Download Trait-based models for functional groups

Trait-based models for functional groups
Jorn Bruggeman
Theoretische biologie
Vrije Universiteit Amsterdam
Context: the project
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Title
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3 PhDs
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biology, physical oceanography, numerical mathematics
Aim:
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“Understanding the ‘organic carbon pump’ in meso-scale ocean
flows”
quantitative prediction of global organic carbon pump from 3D
models
My role:
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‘detailed’ biota modeling in 1D water column, parameterization
for 3D models
Issue: biological complexity
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Marine ecosystems are complex:
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Option: large, detailed models
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ERSEM: 46 state variables, >100 parameters
But:
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Many functional groups (phytoplankton, zooplankton,
bacteria)
Large species variety within functional groups
Few data  little information on biota parameters
Global 3D models need simple models (<10 state variables)
Alternatives?
Trait
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‘quantifiable, species-bound entity’
Here: trait = trade-off
Environment-dependent advantage …
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‘nutrient affinity’
‘light harvesting ability’
‘detritus consumption’
‘predation’
… and environment-independent cost
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increase in maintenance cost
increase in cost for growth
Trait-based population model
nutrient
nutrient uptake
+
structural biomass
+
maintenance
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Marr-Pirt based (food uptake, maintenance, growth)
Trait implementation:
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‘trait biomass’, fixed fraction κ > 0 of ‘structural biomass’
benefit: substrate availability ~ trait biomass
cost in maintenance/growth: sum of cost for structural- and trait
biomass
Dynamic behavior
1 trait, 1 substrate, closed system


dM V
1
X

 j X , M ,V M V  j X , M ,T M T  with M T   M V
 j X , Am M V
dt
y X ,V   y X ,T 
X  K X MT

dM V
dM V
dX
X
  j X , Am M V
 j X , M ,V M V  j X ,M ,T M T   y X ,V  1
   y X ,T  1
dt
X  K X MT
dt
dt
symbol
unit
meaning
MV
biomass
structural biomass
MT
biomass
trait biomass
κ
-
trait value as fraction of structural biomass
X
substrate
substrate
KX
substrate
substrate half-saturation
jX,Am
substrate/time/biomass
maximum structure-specific substrate uptake
jX,M,V
substrate/time/biomass
maintenance for structural biomass
jX,M,T
substrate/time/biomass
maintenance for trait biomass
yX,V
substrate/biomass
substrate req. per structural biomass
yX,T
substrate/biomass
substrate req. per trait biomass
‘Natural’ limits on κ
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Extinction at small trait value:
dM V
 lim
 0 dt
 0
j X , Am M V
lim

Extinction at very high trait value:
dM V
 lim
  dt
 
lim

X
 j X , M ,V M V  j X , M ,T  M V
j
X  K X  MV
  X , M ,V M V
y X ,V   y X ,T
y X ,V
j X , Am M V
X
 j X , M ,V M V  j X , M ,T  M V
j
X  K X  MV
  X , M ,T M V
y X ,V   y X ,T
y X ,T
κ bounds easily calculated (roots of parabola)
Functional group
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One trait-based population = species
Functional group: collection of species
Assumption: infinite biodiversity
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within system, for any trait value, a species is present
Then: continuous trait distribution
For simulation: discretization of trait distribution
Setting: ‘chaotic’ water column
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1D water column
depth-dependent turbulent
diffusion, surface origin:
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Buoyancy (evaporation, cooling)
Shear (wind friction)
Chaotic surface forcing:
meteorological reports
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weather:
• light
• air temperature
• air pressure
• relative humidity
• wind speed
Light intensity
Wind speed
Temperature
Humidity
Closed for mass, open for
energy (surface)
z=0
turbulence
biota
turbulence
biota
turbulence
biota
turbulence
biota
z = -1
z = -2
z = -3
z = -4
Sample simulation
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Functional group: ‘phytoplankton’
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Start in end of winter:
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trait 1: ‘light affinity’
trait 2: ‘nutrient affinity’
light
light harvesting
+
structural biomass
nutrient
deep mixed layer
little primary productivity
uniform trait distribution, low biomass: all
‘species’ start with same low biomass
No predation or explicit mortality (but MarrPirt maintenance)
+
nutrient uptake
maintenance
Results 1
Forcing effect:
log(turbulent diffusion)
Biota response:
total biomass
Results 2
structural biomass
light harvesting biomass
nutrient harvesting biomass
Discussion
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Possible interpretation:
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Deep chlorophyll maximum (observed in ocean)
Succession: large species replaced by small species
(observed in ocean)
However:
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Long term behavior (50 years): dominance of species with
high trait values
Why? Trait biomass serves as reserve, needed in winter
Reflecting: key components
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Trait cost/benefit function
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Continuous trait distribution
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maintenance/growth cost linear in κ
substrate availability linear, assimilation hyperbole in κ
initial distribution?
Chaotic environment
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Long-term behavior (paradox of the plankton: competitive
exclusion?)
Plans
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Add explicit reserves to base model
Study 0D (long-term) behavior
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Other traits
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Competitive exclusion?
Direct measure of body size
Heterotrophy
Predation
Aggregation
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1 adapting population with flexible/constant trait value?
The end…
‘Natural’ limits on κ
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Trait value cannot be negative
Negative growth at high trait value:
j X , Am
X
X  K X  MV
 j X , M ,V   j X , M ,T  0
j X , Am X   X  K X  M V   j X , M ,V   j X ,M ,T 
X  K X  MV
0
 j X , Am X   X  K X M V   j X , M ,V   j X ,M ,T   0
 2 Xj X , M ,T    Xj X , M ,V  j X , M ,T K X M V  j X , Am X   j X , M ,V K X M V  0