EstimateS 8.2 User's Guide
Table of Contents
Richness and Species Diversity
Shared Species and Similarity
Indexes (Shared Species Menu)
Appendix A: Sample-Based Rarefaction
Curve (Expected Species Accumulation Curve)
EstimateS 8.2 is a free software application for Windows and Macintosh operating systems that computes a variety of biodiversity functions, estimators, and indexes based on biotic sampling data. For an overview of major features, click here.
In this Guide, the term sample refers to any list of species or OTUs from a locality, site, quadrat, trap, time unit, clone library, or some other entity. EstimateS expects sets of samples that share some or all species.
Some estimators and indexes require species abundance data (counts) for each species in each sample. This is called abundance data. Other estimators and indexes require only presence/absence (occurrence) data for each species in each sample. This is called incidence data. When comparing the biotic (species) composition of two or more localities (or habitats, treatments, seasons, etc.), you can do so either using abundance data, or using summed incidence data (frequencies of occurence, pooled among samples) for each or two or more sample sets.
Sample-based Rarefaction (species accumulation curves). EstimateS 7 and later versions (indicated as "EstimateS 7+" in this Guide) computes expected species accumulation curves (sample-based rarefaction curves in the terminology of Gotelli & Colwell 2001), with 95% confidence intervals, using the analytical formulas of Colwell et al. (2004), detailed in Appendix A of this Guide. (See also Mao et al. . An equivalent formula for expected richness, but not for the variance, was independently developed by Ugland et al. ). This method is a precise equivalent of, and completely replaces the resampling technique used in previous versions of Estimates for computing these curves (the variable Sobs). The expected richness function is called Mao Tau in EstimateS output.
The traditional, resampled Sobs is nonetheless still produced by EstimateS 7+, so you can see for yourself that Mao Tau is yielding the expected values of Sobs, and so you can still produce non-randomized accumulation curves if you wish.
Because they are computed analytically, Mao Tau and its confidence limits do not require any resampling runs in EstimateS. If expected species accumulation curves (and/or Coleman curves) are all you need, you can set the number of runs to 1 in the Diversity Settings screen. Resampling is still required in Estimates 7+ to compute singletons, doubletons, duplicates, uniques, and all richness estimators for accumulating samples (see below).
To compare datasets in terms of species richness instead of species density, Gotelli & Colwell (2001) recommend rescaling of the expected species accumulation (Mao Tau) curves (and their 95% confidence interval curves) by individuals, instead of leaving them scaled by samples. To allow this rescaling to produce smooth curves, EstimateS 7+ computes the number of individuals for each sampling level, instead of taking the mean for number of individuals, among resampling runs. (If there are N individuals, total, in Q(max) samples, total, the expected number of individuals in Q samples is just [Q / Q(max)] * N; these are the values tabled by EstimateS 7+ for the Individuals column of the output.)
Individual-based Rarefaction. EstimateS also computes classic, individual-based rarefaction curves (in the terminology of Gotelli & Colwell 2001) or Coleman curves for sample-based abundance data. Like sample-based rarefaction curves, these curves are computed analytically, not by resampling.
As discussed by Colwell & Coddington 1994, and independently reported by Brewer & Williamson (1994), Coleman curves and classical rarefaction curves (for sampling without replacement) are identical to three or four decimal places for most datasets. The Coleman curve is orders of magnitude more efficient computationally, so EstimateS computes Coleman curves. See Gotelli & Colwell (2001) and Colwell et al. (2004) for more on Coleman curves.
Because they are computed analytically, Coleman curves do not require any resampling runs in EstimateS. If Coleman (and/or expected species accumulation curves) are all you need, you can set the number or runs to 1 in the Diversity Settings screen. Resampling is still required in Estimates 7 to compute singletons, doubletons, duplicates, uniques, and all richness estimators for accumulating samples (see below).
Rarefaction vs. richness estimation. Please note that neither sample-based rarefaction curves (MaoTau = expected species accumulation curves) nor individual-based rarefaction curves (Coleman curves) are estimators of species richness in the same sense as the other estimators that EstimateS computes. Whereas Chao2, ICE or Jack1, for example, estimate total species richness, including species not present in any sample, rarefaction curves estimate species richness for a sub-sample of the pooled total species richness, based on all species actually discovered.
