Comparing the reliability of networks by spectral analysis

We provide a method for the ranking of the reliability of two networks with the same connectance. Our method is based on the Cheeger constant linking the topological property of a network with its spectrum. We first analyze a set of twisted rings with the same connectance and degree distribution, and obtain the ranking of their reliability using their eigenvalue gaps. The results are generalized to general networks using the method of rewiring. The success of our ranking method is verified numerically for the IEEE57, the Erd\H{o}s-R\'enyi, and the Small-World networks.Comment: 7 pages, 3 figure

The Food Web of Potter Cove (Antarctica): complexity, structure and function

Knowledge of the food web structure and complexity are central to better understand ecosystem functioning. A food-web approach includes both species and energy flows among them, providing a natural framework for characterizing species’ ecological roles and the mechanisms through which biodiversity influences ecosystem dynamics. Here we present for the first time a high-resolution food web for a marine ecosystem at Potter Cove (northern Antarctic Peninsula). Eleven food web properties were analyzed in order to document network complexity, structure and topology. We found a low linkage density (3.4), connectance (0.04) and omnivory percentage (45), as well as a short path length (1.8) and a low clustering coefficient (0.08). Furthermore, relating the structure of the food web to its dynamics, an exponential degree distribution (in- and out-links) was found. This suggests that the Potter Cove food web may be vulnerable if the most connected species became locally extinct. For two of the three more connected functional groups, competition overlap graphs imply high trophic interaction between demersal fish and niche specialization according to feeding strategies in amphipods. On the other hand, the prey overlap graph shows also that multiple energy pathways of carbon flux exist across benthic and pelagic habitats in the Potter Cove ecosystem. Although alternative food sources might add robustness to the web, network properties (low linkage density, connectance and omnivory) suggest fragility and potential trophic cascade effects.Fil: Marina, Tomas Ignacio. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Universidad Nacional de Luján. Instituto de Ecología y Desarrollo Sustentable. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Ecología y Desarrollo Sustentable; ArgentinaFil: Salinas, Vanesa Anabella. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Cordone, Georgina Florencia. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Campana, Gabriela Laura. Universidad Nacional de Luján. Instituto de Ecología y Desarrollo Sustentable. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Ecología y Desarrollo Sustentable; Argentina. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; ArgentinaFil: Moreira, María Eugenia. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Deregibus, Dolores. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; ArgentinaFil: Torre, Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Diversidad y Ecología Animal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Diversidad y Ecología Animal; ArgentinaFil: Sahade, Ricardo Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Diversidad y Ecología Animal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Diversidad y Ecología Animal; ArgentinaFil: Tatian, Marcos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Diversidad y Ecología Animal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Diversidad y Ecología Animal; ArgentinaFil: Barrera Oro, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales ; ArgentinaFil: De Troch, Marleen. University College Ghent; BélgicaFil: Doyle, Santiago Raúl. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Quartino, Maria Liliana. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; ArgentinaFil: Saravia, Leonardo Ariel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Momo, Fernando Roberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Universidad Nacional de Luján. Instituto de Ecología y Desarrollo Sustentable. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Ecología y Desarrollo Sustentable; Argentin

The restoration of ecological interactions: plant-pollinator networks on ancient and restored heathlands

1. Attempts to restore damaged ecosystems usually emphasize structural aspects of biodiversity, such as species richness and abundance. An alternative is to emphasize functional aspects, such as patterns of interaction between species. Pollination is a ubiquitous interaction between plants and animals. Patterns in plant-pollinator interactions can be analysed with a food web or complex-systems approach and comparing pollination webs between restored and reference sites can be used to test whether ecological restoration has taken place. 2. Using an ecological network approach, we compared plant-pollinator interactions on four pairs of restored and ancient heathlands 11 and 14 years following initiation of restoration management. We used the network data to test whether visitation by pollinators had been restored and we calculated pollinator importance indices for each insect species on the eight sites. Finally, we compared the robustness of the restored and ancient networks to species loss. 3. Plant and pollinator communities were established successfully on the restored sites. There was little evidence of movement of pollinators from ancient sites onto adjacent restored sites, although paired sites correlated in pollinator species richness in both years. There was little insect species overlap within each heathland between 2001 and 2004. 4. A few widespread insect species dominated the communities and were the main pollinators. The most important pollinators were typically honeybees (Apis mellifera), species of bumblebee (Bombus spp.) and one hoverfly species (Episyrphus balteatus). The interaction networks were significantly less complex on restored heathlands, in terms of connectance values, although in 2004 the low values might reflect the negative relationship between connectance and species richness. Finally, there was a trend of restored networks being more susceptible to perturbation than ancient networks, although this needs to be interpreted with caution. 5. Synthesis and applications. Ecological networks provide a powerful tool for assessing the outcome of restoration programmes. Our results indicate that heathland restoration does not have to occur immediately adjacent to ancient heathland for functional pollinator communities to be established. Moreover, in terms of restoring pollinator interactions, heathland managers need only be concerned with the most common insect species. Our focus on pollination demonstrates how a key ecological service can serve as a yardstick for judging restoration success

Mutualism supports biodiversity when the direct competition is weak

A key question of theoretical ecology is which properties of ecosystems favour their stability and help maintaining biodiversity. This qu estion recently reconsid- ered mutualistic systems, generating intense controversy about the role of mutu- alistic interactions and their network architecture. Here we show analytically and verify with simulations that reducing the effective intersp ecific competition and the propagation of perturbations positively influences struct ural stability against envi- ronmental perturbations, enhancing persistence. Notewor thy, mutualism reduces the effective interspecific competition only when the direct interspecific competition is weaker than a critical value. This critical competition i s in almost all cases larger in pollinator networks than in random networks with the same connectance. Highly connected mutualistic networks reduce the propagation of e nvironmental perturba- tions, a mechanism reminiscent of MacArthur’s proposal tha t ecosystem complexity enhances stability. Our analytic framework rationalizes p revious contradictory re- sults, and it gives valuable insight on the complex relation ship between mutualism and biodiversity