Introducing the bipartite Package: Analysing 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.