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# Warming impacts in fish food web dynamics

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## Econet 2021

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

[ Azenor/talk_Econet2021](https://github.com/Azenor/talk_Econet2021)

[ @Azenor_Bideault](https://twitter.com/Azenor_Bideault)

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# Food webs are not static objects

.pull-left[
![:scale 120%](images/network1.svg)]

.pull-right[
- Identity of species
- Number of species
- Biomass
- Interactions
- Interaction strength
- Stability] -->

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# Trophic interactions

.center[Are at the core of ecological systems]

![](images/otter.png)

.center[Trophic cascade : Sea otters indirectly enhance kelp abundance by consuming herbivorous sea urchins]

.cite[Estes et al. [2011]]

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# Temperature
.center[Climate change

![:scale 50%](images/global_warming.jpg)

**What are the effects of temperature ?**]

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# Direct effect of temperature

.center[
On populations

![](images/biological_rates_temp1.svg)]

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# Direct effect of temperature

.center[
On their interactions

![](images/biological_rates_temp2.svg)]

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# Effect of temperature

.center[
On the dynamics of food webs

![](images/biological_rates_temp3.svg)

- Alter trophic control
- Decrease stability
- Trigger extinctions]

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# 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

.center[**Hard to disentangle the various effects of temperature**

**How do they propagate from the populations to the community?**]

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# Food webs dynamical properties

.center[![:scale 200%](images/measures_chap2.svg)

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

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# Method

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# Fish food webs at large scale

.center[![:scale 90%](images/map_lat_long.png)]

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# Data

.center[![:scale 90%](images/schema_data.svg)]
 
.cite[Albouy et al [2019], Irigoien et al [2014]]

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# Theoretical approach

.center[**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
- Aij interaction matrix
- gi net growth rate
- Di self regulation
- *ϵ* conversion efficiency

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# Temperature and body-mass dependence of biological rates

.pull-left[
 ![](images/biological_rates_temp12.svg)]

.pull-right[

`\(\large b_i = m_i^\beta b_0e^{-E/kT}\)`

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

.center[**Growth and attack rate**]
.cite[Savage et al [2004], Li et al [2018]]

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# Theoretical approach

.center[**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

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# Self-regulation
.font80[An important but not well known parameter]

.center[**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

.center[**Important to match stability levels observed in nature**]

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# Estimation of species biomass

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

.center[
![:scale 60%](images/hatton.png)]
.cite[Hatton et al [2019]]

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# 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}`

.center[
- using estimations of biological rates and biomass
- allow coexistence
- equilibrium]

.center[**Simulate the dynamics of communities and measure some dynamical properties**]

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# Metrics of community dynamics

.center[
![:scale 200%](images/measures_chap2_1.svg)

**Trophic control (bottom-up vs top-down)**

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

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# Metrics of community dynamics

.center[
![:scale 200%](images/measures_chap2_2.svg)

**Sum species biomass**]

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# Metrics of species dynamics

.center[
![:scale 200%](images/measures_chap2_3.svg)

**Relative change in species biomass**]

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# Metrics of community dynamics

.center[
![:scale 200%](images/measures_chap2_4.svg)

**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]

.cite[Arnoldi et al [2019]]

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# Measures of community dynamics

.center[
![:scale 200%](images/measures_chap2_5.svg)

**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 `\(M\)`]

.cite[Arnoldi et al [in prep]]

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# Simulate warming

.center[![:scale 80%](images/temp_network2.svg)

- 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}`
]

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# Results

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# Moderate effect on community properties

.center[![](images/figure_metric_change_noTSR.svg)]

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# Strong effect at the species level

.center[![:scale 70%](images/figure_biomass_change_noTSR.png)]

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# To conclude

.center[**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

.center[Focus on direct effect of temperature on biological rates and interactions]

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# Entangled effects of temperature

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

![:scale 70%](images/map_expl_variables.svg)

Other variables drive variation in community dynamics 
Indirect effects of warming]

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.pull-left1[

.font180[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
]

.pull-right1[
 
![:scale 200%](images/logo.png)
]