A temporal beta-diversity index to identify sites that have changed in exceptional ways in space-time surveys

Abstract

Aim: This paper presents the statistical bases for temporal beta-diversity analysis, a method to study changes in community composition through time from repeated surveys at several sites. Surveys of that type are presently done by ecologists around the world. A temporal beta-diversity Index (TBI) is computed for each site, measuring the change in species composition between the first (T1) and second surveys (T2). TBI indices can be decomposed into losses and gains; they can also be tested for significance, allowing one to identify the sites that have changed in composition in exceptional ways. This method will be of value to identify exceptional sites in space-time surveys carried out to study anthropogenic impacts, including climate change.

Innovation: The null hypothesis of the TBI test is that a species assemblage is not exceptionally different between T1 and T2, compared to assemblages that could have been observed at this site at T1 and T2 under conditions corresponding to H₀. Tests of significance of coefficients in a dissimilarity matrix are usually not possible because the values in the matrix are interrelated. Here, however, the dissimilarity between T1 and T2 for a site is computed with different data from the dissimilarities used for the T1-T2 comparison at other sites. It is thus possible to compute a valid test of significance in that case. In addition, the paper shows how TBI dissimilarities can be decomposed into loss and gain components (of species, or abundances-per-species) and how a B-C plot can be produced from these components, which informs users about the processes of biodiversity losses and gains through time in space-time survey data.

Main conclusion: Three applications of the method to different ecological communities are presented. This method is applicable worldwide to all types of communities, marine, and terrestrial. R software is available implementing the method.

Keywords: B–C plots; beta diversity; space–time analysis; statistical power; temporal beta diversity; temporal beta diversity index; type I error.

Figure 1

Schematic representation of the first step of the method. Data in matrices Mat.1 (for Time 1) and Mat.2 (for Time 2) are used to compute a vector of TBI dissimilarities D_i for all sites i (data rows). For example, for site i = 1, vectors T1₁ and T2₁ are compared to compute D ₁, the dissimilarity between data at time 1 (T1) and time 2 (T2)

Figure 2

Random permutation of the community composition data is done separately for each species (column), in matrices T1 (left) and T2 (right). This figure shows an example where a permutation of species j brings value y _{1 j} to position y _{9 j} and value y _{5 j} to position y _{1 j}. The exact same permutation, involving all values in column j, is done in matrices T1 (left) and T2 (right). Following similar permutations of all p species, dissimilarities are computed between the two vectors representing each site i, producing the values D_i under permutation

Figure 3

Tikus Island coral data. (a) Changes in dissimilarity D computed from the quantitative coral community compositions between years, and its components B/den (losses) and C/den (gains); den is the denominator of the dissimilarity index D, (2A + B + C) in this figure. The 1981 survey, before the El Niño event, is compared in turn to the 1983, 1984, 1985, 1987, and 1988 surveys. (b) Same for the species occurrence (i.e., presence–absence) data

Figure 4

Tikus Island coral data. Canonical ordination plot obtained by dbRDA for the quantitative coral community compositions data for the 6 years and 10 sites, constrained by a factor representing the 6 survey years. The years are marked by red symbols, and the sites (open circles) for each year are incompletely surrounded by 60% coverage ellipses. Arrows materialize the sequence of years

Figure 5

Chesapeake Bay benthos data. B–C plot comparing the fall surveys of 2005 and 2008, where the 25 brackish sites are plotted using the losses (B/den statistics) and gains (C/den statistics) computed from the species abundance data. Sites are identified by their code of the Chesapeake Bay Benthic Monitoring Program. The sites are represented by symbols corresponding to two water temperature groups observed during the 2005 fall survey. Green line with slope of 1: line where gains equal losses. The red line was drawn parallel to the green line (i.e., with slope = 1) and passing through the centroid of the points. Its position above the green line indicates that, on average, species gains dominated losses from 2005 to 2008

Figure 6

Map of the 25 brackish sites (red symbols) of the Chesapeake Bay ecological survey produced with the RgoogleMaps package in R. Comparison of surveys in years 2005 and 2008, abundance data: point sizes are proportional to the TBI indices (percentage difference D). + signs indicate the 17 sites where gains in abundances‐per‐species dominated; – signs, the 8 sites where losses dominated. The site identification numbers are those found in the Chesapeake Bay data base