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Time class for racing performance of the Quarter Horse: Genetic parameters and trends using Bayesian and multivariate threshold models
Livestock Science 225 (2019) 116–122
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Time class for racing performance of the Quarter Horse: Genetic parameters and trends using Bayesian and multivariate threshold models
T
Ricardo António Silva Fariaa, , Amanda Marchi Maioranoa, Luiz Eduardo Cruz dos Santos Correiaa, Mário Luiz Santana Jrb, Josineudson Augusto II Vasconcelos Silvac ⁎
a
Universidade Estadual Paulista (Unesp), Faculdade de Ciências Agrárias e Veterinárias, PO Box 14884-900 Jaboticabal, São Paulo, Brasil Universidade Federal de Rondonópolis, PO Box 78735-901, Rondonópolis, MT, Brasil c Universidade Estadual Paulista (Unesp), Faculdade de Medicina Veterinária e Zootecnia, PO Box 18618-000 Botucatu, São Paulo, Brasil b
ARTICLE INFO
ABSTRACT
Keywords: Horserace Heritability Hippodrome Repeatability Speed
The aim of this study was to evaluate racing performance in the Quarter Horse breed in Brazil using genetic parameter estimates, breeding values, and genetic trends for a differentiated trait, time class (TC), at four different distances. The speed records comprising races that occurred between 1981 and 2011 were obtained from hippodromes in the states of São Paulo, Ceará, Brasília, and Mato Grosso do Sul. The final archive analysed contained 4263 horses born to 431 stallions and 1716 dams. These animals participated in 3904 races, providing 17,342 records of final racing time. The four TC traits were defined by 5 scores based on the final times (in seconds) of each animal in each race. The scores for formation of the classes were attributed within each race based on the percent difference from winner's time. Time class was evaluated at distances of 301, 320, 365 and 402 m, generating four phenotypic measures: TC301, TC320, TC365 and TC402, respectively. The genetic parameters were estimated by Bayesian inference in multivariate analysis using a threshold animal model. The model included the fixed effects of race, sex and age class of animal in the race, in addition to additive genetic, animal permanent environmental and residual random effects. The mean heritability estimates were of high magnitude and ranged from 0.45 ± 0.06 (TC402) to 0.56 ± 0.04 (TC365). Repeatability estimates ranged from 0.78 ± 0.06 (TC402) to 0.97 ± 0.01 (TC320). The additive genetic and animal permanent environmental correlations were positive, with mean correlations ranging from 0.33 ± 0.06 between TC301 and TC320 to 0.62 ± 0.06 between TC365 and TC402 and from 0.44 ± 0.08 between TC301 and TC320 to 0.58 ± 0.06 between TC365 and TC402, respectively. The mean breeding values transformed by the cumulative distribution function of the standard normal distribution ranged from 54.6 ± 25.3 (TC365) to 57.8 ± 28.5 (TC320) in the group of animals included in the pedigree and born after 1980. The genetic trends observed indicated that TC301 (301 m) exhibited the greatest evolution between 1981 and 2008. The results suggest the possible use of TC traits as selection criteria since they respond positively to selection, permitting genetic gains in breeding programs of racehorses.
1. Introduction The Quarter Horse (QH) breed dates back to the 17th century in the current United States and is a versatile breed used for cutting, conformation and racing. The last attribute, which originated from the Thoroughbred breed, makes the racing line of the QH breed the fastest horse in the world over short distances (Nielsen et al., 2006), with a maximum speed when crossing the finish line of 92.6 km/h. The genetic fitness of horses with high performance in sprint races is complex and
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depends on various environmental factors that will affect the capacity of a horse to become a champion. Racing performance is the main phenotype used to compose selection criteria for speed in horses, with the application of different definitions and traits. In the main racing breed (Thoroughbred) from which QH originated, Sharman and Wilson (2015) observed improvements in final time over the years (1850 to 2012). However, a plateau (stagnation) of racing time was suggested for the first time by Cunningham (1975), and other authors agreed (Gaffney and
Correspondence to: FMVZ - Unesp, DMNA - Fazenda Experimental Lageado, Rua José Barbosa de Barros, n° 1780, CEP: 18.618-307, Botucatu, SP, Brasil. E-mail addresses: [email protected] (R.A.S. Faria), [email protected] (J.A.I.V. Silva).
https://doi.org/10.1016/j.livsci.2019.05.013 Received 8 January 2019; Received in revised form 13 May 2019; Accepted 13 May 2019 Available online 14 May 2019 1871-1413/ © 2019 Elsevier B.V. All rights reserved.
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Cunningham, 1988; Langlois, 1980; Thiruvenkadan et al., 2009) that the animals may have reached their limit of race speed. Nevertheless, Sharman and Wilson (2015) emphasized that this stagnation might be due to the small number of animals studied and the exclusive use of winning time of the animals and elite racing performance. The same phenomenon (plateau) may be happening in the QH breed, but studies are necessary that allow the discussions described for the Thoroughbred breed. Studies on racehorse performance of the QH breed have estimated heritability and repeatability for final time and final rank (Villela et al., 2002), final time and speed index (Corrêa and Mota, 2007), earnings (Silva et al., 2014), and final time (Buttram et al., 1988b), demonstrating little difference in the traits studied and heritability estimates of low and moderate magnitude. These findings indicate the need for identifying a new trait that could be used as a selection criterion. López-Correa et al. (2014) used percent differences in winner's time per race in endurance competitions of Criollo horses in Uruguay. The authors pointed out that one advantage of forming classes (score) from winner's time would be to place animals with small differences in the final racing result on the same level. The authors were thus able to better identify additive genetic variance among horses. Following this line of reasoning, it would be interesting to use a score ranging from 5 to 1 applied to racing performance of horses. The time class (TC) trait was thus developed, in which the animals are ranked based on the percentage comparison of final winner's time in each race. Stock et al. (2007) showed that it is possible to provide reliable estimates for the evaluation of categorical traits similar to TC. The authors estimated (co)variances by simulating phenotypic data using multivariate Bayesian inference under a threshold animal model. The objective of this study was to evaluate the racing performance of QH and to estimate genetic parameters, breeding values and genetic trends for Time Class at different distances.
Table 1 Description of the speed racing data by time class traits and total of the Quarter Horse breed in Brazil. Item
Traits TC301
TC320
TC365
TC402
Animals, n Males, % Races, n Mean animals per race, n Records, n Records males, % Males records 3 years, % Males records 4 years, % Males records 5 years, % Males records 6 years, %
2301 41.3 1039 4.1 4284 42.7 41.0 43.3 43.8 66.7
1490 38.2 464 4.6 2134 38.2 36.4 43.6 68.2 50.6
2638 42.4 1072 4.4 4705 41.6 41.5 42.9 55.0 58.3
2718 44.3 1329 4.7 6219 43.8 41.9 50.4 58.0 78.6
Total 4263 41.9 3904 4.4 17,342 42.4 40.9 45.0 52.7 66.2
TC301 = time class at 301 m; TC320 = time class at 320 m; TC365 = time class at 365 m; TC402 = time class at 402 m. n = number.
to 1.0%, 1.01% to 3.0%, 3.01% to 5.0% and > 5.0% in relation to the final time of the winner, respectively. Time class was defined as four different traits according to distance in each race: TC301, TC320, TC365, and TC402 m (Table 1). 2.3. Data analysis The (co)variance components and genetic parameters (heritability, repeatability, and genetic correlations) of the TC traits were estimated by Bayesian inference in multivariate analysis under a threshold animal model. The analyses were performed using the THRGIBBS1F90 program (Misztal et al., 2002). The Gibbs post-sampling estimates were obtained with the POSTGIBBSF90 program (Misztal et al., 2002). The statistical model used for the four traits (TC301, TC320, TC365, and TC402) included the fixed effects of race, sex and age class of animal, in addition to additive genetic, animal permanent environmental and residual random effects. The effects of hippodrome, racing data or type of racetrack were not considered in the analysis because they are absorbed by including the effect of race. The matrix form of the model can be written as follows:
2. Material and methods 2.1. Data description The racing performance records of QH were provided by the Sorocaba Jockey Club (JCS) and comprised the data of races that occurred between 1981 and 2011 in hippodromes of the states of São Paulo (94.6%) and Ceará, Brasília and Mato Grosso do Sul. The database contained information about the name of the animal, stallion and mare, sex, date of birth, number of races, age of animal, race distance, and final racing time. The phenotype file analysed contained 4263 horses (males and females), born to 431 stallions (range: 1–318 progeny) and 1716 dams (range: 1–12 progeny), which participated in 3904 races. There were 17,342 records of racing time. The quality of the data was analysed using the SAS/STAT® program (SAS, 2011) and animals with incomplete data, pedigree errors and participating in races with fewer than three animals were removed. The age of the animals at race ranged from 2 to 11 years, with a mean of 3.2 years. Two-year-old animals (only 457) were grouped with 3-year-old animals and animals aged 6 years or older were also grouped (only 147). In the analysis of the data, age at race was included as a fixed effect, with four age classes (3, 4, 5, and 6 years). The pedigree file was compiled from the 4263 animals with records and their ascendants up to the fifth generation. The final file contained 6284 animals, born to 873 stallions and 2051 dams.
