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Conference on Applied Statistics in Agriculture 1989 - 1st Annual Conference Proceedings

STATISTICAL ISSUES IN STUDIES OF THERMOREGULATION IN FARM ANIMALS

A. M. Parkhurst

G. L. Hahn

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Recommended Citation Parkhurst, A. M. and Hahn, G. L. (1989). "STATISTICAL ISSUES IN STUDIES OF THERMOREGULATION IN FARM ANIMALS," Conference on Applied Statistics in Agriculture. https://doi.org/10.4148/ 2475-7772.1449

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STATISTICAL ISSUES IN STUDIES OF THERMOREGULATION IN FARM ANIK~LS

A. M. Parkhurst and G. L. Hahn University of Nebraska-Lincoln

and

U. S. Meat Animal Research Center, ARS-USDA, Clay Center, NE Abstract Patterns of tympanic temperature response were identified in ad-lib-fed cattle exposed to constant or cyclic (±7 C) conditions at two levels of air temperature: 10 C and 28 C. Use of time series analysis following the DDS approach of Pandit and Wu indicate the thermoregulatory control dynamics for steers at 28±7 C were markedly different from those at the other conditions. Preliminary evaluations using the ideas of chaos and non-linear dynamics show promise of further characterization of stress responses in farm animals.

Keywords: circadian rhythms, tympanic temperatures, data dependent systems, time series, entrainment, chaos theory, non-linear dynamics, thermal stress

1. Background of Biological Investigation The capability of farm animals to maintain homeothermy through thermoregulation is central to coping with thermal stressors through behavioral or physiological responses. Typical behavioral responses include seeking a more favorable microclimate if available (e.g., shelter from wind or precipitation in cold, or shade from sun and increased utilization of water in hot environments), and altering posture and contacts with other animals to change exposed surface area. Decreased feed intake lowers metabolic heat production and therefore decreases the amount of heat dissipation required in hot weather, while increased feed intake in cold conditions leads to higher metabolic rates. Physiological responses include adjustment of metabolic levels necessary to sustain body processes, vasodilation and increased respiration to increase heat dissipation, or vasoconstriction to conserve body heat. Minimizing the overall impact of thermal stressors is essential to satisfactory performance, health and welfare of farm animals. Variations are cornmon among species and individuals in their ability to adjust to thermal challenges. Disruptions of normal body temperature and thermoregulatory processes can be important criteria for assessing the ability of farm animals to cope with thermal stressors. Thermoregulatory control is a complex process linked primarily to the hypothalamus in the brain. In thermoregulatory studies of animals, body temperature, along with other physiological, environmental and behavioral variables, is observed at regular time intervals. Such time series usually exhibit cyclic fluctuations which are thought by many investigators to be circadian in nature (Aschoff, 1983; Stanier et al., 1984; Hahn, 1988). While much remains to be learned about thermoregulatory control systems in mammals (Cossins and Bowler, 1987), recent evidence indicates an innate monophasic body temperature rhythm in ad-lib-fed animals in the absence of stressors (Hahn, 1988). These innate rhythms, with maxima in late evening and minima in mid-morning, can be altered by environmental stressors (e.g., adverse air temperature, weather events, or transport). Shifts in the mean, amplitude and phase of the circadian body temperature rhythms occur when thermal thresholds characteristic of species and individual animals are exceeded.

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may reflect sinusoidal dynamics with different degrees of damping. Real roots with absolute value close to one can represent constant trend of growth or decay while complex roots close to III may represent circadian rhythms with the period given by the imaginary part.

3. Description of Pilot Controlled-Environment Study Measurements: Tympanic temperatures were recorded hourly by a datalogger from thermocouple sensors inserted into the ear canal of each steer, using techniques previously described (Wiersma and Stott, 1973; Scott et al., 1973). The overall system was carefully calibrated, with obtained accuracy limi ts of .05 C or better. Considerable effort was required to maintain functioning sensors because of breakage, disconnected or chewed leads, and the need to alternate sensors from ear to ear at no more than weekly intervals to minimize ear canal irritation. However, the technique does provide an acceptable index of hypothalamic temperature (Benzinger, 1959, 1964; Guidry and McDowell, 1965; Weirsma and Stott, 1974), which serves as the principal integrator from which animals adjust heat production, loss or retention to maintain thermoregulatory control by animals (Stanier et al., 1984). Treatments: The treatment design was a 2 x 2 factorial consisting of two factors: regime and temperature. The two temperature levels selected represented non- stressing (thermoneutral, 10 C) and potentially stressing (hot, 28 C) conditions, based on prior reports on the effects of temperature on cattle performance and physiological response (c.f., NRC, 1981). Regime levels selected were cyclic and constant temperatures. Cyclic conditions sinusoidally varied ±7 C about either of the mean temperature levels, to approximate naturally-varying spring/fall (thermoneutral) or summer (hot) conditions. Constant conditions represent a contrasting environment often used in environmental research as a basis for comparison. Experiment: In this study, four animals were housed in pairs and each pair received two treatments. All four animals began the study at the non­ stressing temperature. Two of the steers were placed in the constant temperature regime; the other two, in the cyclic regime. Steers were kept in a thermoneutral environment for two weeks, with tympanic temperatures recorded the last eight days. The steers were then subjected to heat stress and the experiment continued for six days. During the experiment, the steers were maintained in individual stalls in controlled-environment chambers at MARC with a photoperiod of 14h light and 10h dark. They were ad-lib-fed a high-energy pelleted ration, supplemented with 1 kg hay/day to maintain rumen function.

