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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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Presentation Transcript
slide2

Collaborators:

Ulrich Brose

Carol Blanchette

Jennifer Dunne

Sonia Kefi

Neo Martinez

Bruce Menge

Sergio Navarrete

Owen Petchey

Philip Stark

Rich Williams

slide4

Predict

Biodiversity

slide5

Biodiversity

Prediction

Changes in Focal Species

slide8

How can we predict the consequences

of species loss in complex ecosystems?

Little Rock Lake Food Web (Martinez 1991)

slide9

How can we predict the consequences

of species loss in complex ecosystems?

1 degree

Little Rock Lake Food Web (Martinez 1991)

slide10

How can we predict the consequences

of species loss in complex ecosystems?

2 degrees

Little Rock Lake Food Web (Martinez 1991)

slide11

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

slide16

<1>

everything needs energy to stay alive

slide17

<2>

BIG things need more energy than small things

slide18

<2>

BIG things need more energy than small things

3/4

( )

allometric scaling of metabolism with body size

slide23

Feeding is

Universal

slide24

Universal

The Only Thing

slide25

Ubiquitous

The Only Thing

slide26

R. Donovan

non-metabolic

interactions

slide28

can we explain

with body size (metabolism)?

ALL interaction strengths

slide29

can we explain

with body size (metabolism)?

ALL interaction strengths

slide30

WHAT

can we explain

with body size (metabolism)?

slide31

WHAT

NOT

can we explain

with body size (metabolism)?

slide34

can we explain

with body size (metabolism)?

ALL interaction strengths

slide35

WHAT

can we explain

with body size (metabolism)?

slide36

WHAT

NOT

can we explain

with body size (metabolism)?

slide37

abundance,

interaction strength,

etc.

?

slide38

abundance,

interaction strength,

etc.

feeding,

body size,

metabolism,

etc.

slide39

abundance,

interaction strength,

etc.

feeding,

body size,

metabolism,

etc.

slide40

can we

describe a metabolic baseline of interactions

in complex networks?

slide41

can we

detrend metabolism

in complex networks?

slide42

Body Size also influences Food Web Structure

Brose et al. 2005 Ecology

Brose et al. 2006 Ecology

Petchey et al. 2008 PNAS

slide43

if each link obeys allometric rules

are those rules preserved at the network scale?

slide44

if each link obeys allometric rules

will body size predict

the effect of species loss in the network?

slide45

does

more complex = more complicated?

slide51

Approach:

<1>

Simulate species dynamics in a wide variety of networks

stochastic variation in

structural and dynamic

parameters

slide52

Approach:

<2>

all feeding links governed by (body size)¾

slide53

Approach:

<3>

delete each species and measure effects on all others

slide54

Approach:

<4>

Track variation for each simulation

interaction strengths

network level structure

neighborhood structure

species attributes

link attributes

slide55

Approach:

<5>

mine the variability for what best explains interaction strengths

slide57

coupled

The Models

slide58

<1>

Food Web Structure: Niche Model

(Williams and Martinez 2000)

<2>

Predator-Prey Interactions: Bio-energetic Model

(Yodzis and Innes 1992, Brose et al. 2005, 2006 Eco Letts)

<3>

Plant population dynamics: Plant-Nutrient Model

(Tilman 1982, Huisman and Weissing 1999)

bioenergetic predator prey dynamics
Bioenergetic Predator-Prey Dynamics

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

slide60

Consumption

# Prey

Bioenergetic Predator-Prey Dynamics

Functional Response

mass-specific metabolic rate

assimilation

efficiency

max metabolic-specific ingestion rate

xi, yiscale with body size

(body size correlated with web structure)

slide61

Nutrient-Dependent

Growth of Plants

Bioenergetic Predator-Prey Dynamics(Plants)

mass-specific

growth rate

metabolic loss

loss to herbivores

ri, xj, y scale with body size

slide62

plant

growth rate

Nutrient-Dependent 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

slide63

Generate a food web (Niche Model)