= X + Z1 + Z2 c + e,
(1)
where y is the vector of observations (TC traits); β is the vector of fixed effects; α is the vector of random effects that represent the additive direct breeding values of the animal; c is the vector of permanent environmental effects; e is the vector of residual random effects, and X, Z1 and Z2 are incidence matrices that relate the observations to the fixed effects, direct additive genetic random effects and uncorrelated permanent environmental random effects, respectively. For the threshold model, the assumption was that the underlying scale has a continuous normal distribution as follows:
U|
N (W , I e2),
(2)
where U is the vector of the underlying scale of order r; Ɵ’=(β’, α’, c’) is the vector of location parameters of order s, with β being defined as systematic effects, α is the additive genetic effect and c is the permanent environmental effect of the animal; W is the known incidence matrix of order r × s; I is the identity matrix of order r × r, and e2 is the residual variance. In multivariate analysis containing categorical variables, according to the Bayesian approach, vectors β, α and c are location parameters of a conditional distribution y | β, α, c. The a priori assumption was that β has a uniform distribution that reflects vague prior knowledge about this vector. Inverse Wishart distributions were attributed to the other components. Thus, the distribution of y, given the scale parameters, can be written as:
2.2. Description of the trait The time class (TC) trait was defined by 5 scores based on the final times (in seconds) of each animal in each race. The scores for formation of the classes were attributed within each race based on the percent difference from winner's time. Class 5 comprises animals with a final time of 0.10% or less in relation to final winner's time, including the winner. Classes 4, 3, 2 and 1 include animals with a final time of 0.11%
( | , a , c, R) N [X + Za a + Wc c, IN R]
(3)
The traits analysed are categorical variables and are determined by 117
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non-observable continuous variables on an underlying scale, in which the initial threshold values are fixed: t1 < t2 … < tj − 1, with t0 = −∞ and tj = ∞, where j is the number of categories. The categories or scores of yi (TC), for each animal i, are defined by Ui on the underlying scale:
Yi = (1) t 0 < Ui < Ui
t1; (2) t1 < Ui
t2; (3) t2 < Ui
t3; (4) t3 < Ui
mean number of animals per race. The smallest amount of information was available for TC320, with 12% of records, 13% of races, and a higher proportion of female participants. The age classes corresponded to 81.3% (≤3 years), 14.6% (4 years), 3.3% (5 years), and 0.9% (≥ 6 years) of all records. Considering all distances (four different traits), females had the largest number of records. However, different values were obtained when the number of records at the different ages was analysed (Table 1). A larger number of records was obtained for males when older animals were considered (≥5 years). The characteristics of the track were the same for all hippodromes and all races were performed in a straight line at the distances studied. The reason for using hippodromes from different states was to cover the whole database. Animals from the hippodromes of Ceará, Brasília and Mato Grosso do Sul (5.4%) were found to be relationship to the animals competing in the hippodromes of the State of São Paulo.
t4; (5) t4 (4)
t5, for i = 1, ...,n ,
where n is the number of observations. After specification of the thresholds t0 to t5, one of the thresholds (t0 to t5) needed to be adjusted to an arbitrary constant. In this study, t1 was set at 0, with the vector of estimable thresholds being defined as t = t2, t3 and t4. A single chain of 1100,000 cycles was defined for Gibbs sampling, with a burn-in period of 100,000 cycles. This number was chosen after verification of the stationary stage of the chain by graphic inspection (Kass et al., 1998). Samples were stored every 20 iterations, totalling 50,000 samples which were used for computing (co)variance components to obtain the posterior mean, standard deviation, median, mode, and highest posterior density at 95% (HPD95) of the genetic parameters. The minimum effective sample size (ESS) of the (co)variance components indicates the number of independent samples with information equivalent to those present in the dependent sample (Sorensen et al., 1995). Thus, the ESS obtained in the present study indicates the convergence of the Gibbs chain. The posterior estimated breeding values (EBV) were obtained using BLUP procedures and the analyses were performed with the THRGIBBS1F90 program (Misztal et al., 2002) using the “OPTION fixed_var mean” tool. The genetic and residual (co)variances obtained in the final analysis of this study were used to calculate EBV. The EVB solutions, obtained from the underlying scale, were transformed by means of a cumulative distribution function (CDF) of the standard normal distribution into a percentage scale and were called estimated breeding value percentage (EBVp). These estimates were calculated with the SAS/STAT® software (SAS, 2011) using the expression:
EBVp = CDF ( NORMAL, x,
,
),
3.2. Genetic parameter estimates 3.2.1. Heritability and repeatability Analysis of the chains generated with the THRGIBSS2F90 program showed that the burn-in period and sampling interval were sufficient to confirm convergence of the chain. For all traits studied, few differences were observed between the measures of central tendency of the estimated parameters, indicating symmetry in the posterior distributions. The minimum ESS of the (co)variance components was > 150 cycles for TC320 and > 1200 cycles for the other traits. The heritability and repeatability estimates for the TC traits were of moderate to high magnitude (Table 2). Heritability estimates ranged from 0.45 ± 0.06 (TC402) to 0.56 ± 0.04 (TC365) and the repeatability estimate was higher than 0.78 (TC402). The measures of central tendency were similar for both heritability and repeatability, with short HPD95 intervals (Table 2). 3.2.2. Genetic correlations The additive genetic correlations between TC traits (Table 3) were moderate between TC301 and TC320 (0.33 ± 0.07) and high between TC365 and TC402 (0.62 ± 0.04). TC402 showed the highest additive genetic correlations with the other traits. The correlations of the animal permanent environment between TC traits were high and ranged from 0.44 ± 0.08 between TC301 and TC320 to 0.58 ± 0.06 between TC365 and TC401, following the same trends as the additive genetic correlations. The residual correlations were close to zero, with a correlation of 0.03 ± 0.06, 0.06 ± 0.03 and 0.02 ± 0.04 for TC301 with TC320, TC365 and TC402, respectively. The residual correlation between the largest distance traits, TC365 and TC402, was 0.04 ± 0.03.
(5)
where x is a numerical random variable, θ is a numerical location parameter, and λ is a numerical scale parameter. The EBVp for the four TC traits refer to 4508 animals born between 1981 and 2008, a period considering the beginning of racing records and the birth of the last breeding animals evaluated. The EBVp for stallions (n = 139) and dams (n = 1118) over the same period are also described. The EBVp were used to calculate genetic trends as the regression of breeding values per year of birth of the animals (from 1981 to 2008). The results are illustrated in a graph as the annual means of the four TC traits and their respective linear trend lines. Additional analyses were performed for all stallions in the pedigree (n = 873), which allowed observation of the genetic relationship between the TC traits based on EBVp, comparing average genetic superiority as a function of the selected proportion of stallions. Trait TC402 was used as the reference (because it contained the largest number of records and the highest earnings), permitting to verify the stallions at 402 m if they were selected based on EBVp for TC301, TC320, TC365, and TC402. We also calculated the regression of EBVp of stallions for TC301, TC320 and TC365 on the EBVp of stallions for TC402 in order to consolidate the results obtained for stallions of the QH breed in Brazil.
Table 2 Descriptive statistics of posterior heritability and repeatability estimates obtained by Bayesian analysis for time class in Quarter Horses. Item Heritability Mean ± SD Median Mode HPD95 Repeatability Mean ± SD Median Mode HPD95
3. Results 3.1. Data
Trait TC301
TC320
TC365
TC402
0.52 ± 0.04 0.52 0.50 0.44–0.66
0.48 ± 0.06 0.48 0.44 0.38–0.60
0.56 ± 0.04 0.56 0.56 0.49–0.63
0.45 ± 0.06 0.46 0.50 0.31–0.55
0.85 ± 0.04 0.84 0.86 0.79–0.93
0.97 ± 0.01 0.98 0.95 0.94–0.99
0.88 ± 0.02 0.88 0.85 0.80–0.91
0.78 ± 0.06 0.79 0.83 0.65–0.87
TC301 = time class at 301 m; TC320 = time class at 320 m; TC365 = time class at 365 m; TC402 = time class at 402 m. HPD95 = highest posterior density at 95%.
Among the traits analysed, TC402 had the largest number of data (Table 1), with 36% of records and 34% of races, as well as the largest 118
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stallions were selected based on the EBVp for the other TC traits. The values observed indicate a reduction in average genetic superiority for TC402 if selection were performed for TC301, TC320 and TC365. However, the fraction of the top 10% of reproducers at the distance of 320 m (TC320) obtained results similar to those of stallions at the distance of 402 m (TC402). After the top 10% of selected stallions, the genetic superiority of 320 m declines and is identical to the distances of 301 and 365 m. The average superiority of the top 50% of stallions (Fig. 2) selected for TC402 is 45.6% (EBVp). If selection were performed for TC301, TC320 and TC365, the superiority in the response of the observed scale would be only 34.1%, 39.1% and 33.6%, respectively. Regression of the EBVp of stallions (Fig. 3) for TC301, TC320 and TC365 on the EBVp of stallions for TC402 confirmed the results shown in Fig. 2. If the offspring of stallions selected for TC402 (Fig. 3) competed at 402 m and obtained an increase of 1.00%, the values of offspring born to stallions selected for TC301, TC320 and TC365 would only be 0.29%, 0.71% and 0.27%, respectively, of this increased unit when competing at 402 m.
Table 3 Additive genetic (above the diagonal) and animal permanent environmental correlations (below the diagonal) between the time class (TC) traits in Quarter Horses. Trait TC301 TC320 TC365 TC402
TC301 ± SD ± ± ± ±
SD SD SD SD
0.44 ± 0.08 0.53 ± 0.06 0.52 ± 0.07
TC320 ± SD
TC365 ± SD
TC402 ± SD
0.33 ± 0.07
0.46 ± 0.06 0.38 ± 0.07
0.52 ± 0.07 0.54 ± 0.07 0.62 ± 0.06
0.45 ± 0.07 0.49 ± 0.08
0.58 ± 0.06
TC301 = time class at 301 m; TC320 = time class at 320 m; TC365 = time class at 365 m; TC402 = time class at 402 m. Table 4 Mean, standard deviation and highest posterior density at 95% (HPD95) of the estimated breeding value percentage (EBVp) for all time class traits in all animals, stallions and dams included in the pedigree (born after 1980) of racing Quarter Horses. Trait TC30a Totala Stallionsa Damsa TC320 Totala Stallionsa Damsa TC365 Totala Stallionsa Damsa TC402 Totala Stallionsa Damsa
Estimated breeding value percentage Mean ± SD,%
HPD95, %
55.2 ± 25.8 47.9 ± 26.2 51.0 ± 26.9
4.57–96.3 2.72–92.0 1.90–95.6
57.8 ± 28.5 47.3 ± 33.2 53.2 ± 29.8
9.12–98.5 3.64–97.3 6.36–97.8
54.6 ± 25.3 47.5 ± 24.6 52.2 ± 26.9
4.81–94.8 6.47–90.8 1.95–95.6
56.9 ± 28.4 48.0 ± 32.4 52.7 ± 28.8
8.76–98.8 4.96–97.9 8.24–97.8
4. Discussion 4.1. Data The difference in the number of records per distance in the data analysed (Table 1) when compared to the racing data of QH in the United States, Mexico and Canada (Buttram et al., 1988a), with a total number of records of 561,738; 368,846 and 92,664 for the distances of 320, 365 and 402 m, respectively, indicates divergence in the training guidelines of horses among countries. The number of animals participating in the distance of 320 m described by Buttram et al. (1988a) was higher than that of the present study, a finding suggesting the lack of interest of Brazilian horse owners for the distance of 320 m. The longest distance (402 m) analysed in the present study is the preference of breeders because of greater earnings (JCS, 2019) and because the breed is specialized at this distance. A higher frequency of competing females (Table 1) has also been described for other racing breeds, Arabian (Ekiz and Kocak, 2005) and Thoroughbred horses (Mota et al., 2005, 1998), as well as for the QH breed (Buttram et al., 1988a; Corrêa and Mota, 2007; Silva et al., 2014). Evaluating all observations (Table 1), there was a trend towards a larger number of females at the four distances studied. However, when the records of older animals (≥5 years) were considered, there was a larger number of male records. Reproductive factors were probably the main reason for the shift in the number of records between sexes with increasing age of the animals, in which mares are removed earlier from competitions for breeding. The use of embryo transfer will permit mares to simultaneously compete and breed. The larger number of female records in the younger age classes remains to be explained.
TC301 = time class at 301 m; TC320 = time class at 320 m; TC365 = time class at 365 m; TC402 = time class at 402 m. HPD95 = highest posterior density at 95%. a Animals, stallions and dams included in the pedigree born after 1980.
3.3. Breeding values 3.3.1. EBV and genetic trends The mean EBVp were similar in the groups studied (total animals, stallions, and dams) for all TC traits (Table 4). The lowest and highest mean EBVp were observed for TC320 in the group of stallions (47.3 ± 33.2) and in the total animal group (57.8 ± 28.5), respectively. The SD values and variation (HPD95) were high and similar in the groups of animals (Table 4). The lowest SD values were observed for the highest mean EBVp. The shortest HPD95 interval ranged from 6.47% to 90.8% (TC365, stallions) and the greatest interval from 1.9% to 95.6% (TC301, dams). The genetic trends (Fig. 1) per year of birth of the animals (1981 to 2008) increased over time for TC301 and TC365, while the genetic trend for TC402 was close to zero. A negative genetic trend was observed for TC320. Oscillations in the annual mean EBVp were observed for all traits, with similar values for TC301 and TC365 and for TC320 and TC402. The difference in the annual mean EBVp (Fig. 1) between the first (1981) and last year (2008) evaluated was 12.3% (TC301), 0.9% (TC320), 7.1% (TC365), and 4.5% (TC402). The annual genetic changes in EBVp were 0.4% (TC301), −0.1% (TC320), 0.3% (TC365), and 0.1% (TC402).
4.2. Genetic parameter estimates 4.2.1. Heritability and repeatability The heritability and repeatability estimates (Table 2) of the traits studied were of moderate to high magnitude. The fact that the definition of the traits is used for the first time to designate phenotypes of horserace records impairs the comparison with other studies. However, considering published studies reporting race records at similar distances, the estimated values were found to be superior. Although the traits were defined differently, the higher values are probably due to the use of categories, grouping animals next to the winner, and to the application of nonlinear models. These approaches may have allowed better identification of additive variance in the population. In Brazil, a combined analysis of QH at distances of 275, 301, 320, 365, 402 and 503, Villela et al. (2002) reported heritability estimates of 0.14 and 0.17 for final rank and final time, respectively. In QH,
3.3.2. Additional analysis of stallions to examine the genetic relationship between TC402 and the other TC traits Considering TC402 as the most important trait, a comparative graph (Fig. 2) was constructed to determine the existence of losses in EBVp if 119
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Fig. 1. Mean estimated breeding value percentage (EBVp) per year for TC301 and TC365 (Fig. 1a) and for TC320 and TC402 (Fig. 1b) and the respective linear genetic trends obtained by regression over the years of birth (1981–2008) of racing Quarter horses in Brazil.
described for QH. Corrêa and Mota (2007) obtained estimates of 0.28 and 0.36 (301 m), 0.27 and 0.48 (365 m) and 0.42 and 0.68 (402 m) for speed index and final rank, respectively. Buttram et al. (1988b) reported repeatability estimates of 0.32 (365, 402 and 796 m), 0.33 (320 m) and 0.40 (201 m) for final time. The high repeatability estimates obtained in this study highlight the importance of repeated data over time for TC, suggesting that its use in selection may provide more accurate evaluations of racehorses. By representing the proportion of total variance attributable to additive and permanent environmental effects (Buttram et al., 1988b), the heritability and repeatability estimates (ignoring dominance and epistasis effects) varied mainly due to the effects of the permanent environment that occurred at the beginning of recording of animal performance, injuries and training, important variables in the life of racing animals. 4.2.2. Genetic correlations The design and execution of breeding programs require knowledge of the correlation estimates between traits in order to identify the causes of genetic and environmental variations that influence the traits due to similar or different physiological mechanisms. The genetic correlations reported in the literature (Corrêa and Mota, 2007; Silva et al., 2014; Villela et al., 2002) for racing performance were similar or higher than those obtained in the present study. Villela et al. (2002) reported a correlation of 0.99 between final time and rank. Corrêa and Mota (2007), evaluating final time, obtained correlations of 0.90 between 301 and 365 m and between 301 and 402 m and of 0.97 between 365 and 402 m. For earnings (Silva et al., 2014), the genetic correlation between ages ranged from 0.81 between 3 and 4 years to 0.99 between 3 years and total. Correlations similar to those of the present study were obtained for speed index in QH (Corrêa and Mota, 2007), with a magnitude of the genetic correlation of 0.67 between 301 and 365 m, of 0.56 between 301 and 402 m, and of 0.73 between 365 and 402 m. In this study (Table 3), the genetic correlations were higher at longer distances, in agreement with other studies investigating sprint race performance in QH (Corrêa and Mota, 2007). Lower genetic correlations were obtained when compared to the literature (Corrêa and Mota, 2007; Silva et al., 2014; Villela et al., 2002), suggesting that the definition of TC distinguishes traits according to distance. Consequently, more reliable genetic parameters are obtained. The genes responsible for performance at a given distance probably differ from those
Fig. 2. Average genetic superiority for TC402 given that the stallions were selected for TC301, TC320, TC365 and TC402 according to the percentage of selection.
Corrêa and Mota (2007) obtained heritabilities of 0.26, 0.40 and 0.41 (final time) and of 0.14, 0.19 and 0.19 (speed index) for distances of 301, 365 and 402 m, respectively. Studying QH in the United States, Mexico and Canada, Buttram et al. (1988b) estimated heritabilities of 0.38 (201 m), 0.24 (320 and 365 m), 0.28 (402 m), and 0.20 (796 m) for final time. The difference in heritabilities between the present study (Table 2) and the literature is due to several factors such as the number of records, years evaluated, presentation of the results (by distance, by age, or both), and differences in the analysis methods used. In addition, the differences in the definition of the traits based on racing performance resulted in higher estimates in the present study. The results suggest that the definition of the trait evaluated, attributing a score per race, reduced environmental variation since it standardizes the environment and permits to detect greater genetic variability. The different traits (TC301, TC320, TC365, and TC402) can thus be used as a selection criterion in breeding programs of racehorses. Given the value of h2 (Table 2) and the young age at selection, greater genetic gain may be achieved with TC301 and TC365. Similarly, the repeatability estimates were higher than those 120
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distances (301 and 320 m), with the animal participating at the beginning of its sporting career when it has less experience in competitions. The residual correlations close to zero suggest that the traits are little influenced by environmental factors that accompany the animal's life, indicating independent environmental effects according to useful life and to period during which the animals run the different racing distances. 4.3. Breeding values 4.3.1. EBV and genetic trends The mean EBVp (Table 4) indicated variability in the TC301, TC320, TC365 and TC402 traits and in the groups of animals studied, confirmed by the SD and HPD95 values. The estimates of the total group were higher than those obtained for stallions, suggesting the existence of animals that are not used as breeding animals but with the capacity to obtain superior offspring. Another factor to be considered is the existence of a reduced number of breeding animals, especially males, and the long generation interval in the Brazilian QH population as described by Faria et al. (2018). The EBVp observed for dams (Table 4) are higher than those of stallions for TC301, TC320, TC365, and TC402. According to Wilson et al. (1988), this finding can be explained by the higher quality of the pedigree information of females. In the present study, all animals with performance records had more information from the maternal grandfather, as described by Wilson et al. (1988). The balance of pedigree information for males and females must be ensured to avoid similar results. The genetic trends (Fig. 1a, b) oscillated over the 28 years evaluated, resulting in small genetic gain during this period. The results indicate the absence of firmness by breeders in maintaining desirable and stable genetic evolution, possibly because of the lack of correct evaluations of breeding animals and of adequate breeding programs for the racing line of the QH breed. The genetic trend for TC301 was the most consistent, followed by the genetic trend for TC365 (Fig. 1a). Environmental effects were more visible at the distance of 320 m (TC320). This distance had the smallest number of records (Table 1) and its prize money is lower than those of the other distances (JCS, 2019). Consequently, animals with poorer physiology and training capacity compete in these races. Furthermore, the lack of selection for this distance implied a reduction of breeding values (Fig. 1b). The genetic trends for TC402 were higher than the trends for TC 320 (Fig. 1b) and lower than those for TC301 and TC365 (Fig. 1a). These trends are influenced (oscillations over time) by the constant changes in the distances at which each animal competed and by the desire of owners to have their horses compete at the distance considered the most important (402 m) for the QH in Brazil. These constant changes in distance resulted in difficulties for the animals, which were unable to acquire the rhythm necessary to achieve success during their sporting career. The animals are less prepared for the physiological and training requirements necessary to be successful, especially in 402-m races (the most demanding distance). The genetic trends reported by Wilson et al. (1988), involving QH competing in the United States, Mexico and Canada, differed from those of this study at the distances of 320 and 402 m and were similar at 365 m. For the QH breed in Brazil, Corrêa and Mota (2007) reported different genetic trends at 301 and 402 m and a similar trend at 365 m. Wilson et al. (1988) described that distances with a larger number of competitions and animals had higher EBV. In contrast, in the present study, the larger number of records at 402 m had no influence on genetic trends. The differences with the literature are due to the different types of evaluation of each trait. However, all of them have the same objective, i.e., to evaluate the performance of horses in sprint races at different times of the animal's sporting life. Suggestions to obtain genetic gains in TC traits include to start breeding at an earlier age (selection of animals based on performance at
Fig. 3. Regressions of the EBVp of stallions for TC301, TC320 and TC365 on the EBVp of stallions for TC402 in racing Quarter Horses.
