The essential role for graphs in allometric analysis

A Revision of the Traditional Analysis Method of Allometry to Allow Extension of the Normality-Borne Complexity of Error Structure: Examining the Adequacy of a Normal-Mixture Distribution-Driven Error Term

Huxley’s model of simple allometry provides a parsimonious scheme for examining scaling relationships in scientific research, resource management, and species conservation endeavors. Factors including biological error, analysis method, sample size, and overall data quality can undermine the reliability of a fit of Huxley’s model. Customary amendments enhance the complexity of the power function-conveyed systematic term while keeping the usual normality-borne error structure. The resulting protocols bear multiple-parameter complex allometry forms that could pose interpretative shortcomings and parameter estimation difficulties, and even being empirically pertinent, they could potentially bear overfitting. A subsequent heavy-tailed Q-Q normal spread often remains undetected since the adequacy of a normally distributed error term remains unexplored. Previously, we promoted the advantages of keeping Huxley’s model-driven systematic part while switching to a logistically distributed error term to improve fit quality. Here, we analyzed eelgrass leaf biomass and area data exhibiting a marked size-related heterogeneity, perhaps explaining a lack of systematization at data gathering. Overdispersion precluded adequacy of the logistically adapted protocol, thereby suggesting processing data through a median absolute deviation scheme aimed to remove unduly replicates. Nevertheless, achieving regularity to Huxley’s power function-like trend required the removal of many replicates, thereby questioning the integrity of a data cleaning approach. But, we managed to adapt the complexity of the error term to reliably identify Huxley’s model-like systematic part masked by variability in data. Achieving this relied on an error term conforming to a normal mixture distribution which successfully managed overdispersion in data. Compared to normal-complex allometry and data cleaning composites present arrangement delivered a coherent Q-Q normal mixture spread and a remarkable reproducibility strength of derived proxies. By keeping the analysis within Huxley’s original theory, the present approach enables substantiating nondestructive allometric proxies aimed at eelgrass conservation. The viewpoint endorsed here could also make data cleaning unnecessary.

Modeling allometric variation: lessons from the metabolic allometry of black carp (Mylopharyngodon piceus)

I used linear and nonlinear regression to re-examine published data on the scaling of metabolic rate vs. body mass in an ontogenetic series of black carp (Mylopharyngodon piceus (Richardson, 1846)). My objective was to expose shortcomings of the conventional procedure for fitting statistical models to bivariate observations (i.e., the procedure that is widely attributed to J.S. Huxley) and simultaneously to outline a more general and utilitarian protocol for analyzing bivariate data in studies of allometry. Authors of the original study on carp reported exponents of 0.83 and 0.78 for two-parameter power functions fitted to observations for resting metabolism and maximum metabolism, respectively. However, metabolic scaling in these fishes actually is described best by straight lines having positive intercepts with the Y axis. The allometric exponent is 1 for a straight line, so interpretations from the current analyses differ substantially from those reached in the original investigation. Contemporary theories for the evolution of optimal body size (e.g., the Metabolic Theory of Ecology) are based on patterns of metabolic allometry that have been estimated by the conventional analytical method. Thus, the current investigation raises questions about generally accepted patterns of metabolic allometry and theoretical models based upon them.