.23	.21	-.04	-.10

Table 3c.
HRC CORRELATIONS

	Rleg rv	Uddr de	Uddr tx	Med sus	Fore at	Fore pl	Fore le
Size	.30	-.46	.17	.24	.16	.05	.18
Stature	.35	-.13	.34	.26	.20	.16	.18
Frt end	.07	.16	.17	.08	.00	-.29	-.17
Chst wi	.37	-.57	.15	.25	.15	.13	.12
Body de	-.22	.10	.16	.16	.15	-.20	-.16
Loin st	.17	.17	.40	.38	.30	.09	.30
Pin wid	.22	-.17	.20	.22	.07	.14	.11
Pin set	.14	.06	.23	.13	.19	.12	.11
Rump an	.00	-.13	.04	-.03	-.11	.30	.24
Bone qu	.60	.19	.44	.41	.52	-.26	.06
Foot an	.03	-.10	-.06	.00	.03	-.38	.00
Heel de	.05	-.12	-.08	.07	-.07	-.39	.06
Setrear	.58	.10	.11	.09	.30	-.07	.07
Rleg sv	-.48	.05	-.28	-.23	-.29	-.24	-.22
Rleg rv	.15	.01	.36	.34	.50	-.03	.13
Uddr de	.01	.11	.54	.25	.40	.21	.06
Uddr tx	.36	.54	.10	.77	.78	.31	.32
Med sus	.34	.25	.77	.07	.56	.20	.31
Fore at	.50	.40	.78	.56	.07	.05	.32
Fore pl	-.03	.21	.31	.20	.05	.03	-.01
Fore le	.13	.06	.32	.31	.32	-.01	.05
Rear he	.29	.37	.63	.56	.67	-.05	.29
Rear wi	.37	-.49	.13	.28	.25	.06	.18
Rear pl	-.31	.20	.06	.11	-.18	.55	-.16
Dy form	.36	.02	.46	.47	.58	-.10	.12
Claw un	.62	.08	.12	.17	.23	-.29	-.06
M speed	.06	-.10	-.09	-.06	-.06	-.03	-.01
Tempera	-.08	-.07	.01	.01	.05	-.09	.21

Table 3d.
HRC CORRELATIONS

	Rear he	Rear wi	Rear pl	Dy form	Claw un	M speed	Tempera
Size	-.15	.58	-.09	.48	.21	.00	.06
Stature	-.02	.38	-.04	.30	.22	-.05	-.02
Frt end	-.02	-.10	-.19	.16	.09	.00	.01
Chst wi	-.17	.56	-.06	.47	.12	.00	.08
Body de	.00	-.09	.19	.48	-.04	-.05	-.06
Loin st	.42	.21	.01	.42	.12	-.03	.00
Pin wid	-.03	.46	.08	.32	.22	-.10	-.07
Pin set	.18	.08	-.06	.16	.19	.05	-.13
Rump an	-.09	.14	-.02	-.11	-.01	-.03	-.05
Bone qu	.48	.13	-.10	.54	.46	.05	-.06
Foot an	-.04	.09	-.21	.19	.46	-.14	.23
Heel de	-.08	.10	-.15	.17	.45	-.06	.21
Setrear	.18	.09	-.30	.26	.35	-.06	-.04
Rleg sv	-.31	-.37	.17	-.11	-.14	.01	-.10
Rleg rv	.29	.37	-.31	.36	.62	.06	-.08
Uddr de	.37	-.49	.20	.02	.08	-.10	-.07
Uddr tx	.63	.13	.06	.46	.12	-.09	.01
Med sus	.56	.28	.11	.47	.17	-.06	.01
Fore at	.67	.25	-.18	.58	.23	-.06	.05
Fore pl	-.05	.06	.55	-.10	-.29	-.03	-.09
Fore le	.29	.18	-.16	.12	-.06	-.01	.21
Rear he	.09	.31	-.09	.24	.04	.02	.00
Rear wi	.31	.11	-.06	.38	.07	.08	.04
Rear pl	-.09	-.06	.07	-.20	-.17	.02	-.10
Dy form	.24	.38	-.20	.05	.15	-.06	.04
Claw un	.04	.07	-.17	.15	.12	.00	-.07
M speed	.02	.08	.02	-.06	.00	.04	-.28
Tempera	.00	.04	-.10	.04	-.07	-.28	.04