responsible at other distances, indicating that an animal that is successful at one distance may not be successful at other distances. In a study on Thoroughbreds (Mota et al., 2005), the shorter distances were run by younger animals (2 and 3 years of age) and the authors showed that the genes are not expressed in the same way during the life of the animal. Analysis of the descriptive data of the present study revealed that the animals obtained superior results at longer distances when they were older. The permanent environmental correlations between distances demonstrated a greater association between TC365 and TC402, indicating that environmental occurrences mainly affect animals at older ages, i.e., when they run these distances. The opposite is observed at the shorter 121
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Supplementary materials
shorter distance (301 m)), to increase the number and variability of families (considering the breeding values of TC trait evaluations independent of other factors), and to use breeding animals for a shorter period of time (selection of females based on performance and breeding values in shorter races). It should be noted that the results of genetic trends were obtained without considering that the TC traits were not used as selection criteria in the QH breed, demonstrating that their introduction in the breed may be promising.
Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.livsci.2019.05.013. References Buttram, S.T., Willham, R.L., Wilson, D.E., 1988a. Genetics of racing performance in the American Quarter Horse: II. Adjustment factors and contemporary groups. J. Anim. Sci. 66, 2800–2807. Buttram, S.T., Wilson, D.E., Willham, R.L., 1988b. Genetics of racing performance in the American Quarter Horse: III. Estimation of variance components. J. Anim. Sci. 66, 2808–2816. Corrêa, M.J.M., Mota, M.D.S., 2007. Genetic evaluation of performance traits in Brazilian Quarter Horse. J. Appl. Genet. 48, 145–151. https://doi.org/10.1007/BF03194672. Cunningham, E., 1975. Genetic studies in horse populations. In: Proc Int. Symp. on Genetics and Horse Breeding. Dublin. Royal Dublin Society, pp. 2–6 17-18 September. Ekiz, B., Kocak, O., 2005. Phenotypic and genetic parameter estimates for racing traits of Arabian horses in Turkey. J. Anim. Breed. Genet. 122, 349–356. https://doi.org/10. 1111/j.1439-0388.2005.00544.x. Faria, R.A.S., Maiorano, A.M., Bernardes, P.A., Pereira, G.L., Silva, M.G.B., Curi, R.A., Silva, J.A.I.V., 2018. Assessment of pedigree information in the Quarter Horse: population, breeding and genetic diversity. Livest. Sci. 214, 135–141. https://doi.org/ 10.1016/j.livsci.2018.06.001. Gaffney, B., Cunningham, E.P., 1988. Estimation of genetic trend in racing performance of thoroughbred horses. Nature. https://doi.org/10.1038/332722a0. JCS, 2019. Results [WWW Document]. Jockey Club Sorocaba. URLhttp://www. jcsorocaba.com.br/resultados/ (Accessed 14 April 2019). Kass, R.E., Carlin, B.P., Gelman, A., Neal, R.M., 1998. Markov Chain Monte Carlo in practice: a roundtable discussion. Am. Stat. 52, 93. https://doi.org/10.2307/ 2685466. Langlois, B., 1980. Heritability of racing ability in thoroughbreds – a review. Livest. Prod. Sci. 7, 591–605. López-Correa, R., Peñagaricano, F., Rovere, G., Urioste, J., 2014. Production Model assessment for ranking traits of Criollo horses participating in endurance trials. In: Proceedings, 10th World Congr. Genet. Appl. to Livest. Prod, pp. 2–5. https://doi. org/10.13140/2.1.3786.9446. Misztal, I., Tsuruta, S., Strabel, T., Auvray, B., Druet, T., Lee, D.H., 2002. BLUPF90 and related programs (BGF90). In: Proceedings of the 7th World Congress on Genetics Applied to Livestock Production, pp. 21–22. https://doi.org/9782738010520. Mota, M.D.S., Abrahão, A.R., Oliveira, H.N., 2005. Genetic and environmental parameters for racing time at different distances in Brazilian Thoroughbreds. J. Anim. Breed. Genet. 122, 393–399. https://doi.org/10.1111/j.1439-0388.2005.00551.x. Mota, M.D.S., Oliveira, H.N., Silva, R.G., Mota, B.M.D.S., 1998. Genetic and environmental factors that affect the best time of Thoroughbred horses in Brazil. J. Anim. Breed. Genet. 115, 123–129. https://doi.org/10.1111/j.1439-0388.1998.tb00335.x. Nielsen, B.D., Turner, K.K., Ventura, B.A., Woodward, A.D., O'Connor, C.I., 2006. Racing speeds of Quarter Horses, Thoroughbreds and Arabians. Equine Vet. J. 38, 128–132. https://doi.org/10.1111/j.2042-3306.2006.tb05528.x. SAS, 2011. SAS/STAT 9.3. SAS Inst. Inc., Cary, NC. Sharman, P., Wilson, A.J., 2015. Racehorses are getting faster. Biol. Lett. 11. https://doi. org/10.1098/rsbl.2015.0310. Silva, A.P.A., Curi, R.A., Langlois, B., Silva, J.A.V, 2014. Genetic parameters for earnings in quarter horse. Genet. Mol. Res. 13, 5840–5848. https://doi.org/10.4238/2014. August.1.2. Sorensen, D., Andersen, S., Gianola, D., Korsgaard, I., 1995. Bayesian inference in threshold models using Gibbs sampling. Genet. Sel. Evol. 27, 229–249. https://doi. org/10.1186/1297-9686-27-3-229. Stock, K.F., Distl, O., Hoeschele, I., 2007. Influence of priors in Bayesian estimation of genetic parameters for multivariate threshold models using Gibbs sampling. Genet. Sel. Evol. 39, 123–137. https://doi.org/10.1186/1297-9686-39-2-123. Thiruvenkadan, A.K., Kandasamy, N., Panneerselvam, S., 2009. Inheritance of racing performance of Thoroughbred horses. Livest. Sci. 121, 308–326. https://doi.org/10. 1016/j.livsci.2008.07.009. Villela, L.C.V., Mota, M.D.S., Oliveira, H.N., 2002. Genetic parameters of racing performance traits of Quarter horses in Brazil. J. Anim. Breed. Genet. 119, 229–234. https://doi.org/10.1046/j.1439-0388.2002.00338.x. Wilson, D.E., Willham, R.L., Buttram, S.T., Hoekstra, J.A., Luecke, G.R., 1988. Genetics of racing performance in the American Quarter Horse: IV. Evaluation using a reduced animal model with repeated records. J. Anim. Sci. 66, 2817–2825.
4.3.2. Additional analysis of stallions to examine the genetic relationship between TC402 and the other time class traits The results (Fig. 2) indicated that, although the correlations between the TC traits were high, the probable genetic gain in 402 m races would be lower when stallions are selected for TC301, TC320 and TC365 rather than for the TC402. One exception was a small group (10%) of animals at 320 m (TC320) with the capacity to exhibit higher EBVp at 402 m (Fig. 3). The values described indicated that selection for each distance has different objectives. The choice of the ideal distance when selecting a stallion depends on different factors. The ideal would be to obtain horses that are capable of producing champion offspring at all distances. However, the present results indicate major difficulties in achieving this goal since, to obtain offspring with high athletic skills at the most popular and competitive distance (402 m), stallions must be selected for TC402. The fact that offspring first compete at shorter distances is part of the physiological evolution and training of athletic horses and the final goal is to be champion at the distance of 402 m. 5. Conclusion The estimation of genetic parameters for sprint racing performance in horses by Bayesian inference in multivariate analysis using a threshold animal model was found to be a suitable alternative for the study of categorical traits transformed from continuous traits because it provides consistent results of high accuracy. The TC traits, evaluating records of sprint racing performance, can be used as a selection criterion by associations, breeders and trainers of QH, with the possibility of genetic gain if applied in breeding programs. Acknowledgments The authors wish to thank the Jockey Clube de Sorocaba (JCS, Brazil) for providing the data used in this study. We thank Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Capes, Brazil) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, Brazil). The authors thank the reviewers of Livestock Science for their suggestions. Funding This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil (Finance Code 001). PhD fellowship granted (PROEX- Program of Academic Excellence) (88882.180634/2018-01) to Ricardo Faria and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, Brazil) productivity grant to Prof. J. Augusto II.
