Estimating species numbers by extrapolation: a cautionary note

Ulrich, Werner

doi:ISSN 1505-2249

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Estimating species numbers by extrapolation: a cautionary note Ulrich, Werner

Object structure

Estimating species numbers by extrapolation: a cautionary note

Estimating species numbers by extrapolation

Ulrich, Werner

Polish Academy of Sciences. Institute of Ecology

Polish Academy of Sciences. Institute of Ecology. Publishing Office

Dziekanów Leśny

2001

Strony 299-305 : ilustracje ; 27 cm ; Bibliografia na stronach 304-305

Czasopismo/Artykuł

species numbers ; extrapolation ; species accumulation curve ; relative abundance distributions ; power fraction ; jackknife-estimator

This paper evaluates the accuracy any estimator of species numbers may achieve if only a limited fraction (up to 3/4) of the species number in the community has been sampled. From the impossibility to infer the relative abundance distribution (RAD) the rare and not sampled species follow it is shown that it is only possible to give a lower and an upper boundary of the species number. The lower boundary may be inferred either from a fit of a log-normal type RAD or by a graphical method. In the latter case, the lower boundary is Smin = (ln (dmin) - 2 icpt) / slope with dmin being the minimal possible relative density in the community and icpt and slope being the intercept and the slope of the geometric series fitted through the linear part of the log-normal distribution. The upper boundary is found through an extrapolation of this geometric series up to dmin [Smax = (ln (dmin) - icpt) / slope]. For any estimator to work dmin has to be known.

Bunge J., Fitzpatrick M. 1993 - Estimating the number of species: a review - J. Am. Stat. Assoc. 88: 364-373.
Burnham K. P., Overton W. S. 1978 - Estimation of the size of a closed population when capture probabilities vary among animals - Biometrika, 65: 623-633.
Burnham K. P., Overton W. S. 1979 - Robust estimation of population size when capture probabilities vary among animals - Ecology, 60: 927-936.
Chao A. 1984 - Non-parametric estimation of the number of classes in a population - Scand. J. Stat. 11: 265-270.
Chao L. 1987 - Estimating the population size for capture-recapture data with unequal catchability - Biometrics, 43: 783-791.
Chao A., Lee S. M. 1992 - Estimating the number of classes via sample coverage - J. Am. Sta. Assac. 87: 210-217.
Chao A., Lee S. M., Jeng S. L. 1992 - Estimation of population size for capture-recapture data when capture probabilities vary by time and individual animal - Biometrics, 48: 201-216.
Colwell R. K., Coddington J. A. 1994 - Estimating terrestrial biodiversity through extrapolation - Phil. Trans. R. Soc. Lond. B 345: 101-118.
De Caprariis P., Lindemann R. H., Collins C. 1976 - A method for determining optimum sample size in species diversity studies - Math. Geol. 8: 575-581.
Edwards L. E. 1997 - A useful procedure for estimating the species richness of spiders - J. Arachnology, 25: 99-105.
Frontier S. 1985 - Diversity and structure in aquatic ecosystems (In : Oceanography and Marine Biology - An Annual Review, Ed. M. Barnes) - Aberdeen, pp. 253-312.
Gregory R. 1994 - Species abundance patterns of British birds - Proc. R. Soc. Lond. B 257: 299-301.
Hilpert H. 1989 - Zur Hautfluglerfauna eines sudbadischen Eichen-Hainbuchenmischwaldes - Spixiana, 12: 57-90.
Hughes R. G. 1986 - Theories and models of species abundance - Am. Nat. 128: 879-899.
Keating K. A. 1998 - Estimating species richness: the Michaelis-Menten model revisited - Oikos, 81: 411-416.
Lauga J., Joachim J. 1987 - L'echantillonnage des populations d'oiseaux par la methode des E.F.P.: interet d'une etude mathemathique de la courbe de richesse cumulee - Acta Oecol. Oecol. Gen. 8: 117-124.
Lee S. M., Chao A. 1994 - Estimating population size via sample coverage for closed capture-recapture models - Biometrics, 50: 88-97.
Miller R. I., Wiegert R. G. 1989 - Documenting completeness, species-area relations, and the species abundance distribution of a regional flora - Ecology, 70: 16-22.
Mingoti S. A., Meeden G. 1992 - Estimating the total number of distinct species using presence and absence data - Biometrics, 48: 863-875.
Moulliot D., Lepretre A., Andrei-Ruiz M.-C., Viale D. 2000 - The fractal model: an new model to describe the species accumulation process and relative abundance distribution (RAD) - Oikos, 90: 333-342.
Nee S., Harvey P. H., May R. M. 1991 - Lifting the veil on abundance patterns - Proc. R. Soc. Lond. B 243: 161-163.
Palmer M. W. 1990 - The estimation of species richness by extrapolation - Ecology, 71: 1195-1198.
Palmer M. W. 1991 - The estimation of species richness: the second-order jackknife reconsidered - Ecology, 72: 1512-1513.
Slocomb J., Dickson K. L. 1978 - Estimating the total number of species in a biological community (In : Biological data in water pollution assessment: quantitative and statistical analyses, Eds K. L. Dickson, J. Cairns Jr., R. J. Livingston) - Philadelphia, pp. 38-52.
Slocomb J., Stauffer B., Dickson K. L. 1977 - On fitting the truncated lognormal distribution to species abundance data using maximum likelihood estimation - Ecology, 58: 693-696.
Soberon M. J., Llorente B. J. 1993 - The use of species accumulation functions for the prediction of species richness - Cons. Biol. 7: 480-488.
Stout J., Vandermeer J. 1975 - Comparison of species richness for stream-inhabiting insects in tropical and mid latitude streams - Am. Nat. 109: 263-280.
Sugihara G. 1980 - Minimal community structure: an explanation of species abundance patterns - Am. Nat. 116: 770-787.
Tackaberry R., Brokaw N., Kellman M., Mallory E. 1997 - Estimating species richness in tropical forest: the missing species extrapolation technique - J. Trop. Ecol. 13: 449-458.
Tokeshi M. 1993 - Species, abundance patterns and community structure - Adv. Ecol. Res. 24: 111-186.
Tokeshi M. 1996 - Power fraction: a new explanation of relative abundance patterns in species-rich assemblages - Oikos, 75: 543-550.
Ulrich W. 1998 - The parasitic Hymenoptera in a beech forest on limestone I: Species composition, species turnover, abundance and biomass - Polish J. Ecol. 46: 261-289.
Ulrich W. 1999a - Estimating species numbers by extrapolation I: Comparing the performance of various estimators using large model assemblages - Pol. J. Ecol. 47: 271-291.
Ulrich W. 1999b - The Hymenoptera of a dry meadow on limestone: species composition, abundance and biomass - Polish J. Ecol. 46: 29-47.
Ulrich W. 1999c - Temporal stability of community structure of the parasitic Hymenoptera in a beech forest on limestone - Pol. J. Ecol. 47: 257-270.
Ulrich W. 2000 - Niche segregation and coexistence of parasitic Hymenoptera of the Aspilota genus group (Hymenoptera, Braconidae) in a beech forest on limestone - Pol. J. Ecol. 48: 225-238.
Ulrich W. 2001: Models of relative abundance distributions I: Model fitting by stochastic models - Pol. J. Ecol.: 49: 145-157.
Walther B. A., Morand S. 1998 - Comparative performance of species richness estimation methods - Parasitology, 116: 395-405.
Winklehner R., Winkler H., Kampichler C. 1997 - Estimating local species richness of epigeic Collembola in temperate dry grassland - Pedobiologia, 41: 154-158.