Sampling without replacement. If you specify randomization of sample order, without replacement, EstimateS selects a single sample at random, computes the richness estimators (and diversity indexes, if requested) based on that sample, selects a second sample, re-computes the estimators using the pooled data from both samples, selects a third, re-computes, and so on until all samples in the matrix are included. Samples are added to the analysis in random order, without replacement (each sample is selected exactly once).
Each distinct randomization accumulates the samples in a different order, but all samples are included in each randomization. The final value for the averaged, random-order species accumulation curve therefore matches, precisely, the total number of observed species. The drawback with this protocol is that the variance, among randomizations, of counts (individuals, singletons, etc.) and of estimators for which no analytical variance is provided, goes goes to zero at the right-hand end of the species accumulation curve. (Standard deviations based on variation among randomizations are identified as "runs" in EstimateS 7+ output. Standard deviations computed analytically are identified as "analytical" in EstimateS 7+ output.)
Sampling with replacement. If you specify randomization of sample order, with replacement, EstimateS selects a single sample at random, computes the richness estimators (and diversity indexes, if requested) based on that sample; then selects two samples at random from the entire set of samples, re-computes the estimators using the pooled data from both samples; then selects three samples at random from the entire set of samples, re-computes, and so on until the pooled number of samples is the same as the full sample set. Samples are added to the analysis in random order, with replacement (each sample can appear in any pooled sample, some may appear in none).
Each distinct randomization thus accumulates the samples in a different order, but in general, not all samples will be included, and some are likely to be chosen twice or more. Therefore, the final value for the averaged, random-order species accumulation curve generally is generally less the total number of observed species, since the missed samples may contain species not found in the samples selected, for any given run. (In fact, the entire species accumulation curve generally lies below the corresponding curve produced by the without replacement option.) The advantage of randomizing samples with replacement is that the variance, among randomizations, of counts (individuals, singletons, etc.) and of estimators for which no analytical variance is provided, remains meaningful at the right- hand end of the species accumulation curve, and can thus be used to compare datasets. (Standard deviations based on variation among randomizations are identified as "runs" in EstimateS 7+ output. Standard deviations computed analytically are identified as "analytical" in EstimateS 7+ output.)
The Mao Tau estimator (Colwell et al. 2004), which for most purposes completely replaces re-sampled Sobs in EstimateS 7+, solves this dilemma for sample-based rarefaction by reproducing the curve expected from the data (the equivalent of sampling without replacement), while yielding the (unconditional) variance by treating the data as a sample from a larger statistical universe. Thus the Mao Tau 95% confidence intervals remain "open" at the right-hand end of the sample-based rarefaction (species accumulation) curve.
Sample accumulation. With or without replacement, as the samples accumulate, more and more information is included in the analysis and the richness estimates generally become more accurate (and diversity indexes tend to stabilize). By following the changes in each estimator or index as the samples accumulate, the performance of different estimators or indexes can be compared.
Number of randomizations. You can tell EstimateS to carry out as many different randomizations of sample order as you wish. By randomizing many times, the effect of sample order can be reduced by averaging over randomizations, producing relatively smooth estimator curves or diversity index curves and allowing a comparison of richness estimators or diversity indexes for your data set that does not depend on the particular order that samples were collected or added to the analysis.
As an option, you can tell EstimateS to add samples in the order they appear in your matrix and compute the estimators and indexes only once, for the sample ordering in the input matrix. (You can also use this option if expected species accumulation curves and/or Coleman curves are all you need.)
An additional options allow an analysis of the effect of patchiness on the performance of the estimators and indexes.
Reporting, exporting, and graphing results. Once the randomizations are complete, the mean value of each estimator or diversity index (and in most cases its standard deviation) is computed for each sample accumulation level and summary results are displayed on the screen (mean values among randomizations, for most estimators). For analysis and graphing, you can export these summary statistical results to a text file that can be opened by any competent spreadsheet, statistical, or graphing application. If you wish to analyze the results of individual randomizations, these can be exported to text file as an option. See Option to Export Results from Individual Randomizations.
The strategy of randomization and estimator evaluation is explained in more detail by Colwell & Coddington (1994). EstimateS was used to compute estimators for the seedbank example shown in Figures 1 and 2 and Table 1 of that paper. A copy of the seedbank data set (Butler & Chazdon 1998) is included when you download EstimateS. You can use this data file for demonstration and verification of proper installation.
The literature on species richness estimators continues to grow in several directions. Key reviews in the 1990s include Bunge & Fitzpatrick (1993) and Colwell & Coddington (1994). For a recent review of the field, see Chao (2004), which, like most key papers cited in this User's Guide, can be downloaded as pdf file.
Chao1 and Chao2 Richness Estimators. In EstimateS 7.5 and later, the classic richness estimators Chao1 and Chao 2 are computed along with log-linear 95% confidence intervals, as suggested by Chao (1987). These asymmetrical confidence intervals, which are based on the assumption that log(Sest - Sobs) is normally distributed, have the common-sense property that the lower confidence bound cannot be less than the observed number of species, Sobs. See Appendix B for details.
Coverage-Based Richness Estimators ICE and ACE.The species richness estimators, ICE (Incidence-based Coverage Estimator) and ACE (Abundance-base Coverage Estimator) are modifications of the Chao & Lee (1992) estimators discussed by Colwell & Coddington (1994). Chazdon et al. (1998) introduced ICE and ACE to the ecological literature. For that paper, they found it necessary and useful to change the notation for the variables involved in the other estimators, to allow a unified system of notation covering the new estimators. This new notation is referenced in Table 1 and detailed in the Appendix C of this User's Guide, replacing the notation of Colwell & Coddington (1994). See Chazdon et al. (1998), which can be downloaded as pdf file, for details and rationale.
There are many possible curvilinear functions, asymptotic and non-asymptotic, that might fit a species accumulation curve (Soberón & Llorente 1993, Colwell & Coddington 1994, Colwell et al. 2004). As a richness estimation option, EstimateS computes the asymptotic function most commonly used, the Michaelis-Menten function (Colwell & Coddington 1994).
EstimateS computes two different Michaelis Menten (MM) richness estimators. In both, the data the program produces represent the estimated MM asymptote based on one, two, three...QdMax samples (see Colwell & Coddington 1994, Fig. 1). The difference is that the first method (MMRuns) computes estimates for values for each pooling level, for each randomization run, then averages over randomization runs. If you have some samples that are much richer than others, randomization runs that, by chance, add a rich sample early in the curve are likely to produce enormous estimates of richness, since the rich sample "shoots" the fitted MM curve suddenly skyward. Thus, MMRuns data are often rather erratic for small numbers of samples, even when 100 runs are randomized.
The second method (MMMeans) computes the estimates for each sample pooling level just once, based on the species accumulation curve, as computed by MaoTau, in EstimateS 7+. Since this curve is computed analytically, it is quite smooth, thus the MM Means estimates are much less erratic than for the MMRuns method. This method is therefore generally recommended over MMRuns.
Note: Although means of Sobs among resampling runs are no longer used to compute MMMeans in Estimates 7 and later, the name MMMeans has been retained to make clear that it is the same as the estimator of that name in previous versions of EstimateS.
In addition to rarefaction and species richness estimators, both of which assess species richness as a measure of diversity, EstimateS computes the four most widely used indexes of species diversity that combine information on richness and relative abundance in different ways (Magurran 2004; Jost 2006, 2007). They are Fisher's alpha (the alpha parameter of a fitted logarithmic series distribution), Shannon diversity (using natural logarithms), exponential Shannon diversity, and Simpson diversity (the reciprocal form). The last two, like species richness itself, are in units of equivalent, equally abundant species. For example, an exponential Shannon index or Simpson index of 4, based on a sample of 10 species of unequal abundance, means that the same value of the index would arise from a sample of 4 species of equal abundance. In terms of sensitivity to rare species, richness is the most sensitive, Simpson diversity the least, and Shannon diversity intermediate. These three (when Shannon is its exponential form) represent particular points in a continuum of diversity indices that share the same mathematical form (Jost 2006, 2007). Fisher's alpha is not part of this continuum.