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Time class for racing performance of the Quarter Horse: Genetic parameters and trends using Bayesian and multivariate threshold models
T
Ricardo António Silva Fariaa, , Amanda Marchi Maioranoa, Luiz Eduardo Cruz dos Santos Correiaa, Mário Luiz Santana Jrb, Josineudson Augusto II Vasconcelos Silvac ⁎
a
Universidade Estadual Paulista (Unesp), Faculdade de Ciências Agrárias e Veterinárias, PO Box 14884-900 Jaboticabal, São Paulo, Brasil Universidade Federal de Rondonópolis, PO Box 78735-901, Rondonópolis, MT, Brasil c Universidade Estadual Paulista (Unesp), Faculdade de Medicina Veterinária e Zootecnia, PO Box 18618-000 Botucatu, São Paulo, Brasil b
ARTICLE INFO
ABSTRACT
Keywords: Horserace Heritability Hippodrome Repeatability Speed
The aim of this study was to evaluate racing performance in the Quarter Horse breed in Brazil using genetic parameter estimates, breeding values, and genetic trends for a differentiated trait, time class (TC), at four different distances. The speed records comprising races that occurred between 1981 and 2011 were obtained from hippodromes in the states of São Paulo, Ceará, Brasília, and Mato Grosso do Sul. The final archive analysed contained 4263 horses born to 431 stallions and 1716 dams. These animals participated in 3904 races, providing 17,342 records of final racing time. The four TC traits were defined by 5 scores based on the final times (in seconds) of each animal in each race. The scores for formation of the classes were attributed within each race based on the percent difference from winner's time. Time class was evaluated at distances of 301, 320, 365 and 402 m, generating four phenotypic measures: TC301, TC320, TC365 and TC402, respectively. The genetic parameters were estimated by Bayesian inference in multivariate analysis using a threshold animal model. The model included the fixed effects of race, sex and age class of animal in the race, in addition to additive genetic, animal permanent environmental and residual random effects. The mean heritability estimates were of high magnitude and ranged from 0.45 ± 0.06 (TC402) to 0.56 ± 0.04 (TC365). Repeatability estimates ranged from 0.78 ± 0.06 (TC402) to 0.97 ± 0.01 (TC320). The additive genetic and animal permanent environmental correlations were positive, with mean correlations ranging from 0.33 ± 0.06 between TC301 and TC320 to 0.62 ± 0.06 between TC365 and TC402 and from 0.44 ± 0.08 between TC301 and TC320 to 0.58 ± 0.06 between TC365 and TC402, respectively. The mean breeding values transformed by the cumulative distribution function of the standard normal distribution ranged from 54.6 ± 25.3 (TC365) to 57.8 ± 28.5 (TC320) in the group of animals included in the pedigree and born after 1980. The genetic trends observed indicated that TC301 (301 m) exhibited the greatest evolution between 1981 and 2008. The results suggest the possible use of TC traits as selection criteria since they respond positively to selection, permitting genetic gains in breeding programs of racehorses.
1. Introduction The Quarter Horse (QH) breed dates back to the 17th century in the current United States and is a versatile breed used for cutting, conformation and racing. The last attribute, which originated from the Thoroughbred breed, makes the racing line of the QH breed the fastest horse in the world over short distances (Nielsen et al., 2006), with a maximum speed when crossing the finish line of 92.6 km/h. The genetic fitness of horses with high performance in sprint races is complex and
⁎
depends on various environmental factors that will affect the capacity of a horse to become a champion. Racing performance is the main phenotype used to compose selection criteria for speed in horses, with the application of different definitions and traits. In the main racing breed (Thoroughbred) from which QH originated, Sharman and Wilson (2015) observed improvements in final time over the years (1850 to 2012). However, a plateau (stagnation) of racing time was suggested for the first time by Cunningham (1975), and other authors agreed (Gaffney and
Correspondence to: FMVZ - Unesp, DMNA - Fazenda Experimental Lageado, Rua José Barbosa de Barros, n° 1780, CEP: 18.618-307, Botucatu, SP, Brasil. E-mail addresses: [email protected] (R.A.S. Faria), [email protected] (J.A.I.V. Silva).
https://doi.org/10.1016/j.livsci.2019.05.013 Received 8 January 2019; Received in revised form 13 May 2019; Accepted 13 May 2019 Available online 14 May 2019 1871-1413/ © 2019 Elsevier B.V. All rights reserved.
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Cunningham, 1988; Langlois, 1980; Thiruvenkadan et al., 2009) that the animals may have reached their limit of race speed. Nevertheless, Sharman and Wilson (2015) emphasized that this stagnation might be due to the small number of animals studied and the exclusive use of winning time of the animals and elite racing performance. The same phenomenon (plateau) may be happening in the QH breed, but studies are necessary that allow the discussions described for the Thoroughbred breed. Studies on racehorse performance of the QH breed have estimated heritability and repeatability for final time and final rank (Villela et al., 2002), final time and speed index (Corrêa and Mota, 2007), earnings (Silva et al., 2014), and final time (Buttram et al., 1988b), demonstrating little difference in the traits studied and heritability estimates of low and moderate magnitude. These findings indicate the need for identifying a new trait that could be used as a selection criterion. López-Correa et al. (2014) used percent differences in winner's time per race in endurance competitions of Criollo horses in Uruguay. The authors pointed out that one advantage of forming classes (score) from winner's time would be to place animals with small differences in the final racing result on the same level. The authors were thus able to better identify additive genetic variance among horses. Following this line of reasoning, it would be interesting to use a score ranging from 5 to 1 applied to racing performance of horses. The time class (TC) trait was thus developed, in which the animals are ranked based on the percentage comparison of final winner's time in each race. Stock et al. (2007) showed that it is possible to provide reliable estimates for the evaluation of categorical traits similar to TC. The authors estimated (co)variances by simulating phenotypic data using multivariate Bayesian inference under a threshold animal model. The objective of this study was to evaluate the racing performance of QH and to estimate genetic parameters, breeding values and genetic trends for Time Class at different distances.
Table 1 Description of the speed racing data by time class traits and total of the Quarter Horse breed in Brazil. Item
Traits TC301
TC320
TC365
TC402
Animals, n Males, % Races, n Mean animals per race, n Records, n Records males, % Males records 3 years, % Males records 4 years, % Males records 5 years, % Males records 6 years, %
2301 41.3 1039 4.1 4284 42.7 41.0 43.3 43.8 66.7
1490 38.2 464 4.6 2134 38.2 36.4 43.6 68.2 50.6
2638 42.4 1072 4.4 4705 41.6 41.5 42.9 55.0 58.3
2718 44.3 1329 4.7 6219 43.8 41.9 50.4 58.0 78.6
Total 4263 41.9 3904 4.4 17,342 42.4 40.9 45.0 52.7 66.2
TC301 = time class at 301 m; TC320 = time class at 320 m; TC365 = time class at 365 m; TC402 = time class at 402 m. n = number.
to 1.0%, 1.01% to 3.0%, 3.01% to 5.0% and > 5.0% in relation to the final time of the winner, respectively. Time class was defined as four different traits according to distance in each race: TC301, TC320, TC365, and TC402 m (Table 1). 2.3. Data analysis The (co)variance components and genetic parameters (heritability, repeatability, and genetic correlations) of the TC traits were estimated by Bayesian inference in multivariate analysis under a threshold animal model. The analyses were performed using the THRGIBBS1F90 program (Misztal et al., 2002). The Gibbs post-sampling estimates were obtained with the POSTGIBBSF90 program (Misztal et al., 2002). The statistical model used for the four traits (TC301, TC320, TC365, and TC402) included the fixed effects of race, sex and age class of animal, in addition to additive genetic, animal permanent environmental and residual random effects. The effects of hippodrome, racing data or type of racetrack were not considered in the analysis because they are absorbed by including the effect of race. The matrix form of the model can be written as follows:
2. Material and methods 2.1. Data description The racing performance records of QH were provided by the Sorocaba Jockey Club (JCS) and comprised the data of races that occurred between 1981 and 2011 in hippodromes of the states of São Paulo (94.6%) and Ceará, Brasília and Mato Grosso do Sul. The database contained information about the name of the animal, stallion and mare, sex, date of birth, number of races, age of animal, race distance, and final racing time. The phenotype file analysed contained 4263 horses (males and females), born to 431 stallions (range: 1–318 progeny) and 1716 dams (range: 1–12 progeny), which participated in 3904 races. There were 17,342 records of racing time. The quality of the data was analysed using the SAS/STAT® program (SAS, 2011) and animals with incomplete data, pedigree errors and participating in races with fewer than three animals were removed. The age of the animals at race ranged from 2 to 11 years, with a mean of 3.2 years. Two-year-old animals (only 457) were grouped with 3-year-old animals and animals aged 6 years or older were also grouped (only 147). In the analysis of the data, age at race was included as a fixed effect, with four age classes (3, 4, 5, and 6 years). The pedigree file was compiled from the 4263 animals with records and their ascendants up to the fifth generation. The final file contained 6284 animals, born to 873 stallions and 2051 dams.
