DOI: 10.5061/dryad.2jm63xst2
title: Estimating total species richness: fitting rarefaction by asymptotic approximation

description: Estimating the number of species in a community is important for
 assessments of biodiversity. Previous species richness estimators are
 mainly based on non-parametric approaches. Although parametric asymptotic
 models have been applied, they received limited attention due to specific
 limitations. Here, we introduce parametric models fitting the
 probability-based rarefied species richness curve that allow us to
 estimate the ‘Total Expected Species’ (TES) in a community based on
 species’ abundance data. We develop two approaches to calculate TES
 (termed ‘TESa’ and ‘TESb’), based on two slightly different mathematical
 assumptions regarding Expected Species (ES) models. We provide R functions
 to calculate both these estimation approaches and their standard
 deviation. The function also enables users to visualize the estimation. We
 test the performance of TESa, TESb and their average (TESab) across
 simulated and empirical data, and compare their bias, precision and
 accuracy with other, commonly used, non-parametric species richness
 estimators; the bias-corrected (bc-)Chao1 and the Abundance-based Coverage
 Estimator (ACE). Simulation reveals that in small samples, TESa shows a
 tendency to over-estimate and TESb to under-estimate overall species
 richness. TESab performs well in bias, precision and accuracy when
 compared to (bc-)Chao1 and ACE estimators. Results from empirical data
 shows that the variance generated from TES estimates is comparable to that
 for (bc-)Chao1 and ACE. Our study demonstrates that rarefaction theory in
 combination with parametric approximation models provides a valuable new
 approach to estimate the species richness of incompletely sampled
 communities. Robust estimates are likely to be obtained where the
 observed number of species is greater than half of the TES estimation.
 When the ratio of TESa to the observed richness is &gt;&gt; 2, we
 suggest the use of TESb or TESab. Although more comprehensive comparisons
 with other estimators are suggested, we encourage researchers to consider
 the TES approach in their biodiversity studies as a complement to current
 existing estimators.
description: There is no empirical data in the submission. The file only
 contains R scripts for functions of ES(), TES() and plot.TES().
description: # ES() calculate the Expected Species' #
 TES() calculate Total Expected Species base on ESa, ESb and their average
 value # plot.TES() provides the fitted curve for
 TES # The argument x for ES() and TES() is a data
 vector representing number of individuals for each species
 # The argument TES_output for plot.TES() is the output from
 TES() # The argument m for ES() is the sample size
 parameter that represents the number of individuals randomly drawn from
 the sample, which by default is set to m=1, but can be changed according
 to the users' requirements. For ESa, m can not be larger than the
 sample size # The argument method is the calculation
 approach of Expected Species used, with two options available as
 "a" and "b" to calculate ESa and ESb, with the default
 set as "a" # The argument knots specifies the
 number of separate sample sizes of increasing value used for the
 calculation of ES between 1 and the endpoint, which by default is set to
 knots=40 # ES() returns a value of Expected
 Species  # TES() returns a list, which contains a table
 of the summary of the estimated values and their standard deviations based
 on TESa, TESb, and TESab, and the model used in the estimation of TES,
 either 'logistic' or 'Weibull'