An R pacakge for species richness estimation

Description

SPECIES provides multiple functions to compute popular estimators for species richness.These estimators include: (1) jackknife estimator by Burnham and Overton 1978, 1979; (2) lower-bound estimator by Chao 1984; (3) coverage-base estimators ACE, ACE-1 by Chao and Lee 1992; (4) coverage-duplication estimator from Poisson-Gamma model by Chao and Bunge 2002; (5) unconditional nonparametric maximum likelihood estimator by Norris and Pollock 1996, 1998; (6) penalized nonparametric maximum likelihood estimator by Wang and Lindsay 2005; and (7) Poisson-compound Gamma model with smooth nonparametric maximum likelihood estimation by Wang 2010.

Details

functions: chao1984, ChaoBunge, ChaoLee1992, jackknife, pcg ,pnpmle, unpmle; data: butterfly, cottontail,EST, insect, microbial, traffic

Author(s)

Ji-Ping Wang, Department of Statistics, Northwestern University

Maintainer: jzwang@northwestern.edu

References

Acinas, S., Klepac-Ceraj, V., Hunt, D., Pharino, C., Ceraj, I., Distel, D., and Polz, M. (2004), Fine-scale phylogenetic architecture of a complex bacterial community. Nature, 430, 551-554.

Bohning, D. and Schon, D., Nonparametric maximum likelihood estimation of population size based on the counting distribution, Journal of the Royal Statistical Society, Series C: Applied Statistics, 54, 721-737.

Burnham, K. P., and Overton,W. S. (1978), Estimation of the Size of a Closed Population When Capture Probabilities Vary Among Animals, Biometrika, 65, 625-633.

Burnham, K. P., and Overton,W. S. (1979), Robust Estimation of Population Size When Capture Probabilities Vary Among Animals, Ecology, 60, 927-936.

Chao, A. (1984), Nonparametric Estimation of the Number of Classes in a Population, Scandinavian Journal of Statistics, 11, 265-270.

Chao, A. (1987). Estimating the population size for capture-recapture data with unequal catchability. Biometrics 43, 783-791.

Chao, A., and Lee, S.-M. (1992), Estimating the Number of Classes via Sample Coverage, Journal of the American Statistical Association, 87, 210-217.

Chao, A., and Bunge, J. (2002), Estimating the Number of Species in a Stochastic Abundance Model, Biometrics, 58, 531-539.

Fisher, R. A., Corbet, A. S., and Williams, C. B. ,(1943), The Relation Between the Number of Species and the Number of Individuals in a Random Sample of an Animal Population, Journal of Animal Ecology, 12, 42-58.

Hong, S. H., and Bunge, J. and Jeon, S.O. and Epstein, S. (2006), Predicting microbial species richness, Proc. Natl. Acad. Sci, 103, 117-122.

Norris, J. L. I., and Pollock, K. H. (1996), Nonparametric MLE Under Two Closed Capture-Recapture Models With Heterogeneity, Biometrics, 52,639-649.

Norris, J. L. I., and Pollock, K. H.(1998), Non-Parametric MLE for Poisson Species Abundance Models Allowing for Heterogeneity Between Species, Environmental and Ecological Statistics, 5, 391-402.

Simar, L. (1976), Maximum likelihood estimation of a compound Poisson process, Annals of Statistics, 4, 1200-1209.

Wang, J.-P. Z. and Lindsay, B. G. (2005), A penalized nonparametric maximum likelihood approach to species richness estimation. Journal of American Statistical Association, 100(471):942-959.

Wang, J.-P., and Lindsay, B.G. (2008), An exponential partial prior for improving NPML estimation for mixtures, Statistical Methodology, 5:30-45.

Wang, J.-P. (2010), Estimating the species richness by a Poisson-Compound Gamma model, Biometrika, 97(3): 727-740.

Wang, J.-P. (2011), SPECIES: An R Package for Species Richness Estimation, Journal of Statistical Software, 40(9), 1-15, URL: http://www.jstatsoft.org/v40/i09/.

