The variations of the numbers of species recorded 1-, 2-, … x-times (singletons, doubletons, … x-tons) with increasing sampling-size : an analytical approach using Taylor expansion.
Résumé
The process of species accumulation, during progressive sampling, results in the regular, monotonic
increase of the number of recorded species with sampling size. On the contrary, the numbers f1(N),
f2(N), f3(N), …, fx(N) of those species recorded 1-, 2-, 3-, …, x-times at sampling-size N all show nonmonotonic
variations with N. The major characteristic elements of this non-monotonic variations
(namely: the maximum reached at ∂fx (N)/∂N = 0 and the inflexion point at ∂2fx (N)/∂N2 = 0) provide
interesting cues regarding the degree of advancement of sampling completeness. Such cues yet
remain undetectable however along the regular, monotonic increase of the species accumulation
curve itself. Although usually unrecorded, the variations of the fx(N) may yet be computed and,
accordingly, the associated cues above thereby made available in practice. This computation
involves the Taylor expansion of the fx(N), making use of recently derived mathematical properties of
the species accumulation process. For common practice, focus is placed upon the variations of the
fx(N) of lower-orders (i.e. f1(N), f2(N), f3(N), f4(N)), which is sufficient to disclose information of particular
relevance in assessing the progress of sampling towards completeness.
Domaines
Biodiversité
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