Warming impacts in fish food web dynamics

Econet 2021

Azenor Bideault, Matthieu Barbier, Arnaud Sentis,
Michel Loreau & Dominique Gravel

Azenor/talk_Econet2021

@Azenor_Bideault

1 / 29

Trophic interactions

Are at the core of ecological systems

Trophic cascade : Sea otters indirectly enhance kelp abundance by consuming herbivorous sea urchins

Estes et al. [2011]

2 / 29

Temperature

Climate change

What are the effects of temperature ?

3 / 29

Direct effect of temperature

On populations

4 / 29

Direct effect of temperature

On their interactions

5 / 29

Effect of temperature

On the dynamics of food webs

Alter trophic control
Decrease stability
Trigger extinctions

6 / 29

No synthetic understanding yet

Most studies explore :

One particular ecological system
Food chains (vs food webs)

with different

experimental design
study system
theoretical framework
model assumptions

Hard to disentangle the various effects of temperature

How do they propagate from the populations to the community?

7 / 29

Food webs dynamical properties

Effects of warming : compare changes in the dynamics at the community and species levels

8 / 29

Method9 / 29

Fish food webs at large scale

10 / 29

Data

Albouy et al [2019], Irigoien et al [2014]

11 / 29

Theoretical approach

Modelling communities to infer their structural and dynamical properties

Lotka-Volterra system

$\begin{align} \dfrac{dB_i}{dt} &= \textrm{production} - \textrm{predation losses} - \textrm{internal losses} \\ \frac{dB_i}{dt} &= g_iB_i + \sum_j \epsilon A_{ij} B_iB_j-\sum_k A_{ki} B_iB_k - D_iB_i^2 \end{align}$

B biomass
A_ij interaction matrix
g_i net growth rate
D_i self regulation
ϵ conversion efficiency

12 / 29

Temperature and body-mass dependence of biological rates

$\large b_i = m_i^\beta b_0e^{-E/kT}$

m body mass
β exponent
b₀, k constants
T temperature
E activation energy

Growth and attack rate Savage et al [2004], Li et al [2018]

13 / 29

Theoretical approach

Modelling communities to infer their structural and dynamical properties

Lotka-Volterra system

$\begin{align} \frac{dB_i}{dt} = g_i + \sum_j \epsilon A_{ij} B_j-\sum_k A_{ki} B_k - D_iB_i \end{align}$

B biomass
A interaction matrix
g net growth rate
D self regulation
ϵ conversion efficiency

14 / 29

Self-regulation

An important but not well known parameter

Intraspecific density dependent regulation
A population’s growth rate is negatively affected by its own population density

Examples :

territoriality
infanticide
intra-guild predation
competition for light

Important to match stability levels observed in nature

15 / 29

Estimation of species biomass

Self-regulation is completely unknown...
Biomass can be inferred from allometric relationship

Hatton et al [2019]

16 / 29

Method to estimate self-regulation

$\begin{align} \frac{dB_i}{dt} = g_iB_i + \sum_j \epsilon A_{ij} B_iB_j-\sum_k A_{ki} B_iB_k - D_iB_i^2 \end{align}$

using estimations of biological rates and biomass
allow coexistence
equilibrium

Simulate the dynamics of communities and measure some dynamical properties

17 / 29

Metrics of community dynamics

Trophic control (bottom-up vs top-down)

$\begin{align} \lambda = \frac{\epsilon A_{21}^2}{D_1D_2} \end{align}$

18 / 29

Metrics of community dynamics

Sum species biomass

19 / 29

Metrics of species dynamics

Relative change in species biomass

20 / 29

Metrics of community dynamics

Variability : temporal biomass variance in response to stochastic pertubations (community average)

$\begin{align} \mathcal{V} = tr(C) \end{align}$ $C$ covariance matrix, solution of the Lyapunov equation $JC+CJ^T = \mathbb I$ with $J$ Jacobian matrix

Arnoldi et al [2019]

21 / 29

Measures of community dynamics

Collectivity : importance of indirect interactions (collectivity = 1, a change in species abundance affect other species far in the network)