Examples

##load library
library(SPECIES)

## "butterfly" is the famous butterfly data by Fisher 1943.

data(butterfly)

##jackknife method
jackknife(butterfly,k=5)

##using only 'ACE' coverage method
ChaoLee1992(butterfly,t=10, method="all")

##using chao1984 lower bound estimator
chao1984(butterfly)

##using Chao and Bunge coverage-duplication method
ChaoBunge(butterfly,t=10)

##penalized NPMLE method
#pnpmle(butterfly,t=15,C=1,b=200)

##unconditonal NPMLE method
#unpmle(butterfly,t=10,C=1,b=200)

##Poisson-compound Gamma method
#pcg(butterfly,t=20,C=1,b=200)

Coverage-duplication estimator for species richness

Description

This function calculates coverage-duplication based estimator from a Poisson-Gamma model by Chao and Bunge 2002.

Usage

       ChaoBunge(n, t = 10,conf = 0.95)

Arguments

Value

The function ChaoBunge returns a list of: Nhat, SE and CI.

Author(s)

Ji-Ping Wang, Department of Statistics, Northwestern University

References

Chao, A. (1984), Nonparametric Estimation of the Number of Classes in a Population, Scandinavian Journal of Statistics, 11, 265-270.

Chao, A., and Bunge, J. (2002), Estimating the Number of Species in a Stochastic Abundance Model, Biometrics, 58, 531-539.

Examples

library(SPECIES)

##load data from the package, 
##"butterfly" is the famous butterfly data by Fisher 1943.

data(butterfly)

##output estimates from all 4 methods using cutoff t=10
ChaoBunge(butterfly,t=10)

Coverage-based estimators for species richness

Description

This function calculates ACE and ACE-1 estimators by Chao and Lee 1992 (ACE-1 provides further bias correction based on ACE).

Usage

       ChaoLee1992(n, t = 10, method = "all",conf = 0.95)

Arguments

Value

The function ChaoLee1992 returns a list of: Nhat, SE and CI.

Author(s)

Ji-Ping Wang, Department of Statistics, Northwestern University

References

Chao, A. (1987). Estimating the population size for capture-recapture data with unequal catchability. Biometrics 43, 783-791.

Chao, A., and Lee, S.-M. (1992), Estimating the Number of Classes via Sample Coverage, Journal of the American Statistical Association, 87, 210-217.

Examples

library(SPECIES)

##load data from the package, 
## "butterfly" is the famous butterfly data by Fisher 1943.

data(butterfly)

##output estimates from all 4 methods using cutoff t=10
ChaoLee1992(butterfly,t=10,method="all")

##output estimates from ACE method using cutoff t=10
ChaoLee1992(butterfly,t=10,method="ACE")

EST data

Description

The Arabidopsis thaliana expressed sequence tag (EST) data originally appeared in Wang and Lindsay 2005. It was recently reanalyzed in Wang 2010. For convenience, the frequency at j=17 is used to denote the total count of species with j\ge17.

References

Wang, J.-P. Z. and Lindsay, B. G. ,(2005), A penalized nonparametric maximum likelilhood approach to species richness estimation. Journal of American Statistical Association, 2005,100(471):942-959

Examples

##load library
library(SPECIES)

##load data that coming with the package.
data(EST)

Fisher's butterfly data

Description

The famous Fisher's butterfly data originally appeared in Fisher 1943. It has been re-analyzed in many publications in the literature.

References

Fisher, R. A., Corbet, A. S., andWilliams, C. B. ,1943, The Relation Between the Number of Species and the Number of Individuals in a Random Sample of an Animal Population, Journal of Animal Ecology, 12, 42-58.

Examples

##load library
library(SPECIES)

##load data that coming with the package.
data(butterfly)

Lower-bound estimator for species richness

Description

This function calculates the lower-bound estimator by Chao 1984.

Usage

       chao1984(n,conf=0.95)

Arguments

Value

The function chao1984 returns a list of: Nhat, SE and CI.

Author(s)

Ji-Ping Wang, Department of Statistics, Northwestern University

References

Chao, A. (1984), Nonparametric Estimation of the Number of Classes in a Population, Scandinavian Journal of Statistics, 11, 265-270.

