The presence–absence matrix reloaded: the use and interpretation of range–diversity plots

Abstract

Aim A great deal of information on distribution and diversity can be extracted from presence-absence matrices (PAMs), the basic analytical tool of many biogeographic studies. This paper presents numerical procedures that allow the analysis of such information by taking advantage of mathematical relationships within PAMs. In particular, we show how range-diversity (RD) plots summarize much of the information contained in the matrices by the simultaneous depiction of data on distribution and diversity.Innovation We use matrix algebra to extract and process data from PAMs. Information on the distribution of species and on species richness of sites is computed using the traditional R (by rows) and Q (by columns) procedures, as well as the new Rq (by rows, considering the structure of columns) and Qr (by columns, considering the structure by rows) methods. Matrix notation is particularly suitable for summarizing complex calculations using PAMs, and the associated algebra allows the implementation of efficient computational programs. We show how information on distribution and species richness can be depicted simultaneously in RD plots, allowing a direct examination of the relationship between those two aspects of diversity. We explore the properties of RD plots with a simple example, and use null models to show that while parameters of central tendency are not affected by randomization, the dispersion of points in RD plots does change, showing the significance of patterns of co-occurrence of species and of similarity among sites.Main conclusion Species richness and range size are both valid measures of diversity that can be analysed simultaneously with RD plots. A full analysis of a system requires measures of central tendency and dispersion for both distribution and species richness.

Is Rich and Rare the Common Share? Describing Biodiversity Patterns to Inform Conservation Practices for South American Anurans

“…This procedure extracts data from rows (i.e., grid cells: species richness) by simultaneously considering the information within columns (i.e., species: range size). This information can be summarized and depicted using range-diversity (RD) plots [17], [18].…”

“…RD plots convey joint information on species richness and range size enabling the exploration of biogeographic patterns of similarity among grid cells, in terms of shared species, and co-occurrence among species [18]. We used the “by sites” version of RD plots [17], in which axes represent the mean proportional per-cell range size and the proportional species richness of cells, in the x - and y -axes, respectively.…”

Species co‐occurrence analysis: pairwise versus matrix‐level approaches

“…I used a F-E algorithm implemented in R to obtain 50,000 random matrices, keeping record of the number of co-occurrences of each pair of species in each iteration, taking advantage of a fast algorithm that computes all pairwise co-occurrences with a single matrix multiplication (Arita et al, 2012). Not surprisingly, I obtained results that were identical to those reported by Veech (2013) and those calculated with pairwise Fisher's exact tests: 14 pairs showing more cooccurrences than expected and one pair showing fewer co-occurrences (P < 0.05 in one-tailed tests).…”

The pairwise approach to analysing species co‐occurrence

“…The main difference is that the latter calculate a co-occurrence metric as a property of the entire presenceabsence matrix whereas the former examine co-occurrence 'species-by-species' (Sfenthourakis et al, 2006;Pitta et al, 2012) to determine whether a particular pair of species is aggregated, segregated or random in occurrence (Gotelli & Ulrich, 2010). A recent approach developed by Arita et al (2012) is best described as a hybrid given that it requires calculations performed on an entire matrix but the metric (proportional species richness) is obtained for each species separately (Table 1). Examples of matrix-level metrics include matrix temperature (Patterson & Atmar, 1986;Atmar & Patterson, 1993), number of unique species combinations (in the matrix), and the variance ratio (Schluter, 1984).…”

“…Used to examine co-occurrence in the context of an entire assemblage and its geographical distribution (among other uses). Arita et al (2012) Causality analysis Pairwise Compares pairwise co-occurrence from two or more types of presence-absence matrix. The geographical matrix is the traditional form where species are recorded from sampling sites; the ecological matrices consist of species assigned to units representing habitat types or other ecological factors.…”