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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.

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Networks and augmented networks

3

0.6

3

0

20

1.2

814

5

12323

12

0.5

3311

196

7.6

12

8

14

1

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Augmented food web: M,N-web

• Mi = average body mass of species i

• Ni = population density of species i

Species 5 (M5, N5)

Species 4 (M4, N4)

Species 2 (M2, N2)

Species 3 (M3, N3)

Species 1 (M1, N1)

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Examples of Real Augmented Food Webs

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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

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Tuesday Lake, 1984

Fish species

Zooplankton species

Phy

topl

ankt

on s

peci

es

Cohen Jonsson, CarpenterPNAS, 2003

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M =

bod

y m

ass

(kg)

Tuesday Lake food web, body mass & pop. density 1984

N = population density (individuals/m3)

Jonsson, Cohen, C

arpenter, Advances in

Ecological R

esearch 2005

Circles = phytoplanktonSquares = zooplanktonDiamonds = fish

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Broadstone Stream, UK

http://www.biology.qmul.ac.uk/research/staff/hildrew/guy.htm

Data are available from other systems.

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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

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Length of linkslo

g(M

)

log(N)

Predator

Prey

d1

d2

Define:Length of link

= d1 + d2

Reuman and Cohen, Journal of Animal Ecology, 2004

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Frequency distribution of link lengthLink lengths were normally distributed.Lengths of all ordered pairs of species were

not normally distributed.

1984

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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

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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

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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

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M,N-web structure varies among communities of different

types

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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).

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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)

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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

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

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What is flux?

Predator

Prey

How much biomass does this predator eat of this preyper unit time?

Want “flux” for all prey-predator pairs

Given a food web and a prey, predator pair …

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What biomass flux occurred along 269 trophic links in 1984,

241 trophic links in 1986?

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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

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Example: Metabolic Action Model

)i of production population(ijF)j ofn consumptio population(

If i = prey and j = predator,

4/3iii MNP 4/3

jjj MNC

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Why estimate flux?Application: animal behavior

Predator

Prey 1 Prey 2

Null-model flux (kg/day)

Measured flux (kg/day)

1/2 1/2

3/41/4

Why the deviation from expectation?

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Other possible applications

• Conservation

• Toxin concentrations going up the food web

• Dynamics and stability of food webs

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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

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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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Toy example of an augmented network: friendship networks40yrs 75yrs

28yrs

50yrs32yrs

0.25 hrs/wk5 hrs/wk

0.5 hrs/wk

1 hr/wk

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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 includemeasures of

the network trafficalong each edge

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Broadstone Stream, UK

-2 0 2 4-6

-4

-2

0

2

-2 0 2 4-6

-4

-2

0

2

log10 pop. density (individuals / m2)

log

10

me

an

ind

ivid

ual b

ody

ma

ss

(ug

dry

mas

s)

Predator mass > prey mass Predator mass < prey mass

Woodward, Speirs, Hildrew, Advances in Ecological Research, 2005

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We also tested our 8 models with other data, too

System System type

Number webs

Avg. # taxa

Lake Neuchatel

Riparian 8 162

Dutch soil Soil 3 29

Preliminary indirect testing shows the MetabolicAction Model is better than the other modelsfor these systems, too.

Lake Neuchatel webs: Carolin Banasek-Richter and Marie-France Cattin BlandenierDutch soil webs: Christian Mulder

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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

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Why estimate flux?Application: conservation

Threatenedspecies

1/10 9/10

1/101/10

8/10

A model can provide guesses on: 1) which prey species is most important for

conservation2) which predator is most destructive

Pred. 2Pred. 1

Prey 1 Prey 3Prey 2