EstimateS does not compute these indexes unless you ask it to. Check the Diversity Indexes checkbox on the Other Options tab of the Diversity Settings screen to enable this option.
As with species richness estimators, EstimateS computes these four indices for each level of sample pooling, from one sample up to the total number in your dataset, allowing you to see whether and when each index stabilizes with increasing numbers of samples. Samples are added to the pool at random. The Runs parameter (on the Randomizations tab of the Diversity Settings screen) specifies how many randomizations EstimateS carries out to compute the mean and bootstrap standard deviation (for all but Fisher's alpha, for which an unconditional SD is computed) for the indices at each level of pooling. You can also specify whether you want the samples to be added to the pool with or without replacement.
This tool allows you to explore the effects of spatial patchiness on species richness estimators, as discussed by Chazdon et al. (1998). If you specify the Shuffle option (Diversity Settings --> Other Options panel), EstimateS uses the following algorithm to reassign individuals at random to samples, within species, with a "tunable" degree of aggregation (patchiness).
If the Patchiness parameter (A) is set to zero. Using the species abundance vector (marginal totals) for all samples pooled, each individual is re-assigned at random to a sample, within species. In other words, the distribution of individuals among species in the input matrix as a whole and the number of samples are maintained, but sample affiliations of individuals are randomized within species. Any patchiness of the original data is removed. (As expected, the mean of randomized sample accumulation curves is indistinguishable from the Coleman curve, which assumes spatial homogeneity, for this setting.)
If the Patchiness parameter (A) is set to a value greater than zero. In this case, the first individual of each species is assigned to a sample at random. The second (if there is one) is assigned to the same sample as the first with probability A, and to a randomly chosen sample with probability (1-A). In other words, the larger you set A, the patchier the pseudo-distribution of individuals becomes. By "tuning" the patchiness of the distribution, you can investigate the effect on the performance of the richness estimators, using real relative-abundance distributions. One could also enter made-up data sets that fit some particular relative abundance distribution(s).
As an option, EstimateS (beginning with Version 8) records and exports results from n individual randomizations to a text file, allowing computation of precision, accuracy, and other analyses (Walther and Moore 2005), using Excel or other applications. To choose this option, select Diversity Settings from the Diversity menu, click the Other Options tab, then check the "Export results for each run to a text file" checkbox. When you click the Compute button (or choose Compute Diversity from the Diversity menu), EstimateS displays an expanatory message, and asks you to name and place the text file that will contain the exported results when the randomizations are complete. The data for each randomization appear in the same format as the summary Diversity results that EstimateS creates by default. (The summary results appear onscreen as usual, and may be exported as usual.) For large datasets, this option takes time, so be patient.
EstimateS offers two random number generators (Diversity menu --> Diversity Settings --> Randomization tab --> Random Number Generator panel). The Strong Hash Encryption generator samples from a 160-bit strong hash (SHA) encryption function, seeded from the computer's clock. This procedure, developed by Jason Swain (personal communication), produces a non-repeating random number series that passes the most demanding tests.
The Difference Equation alternative (Savitch (1992) is based on a seed number that you supply. Thus it permits EstimateS to generate precisely the same results on repeated sets of resampling runs with the same dataset. Unless you require precise repeatability, the Strong Hash Encryption option is recommended.
If you would like to do a visual test of either random number generator, choose Test Random Number Generator from the Special menu.
As discussed by Colwell & Coddington (1994), the problem of estimating the true number of species shared by two (or more) sites or biotas based on sample data presents a difficult but important challenge. The first statistical estimator of shared species was developed by Anne Chao and her colleagues (Chen et al. 1995 in Chinese; Chao et. al. 2000 in English), based on the same statistical strategy as ICE and ACE. Like ACE, the shared species estimator V requires abundance data. Just as ACE augments the observed number of species in a sample by a correction term dependent on the relative abundance of the rarest species (those with fewer than 10 individuals) in the sample, V augments the observed number of shared species by a correction term based on the relative abundance of shared, rare species.
EstimateS computes Chao's shared species estimator for all pairs of samples in the data matrix. A brief presentation of the mathematics behind the shared-species estimator appears in Appendix C of this Guide.
EstimateS computes the ACE estimate of species richness for each sample, as well as the estimate of shared species for each pair of samples.
EstimateS computes four classic indexes of similarity, based on the raw data from the input file: the Classic Jaccard index, the Classic Sørensen incidence-based (qualitative, presence/absence) index, the Bray-Curtis index (= "Sørensen quantitative" index), and the Morisita-Horn index. Dozens of overlap indexes exist in the literature; these were chosen based on the recommendations of Magurran (1998, 2004).
Note: The Bray-Curtis (= "Sørensen quantitative") index and the Morisita-Horn index can be used with either integer or decimal (real number) input data. However, since EstimateS requires all data to be integer counts for estimator computation, all decimal data values are rounded to the nearest integer when imported into EstimateS. For this reason, values of the Sørensen Abundance-based index and the Morisita-Horn index computed by EstimateS will differ slightly from the corresponding indexes computed for corresponding decimal data values, including Magurran's (1998) worked examples (Magurran 1988, pp. 165-166), which are based on decimal data.
Chao's Abundance-based Jaccard and Sørensen indexes are based on the probability that two randomly chosen individuals, one from each of two samples (quadrats, sites, habitats, collections, etc.), both belong to species shared by both samples (but not necessarily to the same shared species). The estimators for these indexes take into account the contribution to the true value of this probability made by species actually present at both sites, but not detected in one or both samples. This approach has been shown to reduce substantially the negative bias that undermines the usefulness of traditional similarity indexes, especially with incomplete sampling of rich communities (Chao et al. 2005).EstimateS 7.5+ computes the raw Chao Abundance-based Jaccard and Sørensen indexes (not corrected for undersampling bias) as well as the estimators of their true values, so that you can assess the effect of the bias correction on the indexes. In addition, the standard errors of the estimators are computed, allowing (for the first time!) statistically rigorous comparison of two or more similarity index values. (To compute 95% confidence intervals, just add and subtract 1.96*SE to/from the index estimate.) Because the Jaccard and Sørensen indexes depend on exactly the same information, which one you use is strictly a matter of taste.
Table 1, below, lists the variables and statistics that EstimateS 8.2.0 computes from the Diversity menu. Table 2 lists the variable and statistics computed from the Shared Species menu.
Table 1: Accumulated species and individuals, richness estimators, species diversity indexes and related variables computed by EstimateS 8.2.0. In the output screen (and exported text files), values for accumulated species, richness estimators, and diversity indexes appear for each level of sample accumulation (Qd =1 to QdMax), as expected values, or as mean values for the number of randomizations you specify. Formulas for the estimators appear in Appendix B .
Table 2: Shared Species estimators, classic similarity indexes, Chao's abundance-based Jaccard and Sorensen similarity indexes and their estimators, and related variables computed by EstimateS 8.2.0. In the output screen (and exported text files), values for these statistics and variables appear for each possible pair of samples. The formula for the shared species estimator appears in Appendix C , and the formulas for Chao's abundance-based Jaccard and Sorensen similarity indexes, and their estimators and variances appears in Appendix D .
Sample Input File: A sample Input File named Seedbank is installed in the EstimateS program folder. Open this file in Excel or a text editor to examine it as you read this section. The Seedbank file is in Format 1. Be sure not to save any changes to this file so it will remain a correct model.
EstimateS was used to compute the species richness estimators for the Seedbank dataset (Butler & Chazdon 1998) that appear in Figures 1 and 2 and Table 1 of Colwell & Coddington (1994). You can use the Seedbank data file for demonstration and verification of proper installation of EstimateS.
File Type, Name and Location: The Input File must be plain text, tab-delimited. The Input File may have any name and may be located in any folder (directory).
Title Record: The first line of the Input File must contain a title, any text will do.
Parameter Record: The second line must contain two obligatory control parameters: the number of species and the number of samples, separated by a TAB character. Additional control parameters are optional, and can be more easily recorded by exporting a new copy of the input file after setting the parameters in EstimateS' Settings screens.
