In sum, we show that contrary to Sugihara's (1981) claim, the distribution of slope values from log-log species-area curves (z) can be accounted for as the distribution of the product of two independent variables r and sy/sx. This strengthens our point that many slope values between 0.2-0.4 are expected independently of biological grounds. We therefore reaffirm our view that slope values between 0.2 and 0.4 may have no biological significance. Rather than trying to interpret the distribution of slope values, attention should be focused on explanations of the observed distributions of the correlation coefficient, r, and the ratio, sy/sx. Elsewhere, Sugihara (1980) continues to advocate Preston's (1962) interpretation of slope values from the power function model of the species-area relationship. He attributes the high frequency of observed slope values near 0.25 as evidence that the underlying relative abundance distribution of species is canonically lognormal. While it is true that the expected slope value given an underlying canonical lognormal relative abundance distribution is near 0.25 (given the assumptions of Preston 1962; May 1975), we have shown that the observed predominance of reported slope values in this region is expected for reasons other than the form of the relative abundance distribution of species. Furthermore, Sugihara (1981) fails to do what he has criticized us for not doing. That is, he has not generated an expected distribution of slopes derived by sampling from an underlying lognormal relative abundance distribution, nor has he compared such a distribution to observed data. Therefore, it is incorrect to interpret slope values near 0.25 to be caused necessarily by what Sugihara (1980) terms the "classical lognormal underpinnings" of the species-area relationship, or to interpret such slope values to indicate the ubiquity of canonical lognormal relative abundance distributions. Contrary to what Sugihara (1980) would have us believe, the frequent occurrence of species-area slopes near 0.25 does not beg for an explanation that lies in its "classical lognormal underpinnings," nor in Sugihara's (1980) views of the ecological basis for lognormal relative abundance distributions.
Citation / Publisher Attribution
E. F. Connor, Earl D. McCoy, and B. J. Cosby. 1983. "Model Discrimination and Expected Slope Values in Species-Area Studies." American Naturalist. 122(6): 789-796.
© 1983 by The University of Chicago.
Scholar Commons Citation
Connor, E. F.; McCoy, Earl D.; and Cosby, B. J., "Model Discrimination and Expected Slope Values in Species-Area Studies" (1983). Integrative Biology Faculty and Staff Publications. Paper 21.