Rarefaction is a method for comparing community diversities that has consistently been abused by paleoecologists: here its assumptions are clarified and advice given on its application. Rarefaction should be restricted to comparison of collections from communities that are taxonomically similar and from similar habitats: the collections should have been obtained by using standardised procedures. The rarefaction curve is a graph of the estimated species richness of sub-samples drawn from a collection, plotted against the size of sub-sample: it is a deterministic transform of the collection's species-abundance distribution. Although rarefaction curves can be compared statistically, it may be more efficient to compare the species-abundance distributions directly. Both types of comparison are discussed in detail.
This paper puts forward the proposition that sedimentation systems generally are in stasis. Three lines of evidence suggest the proposition is largely correct: (1) considerations of how sedimentation systems necessarily operate, (2) observations of active systems, and (3) a reevaluation of ideas about sedimentation rates. There are of course systems to which the proposition cannot apply. A simulation exercise is used to address questions about the stratigraphic effects of stasis. The results show (1) that sedimentation systems that generally are in stasis can be of a variety of types, (2) that stasis is readily preserved in stratigraphic successions, (3) that successions produced by a system in which the time proportion of stasis is high are markedly more complete than successions produced by other systems of the same type, (4) that the proportion of stasis in a system cannot be estimated reliably from stratigraphic successions produced by that system, and (5) that the stratigraphic succession finally left behind by a system is necessarily a systematically biased and partial record of the history of that system. What is always missing is that part of the history before the oldest preserved horizon, which for systems that are in long-term balance will on average be half of the total time.
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