2002-07-08_GENERAL DOCUMENTS - M2002004 (2)

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lit 1972. Whittaker thought the Shannon Index (H' ) was the best all-purpose expression of "equitabiiity' in use. However, Chambers (1983) concluded that proportional - abundance indices (e.&, Shannon- Weiner) were unsuited for revegetation comparisons in revegetation analysis. She lists five troublesome properties of the Shannon Index, two of which bear repeating. First, the response curve is not symmetrical (Peet 1974). Thus, a change at one end of the index is not necessarily proportionate to the same amount of change at the other end, evhhich led Chambers to conclude that Shannon values from different communities are not directly comparable. Second, estimating the variance poses further statistical problems, and an estimate of the variance is of course necessary to construct a confidence interval, calculate a t -rest, etc. The problem is nicely explained by Lyons (1981) who proceeds to devise a formula to estimate the variance of the exponential form of H. Apparently despairing over these challenges, Chambers ( 1983) recommended that similarity indices be used to compare diversity. They certainly facilitate comparisons, that being their derivation, but reliance on similarity indices presupposes a goal of restoring the original plant community (species or growth -form composition), which rarely occurs and seldom is desired. For example, restoring a weedy plant community may be undesirable, and restoring a mature forest within a bond period is impossible. Mining and reclamation destroy some plant habitats, and regulations limit diversity strategies, making similarity an impossible goal. Further, there is a contradiction in comparing the "diversity" of two communities without ever having measured it. Finally, a similarity indeoc seems best suited to measuring beta diversity where composition keys to habitat factors. We are not so pessimistic about the use of the Sheraton Index in reclamation. Magurran (1988) handily cites equations to estimate the variance ell', which can be improved by jackdaiifing, and to calculate "t" to test for the difference between. samples (see pp. 35, 42-43, 148 -149), An analysis of variance is an expanded t-test, so the Shannon values of different communities can be compared relative to habitat or treatment differences. If all else fails, technical standards can set the necessary level for this parameter. Pielou (1986) has come up with a method of directly comparing species diversity of two plant communities (e.g., revegetated and reference area) based on similarities in species occurrence. Her technique is predicated on the fact that within- commmnnity resemblances, measured using "matching coefficients," are higher (more species in common = low diversity) in communities with few species and low evenness. Based on their matching coefficients, samples are divided into two classes as nearly equal as possible, which gives rise to a 2 X 2 table, at which point most ecologists would apply a Chi - square test_ Pielru (147 7) c alls this "a slovenly approach" and provides an example of analysis (1986) that is not terribly clear to the statistically challenged, but probably worth pursuuig. Bete and Between - Habitat Diversity For a transact along a coencline (community gradient), Whittaker (1972, 1975) suggested that this could be measured as half - changes in similarity. MacArthur (1965) measured between- habitat differences using differences (a distance formula) in composition and profile, a similar measurement that underlies an allied concept_ Still following Whittaker ( 1972), "beta differentiation can be expressed by the ratio of the total number of species represented in samples to the mean number per sample." If we read this correctly, it is hard to see how the ratio of richness to species density is anything but a measure of alpha diversity, it focuses on numbers of species, not differences in composition. Even MacArthur (1965) found that actual distinctions between within- and between - habitat diversity could be vague 143 • . -c ?far u t . v!j ceorlc 01: 09PM P4/11 Whittaker ( 1972) defined beta diversity as the extent of differentiation of communities along habitat gradients. Note that this concept hinges on plant species composition denoting habitat factors, which has been an illuminating concept for ecologists as disparate as Whittaker (1956) and Daubeann ire (1968).