Trends and asymptotic limits for racing speed in standardbred trotters

Abstract

Racing data on 44,372 Standardbred trotters in Sweden, spanning a period of nineteen years, were analyzed. Racing speed of any i-th horse was measured as the best average racing time ( k i=sec/km) obtained in a trotting race of a length ≥1640 m, as a 3- to 5-year-old. The distribution of the best average racing time records was found to be asymmetric within the population. A scaled logarithmic function of best average racing time of male horses ( y i=ln( k i−68.2)) was found to be normally distributed (zero skewness and low kurtosis). This means that best average racing time records can be expressed as: k i=e y (i) + x, where the constant x=68.2 sec/km was interpreted as the asymptotic limit for trotting speed in the population of male Standardbred trotters. An equation K birth-year= x(1+e − pt ) was fitted to the data for estimating trends in average, minimum and maximum best average racing time records at time t=(birth-year− z) in Swedish Standardbred trotters. The constants p and z were estimated by least-squares grid search. The trend in the average of best average racing time in male trotters can be predicted by the following expression: Aver K birth-year=68.2(1+e (−0.015 (birth-year−1861))). The corresponding prediction of the fastest racing time records is: Min K birth-year=68.2(1+e (−0.019 (birth-year−1853))). The log linear scale effects may be interpreted as successive reductions in marginal substitution effects of genes and environmental factors affecting racing time as measured on the original scale.