• Asian-Australasian Journal of Animal Sciences
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• v.15 no.8
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• pp.1085-1090
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• 2002

Genetic parameters for birth weights (BWT), calving ease scores observed from calves born by heifers (CEH), and calving ease scores observed from calves born by cows (CEC) were estimated using Bayesian methodology with Gibbs sampling in different threshold animal models. Data consisted of 77,458 records for calving ease scores and birth weights in Gelbvieh cattle. Gibbs samplers were used to obtain the parameters of interest for the categorical traits in two univariate threshold animal models, a bivariate threshold animal model, and a three-trait linear-threshold animal model. Samples of heritabilities and genetic correlations were calculated from the posterior means of dispersion parameters. In a univariate threshold animal model with CEH (model 1), the posterior means of heritabilities for calving ease was 0.35 for direct genetic effects and 0.18 for maternal genetic effects. In the other univariate threshold model with CEC (model 2), the posterior means of heritabilities of CEC was 0.28 for direct genetic effects and 0.18 for maternal genetic effects. In a bivariate threshold model with CEH and CEC (model 3), heritability estimates were similar to those in unvariate threshold models. In this model, genetic correlation between heifer calving ease and cow calving ease was 0.89 and 0.87 for direct genetic effect and maternal genetic effects, respectively. In a three-trait animal model, which contained two categorical traits (CEH and CEC) and one continuous trait (BWT) (model 4), heritability estimates of CEH and CEC for direct (maternal) genetic effects were 0.40 (0.23) and 0.23 (0.13), respectively. In this model, genetic correlation estimates between CEH and CEC were 0.89 and 0.66 for direct genetic effects and maternal effects, respectively. These estimates were greater than estimates between BWT and CEH (0.82 and 0.34) or BWT and CEC (0.85 and 0.26). This result indicates that CEH and CEC should be high correlated rather than estimates between calving ease and birth weight. Genetic correlation estimates between direct genetic effects and maternal effects were -0.29, -0.31 and 0.15 for BWT, CEH and CEC, respectively. Correlation for permanent environmental effects between BWT and CEC was -0.83 in model 4. This study can provide genetic evaluation for calving ease with other continuous traits jointly with assuming that calving ease from first calving was a same trait to calving ease from later parities calving. Further researches for reliability of dispersion parameters would be needed even if the more correlated traits would be concerned in the model, the higher reliability could be obtained, especially on threshold model with property that categorical traits have little information.

• Journal of the Korean Statistical Society
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• v.31 no.2
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• pp.177-198
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• 2002

The estimation of variance components or variance ratios in linear model is an important issue in plant or animal breeding fields, and various estimation methods have been devised to estimate variance components or variance ratios. However, many traits of economic importance in those fields are observed as dichotomous or polychotomous outcomes. The usual estimation methods might not be appropriate for these cases. Recently threshold linear model is considered as an important tool to analyze discrete traits specially in animal breeding field. In this note, we consider a hierarchical Bayesian method for the threshold animal model. Gibbs sampler for making full Bayesian inferences about random effects as well as fixed effects is described to analyze jointly discrete traits and continuous traits. Numerical example of the model with two discrete ordered categorical traits, calving ease of calves from born by heifer and calving ease of calf from born by cow, and one normally distributed trait, birth weight, is provided.

• Journal of Animal Science and Technology
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• v.44 no.2
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• pp.151-164
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• 2002

Genetic variance and covariance components of the linear traits and the ordered categorical traits, that are usually observed as dichotomous or polychotomous outcomes, were simultaneously estimated in a multivariate threshold animal model with concepts of arbitrary underlying liability scales with Bayesian inference via Gibbs sampling algorithms. A multivariate threshold animal model in this study can be allowed in any combination of missing traits with assuming correlation among the traits considered. Gibbs sampling algorithms as a hierarchical Bayesian inference were used to get reliable point estimates to which marginal posterior means of parameters were assumed. Main point of this study is that the underlying values for the observations on the categorical traits sampled at previous round of iteration and the observations on the continuous traits can be considered to sample the underlying values for categorical data and continuous data with missing at current cycle (see appendix). This study also showed that the underlying variables for missing categorical data should be generated with taking into account for the correlated traits to satisfy the fully conditional posterior distributions of parameters although some of papers (Wang et al., 1997; VanTassell et al., 1998) presented that only the residual effects of missing traits were generated in same situation. In present study, Gibbs samplers for making the fully Bayesian inferences for unknown parameters of interests are played rolls with methodologies to enable the any combinations of the linear and categorical traits with missing observations. Moreover, two kinds of constraints to guarantee identifiability for the arbitrary underlying variables are shown with keeping the fully conditional posterior distributions of those parameters. Numerical example for a threshold animal model included the maternal and permanent environmental effects on a multiple ordered categorical trait as calving ease, a binary trait as non-return rate, and the other normally distributed trait, birth weight, is provided with simulation study.

