An empirical comparison of beta diversity indices in establishing prairies.

Whittaker (1960, 1972) first proposed the idea that species diversity has spatial components, with alpha diversity estimating diversity within individual stands (or communities) and beta diversity estimating the number of community types in an area (or in Whittaker’s terminology, ‘‘differentiation of communities along gradients’’). These two values combined make up gamma diversity. Beta diversity is important because it provides the conceptual link between local and regional diversity, more directly measures how soil types, disturbance, and dispersal affect diversity, and is helpful in understanding why species loss is sometimes smaller than predicted by theory (Wilsey et al. 2005). Many interesting and longstanding questions are applied across scales, such as how much diversity is found within islands vs. across islands? Is the number of habitat types (i.e., beta) within islands key to explaining diversity at larger scales or is it the greater population sizes found on large islands? Furthermore, a consideration of both alpha and beta is necessary for understanding how diversity arises and is maintained in diverse systems. For example, in the northern Great Plains, we have found that remnant prairies can contain over 120 plant species within a small area (Wilsey et al. 2005); this occurs because of high diversity at the neighborhood scale where 20–25 species are found per square meter (Martin et al. 2005), and from species accumulation across neighborhoods (i.e., beta). Many different approaches to estimating beta have been forwarded since Whittaker introduced the concept, and many sampling and statistical issues have been discussed. To an empirical ecologist, the key question when deciding which approach to use is ‘‘Will we get different answers to a question depending on the beta measure that we use?’’ Here, I address this question by testing whether commonly used indices (multiplicative and additive measures) differ in their response to a common set of ecological treatments. Whittaker proposed a multiplicative form for beta (mb) as b1⁄4 c/a. A simple way to describe this equation is that alpha is species diversity within communities, and beta is the number of community types in the region (Jost 2007). A major issue with the amongvs. withincommunity approach is that the scale at which a is sampled varies so that alpha is used to estimate point diversity in some studies (e.g., at the scale of a sampling station or quadrat) and is used to estimate something larger (e.g., an island in an island biogeography study) in other studies. This makes sense in that beta describes a general concept of species accumulation across lower levels of organization, but it creates a problem in that one person’s alpha (e.g., an island) is another person’s gamma (e.g., an island, if alpha is at the scale of neighborhoods within the island). The additive form of beta (ab), b 1⁄4 c (mean a), has become popular in recent years (Lande 1996, Veech et al. 2002, Crist et al. 2003) because it can easily be applied at different spatial scales to address these issues in an effective manner. The additive form has the following advantages over the multiplicative form: (1) alpha and beta are in the same units, and (2) it enables estimates of beta even when the boundaries between communities are hard to discern, and thus, (3) it more easily allows multiple levels of beta. With additive beta, one can ask questions about how beta changes with the scale of measurement, and it fits in well with other topics in the popular field of landscape ecology. However, Jost (2007) and Riccota (2007) correctly point out that ab is not mathematically independent of additive a. They recommend using multiplicative forms of beta, alternative forms of additive beta based on numbers equivalents (Jost 2007), or proportions of additive alpha and beta to gamma (a/c and b/c [or propB]; Riccota 2007). To provide a simple ecological example that illustrates their point about a lack of independence: imagine a relatively homogenous field of herbaceous plants surrounded by a very large regional species pool with a consistent amount of species turnover throughout. Three studies are conducted in this same field, each group uses a different sized quadrat to sample, and all have the same sample size. Let us assume that they all sample the field without error. The first uses the smallest-sized quadrat and finds a mean alpha of 20 and gamma of 30. The second uses a medium-sized quadrat and finds a mean alpha of 40 and gamma of 60. The third uses a large-sized quadrat and Manuscript received 2 March 2009; revised 5 May 2009; accepted 8 May 2009. Corresponding Editor: A. M. Ellison. For reprints of this Forum, see footnote 1, p. 1962. 1 E-mail: [email protected] FORUM 1984 Ecology, Vol. 91, No. 7