Accuracy in the estimation of quantitative minimal area from the diversity/area curve

The problem of representativity is fundamental in ecological studies. A qualitative minimal area that gives a good representation of species pool [C.M. Bouderesque, Methodes d'etude qualitative et quantitative du benthos (en particulier du phytobenthos), Tethys 3(1) (1971) 79] can be discerned from a quantitative minimal area which reflects the structural complexity of community [F.X. Niell, Sobre la biologia de Ascophyllum nosodum (L.) Le Jolis en Galicia, Invest. Pesq. 43 (1979) 501]. This suggests that the populational diversity can be considered as the value of the horizontal asymptote corresponding to the curve sample diversity/biomass [F.X. Niell, Les applications de l'index de Shannon a l'etude de la vegetation interdidale, Soc. Phycol. Fr. Bull. 19 (1974) 238]. In this study we develop a expression to determine minimal areas and use it to obtain certain information about the community structure based on diversity/area curve graphs. This expression is based on the functional relationship between the expected value of the diversity and the sample size used to estimate it. In order to establish the quality of the estimation process, we obtained the confidence intervals as a particularization of the functional (h-phi)-entropies proposed in [M. Salicru, M.L. Menendez, D. Morales, L. Pardo, Asymptotic distribution of (h,phi)-entropies, Commun. Stat. (Theory Methods) 22 (7) (1993) 2015]. As an example used to demonstrate the possibilities of this method, and only for illustrative purposes, data about a study on the rocky intertidal seawed populations in the Ria of Vigo (N.W. Spain) are analyzed [F.X. Niell, Estudios sobre la estructura, dinamica y produccion del Fitobentos intermareal (Facies rocosa) de la Ria de Vigo. Ph.D. Mem. University of Barcelona, Barcelona, 1979].