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Identifying compartments in presence–absence matrices and bipartite networks: insights into modularity measures

Authors

  • Elisa Thébault

    Corresponding author
    • Centre National de la Recherche Scientifique (CNRS), UMR 7618 BIOEMCO, (Biogéochimie et Écologie des Milieux Continentaux), Ecole Normale Supérieure, 46 rue d'Ulm, 75005 Paris, France
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Correspondence: Elisa Thébault, CNRS, UMR 7618 BIOEMCO (Biogéochimie et Écologie des Milieux Continentaux), Ecole Normale Supérieure, 46 Rue d'Ulm, 75005 Paris, France.

E-mail: elisa.thebault@ens.fr

Abstract

Aim

The identification of compartments (i.e. clusters of overlapping species ranges across an environmental gradient) is an important methodological challenge for biogeographical studies. Recent developments in network theory offer promising perspectives on this issue using the measurement of modularity. A presence–absence matrix is modular if particular subgroups of species are mainly linked to particular subgroups of sites. Modularity is still rarely considered in biogeographical studies. Here, I compare different modularity indices to investigate which is the most appropriate for studying presence–absence matrices and similar types of networks, such as bipartite networks.

Location

Evaluation was based on 279 data sets from around the world.

Methods

I consider the three most commonly used modularity indices. One was developed for unipartite networks and the other two for bipartite networks. The performance of these indices (detection of a modular pattern, quality of compartment identification) is evaluated on test matrices of known compartmentalization levels with varying sizes and fills. Modularity patterns are then evaluated for 279 presence–absence matrices.

Results

The three modularity measures differ mainly in the identification of the compartments, and less in the statistical significance of the observed modularity. The modularity measure Q3 tends to perform best, whereas Q2 usually performs less well, especially for highly diverse and highly connected networks that include a few extremely well-connected nodes. These modularity indices all reveal the presence of modular patterns in presence–absence matrices.

Main conclusions

The choice of an appropriate modularity index is particularly important when we are interested in the composition of the different compartments. This analysis suggests that compartmentalized structures can be widespread in presence–absence matrices (about 40% of the matrices considered here). Modularity should thus offer interesting perspectives on the understanding of biogeographical patterns.

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