www.FoodWebs.org Structure and Nonlinear Dynamics of Complex Ecological Networks: Neo Martinez * Pacific Ecoinformatics and Computational Ecology Lab www.PEaCELab.net * Rich Williams National Center for Ecological Analysis and Synthesis *Ulrich Brose Biology Dept., Technical University of Darmstadt * Jen Dunne Santa Fe Institute * Eric Berlow White Mountain Research Station, UC San Diego www.FoodWebs.org

Geoffrey B. West*†‡, William H. Woodruff*§, and James H. Brown†¶ Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals (PNAS 2002) Geoffrey B. West*†‡, William H. Woodruff*§, and James H. Brown†¶ *Los Alamos National Laboratory, Los Alamos, NM 87545; †Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501; and ¶Department of Biology, University of New Mexico, Albuquerque, NM 87131

Per Mass Metabolic Maintenance Costs Systematically Decrease with Increasing Body Size.

Invertebrate predacious consumers Histogram of frequency ~ log (consumer-resource body mass ratio) Stats: LOGRATIO N of cases 11451 Minimum -6.519 Maximum 9.112 Mean 0.664 Std. Error 0.010 Standard Dev 1.070 C.V. 1.612 Skewness(G1) 0.355 Average mass ratio indicates that consumers are less than 10 times larger than resources Note that the x-achsis scales logarithmically

Ectotherm vertebrate predacious consumers Histogram of frequency ~ log (consumer-resource body mass ratio) Stats: LOGRATIO N of cases 1327 Minimum -2.782 Maximum 13.341 Mean 3.261 Std. Error 0.060 Standard Dev 2.181 C.V. 0.669 Skewness(G1) 1.220 Average mass ratio indicates that consumers are more than 1000 times larger than resources Note that the x-achsis scales logarithmically

that increase overall species persistence “Devious Strategies” that increase overall species persistence Non-type II functional responses stabilizes chaotic & cyclic dynamics - more ecologically plausible & empirically supported Non-random network topology - especially empirically well-corroborated niche model structure Consumption weighted to low trophic levels eat low on the food chain! Predator-prey Body-size Ratios explains stability explains empirical vertebrate and invertebrate body-size ratios

This work was supported by NSF grants:  Scaling of Network Complexity with Diversity in Food Webs  Effects of Biodiversity Loss on Complex Communities:  A Web-Based Combinatorial Approach  Webs on the Web: Internet Database, Analysis and Visualization of Ecological Networks  Science on the Semantic Web: Prototypes in Bioinformatics Willliams, R. J. and N. D. Martinez . 2000.  Simple rules yield complex food webs.  Nature 404:180-183. Williams, R. J., E. L. Berlow, J. A. Dunne, A-L Barabási. and N. D. Martinez. 2002. Two degrees of Separation in Complex Food Webs. PNAS 99:12917-12922 Dunne, J. A. R. J. Williams and N. D. Martinez. 2002. Food-web structure and network theory: the role of size and connectance. PNAS 99:12917-12922 Brose, U., R.J. Williams, and N.D. Martinez. 2003. The Niche model recovers the negative complexity-stability relationship effect in adaptive food webs.  Science 301:918b-919b Williams, R.J., and N.D. Martinez. 2004. Limits to trophic levels and omnivory in complex food webs: theory and data.  American Naturalist 163: 458-468   Willliams, R. J. and N. D. Martinez . 2004.  Stabilization of Chaotic and Non-permanent Food-web Dynamics. Eur. Phys. J. B 38:297-303 Dunne, J.A., R.J. Williams, and N.D. Martinez Network structure and robustness of marine food webs Marine Ecology Progress Series 273:291-302