Calculate trophic level for each species

Apply plant-nutrient model to plants, predator-prey 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

slide65

Removed Species

R

T

Target Species

slide66

X

R

+

T

slide67

R

T

slide68

per capitaI= (BT+ -BT-)/NR

population I= BT+ -BT-

X

R

-

T

slide69

per capitaI= (BT+ -BT-)/NR

population I= BT+ -BT-

X

R

-

T

slide70

per capitaI= (BT+ -BT-)/NR

population I= BT+ -BT-

X

R

-

T

slide71

per capitaI= (BT+ -BT-)/NR

population I= BT+ -BT-

X

R

-

T

slide72

per capitaI= (BT+ -BT-)/NR

population I= BT+ -BT-

X

R

?

T

T

slide73

per capitaI= (BT+ -BT-)/NR

population I= BT+ -BT-

3° Consumers

2° Consumers

X

R

?

1° Consumers

T

T

1° Prey

2° Prey

3° Prey

slide74

per capitaI= (BT+ -BT-)/NR

population I= BT+ -BT-

3° Consumers

2° Consumers

X

?

R

1° Consumers

T

T

1° Prey

2° Prey

3° Prey

slide75

K = Keystone consumer

NK = Non-Keystone consumer

D = Dominant basal species

S = Subordinate basal species

R = Resource

K

NK1

S1

D

R1

R2

slide76

Consumption

Resource competition

Indirect Facilitation

Keystone Present

K

NK1

+

S1

S2

D

S1

R1

R2

slide77

Consumption

Resource competition

Indirect Facilitation

Keystone Present

K

NK1

+

S1

S2

D

S1

R1

R2

Increased Resources

slide78

Consumption

Resource competition

Indirect Facilitation

Keystone Present

K

NK1

+

S1

Other Competitors

S2

D

S1

Sn

R1

R2

slide79

Consumption

Resource competition

Indirect Facilitation

Secondary Consumers

NK2n

K

NK1

+

S1

D

S1

R1

R2

slide80

Consumption

Resource competition

Indirect Facilitation

NK3n

Tertiary Consumers

Secondary Consumers

NK2n

K

NK1

+

S1

S2

D

S1

R1

R2

slide81

NK4n

and so on…

NK3n

Tertiary Consumers

Secondary Consumers

NK2n

K

NK1

+

S1

S2

D

S1

R1

R2

slide82

K

Top down

+

Horizontal

S1

S2

D

S1

Bottom up

slide83

add

noise

slide85

add noise:

<1>

Web Structure

size, connectance, architecture

slide86

add noise:

<2>

Animal Attributes

metabolic and max consumption rate,

pred-prey body size ratio

functional response type

predator interference

slide87

add noise:

<3>

Plant Attributes

growth rate

half saturation concentrations

slide88

track:

90 predictors to explain

variation in the strengths of

254,032 interactions among

12,116 species in

600 webs

slide89

track:

<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

slide90

attributes of the interaction

+

T

R

-

R

+

prey

predator

prey

predator

-

T

slide91

attributes of the interaction

+

T

R

-

shortest path = 2 degrees

2 degree paths: +, +, -

R

+

prey

predator

prey

predator

-

T

slide92

attributes of the interaction

+

T

R

-

shortest path = 2 degrees

2 degree paths: +, +, -

3 degree paths: +, +, +, -

R

+

prey

predator

prey

predator

-

T

slide93

attributes of the interaction

+

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

un-weighted sum (shortest + next shortest) = +3

weighted sum (shortest + (next shortest / 2)) = +2

slide97

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)

slide98

Per Capita LinearInteraction Strength

= Per Capita RemovalInteraction Strength?

