Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Species Abundance Distribution and Species Accumulation Curve: A General
  Framework and Results   We build a general framework which establishes a one-to-one correspondence
between species abundance distribution (SAD) and species accumulation curve
(SAC). The appearance rates of the species and the appearance times of
individuals of each species are modeled as Poisson processes. The number of
species can be finite or infinite. Hill numbers are extended to the framework.
We introduce a linear derivative ratio family of models, $\mathrm{LDR}_1$, of
which the ratio of the first and the second derivatives of the expected SAC is
a linear function. A D1/D2 plot is proposed to detect this linear pattern in
the data. The SAD of $\mathrm{LDR}_1$ is the Engen's extended negative binomial
distribution, and the SAC encompasses several popular parametric forms
including the power law. Family $\mathrm{LDR}_1$ is extended in two ways:
$\mathrm{LDR}_2$ which allows species with zero detection probability, and
$\mathrm{RDR}_1$ where the derivative ratio is a rational function. We also
consider the scenario where we record only a few leading appearance times of
each species. We show how maximum likelihood inference can be performed when
only the empirical SAC is observed, and elucidate its advantages over the
traditional curve-fitting method.

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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga