Efficiency and robustness in ant networks of galleries

Abstract.Recent theoretical and empirical studies have focused on the topology of large networks of communication/interactions in biological, social and technological systems. Most of them have been studied in the scope of the small-world and scale-free networks’ theory. Here we analyze the characteristics of ant networks of galleries produced in a 2-D experimental setup. These networks are neither small-worlds nor scale-free networks and belong to a particular class of network, i.e. embedded planar graphs emerging from a distributed growth mechanism. We compare the networks of galleries with both minimal spanning trees and greedy triangulations. We show that the networks of galleries have a path system efficiency and robustness to disconnections closer to the one observed in triangulated networks though their cost is closer to the one of a tree. These networks may have been prevented to evolve toward the classes of small-world and scale-free networks because of the strong spatial constraints under which they grow, but they may share with many real networks a similar trend to result from a balance of constraints leading them to achieve both path system efficiency and robustness at low cost.

[1]  M. V. Brian,et al.  Social Insects: Ecology and Behavioral Biology , 1984 .

[2]  Francisco J. Acosta,et al.  Guerilla vs. phalanx strategies of resource capture: growth and structural plasticity in the trunk trail system of the harvester ant Messor barbarus , 1994 .

[3]  W. Tschinkel,et al.  Nest architecture of the ant Formica pallidefulva: structure, costs and rules of excavation , 2004, Insectes Sociaux.

[4]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[5]  A. Barabasi,et al.  Lethality and centrality in protein networks , 2001, Nature.

[6]  W. Tschinkel,et al.  Seasonal life history and nest architecture of a winter-active ant,Prenolepis imparis , 1987, Insectes Sociaux.

[7]  Jie Wu,et al.  Small Worlds: The Dynamics of Networks between Order and Randomness , 2003 .

[8]  R. Pastor-Satorras,et al.  Structure of cycles and local ordering in complex networks , 2004 .

[9]  A. Rinaldo,et al.  Fractal River Basins: Chance and Self-Organization , 1997 .

[10]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[11]  Massimo Marchiori,et al.  Economic small-world behavior in weighted networks , 2003 .

[12]  W. Tschinkel,et al.  Sociometry and sociogenesis of colonies of the harvester ant, Pogonomyrmex badius: distribution of workers, brood and seeds within the nest in relation to colony size and season , 1999 .

[13]  Takao Nishizeki,et al.  Planar Graphs: Theory and Algorithms , 1988 .

[14]  Deryk Osthus,et al.  On random planar graphs, the number of planar graphs and their triangulations , 2003, J. Comb. Theory, Ser. B.

[15]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[16]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[17]  Stefan Bornholdt,et al.  Handbook of Graphs and Networks: From the Genome to the Internet , 2003 .

[18]  R. Solé,et al.  Selection, Tinkering, and Emergence in Complex Networks - Crossing the Land of Tinkering , 2002 .

[19]  J. Jarvis,et al.  The burrow systems and burrowing dynamics of the mole‐rats Bathyergus suillus and Cryptomys hottentotus in the fynbos of the south‐western Cape, South Africa , 1986 .

[20]  R. F. Cancho,et al.  Topology of technology graphs: small world patterns in electronic circuits. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  K. N. Ganeshaiahl,et al.  Topology of the foraging trails of Leptogenys processionalis — why are they branched? , 1991, Behavioral Ecology and Sociobiology.

[22]  Neo D. Martinez,et al.  Network structure and biodiversity loss in food webs: robustness increases with connectance , 2002, Ecology Letters.

[23]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[24]  Diego Garlaschelli,et al.  Universality in food webs , 2004 .

[25]  Andrzej Lingas,et al.  On approximation behavior of the greedy triangulation for convex polygons , 2005, Algorithmica.

[26]  Steven C. Le Comber,et al.  Fractal dimension of African mole-rat burrows , 2002 .

[27]  V.,et al.  Social Insects , 1990, Springer Berlin Heidelberg.

[28]  Ginestra Bianconi,et al.  Number of cycles in off-equilibrium scale-free networks and in the Internet at the Autonomous System Level , 2004 .

[29]  G. Délye,et al.  Observations sur le nid et le comportement constructeur deMessor arenarius (Hyménoptères formicidæ) , 1971, Insectes Sociaux.

[30]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[31]  J. Kruskal.  On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[32]  Pierre-P. Grassé,et al.  Foundation des sociétés, construction , 1984 .

[33]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[34]  R. Matthews,et al.  Ants. , 1898, Science.

[35]  M. Garey.  Johnson: computers and intractability: a guide to the theory of np- completeness (freeman , 1979 .

[36]  F. Frances Yao,et al.  Computational Geometry , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[37]  Marcus Kaiser,et al.  Spatial growth of real-world networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  W. Tschinkel.  Subterranean ant nests: trace fossils past and future? , 2003 .

[39]  W. Tschinkel,et al.  Nest complexity, group size and brood rearing in the fire ant, Solenopsis invicta , 2002, Insectes Sociaux.

[40]  J. Urry.  Complexity , 2006, Interpreting Art.

[41]  S. S. Manna,et al.  LETTER TO THE EDITOR: Scale-free network on Euclidean space optimized by rewiring of links , 2003, cond-mat/0302224.

[42]  Georges Tohmé.  Le nid et le comportement de construction de la fourmiMessor ebeninus, Forel (Hymenoptera, Formicoïdea) , 2005, Insectes Sociaux.

[43]  Ricard V. Solé,et al.  Complexity and fragility in ecological networks , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[44]  Beom Jun Kim,et al.  Attack vulnerability of complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  Robert E. Tarjan,et al.  Finding Minimum Spanning Trees , 1976, SIAM J. Comput..

[46]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .