Multivariate dispersion as a measure of beta diversity

Abstract

Beta diversity can be defined as the variability in species composition among sampling units for a given area. We propose that it can be measured as the average dissimilarity from individual observation units to their group centroid in multivariate space, using an appropriate dissimilarity measure. Differences in beta diversity among different areas or groups of samples can be tested using this approach. The choice of transformation and dissimilarity measure has important consequences for interpreting results. For kelp holdfast assemblages from New Zealand, variation in species composition was greater in smaller holdfasts, while variation in relative abundances was greater in larger holdasts. Variation in community structure of Norwegian continental shelf macrobenthic fauna increased with increases in environmental heterogeneity, regardless of the measure used. We propose a new dissimilarity measure which allows the relative weight placed on changes in composition vs. abundance to be specified explicitly.

How does pedogenesis drive plant diversity?

“…Variance soil properties Represents spatial heterogeneity in soil properties, directly relevant to niche theory [17,29] Multivariate spatial dispersion [70] of soil properties…”

Non-Native Plants Disrupt Dual Promotion of Native Alpha and Beta Diversity

“…Simpson's diversity index yielded qualitatively the same results as species richness. Our measure of beta diversity was the dissimilarity of native species composition between plots within treatments, quantified as the mean distance to individual plots from the group centroid, calculated according to the distance matrix based on Jaccard dissimilarity (Anderson 2004(Anderson , 2006Anderson et al 2006). Bray-Curtis dissimilarity, which takes into account species biomass, yielded qualitatively the same results as Jaccard dissimilarity, which considers only the presence and absence of species.…”

“…We compared this wholly native treatment with other treatments to test for the effects of establishment of Coriaria, Buddleja and other nonnative species on native diversity. We examined removal treatment effects using ANOVA followed by Tukey's HSD test for alpha diversity, using PERMDISP followed by pair-wise a posteriori test (Anderson 2004;Anderson et al 2006) for beta diversity, and using t-tests (to compare plots where all non-native species were excluded and those where all or some non-native species were retained) for gamma diversity. To ensure our results were not biased by exclusion of rare species, we repeated these analyses using all species recorded in plots instead of including only species for which leaf trait data were available.…”

“…Numerous measures of beta diversity have been proposed, each with different strengths and limitations (Koleff et al 2003;Jost 2007Jost , 2010Tuomisto 2010;Veech and Crist 2010;Wilsey 2010). We used Anderson's (2006) measure because it allows betweentreatment difference in beta diversity to be statistically tested and is robust and powerful under a variety of conditions (Anderson 2004(Anderson , 2006Anderson et al 2006;Chase 2007Chase , 2010. Gamma diversity was measured as the total number of native species observed in treatments.…”

Context‐dependent functional dispersion across similar ranges of trait space covered by intertidal rocky shore communities

“…In such trait space , functional richness (Villéger, Mason, & Mouillot, 2008) represents the range occupied by a given community and can be estimated as the number of functional trait combinations. Functional dispersion (Laliberté & Legendre, 2010) is estimated as the mean distance of all species to the weighted centroid of the community in the trait space, being equivalent to the multivariate dispersion (Anderson, Ellingsen, & McArdle, 2006). When the influence of species richness on these indices is statistically removed (Mason, Lanoiselee, Mouillot, Wilson, & Argillier, 2008), functional richness and dispersion are “pure” estimators of the occupied range of functional space and the dispersion in trait combination abundances, respectively (Mason et al., 2012).…”