Chao, A. (1987). Estimating the population size for capture-recapture data with unequal catchability. Biometrics 43, 783-791.

Examples

library(SPECIES)

##load data from the package, 
## \dQuote{butterfly}is the famous butterfly data by Fisher 1943.

data(butterfly)
chao1984(butterfly)

Cottontail data

Description

The cottontail data was analyzed in Chao 1987

References

Chao, A. (1987). Estimating the population size for capture-recapture data with unequal catchability. Biometrics 43, 783-791.

Examples

##load library
library(SPECIES)

##load data that coming with the package.
data(cottontail)

Insects data

Description

The insects data was analyzed in Burnham and Overton 1979. The frequency at j=6 is used to denote the total count of species with j\ge 6.

References

Burnham, K. P., and Overton,W. S. (1979), Robust Estimation of Population Size When Capture Probabilities Vary Among Animals, Ecology, 60, 927-936.

Examples

##load library
library(SPECIES)

##load data that coming with the package.
data(insects)

Jackknife estimator for the species richness

Description

A function implementing the jackknife estimator of the species number by Burnham and Overton 1978 and 1979.

Usage

jackknife(n, k = 5, conf = 0.95)

Arguments

Value

The function jackknife returns a list of: JackknifeOrder, Nhat, SE and CI.

Author(s)

Ji-Ping Wang, Department of Statistics, Northwestern University

References

Burnham, K. P., and Overton,W. S. (1978), Estimation of the Size of a Closed Population When Capture Probabilities Vary Among Animals, Biometrika, 65, 625-633.

Burnham, K. P., and Overton,W. S. (1979), Robust Estimation of Population Size When Capture Probabilities Vary Among Animals, Ecology, 60, 927-936.

Examples

library(SPECIES)

##load data from the package, 
## "butterfly" is the famous tterfly data by Fisher 1943.

data(butterfly)
jackknife(butterfly,k=5)

Microbial species data

Description

The microbial species data originally appeared in Acinas et al 2004. Recently it was re-analyzed by Bohning and Schon 2005, and Wang 2009.

References

Acinas, S., Klepac-Ceraj, V., Hunt, D., Pharino, C., Ceraj, I., Distel, D., and Polz, M. (2004), Fine-scale phylogenetic architecture of a complex bacterial community. Nature, 430, 551-554.

Hong, S. H., and Bunge, J. and Jeon, S.O. and Epstein, S. (2006), Predicting microbial species richness, Proc. Natl. Acad. Sci, 103, 117-122.

Examples

##load library
library(SPECIES)

##load data that coming with the package.
data(microbial)

Poisson-compound Gamma estimator for the species richness

Description

Function to calculate the Poisson-compound Gamma estimators of the species number by Wang 2010. This method is essentially a conditional NPMLE method. The species abundance here is assumed to follow a compound Gamma model. The confidence interval is obtained based on a bootstrap procedure. A Fortran function is called to for the computing. This function requires Fortran compiler installed.

Usage

pcg(n,t=35,C=0,alpha=c(1:10),b=200,seed=NULL,conf=0.95,dis=1)

Arguments

Details

The pcg estimator is computing intensive. The computing of bootstrap confidence interval may take up to a few hours.

Value

The function pcg returns a list of: Nhat, CI (if “C=1”) and AlphaModel.

Author(s)

Ji-Ping Wang, Department of Statistics, Northwestern University

References

Wang, J.-P. (2010), Estimating the species richness by a Poisson-Compound Gamma model, 97(3): 727-740

Examples

library(SPECIES)
##load data from the package, 
## \dQuote{butterfly} is the famous butterfly data by Fisher 1943.

data(butterfly)

##output estimate without confidence interval using cutoff t=15
##pcg(butterfly,t=20,C=0,alpha=c(1:10))

##output estimate with confidence interval using cutoff t=15
#pcg(butterfly,t=20,C=1,alpha=c(1:10),b=200)

Penalized conditional NPML estimator for species richness

Description

This function calculate the penalized conditional NPML estimator of the species number by Wang and Lindsay 2005. This estimator was based on the conditional likelihood of a Poisson mixture model. A penalty term was introduced into the model to prevent the boundary problem discussed in Wang and Lindsay 2008. The confidence interval is calculated based on a bootstrap procedure. A Fortran function is called to for the computing.

