A key property of biodiversity is that it is not homogeneously distributed on Earth. In other words, different sites usually shelter different biological communities. Quantifying the differences among biological communities is, therefore, a major step for understanding how and why biodiversity is distributed in the way it is. The term beta diversity was introduced by Whittaker (1960), and defined as “the extent of change in community composition, or degree of community differentiation, in relation to a complex-gradient of environment, or a pattern of environments”. In his original paper, Whittaker proposed several ways to quantify beta diversity. In its simplest form (which we will call strict sense beta diversity, or multiplicative beta diversity), beta diversity is defined as the ratio between gamma (regional) and alpha (local) diversities (Whittaker, 1960; Jost, 2007). Therefore, beta diversity is the effective number of distinct compositional units in the region (Tuomisto, 2010). In other words, beta diversity quantifies the number of different communities in the region. It is thus clear that beta diversity does not only account for the relationship between local and regional diversity, but also informs about the degree of differentiation among biological communities. This is because alpha and gamma diversities are different if (and only if) the biological communities within the region are different.
Let’s see how beta diversity varies from the minimum to the maximum differentiation of local assemblages in a region. For simplicity, we will quantify biological diversity as species richness (number of species), but alpha, beta and gamma diversities can also be defined to account for richness and relative abundances (see Jost, 2007 for a detailed explanation). When local assemblages are all identical (minimum differentiation), alpha diversity equals gamma diversity, and beta diversity equals 1 (figure below).
Thus, when the mean local species richness (alpha diversity) equals the regional species richness (gamma diversity), their ratio (beta diversity) equals the unity. This means that in this region there is only one distinct compositional unit (i.e. only one “community”).
When local assemblages are all completely different (maximum differentiation), gamma diversity equals the multiplication of alpha diversity by the number of sites (N), so beta diversity equals N, meaning that in this region there are N distinct compositional units (i.e. N different “communities”, figure below).
As seen above, multiplicative beta diversity (gamma/alpha) ranges from 1 to N (number of sites in the region). Therefore, to get a measure of differentiation independent of the number of sites (N) involved in the calculation, one need to standardize beta diversity. For example, the Sørensen index of dissimilarity is just beta-1 divided by N-1, which ranges between 0 and 1, and is independent of the number of sites (N). In general, dissimilarity indices that are monotonic transformations of strict sense beta diversity (i.e. Sørensen and Jaccard indices, see Chao et al., 2012) are appropriate measures of differences among biological communities.
The meaning of “difference” applied to biological communities is not unidimensional. The intuition we all have in mind when thinking on beta diversity or difference between biological assemblages is the replacement of some species by others (see figure below).
However, the nested loss of species from the richest to the poorest locality does also make alpha and gamma diversity to differ, potentially yielding the same value of beta for strikingly different patterns (see figure below).
Of course, the observed patterns can be a combination of both replacement and species loss (see figure below).
In the three situations above (A-C), gamma diversity (12 species) and alpha diversity (mean site diversity = 6 species) are identical, so multiplicative beta diversity (gamma/alpha) and the related dissimilarity indices (e.g., Sørensen, Jaccard) also take identical values.
The Simpson index of dissimilarity (Simpson, 1943; Simpson, 1960) was intended to remove the effects of richness difference in communities. In fact, it considers nested assemblages to be perfectly similar, so it yields the replacement component of beta diversity. In the absence of richness difference, Simpson and Sørensen indices take identical values, so their difference accounts for the nestedness-resultant component of dissimilarity. This leads to a framework in which total dissimilarity (Sørensen or Jaccard indices) can be additively portioned into replacement and nestedness resultant components (see Baselga, 2010; Baselga, 2012 for a detailed explanation of the method). The same approach can be used to separate components of abundance-based dissimilarity (Baselga, 2013; Legendre, 2014; Baselga, 2017), functional dissimilarity (Villeger et al., 2013) and phylogenetic dissimilarity (Leprieur et al., 2012). Functions to compute all these dissimilarity indices are available in R package betapart (see Baselga & Orme, 2012 and updates here).
Baselga, A. (2010) Partitioning the turnover and nestedness components of beta diversity. Global Ecology and Biogeography, 19, 134-143.
Baselga, A. (2012) The relationship between species replacement, dissimilarity derived from nestedness, and nestedness. Global Ecology and Biogeography, 21, 1223-1232.
Baselga, A. (2013) Separating the two components of abundance-based dissimilarity: balanced changes in abundance vs. abundance gradients. Methods in Ecology and Evolution, 4, 552–557.
Baselga A. (2017) Partitioning abundance-based multiple-site dissimilarity into components: balanced variation in abundance and abundance gradients. Methods in Ecology and Evolution, in press
Baselga, A. & Orme, C. D. L. (2012) betapart: an R package for the study of beta diversity. Methods in Ecology and Evolution, 3, 808-812.
Chao, A., Chiu, C.-H. & Hsieh, T. C. (2012) Proposing a resolution to debates on diversity partitioning. Ecology, 39, 2037-2051.
Jost, L. (2007) Partitioning diversity into independent alpha and beta components. Ecology, 88, 2427-2439.
Legendre, P. (2014) Interpreting the replacement and richness difference components of beta diversity. Global Ecology and Biogeography, 23, 1324–1334.
Leprieur, F., Albouy, C., De Bortoli, J., Cowman, P. F., Belwood, D. R. & Mouillot, D. (2012) Quantifying phylogenetic beta diversity: distinguishing between ‘true’ turnover of lineages and phylogenetic diversity gradients. PLoS One, 7, e42760.
Simpson, G. G. (1943) Mammals and the Nature of Continents. American Journal of Science, 241, 1-31.
Simpson, G. G. (1960) Notes on the measurement of faunal resemblance. American Journal of Science, 258, 300-311.
Tuomisto, H. (2010) A diversity of beta diversities: straightening up a concept gone awry. Part 1. Defining beta diversity as a function of alpha and gamma diversity. Ecography, 33, 2-22.
Villeger, S., Grenouillet, G. & Brosse, S. (2013) Decomposing functional ß-diversity reveals that low functional ß-diversity is driven by low functional turnover in European fish assemblages. Global Ecology and Biogeography, 22, 671–681.
Whittaker, R. H. (1960) Vegetation of the Siskiyou Mountains, Oregon and California. Ecological Monographs, 30, 280-338.