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Predictions from data

Predictions from data

Predictions from

Chapter 5. Predictions from dataBy “prediction” in the context of this book is meant the estimation, based on samples, of therichness and other parameters for communities. It also means, in the context of the first section,the estimation of a sample parameter from other parameters as a check on the accuracy of thelogistic-J distribution as a descriptor of samples.In the first section I show how the logistic-J distribution predicts the maximum abundanceaccurately (in the statistical sense) on the basis of other parameters, such as the mean abundanceand the height of the initial peak (at lowest abundance). In subsequent sections I take a closerlook at the sampling process, explaining why no richness estimation process can succeed withoutknowing both the sample intensity and the underlying distribution. I then illustrate thisrequirement with a brief review of some richness estimation methods already in use.The second half of the chapter describes and compares two procedures for estimating communityrichness on the basis of sample richness. Computer experiments make it possible not only todetermine the relative effectiveness of the procedures, but to determine the contributions tosample variance from irregularities present in the community being sampled as well as thosecontributed by the sampling process itself. Distinguishing the two sources of variation, as well astheir influence on the sample, is a crucial step on the way to a fuller understanding of thesampling process in its entirety.Ideally, predictions from theory, at least numerical ones, should come equipped with errorbounds so that biologists who make such predictions have a reliable estimate of the uncertaintythat accompanies them. Ecologists have been slow in coming to the realization enunciated byDoak, Estes et al. (2008): “Over the last decade, there has been increasing recognition thatecological predictions must be advanced with clear statements of their uncertainty.” Such errorbounds are a strict requirement of what I have called exact ecology. In Sections 5.4 and 5.5 it isshown how to derive error estimates based on interval statistics arising from samples.5.1 predicting maximum abundanceThe logistic-J distribution has two parameters that, in the context of the metastudy (see Chapter7), were estimated on the basis of the mean µ of a sample and its initial peak F 1 . Neither of thesemeasurements has any obvious relationship with the maximum abundance !. In the absence ofsome theoretical relationship, one would be hard put to make any prediction whatever about thesize of ! on the basis of either of these measurements, or both, for that matter. Yet, when thetransfer equations (See Appendix B.10.) are solved with the mean µ and F 1 as input, the valuesof " and ! that correspond to F 1 and µ in the logistic-J function are produced. The parameter " isclosely related to F 1 via R, but not readily discernible in a sample histogram. The parameter !,on the other hand, is directly visible, in a sense, as the largest abundance !’ in the sample; thevalue of !’ will be a good estimator of ! if the logistic-J theory is correct, so it forms a relevant1

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