Abstract
Premise of research. The hypothesis of diminishing returns posits that growth by a leaf creates new surface for capturing light but that size of the leaf is ultimately limited by disproportionately large increases in mass of the petiole, the midrib, and/or supporting elements in the lamina itself. The concept is based on numerous investigations of allometric relationships between leaves and their supporting structures. However, most of the studies in question were based on the traditional allometric method, which entails fitting a straight line to logarithmic transformations of the original data and then back transforming the resulting model to form a two-parameter power function in the arithmetic scale. I reexamined data for leaves from four species of tree to show how investigators may be misled by the traditional approach to allometric analysis.Methodology. A two-parameter power function with multiplicative lognormal heteroscedastic error first was fitted to each data set by the traditional allometric method. Four models with additive normal homoscedastic error then were fitted to untransformed data by linear and nonlinear regression, and another four regression models were fitted with additive normal heteroscedastic error. The nine fitted models were evaluated graphically and by applying Akaike’s Information Criterion.Pivotal results. The examples revealed instances in which models fitted by the traditional method failed to follow the path of the original observations, in which allometric exponents were changed substantially by fitting models directly to untransformed data and in which data actually were unsuited from the outset for use in an allometric analysis.Conclusions. Allometric equations that purportedly support the hypothesis of diminishing returns may be inaccurate and misleading. Many problems can be avoided in future research by using linear and nonlinear regression to fit models directly to untransformed observations. The current investigation provides a template for a reliable holistic approach to allometric analysis.
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Claims 4
Claim · model-written summary
Traditional allometric models sometimes failed to follow the original leaf observations.
Verbatim
e0“models fitted by the traditional method failed to follow the path of the original observations”
e1“leaves from four species of tree”
Claim · model-written summary
Fitting models directly to untransformed leaf data substantially changed allometric exponents.
Verbatim
e0“allometric exponents were changed substantially by fitting models directly to untransformed data”
e1“leaves from four species of tree”
Claim · model-written summary
Some leaf datasets were unsuitable for allometric analysis from the outset.
Verbatim
e0“data actually were unsuited from the outset for use in an allometric analysis”
e1“leaves from four species of tree”
Claim · model-written summary
The author recommends fitting linear and nonlinear regression models directly to untransformed observations to avoid allometric analysis problems.
Verbatim
e0“Many problems can be avoided in future research by using linear and nonlinear regression to fit models directly to untransformed observations.”
e1“leaves from four species of tree”