In ecology, beta diversity (β-diversity or true beta diversity) is the ratio between regional and local species diversity. The term was introduced by R. H. Whittaker together with the terms alpha diversity (α-diversity) and gamma diversity (γ-diversity). The idea was that the total species diversity in a landscape (γ) is determined by two different things, the mean species diversity at the local level (α) and the differentiation among local sites (β). Other formulations for beta diversity include "absolute species turnover", "Whittaker's species turnover" and "proportional species turnover". Whittaker proposed several ways of quantifying differentiation, and subsequent generations of ecologists have invented more. As a result, there are now many defined types of beta diversity. Some use beta diversity to refer to any of several indices related to compositional heterogeneity. Confusion is avoided by using distinct names for other formulations. Beta diversity as a measure of species turnover overemphasizes the role of rare species as the difference in species composition between two sites or communities is likely reflecting the presence and absence of some rare species in the assemblages. Beta diversity can also be a measure of nestedness, which occurs when species assemblages in species-poor sites are a subset of the assemblages in more species-rich sites. Moreover, pairwise beta diversity are inadequate in building all biodiversity partitions (some partitions in a Venn diagram of 3 or more sites cannot be expressed by alpha and beta diversity). Consequently, some macroecological and community patterns cannot be fully expressed by alpha and beta diversity. Due to these two reasons, a new way of measuring species turnover, coined Zeta diversity (ζ-diversity), has been proposed and used to connect all existing incidence-based biodiversity patterns. (Wikipedia).
Discussing h-vectors and the g-conjecture. Featuring June Huh from the Institute for Advanced Study at Princeton University. More links & stuff in full description below ↓↓↓ A little extra bit from this interview: https://youtu.be/cFKGX3vAs_Q Shapes in higher dimensions: https://youtu.b
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