On the Description of Equine Somatic Growth Using Nonlinear Functions.

This research aimed to improve our understanding of horse growth using five different sets of mathematical equations, with the goal of improving horse health management.

Study Overview

In this study, the researchers examined the growth curves of horses based on their weight, height, and the ratio of weight to height. Five mathematical models were used to describe this growth – two models that described growth with diminishing returns, and three models that described an eventual leveling off, or asymptotic growth.

• Data was gathered from two breeds of horse (quarter horse males and thoroughbred foals and fillies) from birth to maturity.
• These models were then compared to see which provided the most accurate description of horse growth.

Methodology – Nonlinear Regression and the Marquardt-Levenberg Algorithm

The researchers tasked to estimate the parameters of each model utilized nonlinear regression procedures and a mathematical tool called the Marquardt-Levenberg algorithm.

• Nonlinear regression is a type of statistical analysis that helps model complex data where the effect of predictors (in this case the age of horses) on the outcome variable (the growth) is not a straight line.
• The Marquardt-Levenberg algorithm is a method used in solving non-linear least squares problems; it amends the model parameters to increase the correspondence between the model and the observed data.

Goodness-of-Fit Statistics

To make a comparison between the functions and determine which is most accurate, goodness-of-fit statistical tests were used including the adjusted coefficient of determination and the root mean square error.

• The adjusted coefficient of determination computes the percentage of the variance in the dependent variable (growth) explained by the independent variables (weight, height, and ratio) after adjusting for the number of predictors in the model.
• The root mean square error represents the sample standard deviation of the differences between predicted and observed values – a lower value indicates better fit.

Study Findings

The study found that the Richards, Lopez, and Gompertz equations did not accurately depict the growth in horses, suggesting the curves are not sigmoidal (S-shaped). Instead, the study found that the models that illustrated diminishing returns were the most suitable for describing growth in horses –
indicating that growth slows down as the age increases. These findings provide useful insights to better inform the management of horse health and nutrition.