1. www.FoodWebs.org Structure and Nonlinear Dynamics of
Complex Ecological Networks:
Neo Martinez
* Pacific Ecoinformatics and Computational Ecology Lab
* 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

2. 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

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
Minimum
Maximum
Mean
Std. Error
Standard Dev
C.V
Skewness(G1)
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
Minimum
Maximum
Mean
Std. Error
Standard Dev
C.V
Skewness(G1)
Average mass ratio indicates that consumers are more than 1000 times larger than resources
Note that the x-achsis scales logarithmically

6. 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

7. 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  
Simple rules yield complex food webs.  Nature 404:
Williams, R. J., E. L. Berlow, J. A. Dunne, A-L Barabási. and N. D. Martinez
Two degrees of Separation in Complex Food Webs. PNAS 99:
Dunne, J. A. R. J. Williams and N. D. Martinez
Food-web structure and network theory: the role of size and connectance. PNAS 99:
Brose, U., R.J. Williams, and N.D. Martinez
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
Limits to trophic levels and omnivory in complex food webs: theory and data. 
American Naturalist 163:  
Willliams, R. J. and N. D. Martinez   Stabilization of
Chaotic and Non-permanent Food-web Dynamics. Eur. Phys. J. B 38:
Dunne, J.A., R.J. Williams, and N.D. Martinez
Network structure and robustness of marine food webs
Marine Ecology Progress Series 273: