Food Webs Augmented With Additional Data Structure and

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. 1

Networks and augmented networks 1 3 323 5 2 12 1 0. 5 1. 2 14 11 33 3 12 8 14 0 7. 6 19 8 6 0. 6 20 2

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

Examples of Real Augmented Food Webs 4

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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 7 in each year

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

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

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

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 11

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

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

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 14

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 15

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 16

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

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). 18

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) 19

Results • Communities of some types were betterdescribed 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 20

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

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

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

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 24

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

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

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

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 28

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 29

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Toy example of an augmented network: friendship networks 40 yrs 75 yrs 1 hr/wk 0. 25 hrs/wk 32 yrs 28 yrs 5 hrs/wk 0. 5 hrs/wk 50 yrs 31

Toy example of an augmented network: computer networks 1. 4 GHz One could include the clock speed 4. 0 GHz 2. 2 GHz 1. 7 GHz 3. 2 GHz One could also include measures of the network traffic along each edge 1. 2 GHz 32

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

We also tested our 8 models with other data, too System type Number webs Avg. # taxa Lake Neuchatel Riparian 8 162 Dutch soil Soil 3 29 Lake Neuchatel webs: Carolin Banasek-Richter and Marie-France Cattin Blandenier Dutch soil webs: Christian Mulder Preliminary indirect testing shows the Metabolic Action Model is better than the other models 34 for these systems, too.

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 35 • Various soil food webs

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