Googling Food Webs: Can an Eigenvector Measure Species' Importance for Coextinctions?

A major challenge in ecology is forecasting the effects of species' extinctions, a pressing problem given current human impacts on the planet. Consequences of species losses such as secondary extinctions are difficult to forecast because species are not isolated, but interact instead in a complex network of ecological relationships. Because of their mutual dependence, the loss of a single species can cascade in multiple coextinctions. Here we show that an algorithm adapted from the one Google uses to rank web-pages can order species according to their importance for coextinctions, providing the sequence of losses that results in the fastest collapse of the network. Moreover, we use the algorithm to bridge the gap between qualitative (who eats whom) and quantitative (at what rate) descriptions of food webs. We show that our simple algorithm finds the best possible solution for the problem of assigning importance from the perspective of secondary extinctions in all analyzed networks. Our approach relies on network structure, but applies regardless of the specific dynamical model of species' interactions, because it identifies the subset of coextinctions common to all possible models, those that will happen with certainty given the complete loss of prey of a given predator. Results show that previous measures of importance based on the concept of “hubs” or number of connections, as well as centrality measures, do not identify the most effective extinction sequence. The proposed algorithm provides a basis for further developments in the analysis of extinction risk in ecosystems.

[1]  Owen L. Petchey,et al.  Interaction strengths in food webs: issues and opportunities , 2004 .

[2]  Neo D. Martinez,et al.  Scaling up keystone effects from simple to complex ecological networks , 2005 .

[3]  Tomas Jonsson,et al.  Biodiversity lessens the risk of cascading extinction in model food webs , 2000 .

[4]  Stefano Allesina,et al.  Who dominates whom in the ecosystem? Energy flow bottlenecks and cascading extinctions. , 2004, Journal of theoretical biology.

[5]  Jane Memmott,et al.  Tolerance of pollination networks to species extinctions , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[6]  Jason S. Link,et al.  Does food web theory work for marine ecosystems , 2002 .

[7]  Bo Ebenman,et al.  Early onset of secondary extinctions in ecological communities following the loss of top predators. , 2006, Ecology letters.

[8]  Kurt Bryan,et al.  The $25,000,000,000 Eigenvector: The Linear Algebra behind Google , 2006, SIAM Rev..

[9]  P. Yodzis,et al.  Local trophodynamics and the interaction of marine mammals and fisheries in the Benguela ecosystem , 1998 .

[10]  S. Hall,et al.  Food-web patterns : lessons from a species-rich web , 1991 .

[11]  Robert R. Christian,et al.  Organizing and understanding a winter's seagrass foodweb network through effective trophic levels , 1999 .

[12]  M. Huxham,et al.  Do Parasites Reduce the Chances of Triangulation in a Real Food Web , 1996 .

[13]  Jennifer A. Dunne,et al.  Network structure and robustness of marine food webs , 2004 .

[14]  A. Neutel,et al.  Energetics, Patterns of Interaction Strengths, and Stability in Real Ecosystems , 1995, Science.

[15]  Ernesto Estrada,et al.  Food webs robustness to biodiversity loss: the roles of connectance, expansibility and degree distribution. , 2007, Journal of theoretical biology.

[16]  Bruce Hannon,et al.  Ecological network analysis : network construction , 2007 .

[17]  J. Montoya,et al.  Small world patterns in food webs. , 2002, Journal of theoretical biology.

[18]  Bradford A. Hawkins,et al.  EFFECTS OF SAMPLING EFFORT ON CHARACTERIZATION OF FOOD-WEB STRUCTURE , 1999 .

[19]  F. Jordán,et al.  Quantifying positional importance in food webs: A comparison of centrality indices , 2007 .

[20]  K. Havens,et al.  Scale and Structure in Natural Food Webs , 1992, Science.

[21]  L. G. Abarca-Arenas,et al.  Sociometric Analysis of the Role of Penaeids In the Continental Shelf Food Web Off Veracruz, Mexico Based On By-Catch , 2007 .

[22]  R. Solé,et al.  Ecological networks and their fragility , 2006, Nature.

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

[24]  R. Macarthur Fluctuations of Animal Populations and a Measure of Community Stability , 1955 .

[25]  R. Ulanowicz,et al.  The Seasonal Dynamics of The Chesapeake Bay Ecosystem , 1989 .

[26]  John Harte,et al.  Response of complex food webs to realistic extinction sequences. , 2007, Ecology.

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

[28]  Ernesto Estrada,et al.  Spectral scaling and good expansion properties in complex networks , 2006, Europhysics Letters (EPL).

[29]  J. Roughgarden,et al.  Construction and Analysis of a Large Caribbean Food Web , 1993 .

[30]  Robert E. Ulanowicz,et al.  Quantitative methods for ecological network analysi , 2004, Comput. Biol. Chem..

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

[32]  E. Zavaleta,et al.  Realistic Species Losses Disproportionately Reduce Grassland Resistance to Biological Invaders , 2004, Science.

[33]  Michio Kondoh,et al.  Response to Comment on "Foraging Adaptation and the Relationship Between Food-Web Complexity and Stability" , 2003, Science.

[34]  S. Opitz,et al.  Trophic interactions in Caribbean coral reefs , 1996 .

[35]  Stefano Allesina,et al.  Functional links and robustness in food webs , 2009, Philosophical Transactions of the Royal Society B: Biological Sciences.

[36]  Marta Coll,et al.  Structural Degradation in Mediterranean Sea Food Webs: Testing Ecological Hypotheses Using Stochastic and Mass-Balance Modelling , 2008, Ecosystems.

[37]  G. Polis,et al.  Complex Trophic Interactions in Deserts: An Empirical Critique of Food-Web Theory , 1991, The American Naturalist.

[38]  Dorothea Heiss-Czedik,et al.  An Introduction to Genetic Algorithms. , 1997, Artificial Life.

[39]  Philip H. Warren,et al.  Spatial and temporal variation in the structure of a freshwater food web , 1989 .

[40]  E. Barbier,et al.  Response to Comments on "Impacts of Biodiversity Loss on Ocean Ecosystem Services" , 2007, Science.