www.FoodWebs.org

1
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
2
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
3
Per Mass Metabolic Maintenance Costs
Systematically Decrease with Increasing Body
Size.
4
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
5
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
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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

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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
404180-183. 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 9912917-12922 Dunne, J. A. R. J. Williams
and N. D. Martinez. 2002. Food-web structure
and network theory the role of size and
connectance. PNAS 9912917-12922 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 301918b-919b Willi
ams, 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
38297-303 Dunne, J.A., R.J. Williams, and N.D.
Martinez Network structure and robustness of
marine food webs Marine Ecology Progress Series
273291-302