Post on 01-Nov-2014
description
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
ht
tp
:/
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rb
ar
lo
w.
wo
rd
pr
es
s.
co
m/
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