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. 2006 Aug 14;6:9.
doi: 10.1186/1472-6785-6-9.

Measuring Specialization in Species Interaction Networks

Free PMC article

Measuring Specialization in Species Interaction Networks

Nico Blüthgen et al. BMC Ecol. .
Free PMC article


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.

Conclusion: 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.


Figure 1
Figure 1
Patterns within pollinator networks. Frequency distribution of the species-level specialization index (d') for pollinators and plants from two published networks, one from Britain [32] and one from Argentina [33]. Bars show the number of individuals in each category (label '0' defines 0.00 ≤ d' < 0.05, etc.). Bars are separated for different species, and total number of species in each category is given on top. Arrows indicate cases where bars are invisible due to low numbers of individuals.
Figure 2
Figure 2
Sampling effect in pollinator networks. Rarefaction of sampling effort in a British and an Argentinean pollination web [32,33]. Two network-level measures of specialization – the frequency-based specialization index (H2') and the 'connectance' index (C) – are shown for networks in which the total number of interactions (m) has been reduced by randomly deleting interactions. Black dots show the effect of sampling effort for the original association matrix, gray dots the effect for a null model, i.e. five networks in which partners were randomly associated (same row and column totals as in the original matrix).
Figure 3
Figure 3
Simulated random networks. Behavior of specialization measures in simulated random networks. Each point represents one matrix with random associations, based on specific row and column totals that follow a lognormal distribution. The size of squared matrices in (A) increased from 2 × 2 to 200 × 200. In (B), only the number of rows changed, while the number of columns was fixed at 20, rectangular matrices thus increased from 2 × 20 to 200 × 20. In (C), the network size was fixed at 20 × 20. The total number of interactions (m) increased with matrix size in (A), where each species had on average 20 individuals. In (B), m was fixed at 4000, resulting in a reduced interaction density for larger matrices. In (C), m increased from 20 to 4000. The index H2' and connectance C are specialization measures of the whole matrix and thus reciprocal, while the average number of links (L¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGmbatgaqeaaaa@2DE5@), and weighted mean standardized Kullback-Leibler distance (<d'>) are given for all columns (rows give a similar pattern).

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