The mutually beneficial interactions between plants and their animal pollinators and seed dispersers have been paramount in the generation of Earth's biodiversity. These mutualistic interactions often involve dozens or even hundreds of species that form complex networks of interdependences. Understanding how coevolution proceeds in these highly diversified mutualisms among free-living species presents a conceptual challenge. Recent work has led to the unambiguous conclusion that mutualistic networks are very heterogeneous (the bulk of the species have a few interactions, but a few species are much more connected than expected by chance), nested (specialists interact with subsets of the species with which generalists interact), and built on weak and asymmetric links among species. Both ecological variables (e.g., phenology, local abundance, and geographic range) and past evolutionary history may explain such network patterns. Network structure has important implications for the coexistence and stability of...

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Plant-Animal Mutualistic Networks: The Architecture of Biodiversity

Many analyses of ecological networks in recent years have introduced new indices to describe network properties. As a consequence, tens of indices are available to address similar questions, differing in specific detail, sensitivity in detecting the property in question, and robustness with respect to network size and sampling intensity. Furthermore, some indices merely reflect the number of species participating in a network, but not their interrelationship, requiring a null model approach. Here we introduce a new, free software calculating a large spectrum of network indices, visualizing bipartite networks and generating null models. We use this tool to explore the sensitivity of 26 network indices to network dimensions, sampling intensity and singleton observations. Based on observed data, we investigate the interrelationship of these indices, and show that they are highly correlated, and heavily influenced by network dimensions and connectance. Finally, we re-evaluate five common hypotheses about network properties, comparing 19 pollination networks with three differently complex null models: 1. The number of links per species ("degree") follow (truncated) power law distributions. 2. Generalist pollinators interact with specialist plants, and vice versa (dependence asymmetry). 3. Ecological networks are nested. 4. Pollinators display complementarity, owing to specialization within the network. 5. Plant-pollinator networks are more robust to extinction than random networks. Our results indicate that while some hypotheses hold up against our null models, others are to a large extent understandable on the basis of network size, rather than ecological interrelationships. In particular, null model pattern of dependence asymmetry and robustness to extinction are opposite to what current network paradigms suggest. Our analysis, and the tools we provide, enables ecologists to readily contrast their findings with null model expectations for many different questions, thus separating statistical inevitability from ecological process.

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Indices, Graphs and Null Models: Analyzing Bipartite Ecological Networks

Interactions among species in ecological communities have long fascinated ecologists. Prominent recent examples include pollination webs (Memmott et al., 2004), species-rich predator-prey systems (Tylianakis et al., 2007) and seed dispersal mutualisms (all reviewed in Bluthgen et al., 2007). Many of the topological descriptors used in food webs since the 1960s have limited ecological meaning when only two trophic levels are investigated (for example chain length: Pimm, 1982/2002; Montoya et al., 2006). Here, the network becomes bipartite, i.e. every member of one trophic level is only connected to members of the other trophic level: direct interactions within trophic levels are regarded as unimportant. For bipartite ecological networks very many, more or less different, indices have been proposed to capture important features of the interactions and of the species. For example, species degrees (number of species the target species is linked to) or species strength (sum of level of dependencies of other species on the target) are supposed to quantify the importance of a species in a web. The new R-package bipartite, introduced here, provides functions to viualise webs and calculate a series of indices commonly used to describe pattern in ecological webs. It focusses on webs consisting of only two trophic levels, e.g. pollination webs or predator-prey-webs. We had three types of ecological bipartite webs in mind when writing this package: seed-disperser, plant-pollinator and predatorprey systems. Bipartite networks, as analysed and plotted in the package bipartite, can be represented by a matrix, in which, in our definition, columns represent species in the higher trophic level, and rows species in the lower trophic level. Entries in the matrix represent observed links, either quantitatively (with one to many interactions per link) or qualitatively (binary). Usually such matrices are very sparse, marginal sums (i.e. abundance distributions) highly skewed and average number of interactions per link are low (around 2: Bluthgen et al., 2007). With the package bipartite, presented here, we wanted to overcome two main deficiencies in the field: 1. Lack of software to calculate various indices and topological descriptors of bipartite networks. And 2. No convenient plotting tool for bipartite networks. This article aims to briefly present the two visualisation functions (plotweb and visweb), then present an example output from the calculation of network-level descriptors (using function networklevel) and finally address some miscellaneous issues to do with fitting degree distributions, secondary extinction slopes and null models for bipartite webs. Along with several functions we also include 19 data sets on pollinator networks, taken from the National Center for Ecological Analysis and Synthesis webpage devoted to this topic (www.nceas.ucsb. edu/interactionweb). There are several other bipartite data sets at this repository, and our data include only quantitative plant-pollinator networks.

https://www.uni-goettingen.de/de/document/download/96729eb9d30a6f2dc4403df15854305c-en.pdf/Rnews2008,8_8-11_open.pdf

Introducing the bipartite Package: Analysing Ecological Networks

Summary 1. A fundamental goal of ecological network research is to understand how the complexity observed in nature can persist and how this affects ecosystem functioning. This is essential for us to be able to predict, and eventually mitigate, the consequences of increasing environmental perturbations such as habitat loss, climate change, and invasions of exotic species. 2. Ecological networks can be subdivided into three broad types: ‘traditional’ food webs, mutualistic networks and host‐parasitoid networks. There is a recent trend towards cross-comparisons among network types and also to take a more mechanistic, as opposed to phenomenological, perspective. For example, analysis of network configurations, such as compartments, allows us to explore the role of co-evolution in structuring mutualistic networks and host‐parasitoid networks, and of body size in food webs. 3. Research into ecological networks has recently undergone a renaissance, leading to the production of a new catalogue of evermore complete, taxonomically resolved, and quantitative data. Novel topological patterns have been unearthed and it is increasingly evident that it is the distribution of interaction strengths and the configuration of complexity, rather than just its magnitude, that governs network stability and structure. 4. Another significant advance is the growing recognition of the importance of individual traits and behaviour: interactions, after all, occur between individuals. The new generation of high-quality networks is now enabling us to move away from describing networks based on species-averaged data and to start exploring patterns based on individuals. Such refinements will enable us to address more general ecological questions relating to foraging theory and the recent metabolic theory of ecology. 5. We conclude by suggesting a number of ‘dead ends’ and ‘fruitful avenues’ for future research into ecological networks.

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Ecological networks--beyond food webs.

Uniting pattern and process in plant-animal mutualistic networks: a review.

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. 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. 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.

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Nils Blüthgen

Papers

Measuring specialization in species interaction networks

Specialization, constraints, and conflicting interests in mutualistic networks.