The rest of the Input File contains the input data, which can appear in any one of five alternative formats. When you run the program, you will be asked to specify which of the following formats you used:
Format 1. Species (rows) by Samples (columns) abundance or incidence matrix ("samples" may be collections, quadrats, etc.): one row per species, one column per sample. This is how the demo file (Seedbank) is formatted. The input file may contain any number of initial rows of column labels and/or initial columns of row labels, in which case you must tell EstimateS how many of each there are. (EstimateS simply skips over label rows and columns.)
Format 2. Samples (rows) by Species (columns) abundance or incidence matrix: one row per sample, one column per species. The input file may contain any number of initial rows of column labels and/or initial columns of row labels, in which case you must tell EstimateS how many of each there are. (EstimateS simply skips over label rows and columns.)
Format 3. Species, Sample, Abundance triplets: the first column contains the species number, the second the sample number, and the third the number of individuals (abundance) of that species in that sample. A final (extra) record with "-1" in each column indicates end of input. This "triplet" format a common input format for statistical programs (e.g. SYSTAT.) You can list one row for every sample/species combination, or rows for only those combinations that have non-zero abundances. (The rest are automatically set to zero.) Using the triplet format and storing only non-zero abundance values requires far less file space than storing the full matrix. In fact, this may be the most practical way to store files larger than your spreadsheet will accept. As an option (see below), EstimateS can export a data matrix in this format, after reading it in using one of the other four formats listed here.
Format 4. Sample, Species, Abundance triplets: format as for (3), but the columns are ordered Sample, Species, Abundance.
Format 5. This format is output automatically by Biota, with appropriate row and column labels. For other input files that include column or row labels, use Formats 1 or 2
The required layout for the input (data) file is detailed below. Each [element], shown in square brackets, must be separated from the next by a single TAB character (do not include the line numbers or the brackets in the actual file).
LINE 1: Title Record
[Title]: Any alphanumeric title for the data input file
LINE 2: Parameter Record (all this on one line, separated by TABs)
Required: [SpMax]: Number of species
For data Format 1: Species (i) by Samples (j) abundance or incidence (Nij) matrix
LINES 3 TO (SpMax+2)
[N1,1] [N1,2] ... [N1,j] ... [N1,QdMax]
For data Format 2: Samples (i) by Species (j) abundance or incidence (Nij) matrix
LINES 3 TO (QdMax+2)
[N1,1] [N1,2] ... [N1,j] ... [N1,SpMax]
LINES 3 and beyond
1 1 [N1,1]
LINES 3 and beyond
1 1 [N1,1]
For data Format 5: Samples (i) by Species (j) abundance or incidence (Nij) matrix
LINES 3 TO (QdMax+6)
Line 3: Ignored
1. Launch EstimateS by double-clicking the EstimateS icon or application name or (in Windows) by launching EstimateS from the Programs section of the Start menu.
2. If a file navigation window appears asking you to select a "Data File," choose the file called Statistics.4DD (Windows) or Statistics.data (Mac OS). This default file records the statistical output of Biota.
2. From the File menu in EstimateS, choose Load Input File. The open file window appears.
3. Find the input file and open it. EstimateS presents a confirmation window showing the data set name and the input parameters. (If you want, you can try loading the example Input File called Seedbank.)
4. If the parameters are correct, click the OK button in the dialog. EstimateS loads the file. (Various input data errors will be flagged if they occur. Follow the onscreen instructions if this happens.)
5. To set, change, or check run parameters for the loaded file, choose Diversity Settings from the Diversity menu (richness estimators and diversity indexes), or Shared Species Settings from the Shared Species menu (shared species estimator and similarity indexes). See the description of parameters in the preceding section for details.
6. Launch the computations by clicking the Compute button in a Settings screen, or by choosing Compute Diversity Stats from the Diversity menu (richness estimators and diversity indexes), or Compute Shared Spp Stats from the Shared Species menu (shared species estimator and similarity indexes). EstimateS does the computations and displays the results onscreen. (Clicking a Compute button saves the settings as well as launching the computations.)
