From the article on patterns of Beta Diversity:

https://www.frontiersin.org/articles/10.3389/fevo.2018.00194/full

I understand that beta diversity has 2 components: turnover and nestedness and you want to test whether the different sites reveal differences in the 3 dimentions of biodiversity (taxonomic, phylogenetic, and functional).

I suppose you can calculate the 3 equations as described in the article :

Betasor = b+c /(2a + b + c)

Betasim = min[b,c]/(a + min[b,c])

Betanes = max[b,c] – min[b,c]/(2a+b+c) x a/(a +min[b,c])

In your Excel file you should have :

60 rows for your 60 Quadrates

1 column for the number for each of the 60 Quadrates

1 column for the 3 Sites

3 columns for each Beta

In R you can use an ANOVA to see whether there are differences between Sites:

See e;g;: https://www.scribbr.com/statistics/anova-in-r/

The vegan package offers the betadisper function (https://www.r-bloggers.com/2016/04/a-new-default-plot-for-multivariate-dispersions/). Not sure if this example fits your specific question as not to much info is provided for your question. The example data created in R is how the input should look like. Where the columns are the species/tax and each row an individual sample (quadrate). In this case a wide format (http://www.cookbook-r.com/Manipulating_data/Converting_data_between_wide_and_long_format/). Note that I never really worked with betadisper function as I never had the need for it. Some reading would be required.

This might be useful too although a bit too lengthy:

https://chrischizinski.github.io/rstats/adonis/

R package betapart (https://cran.r-project.org/web/packages/betapart/betapart.pdf) can also be used for calculating nestedness and turnover. First of all, I assume you want to compare the 3 sites? And the quadrates are summarised to get the data for each site? Secondly, the metrics to use depend on the information you sampled within those quardats: species presence/absence or abundance data?

Anyways, in order to calculate the various beta-diversity measures, you will have to bring your data in the form of a p/a matrix as in the screenshot I attached to this message.

You could do this either in Excel or in R. In case you need help with this, you should provide information about how your data is currently organised.

In order to calculate e.g. Sorenson-Index, Simpson-Index (-> turnover), and a nestedness component, you can simply use the betapart function beta.pair with index.family = "sorensen". However, your data has to be transformed to p/a data. The output will be 3 matrices with the different indices calculated between every pair of rows of your input data set. Such can be used for further analyses (your question doesn't reveal what exactly you want to test).

Further information: www.doi.org/10.1111/j.2041-210X.2012.00224.x

I have arranged my data as in the attached screenshot, where CR, DR & AR are different sites and Q1, Q2, .... represents quadrates. I want to analyse the beta diversity and dissimilarities among the three sites. Wim Kaijser Jos Feys Manuel R. Popp

Looks good. Additionally you would need another column just after the first, which indicate the sites, only having like: CR, CR, ..., AR. Assuming df is the dataset you just displayed, the second column would contain the additional site names, you would load the Excel (or csv) into R; you would need to remove these two columns (if the first is not taken as the row names).

library(readxl)

df

you can consult this reference:

Dispersal and neutral sampling mediate contingent effects of disturbance on plant beta‐diversity: A meta‐analysis

By------CP Catano, TL Dickson, JA Myers - Ecology Letters, 2017 - Wiley Online Library