Allometry and Model II Non-linear Regression

For many allometry problems, morphological variables, x and y, can be transformed using logarithms and linear techniques used to estimate parameters and compare samples. Because both x and y are subject to errors, Model II regression has been advocated for such analyses. When data, such as gonad weight or egg number, are analyzed using a more complex allometry equation such as y = αxβ + γ or y = α(x - γ)β, non-linear regression techniques must be used. We present a Model II non-linear analog of reduced major-axis (RMA) regression that minimizes areas similar to triangles that are minimized in RMA regression. Data for two tropical sea urchins, Salmacis belli and Heterocentrotus mammillatus, illustrate the method.