You can also check out the "vegan" package in R (https://cran.r-project.org/web/packages/vegan/vegan.pdf).  There is a function called "rarefy" that will do what you want (and the package has citations for what rarefaction is actually doing, in addition to the citations mentioned above).  To use it, you would do something like the following

# install.packages("vegan")

library(vegan)

dat

Try reading about biodiversity. Magurran wrote a good book on the topic. http://press.princeton.edu/titles/4238.html

One program to calculate measures of biodiversity is a program (free) called EstimateS.

http://viceroy.eeb.uconn.edu/estimates/

One great feature of EstimateS is that it gives you a large number of different calculations. The documentation and references cited therein will help you understand the different options.

You can also check out the "vegan" package in R (https://cran.r-project.org/web/packages/vegan/vegan.pdf).  There is a function called "rarefy" that will do what you want (and the package has citations for what rarefaction is actually doing, in addition to the citations mentioned above).  To use it, you would do something like the following

# install.packages("vegan")

library(vegan)

dat

If you are new to statistics I would suggest you find a mentor, read the Magurran book (see Ebert's post) and use past (see Sozontov's post). The informatics (i.e., the measures you choose) will give you different perspectives on your data. I would discuss this with a mentor experienced in statistical analysis of ecological data. I would also suggest that you spend some time playing with your data set to compare and contrast and to familiarise yourself with any patterns that may occur.

I used PAST ( as mentioned before) on my data and recommend it. It's a free software. You can download from internet.

I strongly recommend the R packages "iNEXT" (for the calculations) and "ggplot2" (for creating publication-quality figures).

In the following link you will find detailed guidelines on how to use these packages:

https://cran.r-project.org/web/packages/iNEXT/vignettes/Introduction.html

In addition, you can use EstimateS software (http://viceroy.eeb.uconn.edu/EstimateS/) to calculate non-parametric estimators of 'true' species richness by following the software's user's guide:(http://viceroy.eeb.uconn.edu/EstimateS/EstimateSPages/EstSUsersGuide/EstimateSUsersGuide.htm).

Good luck.

Dear all,

So I've followed your advice and used EstimateS to calculate many things. But now I have even more questions.

1) I have "Cole Rarefaction" and some Chao values on the output sheet. But what do they mean? Which one of these things is related to rarefaction and how can I read and interpret it? I tried to read it online but the sources I found are either written in a math-heavy language or unrelated to my topic. Now I can't even find a proper source which can tell me what really rarefaction is and what it tells us. Please please please enlighten me. 

2) Why is there a multiple run section? When I run it for multiple runs then I end up with "mean diversity indices" like "Simpson Mean"? There must be a single Simpson's Index for a sample as far as I know. Why does it come up with more than one indices for the same sample? I mean it's the same sample and it should always have the same Simpon's and Shannon's indices. Because everything is the same. I'm really confused now. 

I really am stuck. And thanks for all your support and answers Researchgate family =)

P.S. I also used PAST. I got the diversity profiles graph there too but I don't know how to interpret it either. And none of the rarefaction options work on my table (rows: species, columns: samples). This rarefaction thing is killing me! 

On the EstimateS website (http://viceroy.eeb.uconn.edu/estimates/) there is a list of things on the left side of the screen. In that list there is a "Things you should know" under the EstimateS User's Guide. The answers are there or in the documents that are cited.

To really understand these methods there is no option other than to wade through at least some of the math. This will be very difficult if there is no one in your group interested in math. You might consider that the source paper that describes the method will be math intense. Subsequent papers that use that method may provide somewhat less math intense explanations. So find papers that cite the original work. It does not matter if these papers are on birds, insects, fish, or diatoms. The math is the same.

Some of the indices will change if you run EstimateS multiple times. The problem is how you are interpreting statistics. So I measure the body weight of 5 birds. I get 3, 4, 5, 6, and 7 pounds. The mean is 5. I can recalculate the mean with this data set as many times as I like and I will always get a mean of 5. The problem is that the mean is not really 5. If I go back to the field and measure the weight of 5 different birds it is highly unlikely that I will get exactly the same results. I might get 3.2, 4.1, 4.8, 6.1, and 7.003 pounds and the mean is then 5.0406 pounds. I could do this over and over and I will discover that the mean from a sample of 5 birds will be 5.2 pounds with a standard deviation of 0.6 pounds.

Experiments are not usually run this way, where you collect a sample of 5, and then do that several hundred times to look at the variability in the results given an experiment with a sample size of five. One alternative is to look at an experiment with a sample size of four. So I will calculate a mean from a sample size of four by taking your sample size of five and leaving one value out. I determine which value to leave out using a random number generator. I will do this 10 times and report the mean of these ten times which are themselves the mean of the four observations. In doing this I will get a slightly different answer each time I run the analysis. This is a jackknife approach. This is a stupid activity for this example because the sample size is so small that there are only five possible outcomes. However, this technique works well if you have more data and do more than 10 randomizations. The number will change less as the number of randomizations increases, and where the number of possible permutations is much greater than the number of randomizations.

I could do this another way. I could randomly select a set of five values from the data. I would do this with replacement. So my starting values are 2, 3, 4, 5, 6. My first random draw gets a 5. I keep that value, but the next draw uses the entire data set. So my second draw could also result in 5. My new data set might be 5, 5, 3, 2, 2. I can do this over and over, calculate the mean in each case and then report the mean of all these means. This is a bootstrap approach.

If I have collected 2,000 water birds, and I want to estimate the biodiversity of this group I could estimate biodiversity by leaving out some portion of the data. My answer will change each run of the program.

All statistical estimates have error. Sometimes you can measure this, but often you cannot. Regardless of your ability to measure the error, it is still there.

Does this help?

https://en.wikipedia.org/wiki/Rarefaction_(ecology)

Ecosim is a free download and easy to use: https://www.uvm.edu/~ngotelli/EcoSim/EcoSim.html

Updated commercial version also available: http://www.garyentsminger.com/ecosim/

rarefy: Rarefaction Species Richness

In vegan: Community Ecology Package can do the rarefied/rarefaction richness index in the software R. 

https://rdrr.io/rforge/vegan/man/rarefy.html

Function rarefy gives the expected species richness in random subsamples of size sample from the community. The size of sample should be smaller than total community size, but the function will work for larger sample as well (with a warning) and return non-rarefied species richness (and standard error = 0). If sample is a vector, rarefaction of all observations is performed for each sample size separately. Rarefaction can be performed only with genuine counts of individuals. The function rarefy is based on Hurlbert's (1971) formulation, and the standard errors on Heck et al. (1975).

Function rrarefy generates one randomly rarefied community data frame or vector of given sample size. The sample can be a vector giving the sample sizes for each row. If the sample size is equal to or smaller than the observed number of individuals, the non-rarefied community will be returned. The random rarefaction is made without replacement so that the variance of rarefied communities is rather related to rarefaction proportion than to the size of the sample.

Examples

data(BCI)

S