Empirical growth curve estimation considering multiple seasonal compensatory growths of body weights in Japanese Thoroughbred colts and fillies1

Abstract

Thoroughbred horses are seasonal mating animals, and their foals are born yearly in spring seasons. In northern regions or countries, the foals generally show a typical seasonal compensatory growth pattern, where their growth rate declines in winter and increases in the next spring. In this study, a new empirical approach is proposed to adjust for this compensatory growth when growth curve equations are estimated, by using BW of Japanese Thoroughbred colts and fillies raised in Hidaka, Hokkaido. Based on the traditional Richards growth curve equation, new growth curve equations were developed and fit to the weight-age data. The foals generally experience 2 major winter seasons before their debut in horseracing. The new equations had sigmoid subfunctions that can empirically adjust the first and second year compensatory growths, combined with the Richards biological parameter responsible for the maturity of animals. The unknown parameters included in the equations were estimated by SAS NLMIXED procedure. The goodness-of-fit was examined by using several indices of goodness-of-fit (i.e., Akaike's information criterion, Bayesian information criterion, -2 log likelihood, and residual sum of squares) for the multiple applications of the subfunctions. The indices indicated the best fit of the new equations including both subfunctions for the first and second compensatory growths to the weight-age data. The shapes of the growth curves were improved during the periods of compensatory growth. The proposed method is one of the useful approaches for adjusting multiple seasonal compensatory growths in growth curve estimations of Thoroughbreds and for the management of young horses during the compensatory periods.

Empirical Percentile Growth Curves with Z-scores Considering Seasonal Compensatory Growths for Japanese Thoroughbred Horses

“…Each empirical percentile corresponds to Z-scores of −1.881, −1.282, −0.675, 0.000, 0.675, 1.282 and 1.881, respectively. A Z-score of zero corresponds to the empirical 50 percentile curve, the Equations 4 and 5 become identical to the equations proposed by Onoda et al [17]. …”

“…[16, 17], in which the traditional Richards’ growth curve equation [18] was modified to incorporate CG effects with sigmoid sub-functions f(t) and f’(t) . The sigmoid sub-functions f(t) and f’(t) adjust the first and second year CGs at 432 and 797 (=432 + 365) days of age, respectively, and were adapted to the biological parameters responsible for maturity in the Richards equation [18].…”

“…Thus, the maturity weight of each individual was 575.0 + a i , indicating that the final maturity weight differs according to each individual. Based on Onoda et al [16, 17], the equations for BW for male and female Thoroughbreds are:…”

“…Many studies have investigated the seasonal changes of horses’ growth rates [2, 10, 16, 17, 20, 21]. Mohammed [14] reported that Thoroughbred yearlings were at a high risk of developmental disorders (e.g.…”

“…Concerning body weights for young Thoroughbreds, we have proposed mathematical equations for empirical growth curves considering seasonal CG [16, 17]. These growth curve equations would be useful for the establishment of percentile growth curves considering seasonal CG, because the equations are continuous single variable functions of the age of horses, and the variances of the growth data can be used as the empirical percentiles with Z-scores under the assumption of normal distributions of data.…”