Usage

pnpmle(n,t=15,C=0,b=200,seed=NULL,conf=0.95,dis=1)

Arguments

Value

The function pnpmle returns a list of: Nhat, CI (if “C=1”).

Author(s)

Ji-Ping Wang,Department of Statistics, Northwestern University

References

Wang, J.-P. Z. and Lindsay, B. G. ,2005, A penalized nonparametric maximum likelihood approach to species richness estimation. Journal of American Statistical Association, 2005,100(471):942-959

Wang, J.-P., and Lindsay, B.G., 2008, An exponential partial prior for improving NPML estimation for mixtures, Statistical Methodology, 2008,5:30-45

Examples

library(SPECIES)

##load data from the package, 
## \dQuote{butterfly} is the famous butterfly data by Fisher 1943.
#data(butterfly)

##output estimate without confidence interval using cutoff t=15
#pnpmle(butterfly,t=15,C=0)

##output estimate with confidence interval using cutoff t=15
#pnpmle(butterfly,t=15,C=1, b=200)

Traffic data

Description

The traffice data originally appeared in Simar 1976 where the total number of N is knowns as 9461. Recently it was re-analyzed by Bohning and Schon 2005.

References

Simar, L. (1976), Maximum likelihood estimation of a compound Poisson process, Annals of Statistics, 4, 1200-1209. Bohning, D., and Schon, D. (2005), Nonparametric maximum likelihood estimation of population size based on the counting distribution, Journal of the Royal Statistical Society, Series C: Applied Statistics, 54, 721-737.

Examples

##load library
library(SPECIES)

##load data that coming with the package.
data(traffic)
chao1984(traffic)

Unconditional NPML estimator for the SPECIES number

Description

This function calculate the unconditional NPML estimator of the species number by Norris and Pollock 1996, 1998. This estimator was obtained from the full likelihood based on a Poisson mixture model. The confidence interval is calculated based on a bootstrap procedure.

Usage

unpmle(n,t=15,C=0,method="W-L",b=200,conf=.95,seed=NULL,dis=1)

Arguments

Details

The computing is intensive if method=“N-P” is used particularly when extrapolation is large. It may takes hours to compute the bootstrap confidence interval. If method=“W-L” is used, computing usually is much much faster. Estimates from both methods are often identical.

Value

The function unpmle returns a list of: Nhat, CI (if “C=1”)

Note

The unconditional NPML estimator is unstable from either method='N-P' or method='W-L'. Extremely large estimates may occur. This is also reflected in that the upper confidence bound often greatly vary from different runs of bootstrap procedure. In contrast the penalized NPMLE by pnpmle function is much more stable.

Author(s)

Ji-Ping Wang, Department of Statistics, Northwestern University

References

Norris, J. L. I., and Pollock, K. H. (1996), Nonparametric MLE Under Two Closed Capture-Recapture Models With Heterogeneity, Biometrics, 52,639-649.

Norris, J. L. I., and Pollock, K. H.(1998), Non-Parametric MLE for Poisson Species Abundance Models Allowing for Heterogeneity Between Species, Environmental and Ecological Statistics, 5, 391-402.

Bonhing, D. and Schon, D., (2005), Nonparametric maximum likelihood estimation of population size based on the counting distribution, Journal of the Royal Statistical Society, Series C: Applied Statistics, 54, 721-737.

Wang, J.-P. Z. and Lindsay, B. G. ,(2005), A penalized nonparametric maximum likelihood approach to species richness estimation. Journal of American Statistical Association, 2005,100(471):942-959

Examples

library(SPECIES)

##load data from the package, 
## "butterfly" is the famous butterfly data by Fisher 1943.

data(butterfly)


##output estimate without confidence interval using cutoff t=15
#unpmle(butterfly,t=15,C=0)

##output estimate with confidence interval using cutoff t=15
#unpmle(butterfly,t=15,C=1,b=200)