Network Evolution Based on Centrality

We study the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality. We show that the same network dynamics arises under various centrality measures, and solve analytically the network evolution. During the complete evolution, the network is characterized by nestedness: the neighbourhood of a node is contained in the neighbourhood of the nodes with larger degree. We find a discontinuous transition in the network density between hierarchical and homogeneous networks, depending on the rate of link decay. We also show that this evolution mechanism leads to double power-law degree distributions, with interrelated exponents.Comment: 6 pages, 3 figure

Relative Stability of Core Groups in Pollination Networks in a Biodiversity Hotspot over Four Years

Plants and their pollinators form pollination networks integral to the evolution and persistence of species in communities. Previous studies suggest that pollination network structure remains nested while network composition is highly dynamic. However, little is known about temporal variation in the structure and function of plant-pollinator networks, especially in species-rich communities where the strength of pollinator competition is predicted to be high. Here we quantify temporal variation of pollination networks over four consecutive years in an alpine meadow in the Hengduan Mountains biodiversity hotspot in China. We found that ranked positions and idiosyncratic temperatures of both plants and pollinators were more conservative between consecutive years than in non-consecutive years. Although network compositions exhibited high turnover, generalized core groups – decomposed by a k-core algorithm – were much more stable than peripheral groups. Given the high rate of turnover observed, we suggest that identical plants and pollinators that persist for at least two successive years sustain pollination services at the community level. Our data do not support theoretical predictions of a high proportion of specialized links within species-rich communities. Plants were relatively specialized, exhibiting less variability in pollinator composition at pollinator functional group level than at the species level. Both specialized and generalized plants experienced narrow variation in functional pollinator groups. The dynamic nature of pollination networks in the alpine meadow demonstrates the potential for networks to mitigate the effects of fluctuations in species composition in a high biodiversity area

Structural and dynamical interdependencies in complex networks at meso- and macroscale: nestedness, modularity, and in-block nestedness

Many real systems like the brain are considered to be complex, i.e. they are made of several interacting components and display a collective behaviour that cannot be inferred from how the individual parts behave. They are usually described as networks, with the components represented as nodes and the interactions between them as links. Research into networks mainly focuses on exploring how a network's dynamic behaviour is constrained by the nature and topology of the interactions between its elements. Analyses of this sort are performed on three scales: the microscale, based on single nodes; the macroscale, which explores the whole network; and the mesoscale, which studies groups of nodes. Nonetheless, most studies so far have focused on only one scale, despite increasing evidence suggesting that networks exhibit structure on several scales. In our thesis, we apply structural analysis to a variety of synthetic and empirical networks on multiple scales. We focus on the examination of nested, modular, and in-block nested patterns, and the effects that they impose on each other. Finally, we introduce a theoretical model to help us to better understand some of the mechanisms that enable such patterns to emerge.Molts sistemes, com el cervell o internet, són considerats complexos: sistemes formats per una gran quantitat d'elements que interactuen entre si, que exhibeixen un comportament col·lectiu que no es pot inferir des de les propietats dels seus elements aïllats. Aquests sistemes s'estudien mitjançant xarxes, en les quals els elements constituents són els nodes, i les interaccions entre ells, els enllaços. La recerca en xarxes s'enfoca principalment a explorar com el comportament dinàmic d'una xarxa està definit per la naturalesa i la topologia de les interaccions entre els seus elements. Aquesta anàlisi sovint es fa en tres escales: la microescala, que estudia les propietats dels nodes individuals; la macroescala, que explora les propietats de tota la xarxa, i la mesoescala, basada en les propietats de grups de nodes. No obstant, la majoria dels estudis se centren només en una escala, tot i la creixent evidència que suggereix que les xarxes sovint exhibeixen estructura a múltiples escales. En aquesta tesi estudiarem les propietats estructurals de les xarxes a escala múltiple. Analitzarem les propietats estructurals dels patrons in-block nested i la seva relació amb els patrons niats i modulars. Finalment, introduirem un model teòric per explorar alguns dels mecanismes que permeten l'emergència d'aquests patrons.Muchos sistemas, como el cerebro o internet, son considerados complejos: sistemas formados por una gran cantidad de elementos que interactúan entre sí, que exhiben un comportamiento colectivo que no puede inferirse desde las propiedades de sus elementos aislados. Estos sistemas se estudian mediante redes, en las que los elementos constituyentes son los nodos, y las interacciones entre ellos, los enlaces. La investigación en redes se enfoca principalmente a explorar cómo el comportamiento dinámico de una red está definido por la naturaleza y la topología de las interacciones entre sus elementos. Este análisis a menudo se hace en tres escalas: la microescala, que estudia las propiedades de los nodos individuales; la macroescala, que explora las propiedades de toda la red, y la mesoescala, basada en las propiedades de grupos de nodos. No obstante, la mayoría de los estudios se centran solo en una escala, a pesar de la creciente evidencia que sugiere que las redes a menudo exhiben estructura a múltiples escalas. En esta tesis estudiaremos las propiedades estructurales de las redes a escala múltiple. Analizaremos las propiedades estructurales de los patrones in-block nested y su relación con los patrones anidados y modulares. Finalmente, introduciremos un modelo teórico para explorar algunos de los mecanismos que permiten la emergencia de estos patrones.Tecnologías de la información y de rede

Topological structure of plant-bee networks in four Mexican environments

We analyzed the topological structure (e.g., links per species, connectance, core-periphery analyses, specialization, nestedness, modularity) of plant-bee interactions of four areas in Mexico. We used qualitative data (binary networks). Mexico exhibits a complex geography and community variation that can affect bee networks. Network architecture is variable within large spatial scales, thus our results should vary according to site characteristics (La Mancha and Totula in Veracruz, Carrillo Puerto in Quintana Roo, and the Tehuacan-Cuicatlan valley, in Puebla), type of vegetation, endemism, altitude, size of area sampled. Network topology varied among sites, and the presence of nested or modular patterns was analyzed for robustness to simulated species extinctions. The lowest species richness was recorded for the Quintana Roo site (15 plant, 25 bee species), and the highest for the Tehuacan-Cuicatlan valley site (88 plant, 231 bee species). There was a tendency to have more connected networks when species richness was low and networks with greater species richness had a higher number of interactions. The distribution of interactions differed between environments but not due to network size and all were significantly nested. The robustness to cumulative extinctions showed a different pattern at each site; the most robust network was at Carrillo Puerto, which also was the site with less species. Sites with more endemic species (e.g. Tehuacan) had more specialized interactions, and were more susceptible to extinction