title: Measuring specialization in species interaction networks.
abstract: BACKGROUND
  Network analyses of plant-animal interactions hold valuable biological information. They are often used to quantify the degree of specialization between partners, but usually based on qualitative indices such as 'connectance' or number of links. These measures ignore interaction frequencies or sampling intensity, and strongly depend on network size.
  
  
  RESULTS
  Here we introduce two quantitative indices using interaction frequencies to describe the degree of specialization, based on information theory. The first measure (d') describes the degree of interaction specialization at the species level, while the second measure (H2') characterizes the degree of specialization or partitioning among two parties in the entire network. Both indices are mathematically related and derived from Shannon entropy. The species-level index d' can be used to analyze variation within networks, while H2' as a network-level index is useful for comparisons across different interaction webs. Analyses of two published pollinator networks identified differences and features that have not been detected with previous approaches. For instance, plants and pollinators within a network differed in their average degree of specialization (weighted mean d'), and the correlation between specialization of pollinators and their relative abundance also differed between the webs. Rarefied sampling effort in both networks and null model simulations suggest that H2' is not affected by network size or sampling intensity.
  
  
  CONCLUSIONS
  Quantitative analyses reflect properties of interaction networks more appropriately than previous qualitative attempts, and are robust against variation in sampling intensity, network size and symmetry. These measures will improve our understanding of patterns of specialization within and across networks from a broad spectrum of biological interactions.
authors.affiliation: Department of Animal Ecology and Tropical Biology, University of Würzburg, Biozentrum, Am Hubland, 97074 Würzburg, Germany. bluethgen@biozentrum.uni-wuerzburg.de
authors.forename: Nico
authors.initials: N
authors.lastname: Blüthgen
authors.forename: Florian
authors.initials: F
authors.lastname: Menzel
authors.forename: Nils
authors.initials: N
authors.lastname: Blüthgen
mesh_terms: D000222:Adaptation, Physiological; D000818:Animals; D001118:Argentina; D001516:Bees / Q000502:physiology*; D003198:Computer Simulation; D017753:Ecosystem; D020387:Food Chain; D008954:Models, Biological; D018521:Plant Physiological Phenomena; D011058:Pollen; D011157:Population Dynamics; D013045:Species Specificity; D006113:United Kingdom