Table 4a.
RESIDUAL CORRELATIONS

	Size	Stature	Frt end	Chst wi	Body de	Loin st	Pin wid
Size	.47	.35	.24	.62	.34	.16	-.01
Stature	.35	.30	.05	.09	.06	.37	-.15
Frt end	.24	.05	.53	.20	.11	.13	.08
Chst wi	.62	.09	.20	.63	.28	.10	-.03
Body de	.34	.06	.11	.28	.60	.13	.01
Loin st	.16	.37	.13	.10	.13	.38	.10
Pin wid	-.01	-.15	.08	-.03	.01	.10	.38
Pin set	.09	.07	.00	.04	.10	.43	.06
Rump an	.01	.08	-.15	.02	-.02	.20	.06
Bone qu	-.19	.01	-.15	-.15	-.05	-.08	.12
Foot an	.12	.17	.02	.08	-.01	-.06	.11
Heel de	.12	.19	.07	.07	-.03	.00	.09
Setrear	.05	.07	.06	.01	.00	-.04	.00
Rleg sv	.02	-.06	-.15	.10	.17	-.15	.38
Rleg rv	.04	.05	-.01	.02	-.03	.28	.04
Uddr de	-.37	-.39	-.18	-.30	-.31	-.14	-.41
Uddr tx	-.09	.03	.09	-.09	-.09	-.11	.09
Med sus	.10	.08	.07	.07	.05	-.02	.18
Fore at	.00	-.16	-.06	.01	-.02	.12	-.11
Fore pl	.05	-.03	.00	.05	-.03	.13	.15
Fore le	.10	.04	-.04	.10	.19	.06	.07
Rear he	-.04	-.10	-.11	-.04	-.04	.18	.01
Rear wi	.09	-.02	.02	.12	-.02	-.02	.02
Rear pl	.01	.04	.11	.00	-.10	-.15	.00
Dy form	.20	.26	.19	.09	.26	.53	.28
Claw un	.07	.13	.01	.07	.00	.16	.10
M speed	-.03	-.05	-.03	-.01	.00	-.04	.04
Tempera	.00	.09	.07	-.04	-.05	-.01	-.05

Table 4b.
RESIDUAL CORRELATIONS

	Pin set	Rump an	Bone qu	Foot an	Heel de	Setrear	Rleg sv
Size	.09	.01	-.19	.12	.12	.05	.02
Stature	.07	.08	.01	.17	.19	.07	-.06
Frt end	.00	-.15	-.15	.02	.07	.06	-.15
Chst wi	.04	.02	-.15	.08	.07	.01	.10
Body de	.10	-.02	-.05	-.01	-.03	.00	.17
Loin st	.43	.20	-.08	-.06	.00	-.04	-.15
Pin wid	.06	.06	.12	.11	.09	.00	.38
Pin set	.76	.28	.10	.08	.05	.07	.02
Rump an	.28	.57	-.11	-.03	-.02	.01	-.12
Bone qu	.10	-.11	.52	.02	.08	.27	-.26
Foot an	.08	-.03	.02	.67	.52	.02	-.03
Heel de	.05	-.02	.08	.52	.69	.06	.05
Setrear	.07	.01	.27	.02	.06	.79	.04
Rleg sv	.02	-.12	-.26	-.03	.05	.04	.31
Rleg rv	.02	.03	.27	.10	.06	.24	-.06
Uddr de	-.08	-.17	-.18	.08	.10	-.01	-.12
Uddr tx	.14	-.08	.03	-.04	-.01	.06	.01
Med sus	.11	-.03	-.07	.02	.01	.07	-.09
Fore at	.00	-.06	-.11	.08	.06	.06	-.12
Fore pl	.04	.04	-.20	.04	-.01	.04	-.11
Fore le	.00	-.04	-.01	.03	.04	.06	-.20
Rear he	.09	.10	-.05	-.01	.01	.05	-.16
Rear wi	.13	.01	-.10	.05	.03	.05	-.07
Rear pl	.12	.02	-.14	.02	-.06	.00	.09
Dy form	.25	.06	.12	-.02	.00	.13	.01
Claw un	-.03	-.02	.26	.30	.32	.15	-.03
M speed	.00	-.08	-.04	.02	.03	.01	-.06
Tempera	.01	.02	.05	-.05	-.04	-.06	.14

