Fitting the Gaussian Curve to Ecological Data

An increasing number of models in ecology involve Gaussian curves (or the lognormal, which is the Gaussian with logarithms of the abscissa values). These include models of species distributions along gradients, habitat and niche width, overlap, and packing, and the lognormal distribution of species importances. However, these models cannot be investigated quantitatively unless data can be fitted to Gaussian curves and appropriate statistics determined. Further, the Gaussian data collected by ecologists typically have special properties affecting the fitting process, notably irregular spacing of samples and truncation of the curves, thereby making ours a specialized case (as contrasted with Gaussian data in general). We conclude the best approach for our application to be a variation of parameters algorithm, and present it with a computer program in FORTRAN IV. Applications are given which test field data quantitatively against hypotheses for species distributions along environmental gradients and for dominance—diversity relationships.