R

T

R2 = 0.90

Slope = 0.74

Log (per capita consumption)

Log (R body mass)

slide99

Per Capita RemovalInteraction Strength

R

T

R2 = 0.32

Slope = 0.74

Log |per capita I|

Log (R body mass)

slide100

Per Capita RemovalInteraction Strength

R

T

R2 = 0.14

Slope = 1.3

Log |per capita I|

Log (R body mass)

slide101

Per Capita RemovalInteraction Strength

R

T

R2 = 0.45

Slope = 1.4

Log |per capita I|

Log (R body mass)

slide102

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)

slide103

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)

slide104

population I

(population interaction strength)

slide105

population I

(total effect on T of removing R)

slide106

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

slide107

Log |population I|

Log (T biomass)

slide108

High R Biomass

Low R Biomass

R2 = 0.65

Log |population I|

Log (T biomass)

slide109

Sign

(strong interactions)

Sign

(weak interactions)

positive

Proportion Observed

negative

≥ 1

≥ 1

≤ -1

≤ -1

Weighted Sum Path Signs

Weighted Sum Path Signs

slide110

Summary:

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)

slide114

Is it circular?

BT+ = T biomass (R present)

predicting: (BT+ -BT-)

BT-= T biomass (R removed)

using: BT+

Log (|population I|)

Log (T biomass)

Log (BT+)

slide115

Is it circular?

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

slide117

More Complex is More Simple

population I

per capita I

Proportion of Variation Explained

R2 = 0.73

R2 = 0.88

Number of Species

slide121

Predictions:

<1>

Purely metabolic interactions

should be well predicted by simple attributes of R and T.

slide122

Predictions:

<2>

Deviations from simple metabolic predictions

should point to strong non-metabolic influences.

slide123

Goal:

De-trend the "metabolic baseline" of complex systems

to gain insight into other important ecological processes.

slide127

Whelks

R

T

Mussels

Barnacles

Space

slide128

Field Experiment Conditions

Whelks

R

T

Mussels

Barnacles

Space

slide129

Whelks

R

T

Mussels

Barnacles

Space

slide130

Whelks

R

Metabolic

+

-

-

+

T

-

Mussels

Barnacles

-

-

Space

slide131

Whelks

R

Metabolic

+

Non-Metabolic

+

-

-

+

T

-

Mussels

Barnacles

-

-

Space

slide132

4 blocks

x 3 start dates

x 1-3 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

+

Non-Metabolic

+

+

-

-

-

-

+

+

+

T

T

T

-

-

-

Natural Variation

in Mussels

and Barnacles

slide133

Simulation Results

High R Biomass

Low R Biomass

Log (|per capitaI|)

Log (|population I|)

Log (T biomass)

slide134

Central Tendency

Predicted by Simulations

predicted

High Whelk Biomass

Low Whelk Biomass

Log (|per capitaI|)

Log (|population I|)

Log (Mussel biomass)

slide135

R

Metabolic

predicted

-

High Whelk Biomass

Low Whelk Biomass

T

Log (|per capitaI|)

Log (|population I|)

Log (Mussel biomass)

slide136

R

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)

slide137

R

R

Metabolic

+

Non-Metabolic

Metabolic

+

-

-

-

+

T

T

predicted

observed

Log (|per capitaI|)

R2 = 0.49

Log (|population I|)

R2 = 0.43

Log (Mussel biomass)

Log (Mussel biomass)

slide138

Summary

<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 2-3 simple species attributes (of 90)

<3>

effects dampen with distance

more complex = more simple

<4>

predictable fit and lack-of-fit in field experiment

slide139

Conclusions

<1>

metabolic "webbiness" of life not necessarily a big source of uncertainty.

slide140

Conclusions

<2>

“module” approaches may work best

when embedded in complexity

slide141

Conclusions

<3>

metabolic "null model" may describe

a universal baseline of species interactions in a complex network.

slide142

Conclusions

<4>

"de-trend" metabolism in ecological networks

to better understand non-metabolic interactions and processes

slide143

"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.

slide144

Acknowledgements

Alexander von Humboldt Foundation

slide148

R2 = 0.96

slope = -1.05

High Biomass

R2 = 0.36

slope = -1.17

Low Biomass

R2 = 0.59

slope = -1.4

All Points

slide149

0.15

0.10

Positive

Effects

0.05

Probability

0.15

Negative

Effects

0.10

0.05

Log (|population I|)

slide150

(a)

-

+

n = 5 random subsamples

of 10,000 interactions

+

-