Post on 24-Dec-2019
transcript
Resilience and stability of ecological networks
Elisa Thébault
elisa.thebault@upmc.fr
Why study ecological interaction webs?
Why study ecological interaction webs?
Factors which determine interactions
between species
Network structural patterns
Naisbit et al. 2012
Rezende et al. 2007
Why study ecological interaction webs?
Consequences on ecosystem functioning
and stability
Network structural patterns
Dunne et al. (2004)
Why study ecological interaction webs?
Effects of global change on networks and consequences
Cavalheiro et al. (2008)
Before 1970s, the view is that complexity begets stability
Several arguments:
- Theoretical and experimental evidence that
simple model ecosystems are inherently
unstable
- species-poor islands and artificial
agricultural ecosystems are more prone to
invasions by new species and pests than are
their continental and natural counterparts.
Elton 1958
Before 1970s, the view is that complexity begets stability
Elton 1958 MacArthur 1955 Several arguments:
- Theoretical and experimental evidence that
simple model ecosystems are inherently
unstable
- species-poor islands and artificial
agricultural ecosystems are more prone to
invasions by new species and pests than are
their continental and natural counterparts.
Before 1970s, the view is that complexity begets stability
– Consider a community of k species with population density Ni
– Population dynamics can be described by:
kii NNF
dt
dN,...,1
This traditional view is challenged in the early 1970s
May 1972
A mathematical formulation
n …
… 2 1
1 2 ….. n
– Near equilibrium, the behaviour of the community is related to the eigenvalues of the Jacobian of the system at this point
A = community matrix
aij = interaction strength eqj
iij
N
Fa
This traditional view is challenged in the early 1970s
n …
… 2 1
1 2 ….. n
– Near equilibrium, the behaviour of the community is related to the eigenvalues of the Jacobian of the system at this point
– For a random network with a proportion C of nonzero interaction strengths (connectance), and s the mean interaction strength, the condition for local stability is:
A = community matrix
aij = interaction strength eqj
iij
N
Fa
1kCs
This traditional view is challenged in the early 1970s
These contrasting views are at the origin of the complexity – stability
debate
Tackling this debate is fundamental to understand how the structure of ecological networks affect ecosystem resilience
These contrasting views are at the origin of the complexity – stability
debate
New perspectives on this debate with different definitions of stability
Going beyond May’s work: ecological networks are not random and new model assumptions
Today we will focus on two questions from recent works in this field:
These contrasting views are at the origin of the complexity – stability
debate
New perspectives on this debate with different definitions of stability
Going beyond May’s work: ecological networks are not random and new model assumptions
Today we will focus on two questions from recent works in this field:
These contrasting views are at the origin of the complexity – stability
debate
Stability: a multifaceted concept …
Dynamic stability
Local stability: definition often used in theoretical studies See May
Cycles and Chaos: Associated measures of stability: Variability, amplitude of fluctuations, etc.
Stability: a multifaceted concept …
Dynamic stability Response to disturbances
Resilience and resistance of the community, species persistance, ….
… in relation with many diversity-stability relationships
Ives and Carpenter (2007)
Model of randomly structured competitive communities:
Investigate 13 relationships between diversity and stability
… in relation with many diversity-stability relationships
Ives and Carpenter (2007)
… in relation with many diversity-stability relationships
… in relation with many diversity-stability relationships
Temporal variability of ecosystem functioning: a new perspective on the
diversity-stability debate
Tilman et al. (2006)
Insurance hypothesis
Diversity decreases variability of ecosystem properties through asynchronous responses of species to environmental perturbation Higher diversity
levels
Low diversity
Yachi & Loreau (1999)
Tem
pe
ratu
re T
(°C
)
Time