7. When computations are completed, click the Export button to export the results (see below), or the Done button to dismiss the results screen. (You can always export the results later from a menu command.) The records are saved in the statistics data file (Statistics or another name you have given it), and can be redisplayed at any time by choosing Show Diversity Stats from the Diversity menu (richness estimators and diversity indexes), or Show Shared Spp Stats from the Shared Species menu (shared species estimator and similarity indexes).
1. Export the results to a tab-delimited text file by choosing Export Diversity Stats from the Diversity menu (richness estimators and diversity indexes), or Export Shared Spp Stats from the Shared Species menu (shared species estimator and similarity indexes). You can then open the text file in Excel, a graphing application, or a statistical application to further analyze or graph the data.
2. Export the input data and all current parameter settings to a tab-delimited text file by choosing Export Input File as Triplets from the File menu. EstimateS creates a Format 3 input file, recording all parameter settings. You can reload this file at any time. Triplet files load more quickly than full matrix files (Formats 1, 2, and 5).
3. Save the results in an EstimateS Statistics Data File. The results (statistics) displayed onscreen by EstimateS are actually 4D database records in a file called (initially) Statistics.4DD (Windows) or Statistics.data (Macintosh). When you launch EstimateS, this file is automatically (re)opened. If you want to save this file with the results of the current run and open a new, empty Statistics file (instead of deleting the results next time you run a different input file or the same input file with different parameters), follow these steps:
I have done my best to check all features of EstimateS 8.2.0 for usability and all computations and algorithms for accuracy, but the final responsibility for ensuring that your results are correct must rest with you.
In general, you should have little trouble understanding the output, by referring to Colwell & Coddington (1994), Chazdon et al. (1998), Gotelli & Colwell (2001), Colwell et. al. (2004), Chao et. al. (2005), or if necessary the references in Table 1 and 2.
If you appreciate the effort that has gone into EstimateS, please credit the application and its author in any published work that makes use of results from EstimateS, citing EstimateS as an electronic publication and giving the EstimateS persistent URL (PURL) website address (http://purl.oclc.org/estimates) if the journal permits it. (This "permanent" address automatically transfers the visitor to http://viceroy.eeb.uconn.edu/EstimateS.) Here is one possible form for a References Cited entry:
Colwell, R. K. 2009. EstimateS: Statistical estimation of species richness and shared species from samples. Version 8.2. User's Guide and application published at: http://purl.oclc.org/estimates.
If the journal or book editor will not permit an entry in the References Cited section, you might try this text citation: "...computed using EstimateS (Version 8.2, R. K. Colwell, http://purl.oclc.org/estimates)...."
Failing that, you may be reduced to: "...computed using EstimateS (Version 8.2, R. K. Colwell, unpublished)...," perhaps slipping in the EstimateS website address (http://purl.oclc.org/estimates) in the Acknowledgment section.
I would be most grateful if you would kindly send a reprint of any paper based on your use of the program. Send a pdf to email@example.com, or by post to: Robert K. Colwell, Department of Ecology and Evolutionary Biology, U-43, University of Connecticut, Storrs, CT 06269-3043, USA.
EstimateS is a freeware application. By downloading and using EstimateS, you must agree not to distribute EstimateS in any commercial form.
You are most welcome to use EstimateS in any way you like for your own research, as long as such use is acknowledged as outlined above.
To keep track of EstimateS users and to make sure that the latest version is in use, it is preferable that each new user downloads and registers his or her own copy of EstimateS from http://viceroy.eeb.uconn.edu/estimates or http://purl.oclc.org/estimates, rather than sharing someone else's (e.g. your) copy.
If you do share the program with a colleague, please be sure to make clear that the User's Guide is available online at http://viceroy.eeb.uconn.edu/estimates or http://purl.oclc.org/estimates, to save needless email support questions.
References marked "Download pdf" are available here for downloading.Brewer, A., & M. Williamson. 1994. A new relationship for rarefaction. Biodiversity and Conservation 3:373-379.
Butler, B. J., & R. L. Chazdon. 1998. Species richness, spatial variation, and abundance of the soil seed bank of a secondary tropical rain forest. Biotropica 30:214-222. Download pdf.
