Spontaneous evolution of modularity and network motifs

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  author =       "Nadav Kashtan and Uri Alon",
  title =        "Spontaneous evolution of modularity and network
  journal =      "Proceedings of the National Academy of Sciences",
  year =         "2005",
  volume =       "102",
  number =       "39",
  pages =        "13773--13778",
  month =        sep # " 27",
  keywords =     "genetic algorithms, genetic programming, EHW, NAND,
                 ANN, demes, parallel GA, MFINDER1.2",
  URL =          "http://www.pnas.org/cgi/reprint/102/39/13773.pdf",
  DOI =          "doi:10.1073/pnas.0503610102",
  abstract =     "Biological networks have an inherent simplicity: they
                 are modular with a design that can be separated into
                 units that perform almost independently. Furthermore,
                 they show reuse of recurring patterns termed network
                 motifs. Little is known about the evolutionary origin
                 of these properties. Current models of biological
                 evolution typically produce networks that are highly
                 nonmodular and lack understandable motifs. Here, we
                 suggest a possible explanation for the origin of
                 modularity and network motifs in biology. We use
                 standard evolutionary algorithms to evolve networks. A
                 key feature in this study is evolution under an
                 environment (evolutionary goal) that changes in a
                 modular fashion. That is, we repeatedly switch between
                 several goals, each made of a different combination of
                 subgoals. We find that such modularly varying goals
                 lead to the spontaneous evolution of modular network
                 structure and network motifs. The resulting networks
                 rapidly evolve to satisfy each of the different goals.
                 Such switching between related goals may represent
                 biological evolution in a changing environment that
                 requires different combinations of a set of basic
                 biological functions. The present study may shed light
                 on the evolutionary forces that promote structural
                 simplicity in biological networks and offers ways to
                 improve the evolutionary design of engineered
  notes =        "Elistist selection, high mutation rate, fitness
                 parsimony genotype pressure. pop size=1000 or 2000.
                 crossover. Goal switched every 20 generations. Z-score
                 Z = (Nreal - Nrand) / sigma. Fixed genome genetic
                 algorithm. Quantifying Modularity. Evolution with
                 nonmodular random goals did not yield modular networks.
                 Modularly varying give evolution of modularity and
                 motifs. The two functions had shared subproblems --
                 modularly varying goals MVG. Rapid target function
                 swapping -> Q=0.54 (ie high modularity). But typically
                 used 11 NAND rather than 10 NAND evolved with fixed
                 fitness target. With randomly chosen goals (ie no
                 common sub goals) evolved networks typically are not
                 modular. Modular seed rapidly loses modularity.

                 Fixed? architecture feed forward multi-layer (4 layers)
                 perceptron? MLP. pop size=600. Feedback (output to
                 level -1 etc) allowed in NAND circuit. Every 10
                 generations copies of the 50 best networks from each
                 island were added to each of the other islands,
                 replacing eliminated networks. 4x2 binary picture.
                 Bifan and diamond motifs common but also some
                 anti-motifs less common in evolved modular ANN than
                 occurred in random ANN.

                 Table 5. Modularity measure of several biological
                 networks E. coli transcription network Neuronal network
                 of C. elegans (threshold = 5) Signal transduction in
                 human cells Over the course of many goal changes,
                 modularly varying goals seem to guide the population
                 toward a region of network space that contains fitness
                 peaks for each of the goals in close proximity. This
                 region seems to correspond to modular

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                 This article cites 28 articles, 8 of which you can
                 access for free at:
                 www.pnas.org/cgi/content/full/102/39/13773#BIBL This
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Genetic Programming entries for Nadav Kashtan Uri Alon