Niche differentiation
Pla
nts
an
d h
erb
ivo
res
mo
rtal
ity
rate
s m
T(t)
5 15 25
5 15 25
5 15 25
0
5
10
15
20
25
30
0 500 1000 1500 2000
Degree of niche differentiation
Insurance hypothesis and interactions between species
1 1 P
1 … P
n - 1 P
n
H 1
… H n - 1
H n
P 1
… P n - 1
P n
H 1
… H n - 1
H n
P 1
… P n - 1
P n
H 1
… H n - 1
H n
Environmental fluctuations
Thébault & Loreau (2005)
0
0,2
0,4
0,6
0,8
1
1 2 4 8 16
0
0,1
0,2
0,3
1 2 4 8 16
Plant diversity
CV
of
tota
l he
rbiv
ore
b
iom
ass
P 1 P n - 1 P n
H 1 H n - 1 H n
Specialist herbivores
CV
of
pla
nt
and
he
rbiv
ore
bio
mas
s
Higher degree of niche
differentiation
Plant diversity
synchronous responses
asynchronous responses
highly asynchronous responses
CV
of
tota
l pla
nt
bio
mas
s
0
0,1
0,2
0,3
1 2 4 8 16
Insurance hypothesis and interactions between species
Thébault & Loreau (2005)
0
0,1
0,2
0,3
1 2 4 8 16
0
0,2
0,4
0,6
0,8
1
1 2 4 8 16
0
0,1
0,2
0,3
1 2 4 8 16
0
0,1
0,2
0,3
1 2 4 8 16
0
0,1
0,2
0,3
1 2 4 8 16
0
0,2
0,4
0,6
0,8
1
1 2 4 8 16
Plant diversity
CV
of
tota
l pla
nt
bio
mas
s C
V o
f to
tal h
erb
ivo
re
bio
mas
s
CV
of
pla
nt
and
he
rbiv
ore
bio
mas
s
Plant diversity
synchronous responses
asynchronous responses
highly asynchronous responses
Insurance hypothesis and interactions between species
Thébault & Loreau (2005)
P 1 P n - 1 P n
H 1 H n - 1 H n
P 1
H
P 1
H
P 1
H
0
0,1
0,2
0,3
1 2 4 8 16
0
0,2
0,4
0,6
0,8
1
1 2 4 8 16
0
0,1
0,2
0,3
1 2 4 8 16
0
0,1
0,2
0,3
1 2 4 8 16
0
0,1
0,2
0,3
1 2 4 8 16
0
0,2
0,4
0,6
0,8
1
1 2 4 8 16
Plant diversity
CV
of
tota
l pla
nt
bio
mas
s C
V o
f to
tal h
erb
ivo
re
bio
mas
s
CV
of
pla
nt
and
he
rbiv
ore
bio
mas
s
Plant diversity
synchronous responses
asynchronous responses
highly asynchronous responses
Insurance hypothesis and interactions between species
Thébault & Loreau (2005)
P 1 P n - 1 P n
H 1 H n - 1 H n
P 1 … P n - 1
H 1 … H n - 1
P 1 … P n - 1
H 1 … H n - 1
P 1 … P n - 1
H 1 … H n - 1
P 1 P n - 1 P n
H 1 H n - 1 H n
0
0,1
0,2
0,3
1 2 4 8 16
0
0,2
0,4
0,6
0,8
1
1 2 4 8 16
0
0,1
0,2
0,3
1 2 4 8 16
0
0,1
0,2
0,3
1 2 4 8 16
0
0,1
0,2
0,3
1 2 4 8 16
0
0,2
0,4
0,6
0,8
1
1 2 4 8 16
Plant diversity
CV
of
tota
l pla
nt
bio
mas
s C
V o
f to
tal h
erb
ivo
re
bio
mas
s
CV
of
pla
nt
and
he
rbiv
ore
bio
mas
s
Plant diversity
1 1
synchronous responses
asynchronous responses
highly asynchronous responses
P 1 … P n - 1 P n
H 1 … H n - 1 H n
P 1 … P n - 1 P n
H 1 … H n - 1 H n
P 1 … P n - 1 P n
H 1 … H n - 1 H n
Insurance hypothesis and interactions between species
Thébault & Loreau (2005)
P 1 P n - 1 P n
H 1 H n - 1 H n
0
0,1
0,2
0,3
1 2 4 8 16
0
0,1
0,2
0,3
1 2 4 8 16
0
0,2
0,4
0,6
0,8
1
1 2 4 8 16
P 1 … P n - 1 P n
H 1 … H n - 1 H n
P 1 … P n - 1 P n
H 1 … H n - 1 H n
P 1 … P n - 1 P n
H 1 … H n - 1 H n
0
0,1
0,2
0,3
1 2 4 8 16
0
0,2
0,4
0,6
0,8
1
1 2 4 8 16
Plant diversity
CV
of
tota
l pla
nt
bio
mas
s C
V o
f to
tal h
erb
ivo
re
bio
mas
s
Plant diversity
synchronous responses
asynchronous responses
highly asynchronous responses
0
0,1
0,2
0,3
1 2 4 8 16
CV
of
pla
nt
and
he
rbiv
ore
bio
mas
s
Insurance hypothesis and interactions between species
Thébault & Loreau (2005)
Jiang et al. 2009
Haddad et al. 2010
Diversity promotes ecosystem stability
These contrasting views are at the origin of the complexity – stability
debate
Going beyond May’s work: ecological networks are not random and new model assumptions
- effects of interaction type and network structure - importance of foraging adaptation
Today we will focus on two questions from recent works in this field:
A diversity of interaction networks
Food web
Plant-pollinator network
Host-parasitoid network
Food web
94% food
webs
1% mutualistic
webs
4% parasitic
webs
Proportions of papers on ecological
networks published in the last 50 years
that were related to food webs,
mutualistic webs and parasitic webs
A focus on food webs
A focus on food webs
Schmid-Araya et al. 2002
A focus on food webs
Gauzens et al. 2015
Trophic groups Modules
Gross et al. (2009)
Food web structure and stability
Stouffer et al. (2011)
A growing number of studies on mutualistic webs
Seed dispersal pollination
Nested structure
• Continuum between specialist and generalist species
• Presence of a core of highly connected species
• Asymmetrical specialization Bascompte et al. 2003
A growing number of studies on mutualistic webs
Okuyama & Holland (2008)
Nestedness of mutualistic webs and stability
Rohr et al. (2014)
Gross et al. (2009) Okuyama & Holland (2008)
The links between network structure and stability
The model: dynamics of mutualistic and trophic webs
Na
j
AjpreyPk
kij
ijij
iPiiPii
Np
j
AipreyPk
kji
jiji
iAiiAii
P
PAcPIPr
dt
dP
P
PAcAIAr
dt
dA
1
)(
1
2
1
)(
1
2
Na
j
PimutAk
kij
ijij
iPiiPii
Np
j
AimutPk
kji
jiji
iAiiAii
A
PAcPIPr
dt
dP
P
PAcAIAr
dt
dA
1
)(
1
2
1
)(
1
2
-intrinsic growth rates rP and rA < 0 obligate mutualism
-intrinsic growth rates rP > 0 and rA < 0
-density dependence term -density dependence term
-interaction term saturates with mutualistic partner densities
-interaction term saturates with prey densities
Mutualistic Antagonistic
diversity
con
ne
ctan
ce
n = 24
n = 80
C =
0.0
5
C =
0.2
nestedness
modularity
time
Spec
ies
den
siti
es
The model: network structure and stability
diversity
con
ne
ctan
ce
n = 24
n = 80
C =
0.0
5
C =
0.2
nestedness
modularity
time
Spec
ies
den
siti
es Persistence:
proportion of species persisting at the equilibrium
Resilience:
measure of the speed at which a system returns to its original state after a perturbation
The model: network structure and stability
Results: impact of network structure on species persistence
Antagonistic networks Mutualistic networks
Diversity
Co
nn
ecta
nce
Diversity
Nestedness
Mo
du
lari
ty
Nestedness Thébault & Fontaine 2010
Results: impact of network structure on species persistence
Connectance Diversity
Modularity Nestedness
Persistence
0.07 0.31
- 0.53 - 0.03
- 0.81
0.87 -0.36
0.32
Connectance Diversity
Modularity Nestedness
Persistence
0.12 -0.29
- 0.01 - 0.89
- 0.81
0.86 -0.36
0.35
Mutualistic
opposite effect of network structure on the persistence of mutualistic and trophic networks
Antagonistic
Thébault & Fontaine 2010
Results: impact of network structure on species persistence
indirect effect: 0.40 indirect effect: 0.18 indirect effect: -0.76 indirect effect: -0.31
Importance of nestedness and modularity for network stability
Connectance Diversity
Modularity Nestedness
Persistence
0.07 0.31
- 0.53 - 0.03
- 0.81
0.87 -0.36
0.32
Connectance Diversity
Modularity Nestedness
Persistence
0.12 -0.29
- 0.01 - 0.89
- 0.81
0.86 -0.36
0.35
Mutualistic Antagonistic
Thébault & Fontaine 2010
Results: impact of network structure on resilience
Mutualistic Antagonistic
Connectance Diversity
Modularity Nestedness
Resilience
-0.17 0.49
- 0.17 0.25
- 0.73
0.83 -0.42
0.27
Connectance Diversity
Modularity Nestedness
Resilience
-0.62 -0.28
0.23 0.10
- 0.86
0.90 -0.30
0.26
indirect effect: 0. 32 indirect effect: 0.13 indirect effect: -0.10 indirect effect: -0.04
opposite effect of network structure on the resilience of mutualistic and trophic networks
Thébault & Fontaine 2010
Results: network structure at equilibrium
Thébault & Fontaine 2010
Summary: comparing networks with mutualistic and antagonistic interactions
The relation between structure and stability strongly differ between mutualistic and antagonistic webs Observed differences between herbivory and pollination networks suggest that network structure might differ between mutualistic and antagonistic interactions Importance of the particular architecture of interaction networks in determining their stability
Importance of foraging adaptation
Consumers can’t consume different resource species simultaneously because of the prey’s patchy distribution, the capturing strategy for different preys, consumer’s sensory and cognitive constraints for discriminating between preys.
Bernays and Funk 1999
Kondoh 2003
Importance of foraging adaptation
Kondoh 2003
Importance of foraging adaptation
Take home message Resilience, stability and the structure
of ecological networks
The relationship between network structure and stability depends on the definition of stability and on the mechanisms that determine species interactions
Need to be very careful about stability measures and model assumptions when you consider a study
Is resilience the most appropriate measure to assess the stability of ecological networks and their response to perturbations?
Take home message Resilience, stability and the structure
of ecological networks
Thank you for your attention