A NONLINEAR DYNAMICAL (CHAOS) APPROACH TO THE ANALYSIS OF BROILER GROWTH

Mathematical chaos has been observed in a number of biological areas, suggesting that order can be found in systems previously described as random. Nonlinear analyses were conducted to determine whether periodicity or chaos was evident in the growth responses of broiler chickens. Analyses of the absolute growth rate and growth rate acceleration were conducted for four lines of broilers selected at 14 or 42 d for high or low growth rates (Experiment 1) and for a commercial broiler strain (Experiment 2). Resulting Lyapunov exponents (LE) and correlation dimensions (CD) were statistically evaluated. Time series and return map graphics were analyzed. In both experiments, independence of day-to-day growth responses was indicated by low r2 values. In Experiment 1, there were significant differences between lines in growth rate (low, 9.1 +/- .3; high, 12.9 +/- .5 g/d) and the standard deviation of growth rate (low, 5.8 +/- .2; high 7.3 +/- .3 g/d). There were no significant differences for LE or CD values between lines or day of selection. In general, the positive LE, noninteger values of CD, and return map graphics in both experiments suggested the presence of chaotic dynamics. Evaluation of mathematical chaos in broiler growth may give insight into the dynamics and modeling of growth and diseases associated with growth.