On Fitting the Truncated Lognormal Distribution to Species‐Abundance Data Using Maximum Likelihood Estimation

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Abstract. The truncated lognormal distribution can be used to graduate certain species-abundance data, provided that estimates of the location and scale parameters are obtained. A computer program has been written which groups the data on a log2 scale and numerically solves the maximum likelihood equations for this type of distribution. Results show that the estimates obtained by this method compare well with those of Hald and Cohen. Examples are presented using the diatom data of Hohn and Hellerman, and it is shown that a better fit is obtained by using the entire data set instead of selectively disregarding the most abundant tail intervals. Other published techniques for this type of analysis are also discussed.

The lognormal distribution is not an appropriate null hypothesis for the species–abundance distribution

“…One mathematical attempt to deal with the problems of sampling and discreteness was the development of the Poisson lognormal (Grundy 1951; Cassie 1962; Pielou 1969, 1975, 1977; Bulmer 1974; Slocomb, Stauffer & Dickinson 1977). The argument necessarily has several assumptions about sampling.…”

“…Slocomb et al . (1977) say ‘Pielou (1975) points out that currently available estimates of N [the total number of species] are not satisfactory; this observation is certainly supported by the results presented here and in Bulmer (1974).…”

Estimating the Number of Species: A Review

“…An estimate of C can be obtained by fitting a Gaussian curve to the observed graph, extrapolating the curve to the left, and integrating it over (-oo, + oo ). This method was applied to ecological datasets by Slocomb, Stauffer, and Dickson (1977), who found it unsatisfactory. Palmer ( 1990) studied the method in a botanical experiment with known C and found the resulting estimator to be little better than c itself.…”

Species Abundance in a Forest Community in South China: A Case of Poisson Lognormal Distribution

“…The iteration by equation 5 started from initial values of two parameters that were estimated by fitting a continuous LN distribution to the data on a log scale (Preston 1948;Bliss 1965;Slocomb et al 1977) or by using the moment-matching method. This iteration proceeded with each parameter's step length being 0.001, and terminated when the maximum value of lnL (σ, µ) reached default accuracy in Mathematica 4 (i.e.…”

“…He called this log-transformed abundance an "octave". Since then, the LN has been used widely to model a variety of SA datasets from various communities or collections, such as moths, birds, snakes, and plants, and has attracted increasing attention (Whittaker 1965;Gauch and Chase 1974;Slocomb et al 1977;Coleman 1981;Miller and Wiegert 1989;Xie et al 1995;Engen and Lande 1996;Basset et al 1998;Hill and Hamer 1998;Watt 1998;Harte et al 1999;Fesl 2002;McGill 2003aMcGill , 2003bMcGill , 2003cYin et al 2005). Several approaches have been taken to fit the Gaussian (or LN on a log scale), including the variation of parameters algorithm (Gauch and Chase 1974), maximum likelihood estimate (MLE; Slocomb et al 1977), and the general non-linear least squares method (Yin and Liao 1999;Yin et al 2005).…”