JACKKNIFING AN INDEX OF DIVERSITY

The method of jackknifing is introduced for estimating an index of diversity and several functions of it, and is illustrated with tree data. The method yields approximately normally distributed jackknife estimates and also gives estimated standard deviations, making possible tests of hypotheses and confidence interval estimates. These results apparently can be obtained under the usual conditions of field sampling, where associations within and between species or between quadrats or segments of a traverse may be found. Because of these associations there is no guarantee that the method works; hence an eyeball and a statistical test for the approximate normality of the estimates are given and illustrated with the tree data. The tree data came from 24 quadrats arranged in two blocks of contiguous quadrats. The estimated tree-species diversity, using both indices considered, showed a smooth monotonic decrease over a 19-yr interval providing striking confirmation of the reality of this ecological parameter. The normality tests on this data showed that the normal approximations to the distributions of the jackknife estimates were justified, except in three instances, only one of which seemed to be seriously in error. A conclusion is that it seems reasonable to suppose that in many, if not most, cases, only moderate sample sizes will be needed in practice for the jackknife estimate, at least for forest data.