HR: 1340h
AN: B33C-1052    [Abstracts]
TI: Uncertainty in Power Law Analysis: Influences of Sample Size, Measurement Error, and Analysis Methods
AU: * Hui, D
EM: dafeng@duke.edu
AF: Duke University, Department of Biology, Box 91000, Durham, NC 27708 United States
AU: Luo, Y
EM: yluo@ou.edu
AF: University of Oklahoma, Department of Botany and Microbiology, Norman, OK 73019 United States
AU: Jackson, R B
EM: jackson@duke.edu
AF: Duke University, Department of Biology, Box 91000, Durham, NC 27708 United States
AB: A power function, Y=Y₀ M^beta, can be used to describe the relationship of physiological variables with body size over a wide range of scales, typically many orders of magnitude. One of the key issues in the renewed power law debate is whether the allometric scaling exponent β equals 3/4 or 2/3. The analysis could be remarkably affected by sampling size, measurement error, and analysis methods, but these effects have not been explored systematically. We investigated the influences of these three factors based on a data set of 626 pairs of base metabolic rate and mass in mammals with the calculated β=0.711. Influence of sampling error was tested by re-sampling with different sample sizes using a Monte Carlo approach. Results showed that estimated parameter b varied considerably from sample to sample. For example, when the sample size was n=63, b varied from 0.582 to 0.776. Even though the original data set did not support either β=3/4 or β=2/3, we found that 39.0% of the samples supported β=2/3, 35.4% of the samples supported β=3/4. Influence of measurement error on parameter estimations was also tested using Bayesian theory. Virtual data sets were created using the mass in the above-mentioned data set, with given parameters α and β (β=2/3 or β=3/4) and certain measurement error in base metabolic rate and/or mass. Results showed that as measurement error increased, more estimated bs were found to be significantly different from the parameter β. When measurement error (i.e., standard deviation) was 20% and 40% of the measured mass and base metabolic rate, 15.4% and 14.6% of the virtual data sets were found to be significant different from the parameter β=3/4 and β=2/3, respectively. Influence of different analysis methods on parameter estimations was also demonstrated using the original data set and the pros and cons of these methods were further discussed. We urged cautions in interpreting the power law analysis, especially from a small data sample, and in selecting analysis methods.
DE: 0412 Biogeochemical kinetics and reaction modeling (0414, 0793, 1615, 4805, 4912)
DE: 0414 Biogeochemical cycles, processes, and modeling (0412, 0793, 1615, 4805, 4912)
DE: 0430 Computational methods and data processing
DE: 0466 Modeling
SC: Biogeosciences [B]
MN: Fall Meeting 2005