Accounting for food web information in island biogeography Dominique Gravel, François Massol , Elsa Canard, David Mouillot, Nicolas Mouquet
Nov 01, 2014
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
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
Intr
odu
ctio
nThe question of diversity
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Journée Bioinformatique et Biodiversité 2011 – Jun 29th
Intr
odu
ctio
nThe question of diversity
Diversity
Environment
InteractionsDispersal
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
Intr
odu
ctio
nIsland biogeography
Island
MacArthur & Wilson 1967
Mainland
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
Intr
odu
ctio
nIsland biogeography
c
e
†
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
Intr
odu
ctio
nIsland biogeography
( )1dp c p epdt
= − −c
e
†
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
Intr
odu
ctio
nIsland biogeography
* /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
= − −
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
Intr
odu
ctio
nIsland biogeography
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
Intr
odu
ctio
nThe food web challenge
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
Intr
odu
ctio
nThe food web challenge
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
Intr
odu
ctio
nThe food web challenge
†
Order of colonization events
Chain extinctions
†
Mod
el
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
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
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
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
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
The model
( ) ( )1ii i i i
dpcq p e p
dt= − − + ε
( )1dp c p epdt
= − −
our model
MacArthur & Wilson’s
An
alys
is
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
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
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
Analysis
iq ip iεspecies i
An
alys
is
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
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
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
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
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
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
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
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
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
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
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
• 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
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
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
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
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
no trophic structurewith diet breadth
complete structure
Dat
a fi
ttin
g
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
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
Journée Bioinformatique et Biodiversité 2011 – Jun 29th
Empirical support
Second data set (Piechnik et al. 2008)
poorer fit (high connectance, partial food web data)
Model log likelihood
Classic TIB (Intercept) - 259.3
Trophic – TIB (Analytical) - 259.9
Trophic – TIB (Simulations) - 260.0
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)
The End Journée Bioinformatique et Biodiversité 2011 – Jun 29th
Complexity-diversity?
The End Journée Bioinformatique et Biodiversité 2011 – Jun 29th
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