An elementary dynamic model for non-binary food webs

Information content of colored motifs in complex networks

We study complex networks in which the nodes are tagged with different colors depending on their function (colored graphs), using information theory applied to the distribution of motifs in such networks. We find that colored motifs can be viewed as the building blocks of the networks (much more than the uncolored structural motifs can be) and that the relative frequency with which these motifs appear in the network can be used to define its information content. This information is defined in such a way that a network with random coloration (but keeping the relative number of nodes with different colors the same) has zero color information content. Thus, colored motif information captures the exceptionality of coloring in the motifs that is maintained via selection. We study the motif information content of the C. elegans brain as well as the evolution of colored motif information in networks that reflect the interaction between instructions in genomes of digital life organisms. While we find that colored motif information appears to capture essential functionality in the C. elegans brain (where the color assignment of nodes is straightforward), it is not obvious whether the colored motif information content always increases during evolution, as would be expected from a measure that captures network complexity. For a single choice of color assignment of instructions in the digital life form Avida, we find rather that colored motif information content increases or decreases during evolution, depending on how the genomes are organized, and therefore could be an interesting tool to dissect genomic rearrangements.

Food webs: Experts consuming families of experts

Food webs of habitats as diverse as lakes or desert valleys are known to exhibit common "food-web patterns", but the detailed mechanisms generating these structures have remained unclear. By employing a stochastic, dynamical model, we show that many aspects of the structure of predatory food webs can be understood as the traces of an evolutionary history where newly evolving species avoid direct competition with their relatives. The tendency to avoid sharing natural enemies (apparent competition) with related species is considerably weaker. Thus, "experts consuming families of experts" can be identified as the main underlying food-web pattern. We report the results of a systematic, quantitative model validation showing that the model is surprisingly accurate.