$\begin{align} \phi = \rho(M_{ij}) = \max_i|\lambda_i(M)| \end{align}$

spectral radius of $M_{ij} = A_{ij}/D_i$ , $\lambda_i(M)$ is the ith eigenvalue of matrix $M$

Arnoldi et al [in prep]

22 / 29

Simulate warming

Direct effect of warming on species biological rates
Compute the relative change in community metrics

$\begin{align} \Delta(x) = \textrm{log}_{10}(x_{warm}) - \textrm{log}_{10}(x) \approx (x_{warm} - x)/x \end{align}$

23 / 29

Results24 / 29

Moderate effect on community properties

25 / 29

Strong effect at the species level

26 / 29

To conclude

Warming affects individual species more significantly than communities as an entity

Moderate increase in top-down control and collectivity and decrease in variability
Stronger variation in species biomass, especially species from trophic levels 2 and 3

Focus on direct effect of temperature on biological rates and interactions

27 / 29

Entangled effects of temperature

Apply the framework to identify latitudinal variation in trophic control, variability and collectivity

Other variables drive variation in community dynamics
Indirect effects of warming

28 / 29

Stronger impact of warming at the species level than at the community level

Special thanks to

You for listening
My collaborators and supervisors
Will for the nice template

29 / 29

Warming impacts in fish food web dynamics

Econet 2021

Azenor Bideault, Matthieu Barbier, Arnaud Sentis,
Michel Loreau & Dominique Gravel

Azenor/talk_Econet2021

@Azenor_Bideault

1 / 29

Trophic interactions

Are at the core of ecological systems

Trophic cascade : Sea otters indirectly enhance kelp abundance by consuming herbivorous sea urchins

Estes et al. [2011]

2 / 29

Temperature

Climate change

What are the effects of temperature ?

3 / 29

Direct effect of temperature

On populations

4 / 29

Direct effect of temperature

On their interactions

5 / 29

Effect of temperature

On the dynamics of food webs

Alter trophic control
Decrease stability
Trigger extinctions

6 / 29

No synthetic understanding yet

Most studies explore :

One particular ecological system
Food chains (vs food webs)

with different

experimental design
study system
theoretical framework
model assumptions

Hard to disentangle the various effects of temperature

How do they propagate from the populations to the community?

7 / 29

Food webs dynamical properties

Effects of warming : compare changes in the dynamics at the community and species levels

8 / 29

Method9 / 29

Fish food webs at large scale

10 / 29

Data

Albouy et al [2019], Irigoien et al [2014]

11 / 29

Theoretical approach

Modelling communities to infer their structural and dynamical properties

Lotka-Volterra system

B biomass
A_ij interaction matrix
g_i net growth rate
D_i self regulation
ϵ conversion efficiency

12 / 29

Temperature and body-mass dependence of biological rates

$\large b_i = m_i^\beta b_0e^{-E/kT}$

m body mass
β exponent
b₀, k constants
T temperature
E activation energy

Growth and attack rate Savage et al [2004], Li et al [2018]

13 / 29

Theoretical approach

Modelling communities to infer their structural and dynamical properties

Lotka-Volterra system

$\begin{align} \frac{dB_i}{dt} = g_i + \sum_j \epsilon A_{ij} B_j-\sum_k A_{ki} B_k - D_iB_i \end{align}$

B biomass
A interaction matrix
g net growth rate
D self regulation
ϵ conversion efficiency

14 / 29

Self-regulation

An important but not well known parameter

Intraspecific density dependent regulation
A population’s growth rate is negatively affected by its own population density

Examples :

territoriality
infanticide
intra-guild predation
competition for light

Important to match stability levels observed in nature

15 / 29

Estimation of species biomass

Self-regulation is completely unknown...
Biomass can be inferred from allometric relationship

Hatton et al [2019]

16 / 29

Method to estimate self-regulation

$\begin{align} \frac{dB_i}{dt} = g_iB_i + \sum_j \epsilon A_{ij} B_iB_j-\sum_k A_{ki} B_iB_k - D_iB_i^2 \end{align}$

using estimations of biological rates and biomass
allow coexistence
equilibrium

Simulate the dynamics of communities and measure some dynamical properties

17 / 29

Metrics of community dynamics

Trophic control (bottom-up vs top-down)

