1. Etude du modèle APECOSM en 0D
Calibration des paramètres, des classes de taille
O. Aumont, T. Gorgues
Réunion MACROES, Mai 2011

2. APECOSM: Several problems
The biomass was increasing with weight
In other words, the slope of the biomass spectrum was < 1, for high food levels
F = 0.2
F = 0.7
Biomass
Weight
Weight
The spectrum was strongly unstable
Biomass spectrum
F = 0.2
F = 0.7
Weight (kg)
Years
Weight (kg)
Years

3. Impact of the number of size classes : advection schemes
100, tvd
Slope :
20, upstream : -1.06
20, tvd : -1.13
100, upstream : -1.13
100, tvd :
100, upstream
20, tvd
20, upstream
Biomass spectrum
Weight
Use of a higher order advection scheme reduces the number of necessary size classes

4. Predation function Sigmoidal function similar to a gate function
𝑓 ρ = 1 1+exp α 1 ρ 1 −ρ × 1− 1 1+exp α 2 ρ 2 −ρ 
where r is the predator/prey size ratio
Gaussian function
𝑓 ρ =exp  − log ρ 3 −𝑚 2 2× σ 2   − log ρ 3 −𝑚 2 2× σ 2 
sigma
Gauss (3,2)
Gauss (3,1)

5. Impact of the predation function
Gaussian (m=3,s=2)
Sigma (r1=3, r2=100)
Biomass spectrum
Weight (kg)
year
m=3, s=2
m=3, s=1
m=2, s=2
m=2, s=1
Sigmoidal tends to be unstable which has been previously shown for similar predation selectivity
Decreasing the predator/prey ratio steepens the spectrum
Changing the width improves stability and changes the slope, especially for the small size classes
Slope :
-1.13, -1.15, -1.15, -1.16
Biomass spectrum

6. Introduction of some level of biodiversity
For one species :
𝑑𝑔𝑁 𝑑𝑚 =−μ𝑁
with
𝑔=α×ℎ× 𝑚 𝑛 −𝑘𝑚
If we assume that the community spectrum is as :
𝑁 𝑐 = κ 𝑐 𝑚 −λ
𝑁=κ 𝑚 𝑖𝑛𝑓 𝑚 −𝑛− α 𝑝 αℎ 𝑓 𝑚
Then, we have :
μ= α 𝑝 𝑚 1+𝑛−λ
For an infinity of species :
κ 𝑚 𝑖𝑛𝑓 = κ 𝑐 𝑚 𝑖𝑛𝑓 𝑛−3+ α 𝑝 αℎ
It can be shown that :
(Andersen and Beyer, 2006)

7. Impact of the power of the ingestion function
2/3
2/3
Biodiversité
Biodiversité
0.766
0.766
0.866
0.86
Slopes :
[-1.4, -0.88]
[-0.97, -1.5]
[-1.07, -1.5]
[-1.08, -1.5]
2/3
2/3
Biodiversité
Biodiversité
Biomass
0.766
0.766
0.8666
0.866
Biomass spectrum
Weight (kg)
Weight (kg)
The slope of the size spectrum is extremely sensitive to the power of the ingestion function
A realistic size spectrum should have at equilibrium a slope everywhere below -1
The slope is also sensitive to the mortality function especially for high biomass

8. Impact of the mortality
Quad, 10-18
Quad, 10-19
Linear
biodiversité
Biomass
0.66
Weight (kg)
Weight (kg)
Biomass spectrum
For standard monospecific DEB, the shape is sensitive to the mortality function
For biodiversified DEB, the slope is only weakly altered. The mean biomass is changed.
The choice of the mortality function is often arbitrary and difficult.
Quadratic functions are considered as a good choice, especially for stability reasons.

9. Impact of temperature, food abundance
Weight (kg)
Weight (kg)
Years
Impact of food abundance
Biomass spectrum
f=0.04
f=0.08
f=0.2
f=0.3
f=0.5
f=0.7
Biomass spectrum

10. PISCES en DEB
Gros retard, essentiellement lié à un retard sur le recrutement du post-doc
Le post-doc, Thomas Gorgues a été recruté au 1 mars 2011, soit près d'un an de retard
Avancement actuel :
Passage du zooplancton (micro, meso) en DEB réalisé
Tous les paramètres ont été choisis pour être très proches d'avant
Fonctions de prédation, Taux d'ingestion, maintenance, etc ...
Priorité des 6 prochains mois :
Passage du phytoplancton en DEB : Difficile car n'existe pas réellement dans la littérature