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Collaborators: Ulrich Brose Carol Blanchette Jennifer Dunne Sonia Kefi Neo Martinez Bruce Menge Sergio Navarrete Owen Petchey Philip Stark Rich Williams …. Predictability. Predict. Biodiversity. Biodiversity. Prediction. Changes in Focal Species.
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Ulrich Brose
Carol Blanchette
Jennifer Dunne
Sonia Kefi
Neo Martinez
Bruce Menge
Sergio Navarrete
Owen Petchey
Philip Stark
Rich Williams
…
Biodiversity
How can we predict the consequences
of species loss in complex ecosystems?
Little Rock Lake Food Web (Martinez 1991)
How can we predict the consequences
of species loss in complex ecosystems?
1 degree
Little Rock Lake Food Web (Martinez 1991)
How can we predict the consequences
of species loss in complex ecosystems?
2 degrees
Little Rock Lake Food Web (Martinez 1991)
How can we predict the consequences
of species loss in complex ecosystems?
3 degrees
Little Rock Lake Food Web (Martinez 1991)
Williams et al. PNAS 2002
everything needs energy to stay alive
BIG things need more energy than small things
BIG things need more energy than small things
3/4
( )
allometric scaling of metabolism with body size
Universal
Body Size also influences Food Web Structure
Brose et al. 2005 Ecology
Brose et al. 2006 Ecology
Petchey et al. 2008 PNAS
if each link obeys allometric rules
are those rules preserved at the network scale?
if each link obeys allometric rules
will body size predict
the effect of species loss in the network?
more complex = more complicated?
<1>
Simulate species dynamics in a wide variety of networks
stochastic variation in
structural and dynamic
parameters
<4>
Track variation for each simulation
interaction strengths
network level structure
neighborhood structure
species attributes
link attributes
The Models
Food Web Structure: Niche Model
(Williams and Martinez 2000)
<2>
PredatorPrey Interactions: Bioenergetic Model
(Yodzis and Innes 1992, Brose et al. 2005, 2006 Eco Letts)
<3>
Plant population dynamics: PlantNutrient Model
(Tilman 1982, Huisman and Weissing 1999)
Biomassi at time t
Biomass of each species (i) at time (t) is balance of
1. gain from consuming prey species
2. loss to being consumed by other species
3. loss to metabolism
# Prey
Bioenergetic PredatorPrey Dynamics
Functional Response
massspecific metabolic rate
assimilation
efficiency
max metabolicspecific ingestion rate
xi, yiscale with body size
(body size correlated with web structure)
Growth of Plants
Bioenergetic PredatorPrey Dynamics(Plants)
massspecific
growth rate
metabolic loss
loss to herbivores
ri, xj, y scale with body size
growth rate
NutrientDependent Growth of Plants
Concentration of Nutrients
determined by
Supply
Turnover
Consumption
Growth determined by most limiting Nutrient
Half saturation conc. for uptake of that Nutrient
Generate a food web (Niche Model)
Calculate trophic level for each species
Apply plantnutrient model to plants, predatorprey model to rest.
Assign body sizes based on trophic level (mean pred: prey ratio = 10)
Run simulation with each species deleted individually
to generate a complete removal matrix
Repeat for all species and for 600 Niche Model webs
T
population I= BT+ BT
3° Consumers
2° Consumers
X
R
?
1° Consumers
T
T
1° Prey
2° Prey
3° Prey
population I= BT+ BT
3° Consumers
2° Consumers
X
?
R
1° Consumers
T
T
1° Prey
2° Prey
3° Prey
NK = NonKeystone consumer
D = Dominant basal species
S = Subordinate basal species
R = Resource
K
NK1
S1
D
R1
R2
Resource competition
Indirect Facilitation
Keystone Present
K
NK1
+
S1
S2
D
S1
R1
R2
Increased Resources
Resource competition
Indirect Facilitation
Keystone Present
K
NK1
+
S1
Other Competitors
S2
D
S1
Sn
R1
R2
Resource competition
Indirect Facilitation
NK3n
Tertiary Consumers
Secondary Consumers
NK2n
K
NK1
+
S1
S2
D
S1
R1
R2
noise
<2>
Animal Attributes
metabolic and max consumption rate,
predprey body size ratio
functional response type
predator interference
90 predictors to explain
variation in the strengths of
254,032 interactions among
12,116 species in
600 webs
<1>
Global network structure
<2>
Species attributes of R and T
<3>
Local network structure around each R and T
<4>
Attributes of the interaction
+
T
R

shortest path = 2 degrees
2 degree paths: +, +, 
R
+
prey
predator
prey
predator

T
+
T
R

shortest path = 2 degrees
2 degree paths: +, +, 
3 degree paths: +, +, +, 
R
+
prey
predator
prey
predator

