1. 1 Food Webs Augmented With Additional Data: Structure and Dynamics Daniel C. Reuman, Rockefeller University, New York, U.S.A. Joel E. Cohen, Rockefeller University and Columbia University, New York, U.S.A.

2. 2 Networks and augmented networks 3 0.6 3 0 20 1.2 8 14 5 12 323 1 2 0.5 33 11 19 6 7.6 12 8 14 1

3. 3 Augmented food web: M,N-web M i = average body mass of species i N i = population density of species i Species 5 (M 5, N 5 ) Species 4 (M 4, N 4 ) Species 2 (M 2, N 2 ) Species 3 (M 3, N 3 ) Species 1 (M 1, N 1 )

4. 4 Examples of Real Augmented Food Webs

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7. 7 Tuesday Lake, Michigan Pelagic community only 1984: 25 phytoplankton, 22 zooplankton, 3 fish species Similar data for 1986 Complete food web, average body mass (M) and population density (N) for each species in each year

8. 8 Tuesday Lake, 1984 Fish species Zooplankton species Phytoplankton species Cohen Jonsson, Carpenter PNAS, 2003

9. 9 M = body mass (kg) Tuesday Lake food web, body mass & pop. density 1984 N = population density (individuals/m 3 ) Jonsson, Cohen, Carpenter, Advances in Ecological Research 2005 Circles = phytoplankton Squares = zooplankton Diamonds = fish

10. 10 Broadstone Stream, UK http://www.biology.qmul.ac.uk/research/staff/hildrew/guy.htm Data are available from other systems.

11. 11 Why add data to food webs? Traditional food web directed graphs have sampling problems –Martinez, Ecological Monographs, 1991 –Martinez et al., Ecology, 1999 The food web model is unrealistic –Predator-prey relationships differ –Species with the same prey and same predators differ

12. 12 Length of links log(M) log(N) Predator Prey d1d1 d2d2 Define: Length of link = d 1 + d 2 Reuman and Cohen, Journal of Animal Ecology, 2004

13. 13 Frequency distribution of link length Link lengths were normally distributed. Lengths of all ordered pairs of species were not normally distributed. 1984

14. 14 Niche and Cascade Models Models of food web directed graphs Given a list of species, they select links to emulate the structure of real webs

15. 15 Failures of the Niche and Cascade Models When combined with the M and N data of Tuesday Lake, these models produced webs with non-normal link length distributions M,N structure of food webs interacts with the network structure M,N structure illuminates network structure

16. 16 Better models To reproduce normal link length distributions, assume: –species are divided into 3 body-mass ranked functional groups that can only eat lower groups (e.g., plants, herbivores, carnivores) –species do not eat other species that are too much smaller (perceptual limit) Complete models of M,N-web structure should be proposed and tested

17. 17 M,N-web structure varies among communities of different types

18. 18 Describing M,N structure with linear models For 162 local ecological communities, we tested whether data satisfied the statistical assumptions of standard linear models relating log(M) and log(N).

19. 19 Ecosystem types The 162 communities were of nine types, including: –shores of a lake –inside pitcher plants –7 types of soil community (farms, forest, fields)

20. 20 Results Communities of some types were better- described by linear models than communities of other types M,N-web structure varies by ecosystem type The causes of this structural variation should be studied

21. 21 Use of M,N-webs: biomass flux along trophic links

22. 22 What is flux? Predator Prey How much biomass does this predator eat of this prey per unit time? Want “flux” for all prey-predator pairs Given a food web and a prey, predator pair …

23. 23 What biomass flux occurred along 269 trophic links in 1984, 241 trophic links in 1986?

24. 24 Fluxes are hard to measure Even for a single prey-predator pair Harder still to measure all fluxes We want a model Should estimate flux for all trophic links using M,N-web data

25. 25 Example: Metabolic Action Model If i = prey and j = predator,

26. 26 Why estimate flux? Application: animal behavior Predator Prey 1 Prey 2 Null-model flux (kg/day) Measured flux (kg/day) 1/2 3/41/4 Why the deviation from expectation?

27. 27 Other possible applications Conservation Toxin concentrations going up the food web Dynamics and stability of food webs

28. 28 Future Network models of food web structure that include more information: –An M distribution for each species –Stoichiometric data for each species –Distributions describing predation events Empirical biomass flux measurements to compare to the model

29. 29 Thank you! Questions? References: Reuman & Cohen, Trophic links’ length and slope in the Tuesday Lake food web with species’ body mass and numerical abundance. 2004. Journal of Animal Ecology 73, 852-866. Reuman & Cohen, Estimating relative energy fluxes using the food web, species abundance, and body size. 2005. Advances in Ecological Research 36,137-182. Reuman & Cohen, Allometry of body size and abundance in 166 food webs: tests of the standard linear model. In prep. Email: reumand@rockefeller.edu

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31. 31 Toy example of an augmented network: friendship networks 40yrs75yrs 28yrs 50yrs 32yrs 0.25 hrs/wk 5 hrs/wk 0.5 hrs/wk 1 hr/wk

32. 32 Toy example of an augmented network: computer networks 1.4 GHz 3.2 GHz 1.2 GHz 1.7 GHz 4.0 GHz 2.2 GHz One could include the clock speed One could also include measures of the network traffic along each edge

33. 33 Broadstone Stream, UK log 10 pop. density (individuals / m 2 ) log 10 mean individual body mass (ug dry mass) Predator mass > prey massPredator mass < prey mass Woodward, Speirs, Hildrew, Advances in Ecological Research, 2005

34. 34 We also tested our 8 models with other data, too SystemSystem type Number webs Avg. # taxa Lake Neuchatel Riparian8162 Dutch soilSoil329 Preliminary indirect testing shows the Metabolic Action Model is better than the other models for these systems, too. Lake Neuchatel webs: Carolin Banasek-Richter and Marie-France Cattin Blandenier Dutch soil webs: Christian Mulder

35. 35 Other M,N-webs data sets Tuesday Lake, Michigan, U.S.A.: freshwater pelagic Broadstone Stream, England: freshwater benthic Lake Neuchatel riparian zone, Switzerland Inquiline communities in pitcher plants, Florida, U.S.A. Ythan Estuary, Scotland Caribbean marine food web Various soil food webs

36. 36 Why estimate flux? Application: conservation Threatened species 1/10 9/10 1/10 8/10 A model can provide guesses on: 1) which prey species is most important for conservation 2) which predator is most destructive Pred. 2Pred. 1 Prey 1Prey 3Prey 2