An Estimator of Number of Species from Quadrat Sampling

Haas, Peter J.; Liu, Yushan; Stokes, Lynne

doi:10.1111/j.1541-0420.2005.00390.x

Cited by 21 publications

(38 citation statements)

References 19 publications

(33 reference statements)

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“…Whenâ goes to zero, the estimator is still well-defined and given bŷ Haas et al (2006) proposed a series of nonparametric estimators based on the generalized jackknife procedure. Whenâ goes to zero, the estimator is still well-defined and given bŷ Haas et al (2006) proposed a series of nonparametric estimators based on the generalized jackknife procedure.…”

Section: Cðt þBþmentioning

confidence: 99%

An Incidence-Based Richness Estimator for Quadrats Sampled Without Replacement

Shen

2008

Ecology

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Most richness estimators currently in use are derived from models that consider sampling with replacement or from the assumption of infinite populations. Neither of the assumptions is suitable for sampling sessile organisms such as plants where quadrats are often sampled without replacement and the area of study is always limited. In this paper, we propose an incidence-based parametric richness estimator that considers quadrat sampling without replacement in a fixed area. The estimator is derived from a zero-truncated binomial distribution for the number of quadrats containing a given species (e.g., species i) and a modified beta distribution for the probability of presence-absence of a species in a quadrat. The maximum likelihood estimate of richness is explicitly given and can be easily solved. The variance of the estimate is also obtained. The performance of the estimator is tested against nine other existing incidence-based estimators using two tree data sets where the true numbers of species are known. Results show that the new estimator is insensitive to sample size and outperforms the other methods as judged by the root mean squared errors. The superiority of the new method is particularly noticeable when large quadrat size is used, suggesting that a few large quadrats are preferred over many small ones when sampling diversity.

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Section: Cðt þBþmentioning

confidence: 99%

An Incidence-Based Richness Estimator for Quadrats Sampled Without Replacement

Shen

2008

Ecology

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“…For inclusion in this study, it was computational consideration that decided in favour of the latter. The cluster-sampling Downloaded by [UQ Library] at 11:34 19 November 2014 estimator by Haas et al [24] was tested, but unrealistic assumptions about species sizes and associations of occurrence make it unsuitable for small-sample applications. For forest tree species richness estimation from sample data obtained under cluster sampling, the finite mixture modelling approach by Norris and Pollock [47] and Mao and Colwell [39] has disappointed [37,38].…”

Section: Discussionmentioning

confidence: 99%

“…To date, there is no single uniformly superior estimator of richness [7,37,66]. Rather, the performance of an estimator may be excellent in one Downloaded by [UQ Library] at 11: 34 19 November 2014 population and less so in another for reasons that are difficult to anticipate and discern from the sample data [24]. For the purpose of demonstration, we have chosen SO and five estimators of S in our study (c.f.…”

Section: Estimation Objectives and Performance Assessmentmentioning

confidence: 99%

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A modified bootstrap procedure for cluster sampling variance estimation of species richness

Magnussen

McRoberts

2011

Journal of Applied Statistics

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Variance estimators for probability sample-based predictions of species richness ( S) are typically conditional on the sample (expected variance). In practical applications, sample sizes are typically small, and the variance of input parameters to a richness estimator should not be ignored. We propose a modified bootstrap variance estimator that attempts to capture the sampling variance by generating B replications of the richness prediction from stochastically resampled data of species incidence. The variance estimator is demonstrated for the observed richness (SO), five richness estimators, and with simulated cluster sampling (without replacement) in 11 finite populations of forest tree species. A key feature of the bootstrap procedure is a probabilistic augmentation of a species incidence matrix by the number of species expected to be ‘lost’ in a conventional bootstrap resampling scheme. In Monte-Carlo (MC) simulations, the modified bootstrap procedure performed well in terms of tracking the average MC estimates of richness and standard errors. Bootstrap-based estimates of standard errors were as a rule conservative. Extensions to other sampling designs, estimators of species richness and diversity, and estimates of change are possible.

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“…Good (1953) first addressed the issue of estimating E (C r ) and proposed an empirical Bayesian approach. Examples of bias due to failing to account for sampling without replacement in species richness estimation can be found in , Haas et al (2006), and Chao and Lin (2012). The Good-Turing method has been applied successfully in several disciplines, such as information retrieval (Song and Croft, 1999), computational linguistics (Church and Hanks, 1990), speech recognition (Jelinek, 1998;Chen and Goodman, 1999), species richness estimation (Esty, 1985;, population size estimation , Shannon entropy estimation , and missile coverage estimation (Lo, 1992).…”

Section: Introductionmentioning

confidence: 99%

Good–Turing frequency estimation in a finite population

2014

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Good-Turing frequency estimation (Good, ) is a simple, effective method for predicting detection probabilities of objects of both observed and unobserved classes based on observed frequencies of classes in a sample. The method has been used widely in several disciplines, such as information retrieval, computational linguistics, text recognition, and ecological diversity estimation. Nevertheless, existing studies assume sampling with replacement or sampling from an infinite population, which might be inappropriate for many practical applications. In light of this limitation, this article presents a modification of the Good-Turing estimation method to account for finite population sampling. We provide three practical extensions of the modified method, and we examine performance of the modified method and its extensions in simulation experiments.

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An Estimator of Number of Species from Quadrat Sampling

Cited by 21 publications

References 19 publications

An Incidence-Based Richness Estimator for Quadrats Sampled Without Replacement

An Incidence-Based Richness Estimator for Quadrats Sampled Without Replacement

A modified bootstrap procedure for cluster sampling variance estimation of species richness

Good–Turing frequency estimation in a finite population

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