#### Abstract

Studies of the relationship between animal body temperature and air temperature suggest body temperature is essentially unresponsive until a threshold is reached, then it responds dramatically to increasing air temperature. The goal is to estimate the threshold between the thermoneutral plateau and the beginning of the heat stress challenge. One approach is to fit a polynomial to estimate the knot position and use spline functions to perform linear least squares piecewise polynomial fitting. Another alternative is to use nonlinear regression to estimate the knot or an inflection point of a nonlinear function. In both approaches the cyclic nature of body temperature is ignored. This paper explores the use of nonlinear regression to estimate the knot position and handles the hysteresis effect resulting from the cyclic nature of body temperature. Models are fit to data collected from cattle in chambers subjected to semicontrolled sinusoidal air temperature at the University of Missouri-Columbia Animal Science department and a procedure for estimating the heat stress threshold is proposed.

#### Keywords

hysteresis, nonlinear regression, nonlinear mixed models, heat stress, thresholds

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

SPLINE MODELS FOR ESTIMATING HEAT STRESS THRESHOLDS IN CATTLE

Studies of the relationship between animal body temperature and air temperature suggest body temperature is essentially unresponsive until a threshold is reached, then it responds dramatically to increasing air temperature. The goal is to estimate the threshold between the thermoneutral plateau and the beginning of the heat stress challenge. One approach is to fit a polynomial to estimate the knot position and use spline functions to perform linear least squares piecewise polynomial fitting. Another alternative is to use nonlinear regression to estimate the knot or an inflection point of a nonlinear function. In both approaches the cyclic nature of body temperature is ignored. This paper explores the use of nonlinear regression to estimate the knot position and handles the hysteresis effect resulting from the cyclic nature of body temperature. Models are fit to data collected from cattle in chambers subjected to semicontrolled sinusoidal air temperature at the University of Missouri-Columbia Animal Science department and a procedure for estimating the heat stress threshold is proposed.