= X + Z1 + Z2 c + e,
(1)
where y is the vector of observations (TC traits); β is the vector of fixed effects; α is the vector of random effects that represent the additive direct breeding values of the animal; c is the vector of permanent environmental effects; e is the vector of residual random effects, and X, Z1 and Z2 are incidence matrices that relate the observations to the fixed effects, direct additive genetic random effects and uncorrelated permanent environmental random effects, respectively. For the threshold model, the assumption was that the underlying scale has a continuous normal distribution as follows:
U|
N (W , I e2),
(2)
where U is the vector of the underlying scale of order r; Ɵ’=(β’, α’, c’) is the vector of location parameters of order s, with β being defined as systematic effects, α is the additive genetic effect and c is the permanent environmental effect of the animal; W is the known incidence matrix of order r × s; I is the identity matrix of order r × r, and e2 is the residual variance. In multivariate analysis containing categorical variables, according to the Bayesian approach, vectors β, α and c are location parameters of a conditional distribution y | β, α, c. The a priori assumption was that β has a uniform distribution that reflects vague prior knowledge about this vector. Inverse Wishart distributions were attributed to the other components. Thus, the distribution of y, given the scale parameters, can be written as:
2.2. Description of the trait The time class (TC) trait was defined by 5 scores based on the final times (in seconds) of each animal in each race. The scores for formation of the classes were attributed within each race based on the percent difference from winner's time. Class 5 comprises animals with a final time of 0.10% or less in relation to final winner's time, including the winner. Classes 4, 3, 2 and 1 include animals with a final time of 0.11%
( | , a , c, R) N [X + Za a + Wc c, IN R]
(3)
The traits analysed are categorical variables and are determined by 117
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non-observable continuous variables on an underlying scale, in which the initial threshold values are fixed: t1 < t2 … < tj − 1, with t0 = −∞ and tj = ∞, where j is the number of categories. The categories or scores of yi (TC), for each animal i, are defined by Ui on the underlying scale:
Yi = (1) t 0 < Ui < Ui
t1; (2) t1 < Ui
t2; (3) t2 < Ui
t3; (4) t3 < Ui
mean number of animals per race. The smallest amount of information was available for TC320, with 12% of records, 13% of races, and a higher proportion of female participants. The age classes corresponded to 81.3% (≤3 years), 14.6% (4 years), 3.3% (5 years), and 0.9% (≥ 6 years) of all records. Considering all distances (four different traits), females had the largest number of records. However, different values were obtained when the number of records at the different ages was analysed (Table 1). A larger number of records was obtained for males when older animals were considered (≥5 years). The characteristics of the track were the same for all hippodromes and all races were performed in a straight line at the distances studied. The reason for using hippodromes from different states was to cover the whole database. Animals from the hippodromes of Ceará, Brasília and Mato Grosso do Sul (5.4%) were found to be relationship to the animals competing in the hippodromes of the State of São Paulo.
t4; (5) t4 (4)
t5, for i = 1, ...,n ,
where n is the number of observations. After specification of the thresholds t0 to t5, one of the thresholds (t0 to t5) needed to be adjusted to an arbitrary constant. In this study, t1 was set at 0, with the vector of estimable thresholds being defined as t = t2, t3 and t4. A single chain of 1100,000 cycles was defined for Gibbs sampling, with a burn-in period of 100,000 cycles. This number was chosen after verification of the stationary stage of the chain by graphic inspection (Kass et al., 1998). Samples were stored every 20 iterations, totalling 50,000 samples which were used for computing (co)variance components to obtain the posterior mean, standard deviation, median, mode, and highest posterior density at 95% (HPD95) of the genetic parameters. The minimum effective sample size (ESS) of the (co)variance components indicates the number of independent samples with information equivalent to those present in the dependent sample (Sorensen et al., 1995). Thus, the ESS obtained in the present study indicates the convergence of the Gibbs chain. The posterior estimated breeding values (EBV) were obtained using BLUP procedures and the analyses were performed with the THRGIBBS1F90 program (Misztal et al., 2002) using the “OPTION fixed_var mean” tool. The genetic and residual (co)variances obtained in the final analysis of this study were used to calculate EBV. The EVB solutions, obtained from the underlying scale, were transformed by means of a cumulative distribution function (CDF) of the standard normal distribution into a percentage scale and were called estimated breeding value percentage (EBVp). These estimates were calculated with the SAS/STAT® software (SAS, 2011) using the expression:
EBVp = CDF ( NORMAL, x,
,
),
3.2. Genetic parameter estimates 3.2.1. Heritability and repeatability Analysis of the chains generated with the THRGIBSS2F90 program showed that the burn-in period and sampling interval were sufficient to confirm convergence of the chain. For all traits studied, few differences were observed between the measures of central tendency of the estimated parameters, indicating symmetry in the posterior distributions. The minimum ESS of the (co)variance components was > 150 cycles for TC320 and > 1200 cycles for the other traits. The heritability and repeatability estimates for the TC traits were of moderate to high magnitude (Table 2). Heritability estimates ranged from 0.45 ± 0.06 (TC402) to 0.56 ± 0.04 (TC365) and the repeatability estimate was higher than 0.78 (TC402). The measures of central tendency were similar for both heritability and repeatability, with short HPD95 intervals (Table 2). 3.2.2. Genetic correlations The additive genetic correlations between TC traits (Table 3) were moderate between TC301 and TC320 (0.33 ± 0.07) and high between TC365 and TC402 (0.62 ± 0.04). TC402 showed the highest additive genetic correlations with the other traits. The correlations of the animal permanent environment between TC traits were high and ranged from 0.44 ± 0.08 between TC301 and TC320 to 0.58 ± 0.06 between TC365 and TC401, following the same trends as the additive genetic correlations. The residual correlations were close to zero, with a correlation of 0.03 ± 0.06, 0.06 ± 0.03 and 0.02 ± 0.04 for TC301 with TC320, TC365 and TC402, respectively. The residual correlation between the largest distance traits, TC365 and TC402, was 0.04 ± 0.03.
(5)
where x is a numerical random variable, θ is a numerical location parameter, and λ is a numerical scale parameter. The EBVp for the four TC traits refer to 4508 animals born between 1981 and 2008, a period considering the beginning of racing records and the birth of the last breeding animals evaluated. The EBVp for stallions (n = 139) and dams (n = 1118) over the same period are also described. The EBVp were used to calculate genetic trends as the regression of breeding values per year of birth of the animals (from 1981 to 2008). The results are illustrated in a graph as the annual means of the four TC traits and their respective linear trend lines. Additional analyses were performed for all stallions in the pedigree (n = 873), which allowed observation of the genetic relationship between the TC traits based on EBVp, comparing average genetic superiority as a function of the selected proportion of stallions. Trait TC402 was used as the reference (because it contained the largest number of records and the highest earnings), permitting to verify the stallions at 402 m if they were selected based on EBVp for TC301, TC320, TC365, and TC402. We also calculated the regression of EBVp of stallions for TC301, TC320 and TC365 on the EBVp of stallions for TC402 in order to consolidate the results obtained for stallions of the QH breed in Brazil.
Table 2 Descriptive statistics of posterior heritability and repeatability estimates obtained by Bayesian analysis for time class in Quarter Horses. Item Heritability Mean ± SD Median Mode HPD95 Repeatability Mean ± SD Median Mode HPD95
3. Results 3.1. Data
Trait TC301
TC320
TC365
TC402
0.52 ± 0.04 0.52 0.50 0.44–0.66
0.48 ± 0.06 0.48 0.44 0.38–0.60
0.56 ± 0.04 0.56 0.56 0.49–0.63
0.45 ± 0.06 0.46 0.50 0.31–0.55
0.85 ± 0.04 0.84 0.86 0.79–0.93
0.97 ± 0.01 0.98 0.95 0.94–0.99
0.88 ± 0.02 0.88 0.85 0.80–0.91
0.78 ± 0.06 0.79 0.83 0.65–0.87
TC301 = time class at 301 m; TC320 = time class at 320 m; TC365 = time class at 365 m; TC402 = time class at 402 m. HPD95 = highest posterior density at 95%.
Among the traits analysed, TC402 had the largest number of data (Table 1), with 36% of records and 34% of races, as well as the largest 118
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stallions were selected based on the EBVp for the other TC traits. The values observed indicate a reduction in average genetic superiority for TC402 if selection were performed for TC301, TC320 and TC365. However, the fraction of the top 10% of reproducers at the distance of 320 m (TC320) obtained results similar to those of stallions at the distance of 402 m (TC402). After the top 10% of selected stallions, the genetic superiority of 320 m declines and is identical to the distances of 301 and 365 m. The average superiority of the top 50% of stallions (Fig. 2) selected for TC402 is 45.6% (EBVp). If selection were performed for TC301, TC320 and TC365, the superiority in the response of the observed scale would be only 34.1%, 39.1% and 33.6%, respectively. Regression of the EBVp of stallions (Fig. 3) for TC301, TC320 and TC365 on the EBVp of stallions for TC402 confirmed the results shown in Fig. 2. If the offspring of stallions selected for TC402 (Fig. 3) competed at 402 m and obtained an increase of 1.00%, the values of offspring born to stallions selected for TC301, TC320 and TC365 would only be 0.29%, 0.71% and 0.27%, respectively, of this increased unit when competing at 402 m.