$\begin{align} \lambda = \frac{\epsilon A_{21}^2}{D_1D_2} \end{align}$

18 / 29

Metrics of community dynamics

Sum species biomass

19 / 29

Metrics of species dynamics

Relative change in species biomass

20 / 29

Metrics of community dynamics

Variability : temporal biomass variance in response to stochastic pertubations (community average)

$\begin{align} \mathcal{V} = tr(C) \end{align}$ $C$ covariance matrix, solution of the Lyapunov equation $JC+CJ^T = \mathbb I$ with $J$ Jacobian matrix

Arnoldi et al [2019]

21 / 29

Measures of community dynamics

Collectivity : importance of indirect interactions (collectivity = 1, a change in species abundance affect other species far in the network)

$\begin{align} \phi = \rho(M_{ij}) = \max_i|\lambda_i(M)| \end{align}$

spectral radius of $M_{ij} = A_{ij}/D_i$ , $\lambda_i(M)$ is the ith eigenvalue of matrix $M$

Arnoldi et al [in prep]

22 / 29

Simulate warming

Direct effect of warming on species biological rates
Compute the relative change in community metrics

$\begin{align} \Delta(x) = \textrm{log}_{10}(x_{warm}) - \textrm{log}_{10}(x) \approx (x_{warm} - x)/x \end{align}$

23 / 29

Results24 / 29

Moderate effect on community properties

25 / 29

Strong effect at the species level

26 / 29

To conclude

Warming affects individual species more significantly than communities as an entity

Moderate increase in top-down control and collectivity and decrease in variability
Stronger variation in species biomass, especially species from trophic levels 2 and 3

Focus on direct effect of temperature on biological rates and interactions

27 / 29

Entangled effects of temperature

Apply the framework to identify latitudinal variation in trophic control, variability and collectivity

Other variables drive variation in community dynamics
Indirect effects of warming

28 / 29

Stronger impact of warming at the species level than at the community level

Special thanks to

You for listening
My collaborators and supervisors
Will for the nice template

29 / 29

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Warming impacts in fish food web dynamics

Econet 2021

Azenor Bideault, Matthieu Barbier, Arnaud Sentis, Michel Loreau & Dominique Gravel

Trophic interactions

Temperature

Direct effect of temperature

Direct effect of temperature

Effect of temperature

No synthetic understanding yet

Food webs dynamical properties

Method

Fish food webs at large scale

Data

Theoretical approach

Temperature and body-mass dependence of biological rates

Theoretical approach

Self-regulation

Estimation of species biomass

Method to estimate self-regulation

Metrics of community dynamics

Metrics of community dynamics

Metrics of species dynamics

Metrics of community dynamics

Measures of community dynamics

Simulate warming

Results

Moderate effect on community properties

Strong effect at the species level

To conclude

Entangled effects of temperature

Trophic interactions

Help

Talk template

Warming impacts in fish food web dynamics

Econet 2021

Azenor Bideault, Matthieu Barbier, Arnaud Sentis, Michel Loreau & Dominique Gravel

Trophic interactions

Temperature

Direct effect of temperature

Direct effect of temperature

Effect of temperature

No synthetic understanding yet

Food webs dynamical properties

Method

Fish food webs at large scale

Data

Theoretical approach

Temperature and body-mass dependence of biological rates

Theoretical approach

Self-regulation

Estimation of species biomass

Method to estimate self-regulation

Metrics of community dynamics

Metrics of community dynamics

Metrics of species dynamics

Metrics of community dynamics

Measures of community dynamics

Simulate warming

Results

Moderate effect on community properties

Strong effect at the species level

To conclude

Entangled effects of temperature

Azenor Bideault, Matthieu Barbier, Arnaud Sentis,
Michel Loreau & Dominique Gravel

Azenor Bideault, Matthieu Barbier, Arnaud Sentis,
Michel Loreau & Dominique Gravel