An R package for estimating the number of species represented at least r times

Description

preseqR provides functions to estimate the number of species represented at least r times in a random sample based on an initial sample. Functions work through rational function approximations to a modified Good and Toulmin's (1956) non-parametric empirical Bayes power series estimator. The rational function approximation is then boosted to an estiamtor for the number species represented at least r times, based on a relation bewteen the number of species represented at least r times and the number of species represented at least once.

Details

functions:

ds.mincount.bootstrap

ds.mincount

ztpois.mincount

ztnb.mincount

boneh.mincount

chao.mincount

pois.mincount

nb.mincount

preseqR.ztnb.em

preseqR.simu.hist

preseqR.nonreplace.sampling

preseqR.interpolate.mincount

data: FisherButterflyHist, ShakespeareWordHist

Author(s)

Chao Deng, Timothy Daley, and Andrew D. Smith

Maintainer: Chao Deng <chaodeng@usc.edu>

References

Baker, G. A., & Graves-Morris, P. (1996). Pade approximants (Encyclopedia of Mathematics and its Applications vol 59).

Boneh, S., Boneh, A., & Caron, R. J. (1998). Estimating the prediction function and the number of unseen species in sampling with replacement. Journal of the American Statistical Association, 93(441), 372-379.

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

Chao, A., & Shen, T. J. (2004). Nonparametric prediction in species sampling. Journal of agricultural, biological, and environmental statistics, 9(3), 253-269.

Cohen Jr, A. C. (1960). Estimating the parameters of a modified Poisson distribution. Journal of the American Statistical Association, 55(289), 139-143.

Daley, T., & Smith, A. D. (2013). Predicting the molecular complexity of sequencing libraries. Nature methods, 10(4), 325-327.

Deng C, Daley T and Smith AD (2015). Applications of species accumulation curves in large-scale biological data analysis. Quantitative Biology, 3(3), 135-144. URL http://dx.doi.org/10.1007/s40484-015-0049-7.

Efron, B., & Thisted, R. (1976). Estimating the number of unseen species: How many words did Shakespeare know?. Biometrika, 63(3), 435-447.

Efron, B. (1979). Bootstrap methods: another look at the jackknife. The annals of Statistics, 1-26.

Efron, B., & Tibshirani, R. J. (1994). An introduction to the bootstrap. CRC press.

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.

Good, I. J., & Toulmin, G. H. (1956). The number of new species, and the increase in population coverage, when a sample is increased. Biometrika, 43(1-2), 45-63.

Heck Jr, K. L., van Belle, G., & Simberloff, D. (1975). Explicit calculation of the rarefaction diversity measurement and the determination of sufficient sample size. Ecology, 1459-1461.

Kalinin V (1965). Functionals related to the poisson distribution and statistical structure of a text. Articles on Mathematical Statistics and the Theory of Probability pp. 202-220.