Species Richness v2.1
Introduction
The Species Richness eco-tool implements a variety of analyses that take as their input a “species by sample” matrix of observed abundances. For the most part, these are a subset of the analyses performed by the downloadable software package EstimateS (Colwell 1994–present). The analyses include various summary statistics, as well as a number of estimators of true species richness, including Chao 1, Chao 2, ACE, ICE, first-order jackknife, second-order jackknife, and bootstrap (see Colwell and Coddington 1994 for an overview of these estimators). Variances (and hence confidence intervals) for these estimators are calculated based on analytical results (for Chao 1 and Chao 2) or on multiple random resamples with replacement (for everything else). Finally, the eco-tool calculates a sample-based rarefaction curve, with confidence intervals, using the analytical method described in Colwell et al. 2004, as well as the individual-based rarefaction curve for comparison. These curves are plotted, and both the figures and the curve data are provided for download.
Differences between the eco-tool and EstimateS
- In EstimateS, the user chooses between resampling with or without replacement in any one run. The eco-tool does both. Both types of resampling are useful. Resampling without replacement allows one to calculate a non-biased mean value of a estimator (such as Chao 2) at smaller sample sizes. This allows one to see if the statistic is approaching an asymptote as the number of samples increases. Any estimator which has not reached an asymptote is a minimum estimate, and should be used with caution. Resampling with replacement produces bootstrap estimates of the variance of a statistic at all sample sizes, including the full data sample (but would produce downward-biased estimates of the mean value). Both these estimates — the mean and the variance — are used to plot how each calculated statistic varies with sample size, up to the full sample.
- The eco-tool calculates the classic individual rarefaction curve, rather than the Coleman approximation used by EstimateS. The differences are negligible.
What the Eco-Tool does (that EstimateS does not)
- The eco-tool performs two tests of the assumption of sample set homogeneity that underlies these methods. The tests only make sense if the samples are ordered in some way; if they are not, you can ignore the results of the tests. The first test is for a trend in the rate of observation per unit effort, which is most useful when your samples are ordered in time. A trend may indicate immigration, emigration, or perhaps depletion caused by the sampling process itself. A large trend will invalidate any estimates of species richness. The other test is for a trend in community composition, using canonical correspondence analysis with sample order as a predictor. This is relevant when your samples are ordered in either space or time (or both). A trend here indicates progressive change in community composition over time (e.g., seasonality) or space (e.g., an ecotone), and should also cause the researcher to re-examine his or her assumptions.
- The eco-tool generates two sets of confidence intervals for the sample rarefaction curves, rather than one. One set assumes that the true species richness is given by the Chao 2 estimator (as per EstimateS). The other assumes that the true species richness is given by the upper bound of the 95% confidence interval for the Chao 2 estimator. This is a conservative approach — probably overly-conservative!
- The eco-tool plots the rarefaction curves and the resampling curves.
What the Eco-Tool does NOT do (that EstimateS does)
- The eco-tool does not (currently) output all the resampling data in numerical form, but just the rarefaction curves. A future update will include the option to download all the data as a text file.
- The eco-tool does not let you set your own seed for the random number generator. If you would like this functionality, please ask. (Choosing the seed lets you repeat runs with exactly the same randomaizations.)
- EstimateS calculates the Michaelis-Menten curve-fit estimate of species richness. The eco-tool does not do any curve fitting. The first version of this eco-tool fit a variety of curves (see the Archive), but these methods are generally regarded as unreliable.
- For a long time EstimateS has had the ability to calculate diversity indices (Simpson’s, Shannon-Weiner), and as of v7.5 it can also calculate Anne Chao’s new Sørensen and Jaccard similarity estimators (Chao et al. 2005). These features may be added to the eco-tool in the future.
Why duplicate EstimateS, even in part? Does Rob Colwell know about this?
Good questions! The eco-tool provides access to many of the same calculations for those who, for one reason or another, cannot use the latest versions of EstimateS. This may include those with access only to very old computers, or those using UNIX. The eco-tool provides plots for instant visual feedback, and the web-page nature of the output means that explanatory text can accompany the statistics. It is also easier (therefore quicker) to fix bugs and implement updates in the higher-level code that runs the eco-tool. The source code is available for download in a fully-annotated Mathematica notebook, with example data built in, so it can be verified and/or customized. Finally, it is always good to have an alternative source of calculations to compare against, as this is how mistakes are found!
And yes, Rob knows and approves.
References
Colwell, R. K and J. A. Coddington (1994) Estimating terrestrial biodiversity through extrapolation. Phil. Trans Roy. Soc. Lond. B 345: 101–118.
Colwell, R. K. 1994–present. EstimateS: statistical estimation of species richness and shared species from samples. http://viceroy.eeb.uconn.edu/estimates. [Persistent URL: http://purl.oclc.org/estimates.]
Colwell, R. K., C. X. Mao and J. Chang (2004) Interpolating, extrapolating, and comparing incidence-based species accumulation curves. Ecology 85: 2717–2727.
Gotelli, N. and R. K. Colwell (2001) Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness. Ecology Letters 4: 379–391.
Chao, A., Chazdon, R. L., Colwell, R. K. and Shen, T.-J.(2005). A new statistical approach for assessing similarity of species composition with incidence and abundance data. Ecology Letters 8: 148–159.