Beta diversity is estimated when you have plots or samples of sites separated by different distances but how to calculate it if you have only one big plot? An approach is to take regularly spaced sub-samples as in: Münkemüller et al. (2012). From diversity indices to community assembly processes: a test with simulated data, Ecography 35: 468–480. But maybe there are better ways.
It's a question of scale choice. Beta diversity measures species turnover among habitats, or sites, or plots, or in your case, samples within plots. That's the easy part. Choosing the particular metric of beta diversity is challenging. Koleff et al 2003 reviewed 24 metrics....probably a good place to start.
I'll be interested to hear other answers. We just completed ID work on 370 benthic samples taken at 500m grid intervals in a bay on the Vermont/Quebec border. We have some primary questions in mind relating to habitat variables, but I'm sure we can spin off some other interesting analyses on a data matrix of this size.
The most important for your work, Declan, are the previous hypothesis you have about your community, think carefully about hypothesis before analyze data.
One interesting new beta-diversity is derived from Shannon Entropy
Marcon E, Hérault B, Baraloto C, Lang G (2012) The decomposition of Shannon’s entropy and a confidence interval for beta diversity. Oikos 121: 516–522.
I found one measure suitable for continuous data beta-diversity or species turnover: how rapidly increasing the distance r decreases the probability F(r) that two randomly chosen trees a distance r apart are the same species (Condit et al., 2002).
The way to calculate this F(r) is to draw pairs of individuals at random compute distance and calculate frequency of individuals of the same species at intervals r+dr, choosing dr as 1/100 of the length of the sample (Chave 2002).
Chave J, Leigh EG (2002) A Spatially Explicit Neutral Model of [beta]-Diversity in Tropical Forests. Theoretical Population Biology 62: 153–168.
Condit R, Pitman N, Jr. EGL, Chave J, Terborgh J, et al. (2002) Beta-Diversity in Tropical Forest Trees. Science 295: 666–669.
Interesting question, but once you got it what do you do with that? I am sorry to be rude and provocative but the real problem is what are you actually going to do with it. Species richness, the number of different species in an ecosystem, was for a long time the predominant measure of global biodiversity. This is now changing rapidly (see a recent paper in Nature) as researchers are realizing that rather than considering the sheer number of species, it is which specific species that are present that is crucial for ecological functions. So, I am afraid that alpha, beta and gamma biodiversity will have less relevance in the future for conservation purposes.
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