Mathematical models to define growth patterns in indigenous horses of India

Abstract

The objective of the study was to define the nature of growth and to establish the standards of growth in Marwari, Manipuri and Zanskari horses. Mathematical functions for the prediction of growth in Marwari horses were derived utilising 1112 records of body weight. The body weight standards of Marwari horses from birth to 11 ½ years of age were defined and found to be close to that of Arabian horses. The Logarithmic, Power, S and Cubic functions were derived with respective R2 values of 0.955, 0.833, 0.897 and 0.980 for average body weights to explain the age-weight relationship in Marwari horses from birth to 11 ½ years of age. Looking at the distribution of observed data along the course of predicted curve and goodness of fit on average body weight, the Cubic equation Ŷ = 68.136 + 10.744 (x) - 0.12189 (x)2 + 0.00044177 (x)3 can reliably be utilized for prediction of body weight with respect to age. Similarly, the Cubic equations with R2 value of 0.965 and 0.958 were derived respectively for Manipuri and Zanskari horses. The two roots of Cubic function were derived to define the points of inflection of growth curve. The study indicated that the initial growth phase in Marwari, Manipuri and Zanskari continues up to the age of 73.22, 72 and 67.4 months respectively and there after it remains static; and the cubic function can reliably be used to explain the nature of growth in Marwari, Manipuri and Zanskari breeds of horses.