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Title: GENETIC ANALYSIS OF DISCRETE REPRODUCTIVE TRAITS IN SHEEP USING LINEAR AND NONLINEAR MODELS: I. ESTIMATION OF GENETIC PARAMETERS

Author
item MATOS, CAP
item THOMAS, D
item GIANOLA, D
item TEMPELMAN, R
item Young, Lawrence

Submitted to: Journal of Animal Science
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 8/1/1996
Publication Date: N/A
Citation: N/A

Interpretive Summary: Measurements of reproductive traits of sheep, such as fertility and litter size, fall into a relatively few distinct or discrete classes. Ewes either conceive or don't conceive and give birth to 1, 2, 3, 4, 5 or, occasionally, 6 lambs. Most genetic analyses are based on linear statistical methodologies developed for traits that show a continuous distribution such as weaning weight where individual lamb weights may rang from 15.0 to 45.0 pounds. The purpose of this research was to evaluate linear and nonlinear models for analysis of discrete traits. As the heritability of the trait increased, the difference between estimates of genetic parameters obtained with the various models decreased. Problems were encountered when estimating variance components with the nonlinear Poisson and Negative Binomial models. In general, the nonlinear threshold model yielded higher estimates of heritabilities and repeatabilities than did linear models. Heritabilities more often exceeded repeatabilities wit threshold models than with linear models which is contrary to genetic expectations. The results indicate that among the nonlinear models, only the threshold model appears to offer advantages over traditional linear models. Results also indicated that models utilizing genetic relationships among animals through the sire and dam, rather than just the sire, may be especially pertinent in the analysis of discrete traits.

Technical Abstract: Repeated records of fertility, litter size and ovulation rate in Rambouillet ewes, and of fertility and litter size in Finnsheep ewes were used to estimate heritabilities and repeatabilities with linear and nonlinear models. Linear sire (LSM), animal (LAM) and ewe (LEM) models were used with all traits. Threshold sire (TSM), animal (TAM) and ewe (TEM) models were also used with all traits. Litter size and ovulation rate were also analyzed with Poisson sire (PSM) and animal (PAM) models, and with Negative Binomial sire (NBSM) and animal (NBAM) models. All models included sire, animal or ewe, permanent environment, and residual as random effects and appropriate fixed effects such as ewe age, condition score, or breeding weight. Poisson and Negative Binomial analyses yielded results difficult to interpret due to problems in variance component estimation. Heritabilities obtained with LAM were, in general, greater than those obtained with LSM, except for ovulation rate. LAM estimates of heritability for the Rambouillet were .03, .16 and .23 for fertility, litter size and ovulation rate, respectively. For Finnsheep, heritabilities were .04 for fertility and .08 for litter size. Heritabilities obtained with threshold models were larger than those found with linear models for all traits. In general, repeatabilities were consistent among different models. LAM repeatabilities were .10, .21 and .23 for fertility, litter size and ovulation rate, respectively, in the Rambouillet and .13 and .11 for fertility and litter size, respectively, in the Finnsheep. Heritabilities exceeding repeatabilities were observed more frequently with TSM than with LSM. This suggests that the animal models may be even more pertinent with categorical than with continuous data.