• Animal Bioscience
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• v.34 no.1
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• pp.20-25
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• 2021

Objective: The objective of the study was to investigate the possibility of utilizing an early litter size trait as an indirect selection trait for longevity and to estimate genetic parameters between sow stayability and litter size at different parities using a linear-threshold model for longevity in Thai Large White (LW) and Landrace (LR) populations. Methods: The data included litter size at first, second, and third parities (NBA1, NBA2, and NBA3) and sow stayability from first to fourth farrowings (STAY14). The data was obtained from 10,794 LR and 9,475 LW sows. Genetic parameters were estimated using the multiple-trait animal model. A linear-threshold model was used in which NBA1, NBA2, and NBA3 were continuous traits, while STAY14 was considered a binary trait. Results: Heritabilities for litter size were low and ranged from 0.01 to 0.06 for both LR and LW breeds. Similarly, heritabilities for stayability were low for both breeds. Genetic associations between litter size and stayability ranged from 0.43 to 0.65 for LR populations and 0.12 to 0.55 for LW populations. The genetic correlation between NBA1 and STAY14 was moderate and in a favorable direction for both LR and LW breeds (0.65 and 0.55, respectively). Conclusion: A linear-threshold model could be utilized to analyze litter size and sow stayability traits. Furthermore, selection for litter size at first parity, which was the genetic trait correlated with longevity, is possible when one attempts to improve lifetime productivity in Thai swine populations.

• Asian-Australasian Journal of Animal Sciences
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• v.18 no.8
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• pp.1088-1097
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• 2005

Main objectives of this study were to investigate accuracy, bias and power of linear and threshold model segregation analysis methods for detection of major genes in categorical traits in farm animals. Maximum Likelihood Linear Model (MLLM), Bayesian Linear Model (BALM) and Bayesian Threshold Model (BATM) were applied to simulated data on normal, categorical and binary scales as well as to disease data in pigs. Simulated data on the underlying normally distributed liability (NDL) were used to create categorical and binary data. MLLM method was applied to data on all scales (Normal, categorical and binary) and BATM method was developed and applied only to binary data. The MLLM analyses underestimated parameters for binary as well as categorical traits compared to normal traits; with the bias being very severe for binary traits. The accuracy of major gene and polygene parameter estimates was also very low for binary data compared with those for categorical data; the later gave results similar to normal data. When disease incidence (on binary scale) is close to 50%, segregation analysis has more accuracy and lesser bias, compared to diseases with rare incidences. NDL data were always better than categorical data. Under the MLLM method, the test statistics for categorical and binary data were consistently unusually very high (while the opposite is expected due to loss of information in categorical data), indicating high false discovery rates of major genes if linear models are applied to categorical traits. With Bayesian segregation analysis, 95% highest probability density regions of major gene variances were checked if they included the value of zero (boundary parameter); by nature of this difference between likelihood and Bayesian approaches, the Bayesian methods are likely to be more reliable for categorical data. The BATM segregation analysis of binary data also showed a significant advantage over MLLM in terms of higher accuracy. Based on the results, threshold models are recommended when the trait distributions are discontinuous. Further, segregation analysis could be used in an initial scan of the data for evidence of major genes before embarking on molecular genome mapping.

• Animal Bioscience
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• v.36 no.8
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• pp.1151-1155
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• 2023

Objective: This study analyzes interactions of body condition score (BCS) with other factors and the effect of BCS on estimates of genetic paremeters of conception rate (CR) in Japanese Black cows. Methods: Factors affecting CR were analyzed through the linear mixed model, and genetic parameters of CR were estimated through the threshold animal model. Results: The interactions between BCS and each season and the number of artificial inseminations (AI) was significant (p<0.05), but that between BCS and parity showed no significance for CR. High CR was observed with BCS 3 in autumn (0.56±0.01) and BCS 4 in summer (0.56±0.02). The highest CR with BCS 3 (0.56±0.02) and BCS 4 (0.55±0.01) was observed at first AI. With BCS 5, however, the highest CR (0.55±0.08) was observed at second AI. Conclusion: The model with BCS was notably conducive to the estimation of genetic parameters because of a low deviance information criterion of heritability that, nevertheless, was slightly lower than the model without BCS.

