Massol bio info2011

Accounting for food web

information in island

biogeography

Dominique Gravel, François Massol,

Elsa Canard, David Mouillot, Nicolas Mouquet

Journée Bioinformatique et Biodiversité 2011 – Jun 29th

Intr

odu

ctio

nOutline

1. Introduction

2. The model

3. Analysis

4. Fit to existing data

5. Conclusions & perspectives


Intr

odu

ctio

nThe question of diversity

ht

tp

:/

/m

rb

ar

lo

w.

wo

rd

pr

es

s.

co

m/


Intr

odu

ctio

nThe question of diversity

Diversity

Environment

InteractionsDispersal


Intr

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nIsland biogeography

Island

MacArthur & Wilson 1967

Mainland


Intr

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c

e

†


Intr

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ctio


( )1dp c p epdt

= − −c

e

†


Intr

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ctio


* /1 /

c epc e

=+

islands closer to the mainland are easier to colonize

larger islands are less prone to species extinctions

( )1dp c p epdt

= − −


Intr

odu

ctio



Intr

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nThe food web challenge


Intr

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ctio



Intr

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†

Order of colonization events

Chain extinctions

†

Mod

el


The modelStructuring assumptions:

1. a species cannot colonize unless one prey species is already present

2. a species that loses its last prey species gets extinct

Mod

el


The model

[ ]Ei ip X=iX random variable for the occurrence of species i (= 0 or 1)

iY indicator for the occurrence of at least one prey of species i

iε rate at which species i loses its last prey species

( ) ( )1ii

i i idp

cq p e pdt

= − − + ε

[ ]|E 0i i iq Y X= =

Mod

el


The model

( ) ( )1ii i i i

dpcq p e p

dt= − − + ε

( )1dp c p epdt

= − −

our model

MacArthur & Wilson’s

An

alys

is


AnalysisStructuring assumptions:

1. a species cannot colonize unless one prey species is already present

2. a species that loses its last prey species gets extinct

Approximation for analysis:1. consumers are structured by their diet breadth (g)2. preys of the same predator occur independently3. prey presence is independent of predator presence

An

alys

is


Analysis

iq ip iεspecies i

An

alys

is


Analysis

iq ip iεspecies i

( )E 1 |1 0i

i j ij G

X Xq∈

= − =⎡ ⎤

−⎢ ⎥⎣ ⎦∏

before approximations

( )( )

/1 /

i ii

i i

cq ep

cq e+

=+ +

εε

( ) ( )1 | 1Ei i

i j j k ij

k jkG G

e X X X∈ ∈

≠

⎡ ⎤⎢ ⎥+⎢ ⎥⎢ ⎥⎣ ⎦

= − =∏∑ε ε

iG set of prey species for species i

An

alys

is


Analysis

iq ip iεspecies i

( )•log 11 i PpG

iq e −≈ −

after approximations

( )( )

/1 /

i ii

i i

cq ep

cq e+

=+ +

εε

( )•log 1• •

•1i P

G pi i

P

pp

G e −⎛ ⎞≈ ⎜ ⎟⎜ ⎟

⎠−⎝

εε

iG # of prey species for species i• Px average of x among regional species

An

alys

is


Analysis

gq gp gεdiet breadth g

after approximations

( ) ( )

( ) ( ) ( )

log 1

log 1 log 1

/ 1

1 / 1 1

g P

g gP P

g

g g g

p

p p

c e ep

c e e ge

−

− −

⎛ ⎞−⎜ ⎟⎝ ⎠

⎛ ⎞≈

⎛ ⎞+ − +⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

• Px average of x among regional species

An

alys

is


c/e

Analysis

0 5 10 15 20

0.2

0.4

0.6

0.8

1.0p

2

1.5

0.05

/ 0.5g

B

g

P P

σ

=

=

=p1

pB

• gpp σ±

An

alys

is


Analysis

c/e

p

2

1.5

0.05

/ 0.5g

B

g

P P

σ

=

=

=

0.0 0.5 1.0 1.5 2.0

0.1

0.2

0.3

0.4

0.5

0.6

p1

pB

• gpp σ±

Dat

a fi

ttin

g


• dataset: Havens (1992)• 50 Adirondack lakes• 210 species (13-75)• 107 primary producers• 103 consumers• 2020 links (17-577)• low connectance (0.09)

Empirical support?

Dat

a fi

ttin

g


Empirical support

Estimation of c/e for each lake by maximum likelihood

Model log likelihood

Classic TIB (Intercept) - 2428.2

Trophic – TIB (Analytical) - 2416.8

Trophic – TIB (Simulations) - 2392.4

Dat

a fi

ttin

g


Empirical support

Estimation of c/e for each lake by maximum likelihood





no trophic structurewith diet breadth

complete structure

Dat

a fi

ttin

g


Empirical support

• second dataset: Piechnik et al. (2008)• 6 islands (Florida keys)• sampled before total defaunation in the 60’s• 250 species (arthropods only, 15-38 per island)• no primary producer, but 120 taxa (herbivores &

detritivores) are not constrained• 130 consumers• 13068 feeding links (32-331 per island)• high connectance (0.21)

Dat

a fi

ttin

g


Empirical support

Second data set (Piechnik et al. 2008)

poorer fit (high connectance, partial food web data)





no trophic structurewith diet breadth

complete structure

The End Journée Bioinformatique et Biodiversité 2011 – Jun 29th

Conclusions & Perspectives

Conclusions:– richer/more precise predictions than TIB with no

additional parameter– captures phenomena occurring in low connectance

webs– integrates interactions in dispersal-based model

Perspectives:– application to other biological networks in space– refining approximations– testing against other models (e.g. group-dependent rates)


Complexity-diversity?


Thank you!

Dataset: J. Dunne

Comments on paper

C. Albert, D. Alonso, J. Chase, J. E. Cohen, S. M. Gray, R. D. Holt, O. Kaltz, M. Loreau

Technology

Massol bio info2011