Table 4c.
RESIDUAL CORRELATIONS

	Rleg rv	Uddr de	Uddr tx	Med sus	Fore at	Fore pl	Fore le
Size	.04	-.37	-.09	.10	.00	.05	.10
Stature	.05	-.39	.03	.08	-.16	-.03	.04
Frt end	-.01	-.18	.09	.07	-.06	.00	-.04
Chst wi	.02	-.30	-.09	.07	.01	.05	.10
Body de	-.03	-.31	-.09	.05	-.02	-.03	.19
Loin st	.28	-.14	-.11	-.02	.12	.13	.06
Pin wid	.04	-.41	.09	.18	-.11	.15	.07
Pin set	.02	-.08	.14	.11	.00	.04	.00
Rump an	.03	-.17	-.08	-.03	-.06	.04	-.04
Bone qu	.27	-.18	.03	-.07	-.11	-.20	-.01
Foot an	.10	.08	-.04	.02	.08	.04	.03
Heel de	.06	.10	-.01	.01	.06	-.01	.04
Setrear	.24	-.01	.06	.07	.06	.04	.06
Rleg sv	-.06	-.12	.01	-.09	-.12	-.11	-.20
Rleg rv	.63	.01	.07	.06	-.02	-.16	.11
Uddr de	.01	.28	.13	.04	.11	.13	-.09
Uddr tx	.07	.13	.49	.36	.10	-.04	.17
Med sus	.06	.04	.36	.64	.07	.09	.10
Fore at	-.02	.11	.10	.07	.50	.01	.07
Fore pl	-.16	.13	-.04	.09	.01	.52	.05
Fore le	.11	-.09	.17	.10	.07	.05	.51
Rear he	.02	.05	.09	.12	.07	-.14	.02
Rear wi	.09	-.26	-.01	.17	.08	-.04	.10
Rear pl	-.05	.00	-.13	.17	-.11	.21	.21
Dy form	-.02	-.33	-.11	-.02	-.15	-.37	.20
Claw un	.32	.14	.19	.08	.08	-.03	-.07
M speed	.01	-.02	.02	-.01	.01	.00	-.08
Tempera	-.05	.18	.01	-.01	.03	-.04	.01

Table 4d.
RESIDUAL CORRELATIONS

	Rear he	Rear wi	Rear pl	Dy form	Claw un	M speed	Tempera
Size	-.04	.09	.01	.20	.07	-.03	.00
Stature	-.10	-.02	.04	.26	.13	-.05	.09
Frt end	-.11	.02	.11	.19	.01	-.03	.07
Chst wi	-.04	.12	.00	.09	.07	-.01	-.04
Body de	-.04	-.02	-.10	.26	.00	.00	-.05
Loin st	.18	-.02	-.15	.53	.16	-.04	-.01
Pin wid	.01	.02	.00	.28	.10	.04	-.05
Pin set	.09	.13	.12	.25	-.03	.00	.01
Rump an	.10	.01	.02	.06	-.02	-.08	.02
Bone qu	-.05	-.10	-.14	.12	.26	-.04	.05
Foot an	-.01	.05	.02	-.02	.30	.02	-.05
Heel de	.01	.03	-.06	.00	.32	.03	-.04
Setrear	.05	.05	.00	.13	.15	.01	-.06
Rleg sv	-.16	-.07	.09	.01	-.03	-.06	.14
Rleg rv	.02	.09	-.05	-.02	.32	.01	-.05
Uddr de	.05	-.26	.00	-.33	.14	-.02	.18
Uddr tx	.09	-.01	-.13	-.11	.19	.02	.01
Med sus	.12	.17	.17	-.02	.08	-.01	-.01
Fore at	.07	.08	-.11	-.15	.08	.01	.03
Fore pl	-.14	-.04	.21	-.37	-.03	.00	-.04
Fore le	.02	.10	.21	.20	-.07	-.08	.01
Rear he	.57	.17	-.07	-.08	.08	-.01	.01
Rear wi	.17	.60	-.15	.01	.12	-.01	-.02
Rear pl	-.07	-.15	.45	-.29	.08	.03	-.02
Dy form	-.08	.01	-.29	.43	.07	.02	-.09
Claw un	.08	.12	.08	.07	.70	.01	-.04
M speed	-.01	-.01	.03	.02	.01	.88	-.15
Tempera	.01	-.02	-.02	-.09	-.04	-.15	.82

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