4. Statistical Analysis The analysis focuses on identifying patterns of response over time. Resul ts are used to support assumptions proposed in the literature as reviewed above and/or to generate new constructs or models for thermoregulatory systems. Visual inspection of the time series data indicates a dynamic process (Figure 1 ) and because of the suspected heterogeneity among animals, data from each steer were analyzed separately. Individual analyses were also made for each treatment, since the parameters of interest were more likely to remain constant wi thin rather than between the treatment segments. In addition, a 24h washout period was imposed between the thermoneutral and thermal stress conditions, with measurements at the beginning of the thermal stress conditions omitted from the analyses in an attempt to eliminate

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24

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close to the limit cycle of the internal biorhythm, the resulting periodic motion can become entrained at the stressor frequency. Thus, the conclusion of a sinusoidal function of period 24 for thermal stress treatment is reaffirmed. The phase diagrams for the other treatments suggest a different story. The attractor for the cyclic thermoneutral condition appears almost periodic or quasiperiodic, (Figure 3a). This could happen because the periodic force of the treatment is too small to become entrained and what is displayed is a combination of oscillators. For constant thermal stress, the attractor may be periodic, but, it is difficult to tell because the process rises to a threshold and then decreases, (Figure 3d). The most complex condition is the constant thermoneutral state, (Figure 3c). This process may also be quasiperiodic. It could be dominated by a combination of oscillators and the attractor could become strange suggesting a chaotic process. The above observations are also supported by the use of the Fourier spectrum (Figure 4). In each case, the peak at approximately 24h indicates a diurnal cycle. However, the multiharmonics in the neutral conditions suggest that is far from the whole story. These phenomena require further study and may be addressed by Poincare maps, surfaces in a three dimensional phase space or other tools used to identify routes to chaos (Berge et al., 1984; Moon, 1987).

5. Issues Generated by the Statistical Analysis The DDS approach involves a sequence of F tests, multiple t-tests, and tests for autocorrelation as statistical issues in estimating dimensionality. There are also issues of size of sampling intervals, length of series, magnitude of signal-to-noise ratio and statistical graphics needed to detect and illustrate treatment differences. There are questions about the robustness of the DDS procedure in modeling data with deterministic periodicity and trends. The concept of stochastic periodicity (Box and Jenkins, 1976) needs to be re-examined especially in light of chaos. And, since the characteristic roots are useful not only in detecting periodicity and trends, but also in interpreting Green's function, attention needs to be given to more conditional tests for eigenvalues. However, the most intriguing statistical issues raised in this paper are generated by consideration of chaos, the study of non-linear dynamic systems. Some rudimentary questions are: When is a system linear or nonlinear? Is the ability to differentiate among attractors dependent on the signal to noise ratio? Is it possible to distinguish among periodic, aperiodic or quasi~periodic,chaotic, and random events, especially in the presence of self-excited vibrations? Physicists, engineers and mathematicians are developing new ways to describe the dynamics of nonlinear systems. Statisticians need to respond with equally inventive ways of estimating those ever changing parameters (Priestley, 1988; Tong, 1983).

6. Further Considerations It may be fruitful to conceptualize thermoregulation in terms of non­ linear oscillators, such as those used in modeling human responses as mentioned above (Strogatz 1987) and in Glass and Mackey (1988). The primary oscillator(s) represents the animal's own biorhythm. In the thermoneutral zone, it is a self-excited function. It is not constrained by an external driving force. However, as the ambient temperature is increased, so is the amplitude of the external driving force(s) the secondary

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26

oscills.tor(s). over beyond drives stress. lmpact al., fractal to apparent control

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thermoregulatory

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or go et an Conference on Applied Statistics in Agriculture Kansas27 State University

TABLES

TABLE 1. Dimension of ARMA Model for each Treatment

Sample 1 Sample 2 NEUTRAL STRESS NEUTRAL STRESS CYCLIC ( 4 , 3 ) (3 , 1) (6,5) (2,1) CONSTANT (1,1) ( 2 , 0) (2,0) (3,1)

TABLE 2. Periods Indicated by Conjugate Roots of Length One

Sample 1 Sample 2 NEUTRAL STRESS NEUTRAL STRESS CYCLIC 2.24* 24.58 23.70+ 24.90 CONSTANT

* Coefficients not significant, (a = 1%) + Roots for autoregression and moving average cancel. - No roots of length one.

TABLE 3 . Parameters of Stationary Process Temperature Tym12anic Chamber Sample 1 Sample 2

MEAN ( 0 C) 40.15 40.25 28.56 AMPLITUDE 0.97 0.87 6.37 PHASE ANGLE (rad. ) 2.44 2.48 1. 47 PHASE SHIFT (rad. ) -1.17 1.13 0.60

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28

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CYCLIC THERMONEUTHALTHE~RMONEUTHAL SPECTRAL ANALYSIS CYCLIC THERMALTIIE:RMAL STRESS STEERSTETR 186 SPECTRAL ANALYSIS STEER 188185

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