Estimating number of species

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Species richness, that is the total number of species existing in a given area, is a common biodiversity indicator because it is simple and intuitive. However, determining the number of species (either in total or for a species group such as trees) in a given region is difficult and time consuming. Full enumeration of individuals and species is expensive. The unbiased sample-based estimation of species richness has been studied for decades. In the 1920s, Arrhenius (1921[1], 1923[2]) used extrapolation techniques to estimate species richness, and later the great R.A. Fisher (Fisher et al., 1943[3]) initiated intensive research into this matter. Bunge and Fitzpatrick (1993[4]), revealing an extraordinary variety of estimators and estimation procedures, provided an excellent theoretical review of existing species richness estimators. Up till now, however, there is no unbiased estimator available.

Species richness estimators were frequently applied to various taxa; application of the estimators to tree species from forest inventories include Chazdon et al. (1998[5]), Condit et al. (1996[6]); Hellmann and Fowler (1999[7]), Magnussen et al. (2006[8]), Palmer (1990[9], 1991[10]) and Schreuder et al.(1999[11]).

Walther and Moore (2005[12]) gathered an extensiv list of additional studies and summarized them by the species richness estimators. They also provided various definitions and measures of bias, precision and accuracy to evaluate the estimators´ performances. Colwell and Coddington (1994[13]) and Gotelli and Colwell (2001[14]) provided in depth discussion on issues related to pitfalls and cautions.

There are at least two species richness estimation softwares: EstimateS (Colwell, 2007[15]) and SPADE (Chao and Shen, 2006[16]), both easily accessible.

Estimation of species richness for larger regions is a generic sampling issue. The basic question is in principle the same as with the estimation of growing stock or tree size in a given region. However, there is also a basic difference with respect to statistical analysis: while growing stock and tree size are metric variables – species richness is a nominal variable. Thus, conventional models such as expansion factor in estimating metric variables on a per unit area basis are not applicable to species richness estimation.

Large area forest inventories such as national forest inventories are carried out in many regions so as to provide baseline information for forest and related policy formulation. A relatively large number (commonly between about 500 and several 1000s) of relatively small field plots (commonly of areas between about 0.1 and 1 ha), usually laid out in a systematic grid over the entire inventory area, constitute the backbone of estimation (for example FAO 2003[17]). While the area of one field plot is small, the total tallied sample area is large. Thus, such data set should be, also because of the homogeneous geographical cover, an excellent basis for species richness estimation in the inventory region.

This chapter discusses some issues in this context and is largely based on based on (Lam and Kleinn 2008[18]) and we look here exclusively at estimating the number of tree species. However, the principles can, of course, be applied to any other taxa group.


Figure 1 Typical example for the distribution of species in a natural forest where the about 270 observed species were ordered by the number of observed individuals: some few species occur in larger numbers but there are also many species that are only observed once in the entire inventory. In this example, the by far most abundant “species” is the class “not identified” (Kleinn 2007[19]).

The only undisputed estimation for species richness is in making a statement about the lower bound of species present: the number of observed species in the sample. There are numerous approaches to extrapolate the observed number of species to the estimated total number of species, but unbiased estimators do not exist (yet) and different studies identify different estimators as appropriate or best. It is, therefore, practically impossible to give a general recommendation about a best approach for the estimation of species richness. In particular in tropical forests with large numbers of tree species, monitoring of species richness is of major interest in the context of biodiversity monitoring.

When the species present do occur all in larger numbers of individuals, the likelihood that all species are observed is large and the number of observed species can be used as estimate for the total number of species. While this may happen in managed and planted forests, it is often the rarer species that make up for a large number of species and these have a large likelihood not to be in the sample. An example for the frequency distribution from a tropical forest inventory is given in Figure 1; there, some species occur in larger number on the total of all sample plots, but many species were found only once in the sample.

The number of these singletons is usually a relevant input to the extrapolation of species richness. In this example, the most abundant “species” is the group “not identified” – and this constitutes a major issue in the estimation of tree species richness above all in tropical forests (see also the following chapter); it is interesting to note that observation errors such as lack of identification, or even more difficult: wrongly identified species, are usually a lesser concern in research on estimating species richness.

Many estimators have been developed and most of them have the number of singletons and doubletons and the number of actually observed species as input variables. We list some of these estimators based on Schreuder et al. 1999 but leave here out a wider class of jackknife based estimators as dealt with, for example, in Burnham and Overton (1978, 1979) or in Lam and Kleinn (2008). There may even be cases in which application of an estimator produces an estimated number of species that is lower than the number of observed species; of course, this is an unwanted characteristic of an estimator and it points to the fact that none of them has the property of unbiasedness.

Species identification

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Species estimation in large area forest inventory


  • EstimateS is a free software application that computes a variety of biodiversity functions, estimators, and indices.


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  4. Bunge J. and M. Fitzpatrick. 1993. Estimating the number of species: a review. J. Am. Stat. Assoc. 88, 364–373.
  5. Chazdon R.L., R.K. Colwell, J.S. Denslow and M.R. Guariguata. 1998. Statistical methods for estimating species richness of woody regeneration in primary and secondary rain forests of Northeastern Costa Rica. In: Dallmeier F and JA Comisky. (Eds.), Forest biodiversity research, monitoring and modelling. The Parthenon Publishing Group, Paris, France, pp. 285–309.
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  11. Schreuder, H.T., R.C. Czaplewski and R.G. Bailey. 1999. Combining mapped and statistical data in forest ecological inventory and monitoring-supplementing an existing system. Env Mon Asst 56:269-291.
  12. Walther B.A. and J.L. Moore. 2005. The concepts of bias, precision and accuracy, and their use in testing the performance of species richness estimators, with a literature review of estimator performance. Ecography 28, 815–829
  13. Colwell R.K. and J.A. Coddington. 1994. Estimating terrestrial biodiversity through extrapolation. Philos. T. Roy. Soc. B. 345, 101–118.
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  15. Colwell R.K. 2007. EstimateS: Statistical estimation of species richness and shared species from samples. Version 8.0. User's Guide and application published at:
  16. Chao A. and T.J. Shen. 2006. Program SPADE (Species Prediction And Diversity Estimation). Program User’s Guide published at
  17. FAO. 2003. Workshop on the FAO approach to national forest resources assessment and ongoing project. FAO Forest Resources Assessment Working Paper No.70/E. Food and Agriculture Organization of the United Nations, Rome. 25p.
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  19. Kleinn, C. 2007. Lecture Notes for the Teaching Module Forest Inventory. Department of Forest Inventory and Remote Sensing. Faculty of Forest Science and Forest Ecology, Georg-August-Universität Göttingen. 164 S.

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