Chao, A. 1984. Non-parametric estimation of the number of classes in a population. Scandinavian Journal of Statistics 11, 265-270. Download pdf.
Chao, A. 1987. Estimating the population size for capture-recapture data with unequal catchability. Biometrics 43, 783-791. Download pdf.
Chao, A. 2005. Species richness estimation, Pages 7909-7916 in N. Balakrishnan, C. B. Read, and B. Vidakovic, eds. Encyclopedia of Statistical Sciences. New York, Wiley. Download pdf.
Chao, A., R. L. Chazdon, R. K. Colwell, and T.-J. Shen. 2005. A new statistical approach for assessing compositional similarity based on incidence and abundance data. Ecology Letters 8:148-159. Download pdf. Spanish Version: Download pdf.
Chao, A., R. L. Chazdon, R. K. Colwell, and T.-J. Shen. 2006. Abundance-based similarity indices and their estimation when there are unseen species in samples. BiometricsBiometrics 62, 361-371. Download pdf.
Chao, A., W.-H. Hwang, Y.-C. Chen, and C.-Y. Kuo. 2000. Estimating the number of shared species in two communities. Statistica Sinica 10:227-246. Download pdf.
Chao, A. & S.-M Lee. 1992 Estimating the number of classes via sample coverage. Journal of the American Statistical Association 87, 210-217. Download pdf.
Chao, A., M.-C. Ma, & M. C. K. Yang. 1993. Stopping rules and estimation for recapture debugging with unequal failure rates. Biometrika 80, 193-201. Download pdf.
Chazdon, R. L., R. K. Colwell, J. S. Denslow, & M. R. Guariguata. 1998. Statistical methods for estimating species richness of woody regeneration in primary and secondary rain forests of NE Costa Rica. Pp. 285-309 in F. Dallmeier and J. A. Comiskey, eds. Forest biodiversity research, monitoring and modeling: Conceptual background and Old World case studies. Parthenon Publishing, Paris. Download pdf.
Chen, Y.-C., W.-H. Hwang, A. Chao, & C.-Y. Kuo. 1995. Estimating the number of common species. Analysis of the number of common bird species in Ke-Yar Stream and Chung-Kang Stream. (In Chinese with English abstract.) Journal of the Chinese Statistical Association 33, 373-393.
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The resampling-based Sobs curve computed by previous versions of EstimateS was an approximation to the curve computed by this analytical method. For details and interpretation, see Colwell et al. (2004).
stand for the number of species found in exactly j samples of the empirical sample set,
which has a total of H
samples. Thus s1 is the number of species found in
precisely 1 sample, s2
is the number of species found in precisely 2 samples, and so on. The
observed richness in the empirical sample set is therefore
For sample-based rarefaction (species
accumulation based on samples),
where the combinatorial coefficients are defined by
Because the coefficient alpha in equation (1) is 0 for h = H, estimated richness for the full empirical sample set is
95% confidence intervals
Please note that nonparametic estimators of species richness are minimum estimators: their computed values should be viewed as lower bounds of total species numbers, given the information in a sample or sample set.
Definition of variables
Chao 1 and Chao2: Different equations are used to compute the Chao1 and Chao2 richness estimators, their estimated variance, and the corresponding log-linear 95% confidence intervals, depending on (1) the number of singletons and doubletons (in abundance-based data) or uniques and duplicates (for incidence-based data), and (2) the settings you select "Chao 1 and Chao 2 bias correction" panel in the Estimators tab of the Diversity Settings screen (Diversity menu). The table below specifies the equations used in each case. The equations referred to appear below the table. This section was developed in personal communication with Anne Chao, Institute of Statistics, National Tsing Hua University, Taiwan, to whom I am most grateful.
Equations referenced in the table above:
This appendix and its implementation in EstimateS is based on Chao et al. (2000) and on personal communication with Anne Chao, Institute of Statistics, National Tsing Hua University, Taiwan.
Definition of variables
Sample coverage for rare, shared species is estimated by
This appendix and its implementation in EstimateS is based on Chao et al. (2005) and on personal communication with Anne Chao, Institute of Statistics, National Tsing Hua University, Taiwan.