T
+
T
R

shortest path = 2 degrees
2 degree paths: +, +, 
3 degree paths: +, +, +, 
4 degree paths: 
R
+
prey
predator
prey
predator

T
sign shortest path = +1
sign next shortest path = +2
unweighted sum (shortest + next shortest) = +3
weighted sum (shortest + (next shortest / 2)) = +2
Each Feeding Interaction Scales with (Body Size)3/4
R
T
R2 = 0.90
Slope = 0.74
Log (per capita consumption)
Log (R body mass)
Per Capita LinearInteraction Strength
= Per Capita RemovalInteraction Strength?
R
T
R2 = 0.90
Slope = 0.74
Log (per capita consumption)
Log (R body mass)
Per Capita Interaction Strength
Per Capita RemovalInteraction Strength
R
High R Biomass
Low R Biomass
T
Residuals
Log per capita I
Log (R body mass)
Log (T biomass)
Per Capita Interaction Strength
R
T
R2 = 0.88
Log per capita I
Predicted by:
Log (T biomass) +
Log (R biomass) +
Log (R body mass)
(population interaction strength)
(total effect on T of removing R)
Classification and Regression Trees (CART)
on log transformed Interaction Strengths
of the 90 variables tracked
best predictors of
absolute magnitude of log(population I)
T biomass
R biomass
(Degrees Separated)
R2 = 0.65
Log (T biomass)
(strong interactions)
Sign
(weak interactions)
positive
Proportion Observed
negative
≥ 1
≥ 1
≤ 1
≤ 1
Weighted Sum Path Signs
Weighted Sum Path Signs
1. 3/4 scaling disappears
in complex networks
Log (per capita linear I)
High R Biomass
Low R Biomass
(a)
2. strongest per capita I:
large bodied, low biomass R
effects on high biomass T
R2 = 0.88
Residuals from (a)
Log (per capitaI)
3. strongest population I:
high biomass R
effects on high biomass T
R2 = 0.65
Log (population I)
Log (population I)
Log (R Body Mass)
Log (T biomass)
BT+ = T biomass (R present)
predicting: (BT+ BT)
BT= T biomass (R removed)
using: BT+
Log (population I)
Log (T biomass)
Log (BT+)
predicting: (BT+ BT) 2° extinction of T
using: BT+
reshuffled interactions
Log (population I)
Log (T biomass)
Log (T biomass)
Log (BT+)
Log (BT+)
R2 = 0.19
R2 = 0.59
population I
per capita I
Proportion of Variation Explained
R2 = 0.73
R2 = 0.88
Number of Species
<1>
Purely metabolic interactions
should be well predicted by simple attributes of R and T.
<2>
Deviations from simple metabolic predictions
should point to strong nonmetabolic influences.
Detrend the "metabolic baseline" of complex systems
to gain insight into other important ecological processes.
Predict
Fail
x 3 start dates
x 13 yrs
Experimental Design
R
Whelks
Mussels
T
Barnacles
Whelks
Excluded
Low Whelk
Biomass
High Whelk
Biomass
R
R
Metabolic


T
T
T
R
R
Metabolic
+
NonMetabolic
+
+




+
+
+
T
T
T



Natural Variation
in Mussels
and Barnacles
Predicted by Simulations
predicted
High Whelk Biomass
Low Whelk Biomass
Log (per capitaI)
Log (population I)
Log (Mussel biomass)
Metabolic
predicted

High Whelk Biomass
Low Whelk Biomass
T
Log (per capitaI)
Log (population I)
Log (Mussel biomass)
R
Metabolic
+
predicted


High Whelk Biomass

Low Whelk Biomass
+
T
T
observed
High Whelk Biomass
Low Whelk Biomass
Log (per capitaI)
R2 = 0.49
Log (population I)
R2 = 0.43
Log (Mussel biomass)
R
Metabolic
+
NonMetabolic
Metabolic
+



+
T
T
predicted
observed
Log (per capitaI)
R2 = 0.49
Log (population I)
R2 = 0.43
Log (Mussel biomass)
Log (Mussel biomass)
<1>
¾ power law signal disappears and
new simple patterns emerge in a network context.
<2>
magnitude of per capita and population I
explained by 23 simple species attributes (of 90)
<3>
effects dampen with distance
more complex = more simple
<4>
predictable fit and lackoffit in field experiment
<3>
metabolic "null model" may describe
a universal baseline of species interactions in a complex network.
<4>
"detrend" metabolism in ecological networks
to better understand nonmetabolic interactions and processes
"I would not give a fig for simplicity on this side of complexity,
but I'd give my life for the simplicity on the other side of complexity"
Oliver Wendell Holmes, Jr.
Alexander von Humboldt Foundation
slope = 1.05
High Biomass
R2 = 0.36
slope = 1.17
Low Biomass
R2 = 0.59
slope = 1.4
All Points