Table 3 Additive genetic (above the diagonal) and animal permanent environmental correlations (below the diagonal) between the time class (TC) traits in Quarter Horses. Trait TC301 TC320 TC365 TC402
TC301 ± SD ± ± ± ±
SD SD SD SD
0.44 ± 0.08 0.53 ± 0.06 0.52 ± 0.07
TC320 ± SD
TC365 ± SD
TC402 ± SD
0.33 ± 0.07
0.46 ± 0.06 0.38 ± 0.07
0.52 ± 0.07 0.54 ± 0.07 0.62 ± 0.06
0.45 ± 0.07 0.49 ± 0.08
0.58 ± 0.06
TC301 = time class at 301 m; TC320 = time class at 320 m; TC365 = time class at 365 m; TC402 = time class at 402 m. Table 4 Mean, standard deviation and highest posterior density at 95% (HPD95) of the estimated breeding value percentage (EBVp) for all time class traits in all animals, stallions and dams included in the pedigree (born after 1980) of racing Quarter Horses. Trait TC30a Totala Stallionsa Damsa TC320 Totala Stallionsa Damsa TC365 Totala Stallionsa Damsa TC402 Totala Stallionsa Damsa
Estimated breeding value percentage Mean ± SD,%
HPD95, %
55.2 ± 25.8 47.9 ± 26.2 51.0 ± 26.9
4.57–96.3 2.72–92.0 1.90–95.6
57.8 ± 28.5 47.3 ± 33.2 53.2 ± 29.8
9.12–98.5 3.64–97.3 6.36–97.8
54.6 ± 25.3 47.5 ± 24.6 52.2 ± 26.9
4.81–94.8 6.47–90.8 1.95–95.6
56.9 ± 28.4 48.0 ± 32.4 52.7 ± 28.8
8.76–98.8 4.96–97.9 8.24–97.8
4. Discussion 4.1. Data The difference in the number of records per distance in the data analysed (Table 1) when compared to the racing data of QH in the United States, Mexico and Canada (Buttram et al., 1988a), with a total number of records of 561,738; 368,846 and 92,664 for the distances of 320, 365 and 402 m, respectively, indicates divergence in the training guidelines of horses among countries. The number of animals participating in the distance of 320 m described by Buttram et al. (1988a) was higher than that of the present study, a finding suggesting the lack of interest of Brazilian horse owners for the distance of 320 m. The longest distance (402 m) analysed in the present study is the preference of breeders because of greater earnings (JCS, 2019) and because the breed is specialized at this distance. A higher frequency of competing females (Table 1) has also been described for other racing breeds, Arabian (Ekiz and Kocak, 2005) and Thoroughbred horses (Mota et al., 2005, 1998), as well as for the QH breed (Buttram et al., 1988a; Corrêa and Mota, 2007; Silva et al., 2014). Evaluating all observations (Table 1), there was a trend towards a larger number of females at the four distances studied. However, when the records of older animals (≥5 years) were considered, there was a larger number of male records. Reproductive factors were probably the main reason for the shift in the number of records between sexes with increasing age of the animals, in which mares are removed earlier from competitions for breeding. The use of embryo transfer will permit mares to simultaneously compete and breed. The larger number of female records in the younger age classes remains to be explained.
TC301 = time class at 301 m; TC320 = time class at 320 m; TC365 = time class at 365 m; TC402 = time class at 402 m. HPD95 = highest posterior density at 95%. a Animals, stallions and dams included in the pedigree born after 1980.
3.3. Breeding values 3.3.1. EBV and genetic trends The mean EBVp were similar in the groups studied (total animals, stallions, and dams) for all TC traits (Table 4). The lowest and highest mean EBVp were observed for TC320 in the group of stallions (47.3 ± 33.2) and in the total animal group (57.8 ± 28.5), respectively. The SD values and variation (HPD95) were high and similar in the groups of animals (Table 4). The lowest SD values were observed for the highest mean EBVp. The shortest HPD95 interval ranged from 6.47% to 90.8% (TC365, stallions) and the greatest interval from 1.9% to 95.6% (TC301, dams). The genetic trends (Fig. 1) per year of birth of the animals (1981 to 2008) increased over time for TC301 and TC365, while the genetic trend for TC402 was close to zero. A negative genetic trend was observed for TC320. Oscillations in the annual mean EBVp were observed for all traits, with similar values for TC301 and TC365 and for TC320 and TC402. The difference in the annual mean EBVp (Fig. 1) between the first (1981) and last year (2008) evaluated was 12.3% (TC301), 0.9% (TC320), 7.1% (TC365), and 4.5% (TC402). The annual genetic changes in EBVp were 0.4% (TC301), −0.1% (TC320), 0.3% (TC365), and 0.1% (TC402).
4.2. Genetic parameter estimates 4.2.1. Heritability and repeatability The heritability and repeatability estimates (Table 2) of the traits studied were of moderate to high magnitude. The fact that the definition of the traits is used for the first time to designate phenotypes of horserace records impairs the comparison with other studies. However, considering published studies reporting race records at similar distances, the estimated values were found to be superior. Although the traits were defined differently, the higher values are probably due to the use of categories, grouping animals next to the winner, and to the application of nonlinear models. These approaches may have allowed better identification of additive variance in the population. In Brazil, a combined analysis of QH at distances of 275, 301, 320, 365, 402 and 503, Villela et al. (2002) reported heritability estimates of 0.14 and 0.17 for final rank and final time, respectively. In QH,
3.3.2. Additional analysis of stallions to examine the genetic relationship between TC402 and the other TC traits Considering TC402 as the most important trait, a comparative graph (Fig. 2) was constructed to determine the existence of losses in EBVp if 119
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Fig. 1. Mean estimated breeding value percentage (EBVp) per year for TC301 and TC365 (Fig. 1a) and for TC320 and TC402 (Fig. 1b) and the respective linear genetic trends obtained by regression over the years of birth (1981–2008) of racing Quarter horses in Brazil.
described for QH. Corrêa and Mota (2007) obtained estimates of 0.28 and 0.36 (301 m), 0.27 and 0.48 (365 m) and 0.42 and 0.68 (402 m) for speed index and final rank, respectively. Buttram et al. (1988b) reported repeatability estimates of 0.32 (365, 402 and 796 m), 0.33 (320 m) and 0.40 (201 m) for final time. The high repeatability estimates obtained in this study highlight the importance of repeated data over time for TC, suggesting that its use in selection may provide more accurate evaluations of racehorses. By representing the proportion of total variance attributable to additive and permanent environmental effects (Buttram et al., 1988b), the heritability and repeatability estimates (ignoring dominance and epistasis effects) varied mainly due to the effects of the permanent environment that occurred at the beginning of recording of animal performance, injuries and training, important variables in the life of racing animals. 4.2.2. Genetic correlations The design and execution of breeding programs require knowledge of the correlation estimates between traits in order to identify the causes of genetic and environmental variations that influence the traits due to similar or different physiological mechanisms. The genetic correlations reported in the literature (Corrêa and Mota, 2007; Silva et al., 2014; Villela et al., 2002) for racing performance were similar or higher than those obtained in the present study. Villela et al. (2002) reported a correlation of 0.99 between final time and rank. Corrêa and Mota (2007), evaluating final time, obtained correlations of 0.90 between 301 and 365 m and between 301 and 402 m and of 0.97 between 365 and 402 m. For earnings (Silva et al., 2014), the genetic correlation between ages ranged from 0.81 between 3 and 4 years to 0.99 between 3 years and total. Correlations similar to those of the present study were obtained for speed index in QH (Corrêa and Mota, 2007), with a magnitude of the genetic correlation of 0.67 between 301 and 365 m, of 0.56 between 301 and 402 m, and of 0.73 between 365 and 402 m. In this study (Table 3), the genetic correlations were higher at longer distances, in agreement with other studies investigating sprint race performance in QH (Corrêa and Mota, 2007). Lower genetic correlations were obtained when compared to the literature (Corrêa and Mota, 2007; Silva et al., 2014; Villela et al., 2002), suggesting that the definition of TC distinguishes traits according to distance. Consequently, more reliable genetic parameters are obtained. The genes responsible for performance at a given distance probably differ from those
Fig. 2. Average genetic superiority for TC402 given that the stallions were selected for TC301, TC320, TC365 and TC402 according to the percentage of selection.
Corrêa and Mota (2007) obtained heritabilities of 0.26, 0.40 and 0.41 (final time) and of 0.14, 0.19 and 0.19 (speed index) for distances of 301, 365 and 402 m, respectively. Studying QH in the United States, Mexico and Canada, Buttram et al. (1988b) estimated heritabilities of 0.38 (201 m), 0.24 (320 and 365 m), 0.28 (402 m), and 0.20 (796 m) for final time. The difference in heritabilities between the present study (Table 2) and the literature is due to several factors such as the number of records, years evaluated, presentation of the results (by distance, by age, or both), and differences in the analysis methods used. In addition, the differences in the definition of the traits based on racing performance resulted in higher estimates in the present study. The results suggest that the definition of the trait evaluated, attributing a score per race, reduced environmental variation since it standardizes the environment and permits to detect greater genetic variability. The different traits (TC301, TC320, TC365, and TC402) can thus be used as a selection criterion in breeding programs of racehorses. Given the value of h2 (Table 2) and the young age at selection, greater genetic gain may be achieved with TC301 and TC365. Similarly, the repeatability estimates were higher than those 120
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distances (301 and 320 m), with the animal participating at the beginning of its sporting career when it has less experience in competitions. The residual correlations close to zero suggest that the traits are little influenced by environmental factors that accompany the animal's life, indicating independent environmental effects according to useful life and to period during which the animals run the different racing distances. 4.3. Breeding values 4.3.1. EBV and genetic trends The mean EBVp (Table 4) indicated variability in the TC301, TC320, TC365 and TC402 traits and in the groups of animals studied, confirmed by the SD and HPD95 values. The estimates of the total group were higher than those obtained for stallions, suggesting the existence of animals that are not used as breeding animals but with the capacity to obtain superior offspring. Another factor to be considered is the existence of a reduced number of breeding animals, especially males, and the long generation interval in the Brazilian QH population as described by Faria et al. (2018). The EBVp observed for dams (Table 4) are higher than those of stallions for TC301, TC320, TC365, and TC402. According to Wilson et al. (1988), this finding can be explained by the higher quality of the pedigree information of females. In the present study, all animals with performance records had more information from the maternal grandfather, as described by Wilson et al. (1988). The balance of pedigree information for males and females must be ensured to avoid similar results. The genetic trends (Fig. 1a, b) oscillated over the 28 years evaluated, resulting in small genetic gain during this period. The results indicate the absence of firmness by breeders in maintaining desirable and stable genetic evolution, possibly because of the lack of correct evaluations of breeding animals and of adequate breeding programs for the racing line of the QH breed. The genetic trend for TC301 was the most consistent, followed by the genetic trend for TC365 (Fig. 1a). Environmental effects were more visible at the distance of 320 m (TC320). This distance had the smallest number of records (Table 1) and its prize money is lower than those of the other distances (JCS, 2019). Consequently, animals with poorer physiology and training capacity compete in these races. Furthermore, the lack of selection for this distance implied a reduction of breeding values (Fig. 1b). The genetic trends for TC402 were higher than the trends for TC 320 (Fig. 1b) and lower than those for TC301 and TC365 (Fig. 1a). These trends are influenced (oscillations over time) by the constant changes in the distances at which each animal competed and by the desire of owners to have their horses compete at the distance considered the most important (402 m) for the QH in Brazil. These constant changes in distance resulted in difficulties for the animals, which were unable to acquire the rhythm necessary to achieve success during their sporting career. The animals are less prepared for the physiological and training requirements necessary to be successful, especially in 402-m races (the most demanding distance). The genetic trends reported by Wilson et al. (1988), involving QH competing in the United States, Mexico and Canada, differed from those of this study at the distances of 320 and 402 m and were similar at 365 m. For the QH breed in Brazil, Corrêa and Mota (2007) reported different genetic trends at 301 and 402 m and a similar trend at 365 m. Wilson et al. (1988) described that distances with a larger number of competitions and animals had higher EBV. In contrast, in the present study, the larger number of records at 402 m had no influence on genetic trends. The differences with the literature are due to the different types of evaluation of each trait. However, all of them have the same objective, i.e., to evaluate the performance of horses in sprint races at different times of the animal's sporting life. Suggestions to obtain genetic gains in TC traits include to start breeding at an earlier age (selection of animals based on performance at
Fig. 3. Regressions of the EBVp of stallions for TC301, TC320 and TC365 on the EBVp of stallions for TC402 in racing Quarter Horses.
