Spatial Components of Biodiversity

The terms alpha, beta, and gamma diversity were all introduced by R. H. Whittaker to describe the spatial component of biodiversity.

Imagine that you have a landscape containing of a number of separate sites and habitats. Alpha diversity is just the diversity of each site (local species pool). Beta diversity represents the differences in species composition among sites. Gamma diversity is the diversity of the entire landscape (regional species pool).

Among these, alpha and gamma diversity are fairly straightforward. It's harder to grasp what beta diversity means, since it's usually used quite loosely. It's something of a bridge from the local (alpha) to the regional (gamma) scale. You can interpret it as a metric of turnover or dissimilarity between sites, however you want to measure that. You can interpret it as a rate of accumulation of diversity with an increasing number of sites sampled. You can even calculate it as:

Beta=Gamma/Alpha
β=γα

It's fair to be pluralistic about conceptions of beta diversity: In other words, pick a formulation that works with the question and the data you have. You can find plenty of papers that review the different meanings and uses of beta diversity, for example Anderson et al. (2011) Ecol. Lett. 14. One important distinction this paper points out is that beta diversity can refer either to directional variation along an environmental gradient, or non-directional variation among sample units in an area.