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Aim The nestedness temperature of presence-absence matrices is currently calculated with the nestedness temperature calculator (NTC). In the algorithm implemented by the NTC: (1) the line of perfect order is not uniquely defined, (2) rows and columns are reordered in such a way that the packed matrix is not the one with the lowest temperature, and (3) the null model used to determine the probabilities of finding random matrices with the same or lower temperature is not adequate for most applications. We develop a new algorithm, BINMATNEST (binary matrix nestedness temperature calculator), that overcomes these difficulties.Methods BINMATNEST implements a line of perfect order that is uniquely defined, uses genetic algorithms to determine the reordering of rows and columns that leads to minimum matrix temperature, and provides three alternative null models to calculate the statistical significance of matrix temperature. ResultsThe NTC performs poorly when the input matrix has checkerboard patterns. The more efficient packing of BINMATNEST translates into matrix temperatures that are lower than those computed with the NTC. The null model implemented in the NTC is associated with a large frequency of type I error, while the other null models implemented in BINMATNEST (null models 2 and 3) are conservative. Overall, null model 3 provides the best performance. The nestedness temperature of a matrix is affected by its size and fill, but the probability that such a temperature is obtained by chance is not. BINMATNEST reorders the input matrix in such a way that, if fragment size/isolation plays a role in determining community structure, there will be a significant rank correlation between the size/ isolation of the fragments and the way that they are ordered in the packed matrix. Main conclusionsThe nestedness temperature of presence-absence matrices should not be calculated with the NTC. The algorithm implemented by BINMATNEST is more robust, allowing for across-study comparisons of the extent to which the nestedness of communities departs from randomness. The sequence in which BINMATNEST reorders habitat fragments provides information about the causal role of immigration and extinction in shaping the community under study.

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The structural organization of mutualism networks, typified by interspecific positive interactions, is important to maintain community diversity. However, there is little information available about the effect of introduced species on the structure of such networks. We compared uninvaded and invaded ecological communities, to examine how two species of invasive plants with large and showy flowers (Carpobrotus affine acinaciformis and Opuntia stricta) affect the structure of Mediterranean plant-pollinator networks. To attribute differences in pollination to the direct presence of the invasive species, areas were surveyed that contained similar native plant species cover, diversity and floral composition, with or without the invaders. Both invasive plant species received significantly more pollinator visits than any native species and invaders interacted strongly with pollinators. Overall, the pollinator community richness was similar in invaded and uninvaded plots, and only a few generalist pollinators visited invasive species exclusively. Invasive plants acted as pollination super generalists. The two species studied were visited by 43% and 31% of the total insect taxa in the community, respectively, suggesting they play a central role in the plant-pollinator networks. Carpobrotus and Opuntia had contrasting effects on pollinator visitation rates to native plants: Carpobrotus facilitated the visit of pollinators to native species, whereas Opuntia competed for pollinators with native species, increasing the nestedness of the plant-pollinator network. These results indicate that the introduction of a new species to a community can have important consequences for the structure of the plant-pollinator network.

Recent attempts to examine the biological processes responsible for the general characteristics of mutualistic networks focus on two types of explanations: nonmatching biological attributes of species that prevent the occurrence of certain interactions (“forbidden links”), arising from trait complementarity in mutualist networks (as compared to barriers to exploitation in antagonistic ones), and random interactions among individuals that are proportional to their abundances in the observed community (“neutrality hypothesis”). We explored the consequences that simple linkage rules based on the first two hypotheses (complementarity of traits versus barriers to exploitation) had on the topology of plant–pollination networks. Independent of the linkage rules used, the inclusion of a small set of traits (two to four) sufficed to account for the complex topological patterns observed in real-world networks. Optimal performance was achieved by a “mixed model” that combined rules that link plants and pollinators whose trait ranges overlap (“complementarity models”) and rules that link pollinators to flowers whose traits are below a pollinator-specific barrier value (“barrier models”). Deterrence of floral parasites (barrier model) is therefore at least as important as increasing pollination efficiency (complementarity model) in the evolutionary shaping of plant–pollinator networks.