responsible at other distances, indicating that an animal that is successful at one distance may not be successful at other distances. In a study on Thoroughbreds (Mota et al., 2005), the shorter distances were run by younger animals (2 and 3 years of age) and the authors showed that the genes are not expressed in the same way during the life of the animal. Analysis of the descriptive data of the present study revealed that the animals obtained superior results at longer distances when they were older. The permanent environmental correlations between distances demonstrated a greater association between TC365 and TC402, indicating that environmental occurrences mainly affect animals at older ages, i.e., when they run these distances. The opposite is observed at the shorter 121
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Supplementary materials
shorter distance (301 m)), to increase the number and variability of families (considering the breeding values of TC trait evaluations independent of other factors), and to use breeding animals for a shorter period of time (selection of females based on performance and breeding values in shorter races). It should be noted that the results of genetic trends were obtained without considering that the TC traits were not used as selection criteria in the QH breed, demonstrating that their introduction in the breed may be promising.
Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.livsci.2019.05.013. References Buttram, S.T., Willham, R.L., Wilson, D.E., 1988a. Genetics of racing performance in the American Quarter Horse: II. Adjustment factors and contemporary groups. J. Anim. Sci. 66, 2800–2807. Buttram, S.T., Wilson, D.E., Willham, R.L., 1988b. Genetics of racing performance in the American Quarter Horse: III. Estimation of variance components. J. Anim. Sci. 66, 2808–2816. Corrêa, M.J.M., Mota, M.D.S., 2007. Genetic evaluation of performance traits in Brazilian Quarter Horse. J. Appl. Genet. 48, 145–151. https://doi.org/10.1007/BF03194672. Cunningham, E., 1975. Genetic studies in horse populations. In: Proc Int. Symp. on Genetics and Horse Breeding. Dublin. Royal Dublin Society, pp. 2–6 17-18 September. Ekiz, B., Kocak, O., 2005. Phenotypic and genetic parameter estimates for racing traits of Arabian horses in Turkey. J. Anim. Breed. Genet. 122, 349–356. https://doi.org/10. 1111/j.1439-0388.2005.00544.x. Faria, R.A.S., Maiorano, A.M., Bernardes, P.A., Pereira, G.L., Silva, M.G.B., Curi, R.A., Silva, J.A.I.V., 2018. Assessment of pedigree information in the Quarter Horse: population, breeding and genetic diversity. Livest. Sci. 214, 135–141. https://doi.org/ 10.1016/j.livsci.2018.06.001. Gaffney, B., Cunningham, E.P., 1988. Estimation of genetic trend in racing performance of thoroughbred horses. Nature. https://doi.org/10.1038/332722a0. JCS, 2019. Results [WWW Document]. Jockey Club Sorocaba. URLhttp://www. jcsorocaba.com.br/resultados/ (Accessed 14 April 2019). Kass, R.E., Carlin, B.P., Gelman, A., Neal, R.M., 1998. Markov Chain Monte Carlo in practice: a roundtable discussion. Am. Stat. 52, 93. https://doi.org/10.2307/ 2685466. Langlois, B., 1980. Heritability of racing ability in thoroughbreds – a review. Livest. Prod. Sci. 7, 591–605. López-Correa, R., Peñagaricano, F., Rovere, G., Urioste, J., 2014. Production Model assessment for ranking traits of Criollo horses participating in endurance trials. In: Proceedings, 10th World Congr. Genet. Appl. to Livest. Prod, pp. 2–5. https://doi. org/10.13140/2.1.3786.9446. Misztal, I., Tsuruta, S., Strabel, T., Auvray, B., Druet, T., Lee, D.H., 2002. BLUPF90 and related programs (BGF90). In: Proceedings of the 7th World Congress on Genetics Applied to Livestock Production, pp. 21–22. https://doi.org/9782738010520. Mota, M.D.S., Abrahão, A.R., Oliveira, H.N., 2005. Genetic and environmental parameters for racing time at different distances in Brazilian Thoroughbreds. J. Anim. Breed. Genet. 122, 393–399. https://doi.org/10.1111/j.1439-0388.2005.00551.x. Mota, M.D.S., Oliveira, H.N., Silva, R.G., Mota, B.M.D.S., 1998. Genetic and environmental factors that affect the best time of Thoroughbred horses in Brazil. J. Anim. Breed. Genet. 115, 123–129. https://doi.org/10.1111/j.1439-0388.1998.tb00335.x. Nielsen, B.D., Turner, K.K., Ventura, B.A., Woodward, A.D., O'Connor, C.I., 2006. Racing speeds of Quarter Horses, Thoroughbreds and Arabians. Equine Vet. J. 38, 128–132. https://doi.org/10.1111/j.2042-3306.2006.tb05528.x. SAS, 2011. SAS/STAT 9.3. SAS Inst. Inc., Cary, NC. Sharman, P., Wilson, A.J., 2015. Racehorses are getting faster. Biol. Lett. 11. https://doi. org/10.1098/rsbl.2015.0310. Silva, A.P.A., Curi, R.A., Langlois, B., Silva, J.A.V, 2014. Genetic parameters for earnings in quarter horse. Genet. Mol. Res. 13, 5840–5848. https://doi.org/10.4238/2014. August.1.2. Sorensen, D., Andersen, S., Gianola, D., Korsgaard, I., 1995. Bayesian inference in threshold models using Gibbs sampling. Genet. Sel. Evol. 27, 229–249. https://doi. org/10.1186/1297-9686-27-3-229. Stock, K.F., Distl, O., Hoeschele, I., 2007. Influence of priors in Bayesian estimation of genetic parameters for multivariate threshold models using Gibbs sampling. Genet. Sel. Evol. 39, 123–137. https://doi.org/10.1186/1297-9686-39-2-123. Thiruvenkadan, A.K., Kandasamy, N., Panneerselvam, S., 2009. Inheritance of racing performance of Thoroughbred horses. Livest. Sci. 121, 308–326. https://doi.org/10. 1016/j.livsci.2008.07.009. Villela, L.C.V., Mota, M.D.S., Oliveira, H.N., 2002. Genetic parameters of racing performance traits of Quarter horses in Brazil. J. Anim. Breed. Genet. 119, 229–234. https://doi.org/10.1046/j.1439-0388.2002.00338.x. Wilson, D.E., Willham, R.L., Buttram, S.T., Hoekstra, J.A., Luecke, G.R., 1988. Genetics of racing performance in the American Quarter Horse: IV. Evaluation using a reduced animal model with repeated records. J. Anim. Sci. 66, 2817–2825.
4.3.2. Additional analysis of stallions to examine the genetic relationship between TC402 and the other time class traits The results (Fig. 2) indicated that, although the correlations between the TC traits were high, the probable genetic gain in 402 m races would be lower when stallions are selected for TC301, TC320 and TC365 rather than for the TC402. One exception was a small group (10%) of animals at 320 m (TC320) with the capacity to exhibit higher EBVp at 402 m (Fig. 3). The values described indicated that selection for each distance has different objectives. The choice of the ideal distance when selecting a stallion depends on different factors. The ideal would be to obtain horses that are capable of producing champion offspring at all distances. However, the present results indicate major difficulties in achieving this goal since, to obtain offspring with high athletic skills at the most popular and competitive distance (402 m), stallions must be selected for TC402. The fact that offspring first compete at shorter distances is part of the physiological evolution and training of athletic horses and the final goal is to be champion at the distance of 402 m. 5. Conclusion The estimation of genetic parameters for sprint racing performance in horses by Bayesian inference in multivariate analysis using a threshold animal model was found to be a suitable alternative for the study of categorical traits transformed from continuous traits because it provides consistent results of high accuracy. The TC traits, evaluating records of sprint racing performance, can be used as a selection criterion by associations, breeders and trainers of QH, with the possibility of genetic gain if applied in breeding programs. Acknowledgments The authors wish to thank the Jockey Clube de Sorocaba (JCS, Brazil) for providing the data used in this study. We thank Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Capes, Brazil) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, Brazil). The authors thank the reviewers of Livestock Science for their suggestions. Funding This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil (Finance Code 001). PhD fellowship granted (PROEX- Program of Academic Excellence) (88882.180634/2018-01) to Ricardo Faria and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, Brazil) productivity grant to Prof. J. Augusto II.
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