• Journal of Animal Science and Technology
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• v.48 no.2
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• pp.161-168
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• 2006

Genetic parameters for linear type and composite traits were estimated by using Bayesian inference via Gibbs sampling with a multiple threshold animal model in Holstein cows. Fifteen linear type traits and 5 composite traits were included to estimate genetic variance and covariance components in the model. In this study, 30,204 records were obtained in the cows from 305 sires. Heritability estimates for linear type traits had the estimates as high as 0.28~0.64. Heritability estimates for composite traits were also high, when the traits were assumed to be categorical traits. Final score was more correlated with the composite traits than with the linear type traits.

• Asian-Australasian Journal of Animal Sciences
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• v.18 no.12
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• pp.1669-1674
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• 2005

Maximum likelihood methodology was applied to analyze the efficiency and statistical power of interval mapping by using a threshold model. The factors that affect QTL detection efficiency (e.g. QTL effect, heritability and incidence of categories) were simulated in our study. Daughter design with multiple families was applied, and the size of segregating population is 500. The results showed that the threshold model has a great advantage in parameters estimation and power of QTL mapping, and has nice efficiency and accuracy for discrete traits. In addition, the accuracy and power of QTL mapping depended on the effect of putative quantitative trait loci, the value of heritability and incidence directly. With the increase of QTL effect, heritability and incidence of categories, the accuracy and power of QTL mapping improved correspondingly.

• Animal Bioscience
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• v.34 no.2
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• pp.185-191
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• 2021

Objective: The objective of this study was to estimate the genetic parameters for worm resistance (WR) and associated characteristics, using the linear-threshold animal model via Bayesian inference in single- and multiple-trait analyses. Methods: Data were collected from a herd of Santa Inês breed sheep. All information was collected with animals submitted to natural contamination conditions. All data (number of eggs per gram of feces [FEC], Famacha score [FS], body condition score [BCS], and hematocrit [HCT]) were collected on the same day. The animals were weighed individually on the day after collection (after 12-h fasting). The WR trait was defined by the multivariate cluster analysis, using the FEC, HCT, BCS, and FS of material collected from naturally infected sheep of the Santa Inês breed. The variance components and genetic parameters for the WR, FEC, HCT, BCS, and FS traits were estimated using the Bayesian inference under the linear and threshold animal model. Results: A low magnitude was obtained for repeatability of worm-related traits. The mean values estimated for heritability were of low-to-high (0.05 to 0.88) magnitude. The FEC, HCT, BCS, FS, and body weight traits showed higher heritability (although low magnitude) in the multiple-trait model due to increased information about traits. All WR characters showed a significant genetic correlation, and heritability estimates ranged from low (0.44; single-trait model) to high (0.88; multiple-trait model). Conclusion: Therefore, we suggest that FS be included as a criterion of ovine genetic selection for endoparasite resistance using the trait defined by multivariate cluster analysis, as it will provide greater genetic gains when compared to any single trait. In addition, its measurement is easy and inexpensive, exhibiting greater heritability and repeatability and a high genetic correlation with the trait of resistance to worms.

• Asian-Australasian Journal of Animal Sciences
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• v.32 no.3
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• pp.334-340
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• 2019

Objective: The objective of this study was to investigate the genetic components of daily milk yield and to re-rank bulls in South Korea by estimated breeding value (EBV) under heat stress using the temperature-humidity index (THI). Methods: This study was conducted using 125,312 monthly test-day records, collected from January 2000 to February 2017 for 19,889 Holstein cows from 647 farms in South Korea. Milk production data were collected from two agencies, the Dairy Cattle Genetic Improvement Center and the Korea Animal Improvement Association, and meteorological data were obtained from 41 regional weather stations using the Automated Surface Observing System (ASOS) installed throughout South Korea. A random regression model using the THI was applied to estimate genetic parameters of heat tolerance based on the test-day records. The model included herd-year-season, calving age, and days-in-milk as fixed effects, as well as heat tolerance as an additive genetic effect, permanent environmental effect, and direct additive and permanent environmental effect. Results: Below the THI threshold (${\leq}72$; no heat stress), the variance in heat tolerance was zero. However, the heat tolerance variance began to increase as THI exceeded the threshold. The covariance between the genetic additive effect and the heat tolerance effect was -0.33. Heritability estimates of milk yield ranged from 0.111 to 0.176 (average: 0.128). Heritability decreased slightly as THI increased, and began to increase at a THI of 79. The predicted bull EBV ranking varied with THI. Conclusion: We conclude that genetic evaluation using the THI function could be useful for selecting bulls for heat tolerance in South Korea.