scholarly journals A Truncation Model for Estimating Species Richness

2018 ◽  
Vol 15 (2) ◽  
Author(s):  
Babagnidé François Koladjo ◽  
Mesrob I. Ohannessian ◽  
Elisabeth Gassiat
Keyword(s):  
Species Richness ◽  
Lower Bound ◽  
Regularity Conditions ◽  
Model Parameters ◽  
Conditional Likelihood ◽  
Abundance Distribution ◽  
Species Richness Estimation ◽  
Class Of Estimators ◽  
Truncation Threshold ◽  
Asymptotically Efficient

Abstract We propose a truncation model for the abundance distribution in species richness estimation. This model is inherently semiparametric and incorporates an unknown truncation threshold between rare and abundant observations. Using the conditional likelihood, we derive a class of estimators for the parameters in this model by stepwise maximization. The species richness estimator is given by the integer maximizing the binomial likelihood, given all other parameters in the model. Under regularity conditions, we show that our estimators of the model parameters are asymptotically efficient. We recover Chaos lower bound estimator of species richness when the parametric part of the model is single-component Poisson. Thus our class of estimators strictly generalized the latter. We illustrate the performance of the proposed method in a simulation study, and compare it favorably to other widely-used estimators. We also give an application to estimating the number of distinct vocabulary words in French playwright Molière’s Tartuffe.

Estimation of the Common Probability of Success for Several Binomials —A Simulation Study

1998 ◽  
Vol 48 (1-2) ◽  
pp. 61-72
Author(s):  
Joydeep Bhanja
Keyword(s):  
Lower Bound ◽  
Simulation Study ◽  
Regularity Conditions ◽  
Moment Estimate ◽  
Probability Of Success ◽  
Finite Set ◽  
The Common ◽  
Asymptotically Efficient ◽  
Common Probability

In this paper we consider an example where for each i, i = 1,2, ... , n, the observations Xij , j = 1, 2, ... , k are i.i.d . Binomial ( ni, θ). Based on a theory developed by us earlier, we propose estimates of θ which are asymptotically efficient under the assumption that k ≥ 2, the ni 's come from a finite set { 1, 2, ... , q} and some mild regularity conditions on the sequence { ni} and θ hold. We present the results of a simulation whlch indicate, among other thlngs, the asymptotic lower bound to variance is lower than or approximately equal to simulated Variances and a simple moment estimate of θ does as well as the asymptotically efficient estimates.

scholarly journals An Algebraic Derivation of Chao’s Estimator of the Number of Species in a Community Highlights the Condition Allowing Chao to Deliver Centered Estimates

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Jean Béguinot
Keyword(s):  
Species Richness ◽  
Lower Bound ◽  
Species Abundance ◽  
Nonparametric Estimator ◽  
Species Abundance Distribution ◽  
Abundance Distribution ◽  
Limited Size ◽  
Total Species Richness ◽  
Log Normal ◽  
Total Species

Anne Chao proposed a very popular, nonparametric estimator of the species richness of a community, on the basis of a limited size sampling of this community. This expression was originally derived on a statistical basis as a lower-bound estimate of the number of missing species in the sample and provides accordingly a minimal threshold for the estimation of the total species richness of the community. Hereafter, we propose an alternative, algebraic derivation of Chao’s estimator, demonstrating thereby that Chao’s formulation may also provide centered estimates (and not only a lower bound threshold), provided that the sampled communities satisfy a specific type of SAD (species abundance distribution). This particular SAD corresponds to the case when the number of unrecorded species in the sample tends to decrease exponentially with increasing sampling size. It turns out that the shape of this “ideal” SAD often conforms approximately to the usually recorded types in nature, such as “log-normal” or “broken-stick.”. Accordingly, this may explain why Chao’s formulation is generally recognized as a particularly satisfying nonparametric estimator.

scholarly journals Species richness estimation: Estimator performance and the influence of rare species

2010 ◽  
Vol 8 (6) ◽  
pp. 294-303 ◽  
Author(s):  
Katharina Reichert ◽  
Karl Inne Ugland ◽  
Inka Bartsch ◽  
Joaquín Hortal ◽  
Julie Bremner ◽  
...  
Keyword(s):  
Species Richness ◽  
Rare Species ◽  
Richness Estimation ◽  
Species Richness Estimation

scholarly journals Variations in Total Species Richness and the Unevenness of Species Abundance Distribution between Two Distant Conus Communities (Neogastropoda): A Case Study in Mannar Gulf (India)

