Hi all, I am a student and my statistics knowledge is minimal. I have three data sets for three sites. I sampled insects over 12 months. The sample sizes are not the same (12 for two sites and 24 for one site); I want to compare the sites in terms of species richness. I recently downloaded EstimateS 9.1.0 and still trying to get my head around it.
Please advise on how can i best use the DIVERSITY OPTIONS in the software.
Thanks
Chao1 is an estimator based on abundance. This means that the data it requires refer to the abundance of individuals belonging to a certain class in a sample. A sample is any list of species in a site, location, quadrant, country, unit of time, trap, etcetera. As we know, there are many species that are only represented by a few individuals in a sample (rare species), compared to the common species, which can be represented by numerous individuals. The Chao1 estimator is based on the presence of the former. That is, we need to know how many species are represented by only one individual in the sample (singletons), and how many species are represented by exactly two individuals (doubletons): Sest = Sobs + F2 / 2G, where: Sest is the number of classes ( in this case, number of species) that we want to know, Sobs is the number of species observed in a sample, F is the number of singletons and G is the number of doubletons. In the programEstimates a corrected formula has also been integrated for this model, which is applied when the number of doubletons is zero: Sest = Sobs + ((F2 / 2G + 1) - (FG / 2 (G + 1) 2)).
Chao2 is the estimator based on the incidence. This means that it needs presence-absence data of a species in a given sample, that is, only if the species is present and how many times is that species in the sample set: Sest = Sobs + (L2 / 2M), where: L is the number of species that occur only in one sample ("unique" species), and M is the number of species that occur in exactly two samples ("double" or "duplicate" species). For example, if we have a set of grids, we need to know how many species are in a grid and how many species are in two. The formula corrected in Estimates, which is applied when the number of doubles is zero, is: Sest = Sobs + ((L2 / 2M + 1) - (LM / 2 (M + 1) 2)). To use both estimators in ESTIMATES, data in the form of a matrix is needed, where rows and columns can represent samples and species indistinctly; it is necessary to establish the order once the program has started. Estimates also allows the calculation of the standard deviation of the two estimators. Once several randomisations are made (50 recommended, but can be 100 or more), with or without replacement, and when the total number of samples has been used, the final value of the estimator is obtained and the results can be plotted. The number of samples is presented on the x axis, and the number of species in the dependent variable. Thus, the Sest and the Sobs can be compared. But the final graph is interpreted differently from the conventional one: when you have the total number of samples, there is a certain separation between the curve of the Sest and the Sobs. That separation would be indicating how many species are missing to register in that community. The more separated they are, we would expect that the total number of species that contains the place is greater than the one that we currently know.
For additional information please read the following chapter Estimating species richness in the following link:
https://www.uvm.edu/~ngotelli/manuscriptpdfs/Chapter%204.pdf
The first problem is that any sampling strategy will miss some species. The first sample has all new species (for your study) because it is the first sample. The second sample will have many new species, but some species will have been captured in the first sample. As more samples are gathered, fewer and fewer new species will be recovered. Eventually (with thousands of samples) the rate of getting new species will equal the speciation rate of the existing species plus the immigration rate (invasion) of new species from other geographic regions.
The diversity indices are simply trying to figure out how many species are actually present based on the sampling effort and the observed diversity.
Chao1 is an estimator based on abundance. This means that the data it requires refer to the abundance of individuals belonging to a certain class in a sample. A sample is any list of species in a site, location, quadrant, country, unit of time, trap, etcetera. As we know, there are many species that are only represented by a few individuals in a sample (rare species), compared to the common species, which can be represented by numerous individuals. The Chao1 estimator is based on the presence of the former. That is, we need to know how many species are represented by only one individual in the sample (singletons), and how many species are represented by exactly two individuals (doubletons): Sest = Sobs + F2 / 2G, where: Sest is the number of classes ( in this case, number of species) that we want to know, Sobs is the number of species observed in a sample, F is the number of singletons and G is the number of doubletons. In the programEstimates a corrected formula has also been integrated for this model, which is applied when the number of doubletons is zero: Sest = Sobs + ((F2 / 2G + 1) - (FG / 2 (G + 1) 2)).
Chao2 is the estimator based on the incidence. This means that it needs presence-absence data of a species in a given sample, that is, only if the species is present and how many times is that species in the sample set: Sest = Sobs + (L2 / 2M), where: L is the number of species that occur only in one sample ("unique" species), and M is the number of species that occur in exactly two samples ("double" or "duplicate" species). For example, if we have a set of grids, we need to know how many species are in a grid and how many species are in two. The formula corrected in Estimates, which is applied when the number of doubles is zero, is: Sest = Sobs + ((L2 / 2M + 1) - (LM / 2 (M + 1) 2)). To use both estimators in ESTIMATES, data in the form of a matrix is needed, where rows and columns can represent samples and species indistinctly; it is necessary to establish the order once the program has started. Estimates also allows the calculation of the standard deviation of the two estimators. Once several randomisations are made (50 recommended, but can be 100 or more), with or without replacement, and when the total number of samples has been used, the final value of the estimator is obtained and the results can be plotted. The number of samples is presented on the x axis, and the number of species in the dependent variable. Thus, the Sest and the Sobs can be compared. But the final graph is interpreted differently from the conventional one: when you have the total number of samples, there is a certain separation between the curve of the Sest and the Sobs. That separation would be indicating how many species are missing to register in that community. The more separated they are, we would expect that the total number of species that contains the place is greater than the one that we currently know.
For additional information please read the following chapter Estimating species richness in the following link:
https://www.uvm.edu/~ngotelli/manuscriptpdfs/Chapter%204.pdf
Hi, Tebogo Khoza.
I agree with Timothy A Ebert,
Both Chao-1 and Chao-2 are non-parametric estimators (distribution-free). Chao-2 estimates the number of species that occur in only one or two samples based on incidences (see more in Chao, 1984). While Chao-1 estimates the number of species that are represented only by a single individual (singletons) or by two individuals (doubletons) in that sample based on abundances.
You can also see Hill numbers or effective number of species (see Chao & Jost 2015), which are other ways to compare diversity in the SPADE program (Species Prediction And Diversity Estimation, http: //chao.stat.nthu. edu.tw/wordpress/software_download/).
Here are some articles that will help you.
Hi again, how do I plot Species accumulation and Rarefaction curves based on the Chao1 and Chao2 results I obtained for my data? Can I do the typical line graph on Microsoft Excel?
Hi,
You can use the EstimateS and Spade programs. I also leave the links of the pages.
http://chao.stat.nthu.edu.tw/wordpress/software_download/
chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/http://chao.stat.nthu.edu.tw/wordpress/wp-content/uploads/software/SPADE_UserGuide.pdf
http://viceroy.eeb.uconn.edu/estimates/
If you need something with pleasure.
Regards
You can also make use of the R package iNEXT, see paper: Article iNEXT: An R package for rarefaction and extrapolation of spe...
For microbiome data, you can visit this page to get Chao estimation
https://microbiome.github.io/tutorials/Diversity.html
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