Population Dynamics on Complex Food Webs

In this work we analyze the topological and dynamical properties of a simple model of complex food webs, namely the niche model. In order to underline competition among species, we introduce "prey" and "predators" weighted overlap graphs derived from the niche model and compare synthetic food webs with real data. Doing so, we find new tests for the goodness of synthetic food web models and indicate a possible direction of improvement for existing ones. We then exploit the weighted overlap graphs to define a competition kernel for Lotka–Volterra population dynamics and find that for such a model the stability of food webs decreases with its ecological complexity.

[1]  Joel E. Cohen,et al.  A Stochastic Theory of Community Food Webs , 1990 .

[2]  Cristóbal López,et al.  Species clustering in competitive Lotka-Volterra models. , 2007, Physical review letters.

[3]  R. May,et al.  Systemic risk in banking ecosystems , 2011, Nature.

[4]  P. Abrams.  SOME COMMENTS ON MEASURING NICHE OVERLAP , 1980 .

[5]  Guido Caldarelli,et al.  The corporate boards networks , 2004 .

[6]  Jordi Bascompte,et al.  Understanding food-web persistence from local to global scales. , 2010, Ecology letters.

[7]  Guido Caldarelli,et al.  Scale-Free Networks , 2007 .

[8]  R. Guimerà,et al.  QUANTITATIVE PATTERNS IN THE STRUCTURE OF MODEL AND EMPIRICAL FOOD WEBS , 2004, q-bio/0401023.

[9]  Guido Caldarelli,et al.  Universal scaling relations in food webs , 2003, Nature.

[10]  Owen L Petchey,et al.  Size, foraging, and food web structure , 2008, Proceedings of the National Academy of Sciences.

[11]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.

[12]  J. E. Cohen,et al.  Food webs and niche space. , 1979, Monographs in population biology.

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

[14]  G. Caldarelli,et al.  Assortative model for social networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  J. Bascompte,et al.  Compartmentalization increases food-web persistence , 2011, Proceedings of the National Academy of Sciences.

[16]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[17]  G. Caldarelli,et al.  The fractal properties of Internet , 2000, cond-mat/0009178.

[18]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[19]  Jean-Pierre Gabriel,et al.  Phylogenetic constraints and adaptation explain food-web structure , 2004, Nature.

[20]  Neo D. Martinez,et al.  Simple rules yield complex food webs , 2000, Nature.

[21]  D. Garlaschelli,et al.  Self-organized network evolution coupled to extremal dynamics , 2006, cond-mat/0611201.

[22]  Roger Guimerà,et al.  Analytical solution of a model for complex food webs. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Charles M. Newman,et al.  A stochastic theory of community food webs I. Models and aggregated data , 1985, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[24]  Neo D. Martinez,et al.  Two degrees of separation in complex food webs , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[25]  Roger Guimerà,et al.  Robust patterns in food web structure. , 2001, Physical review letters.

[26]  Neo D. Martinez,et al.  Food-web structure and network theory: The role of connectance and size , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[27]  Kazuto Nakada,et al.  A General Model for Food Web Structure , 2008 .

[28]  Guido Caldarelli,et al.  Loops structure of the Internet at the autonomous system level. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Daniel B. Stouffer,et al.  Origin of compartmentalization in food webs. , 2010, Ecology.

[30]  Stefano Allesina,et al.  Googling Food Webs: Can an Eigenvector Measure Species' Importance for Coextinctions? , 2009, PLoS Comput. Biol..

[31]  L. Amaral,et al.  A robust measure of food web intervality , 2006, Proceedings of the National Academy of Sciences.

[32]  R. May,et al.  Stability and Complexity in Model Ecosystems , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[33]  M. Newman.  Random Graphs as Models of Networks , 2002, cond-mat/0202208.

[34]  Carlos J. Melián,et al.  Food web structure and habitat loss , 2002 .