2019 ◽  
pp. 1-18
Author(s):  
Jean Béguinot
Keyword(s):  
Species Richness ◽  
Species Composition ◽  
Species Abundance ◽  
Species Abundance Distribution ◽  
Abundance Distribution ◽  
Marine Gastropods ◽  
Total Species Richness ◽  
Species Recruitment ◽  
Total Species

The genus Conus forms a conspicuous and rather homogeneous group within marine Gastropods. This makes it all the more interesting to focus on the sub-communities formed by Conus species and to analyze the potential specificities in the internal organization of species in these communities, in particular species richness, species abundance distribution and the effect of geographical distance between communities on differences in their respective species composition. Accordingly, two Conus communities along the coast in Mannar Gulf (India), separated by 80 km, are considered. Reliable analysis requires, first, to treat exhaustive data from complete samplings or, else – as here – to implement an appropriate extrapolation procedure to complete numerically the partial samplings. After numerical completion, substantial differences were highlighted between the two communities, not only in terms of true (total) species richness but, even more, as regards the profile and the average unevenness of the distributions of species abundance. Also, significant dissimilarity in species composition was found between the two communities, that may be tentatively attributed to either deterministic distance decay in similarity of species composition or, alternatively, to the persistence in the stochastic process of species recruitment from the regional stock of Conus planktonic larvae. This preliminary study yet requests to be complemented by other similar case studies, before drawing any safer interpretative conclusions.

scholarly journals Diversity, Composition, and Abundance Distribution of Birds in Kariangau Industrial Zone, Balikpapan City, East Borneo

2018 ◽  
Vol 10 (3) ◽  
pp. 605-612
Author(s):  
Alexander Kurniawan Sariyanto Putera ◽  
Yeni Aryati Mulyani ◽  
Dyah Perwitasari Farajallah ◽  
Stanislav Lhota ◽  
Tadeas Toulec
Keyword(s):  
Species Richness ◽  
Species Composition ◽  
Diversity Index ◽  
Future Research ◽  
Industrial Zone ◽  
Abundance Distribution ◽  
Bird Abundance ◽  
Rarefaction Analysis ◽  
Similarity Indices ◽  
Boat Traffic

The Kariangau Industrial Zone extends industry from Balikpapan city in the Central Balikpapan to the coast in Western Balikpapan, forming a part of Balikpapan Bay. Our study aimed to estimate the diversity, species composition, and the abundance distribution of birds at the industrial zone of Balikpapan City. Our study contained six replicates each of boat transects on four rivers, the Somber, Getah, Paka Dua, and Wain rivers during the months of May and June 2017. We calculated the Margalef diversity and Bray–Curtis similarity indices to estimate diversity and species composition, whereas bird abundance distributions were analyzed using Paleontological Statistics (PAST) version 3.12. The Getah river had the highest diversity index (4.846), followed by the Somber (3.988), Wain (3.510), and Paka Dua (3.050) rivers. The Bray–Curtis index revealed high similarity in species composition between the Wain and Paka Dua. Our rarefaction analysis showed that the Wain and Paka Dua rivers were well sampled and had lower species richness, with low differences between the observed and expected species richness, than the Somber and Getah rivers. Fisher Log Series Model also showed abundance distribution being highest at Getah (11.170), and lowest at the Paka Dua Rivers (5.221). This observation may be due to heightened industrial activities and boat traffic on each river. Our study provides a useful baseline for future research on the bird assemblages on Balikpapan Bay.

A multiple-threshold AR(1) model

1985 ◽  
Vol 22 (02) ◽  
pp. 267-279 ◽  
Author(s):  
K. S. Chan ◽  
Joseph D. Petruccelli ◽  
H. Tong ◽  
Samuel W. Woolford
Keyword(s):  
Least Squares ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Regularity Conditions ◽  
Model Parameters ◽  
Asymptotically Normal ◽  
Least Squares Estimators ◽  
Multiple Threshold ◽  
Necessary And Sufficient ◽  
Strongly Consistent

We consider the model Zt = φ (0, k)+ φ(1, k)Zt –1 + at (k) whenever r k−1<Z t−1≦r k , 1≦k≦l, with r 0 = –∞ and rl =∞. Here {φ (i, k); i = 0, 1; 1≦k≦l} is a sequence of real constants, not necessarily equal, and, for 1≦k≦l, {at (k), t≧1} is a sequence of i.i.d. random variables with mean 0 and with {at (k), t≧1} independent of {at (j), t≧1} for j ≠ k. Necessary and sufficient conditions on the constants {φ (i, k)} are given for the stationarity of the process. Least squares estimators of the model parameters are derived and, under mild regularity conditions, are shown to be strongly consistent and asymptotically normal.

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