A protocol to compare nestedness among submatrices
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ORIGINAL ARTICLE
A protocol to compare nestedness among submatrices Giovanni Strona • Fabrizio Stefani Paolo Galli • Simone Fattorini
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Received: 30 March 2012 / Accepted: 10 September 2012 / Published online: 28 September 2012 Ó The Society of Population Ecology and Springer 2012
Abstract Searching for nestedness has become a popular exercise in community ecology. Significance of a nestedness index is usually evaluated using z values, and finding that a matrix is nested is typically a common result. However, nestedness is not likely to be spread uniformly within a matrix of species presence/absence per site. Selected parts of the matrix may show a degree of nestedness significantly higher (or lower) than expected from the overall pattern. Here we describe a procedure to assess if a particular submatrix (i.e., a peculiar combination of rows and columns extracted from the complete matrix) is more or less nested than expected for an assortment of sites and species taken at random from the same overall matrix. The idea is to obtain several submatrices of different sizes from the same overall matrix and to calculate their z values. A regression is then performed between z values of submatrices and their sizes. A nestedness index independent of matrix size is suggested as the deviation of the z value of a particular submatrix from that expected according to the regression line. We applied our protocol to 55 matrices with different nestedness indices under various null-models and, for purpose of demonstration, we discussed in detail a single case study regarding various animal groups of the Aegean Islands (Greece). The obtained results strongly
G. Strona (&) F. Stefani P. Galli S. Fattorini Department of Biotechnology and Biosciences, Water Ecology Team (WET), University of Milano Bicocca, Piazza della Scienza 2, 20126 Milan, Italy e-mail: [email protected] S. Fattorini Azorean Biodiversity Group (CITA-A) and Platform for Enhancing Ecological Research and Sustainability (PEERS), Departamento de Cieˆncias Agra´rias, Angra do Heroı´smo, Universidade dos Ac¸ores, Terceira, Ac¸ores, Portugal
encourage further research to focus not only on the question whether a matrix is nested or not, but also on where and why nestedness is confined. Keywords Aegean Islands Biogeography Mediterranean Null model Paleogeography
Introduction Nestedness analysis is a technique aimed at investigating species distribution patterns. In a perfectly nested distribution, species occurring at a particular site are always present in more species-rich sites, whereas species absent from this particular site never occur in less species-rich sites (Patterson and Atmar 1986). In the last 20 years, searching for nestedness has become a popular exercise in disparate fields, including community ecology, ecological networks, biogeography, conservation biology, and parasitology (Kadmon 1995; Worthen 1996; Hadly and Maurer 2001; Fleishman et al. 2002; Azeria et al. 2006; Ulrich et al. 2009; Joppa et al. 2010). A common practice to asses
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