Download A biodiversity-inspired approach to marine ecosystem modeling

A biodiversity-inspired approach to
marine ecosystem modelling
Jorn Bruggeman
Dept. of Theoretical Biology
Vrije Universiteit Amsterdam
Intro: it used to be so simple…
NO3-
NH4+
nitrogen
Le Quére et al. (2005):
10 plankton types
assimilation
phytoplankton
DON
death
labile
zooplankton
death
detritus
stable
Layout
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Theory: modeling biodiversity
Test case 1: the phytoplankton community
Intermezzo: a simple approximation
Test case 2: mixotrophy, phytoplankton and bacteria
Conclusion and outlook
Modeling biodiversity: step 1
The “omnipotent” population
biomass
N2 fixation
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Standardization: one model to describe any species
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Dynamic Energy Budget theory (Kooijman 2000)
Species differ in allocation to metabolic strategies
Allocation parameters: traits
Modeling biodiversity: step 2
Continuity in traits
Phototrophs and heterotrophs: a section through diversity
bact 1
heterotrophy
bact 3
?
bact 2
?
?
mix 1
mix 2
mix 3
mix 4
?
phyt 1
?
phyt 2
?
phyt 3
phototrophy
phyt 2
Modeling biodiversity: step 3
“Everything is everywhere; the environment selects”
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Every possible species present at all times
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The environment changes
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implementation: continuous immigration of trace amounts of all species
similar to: constant variance of trait distribution (Wirtz & Eckhardt 1996)
external forcing: periodicity of light, mixing, …
ecosystem dynamics: depletion of nutrients, …
Changing environment drives succession
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niche presence = time- and space-dependent
trait value combinations define species & niche
trait distribution will change in space and time
Test case 1: phytoplankton diversity
Trait 1: investment in light harvesting
light harvesting
+
+
maintenance
structural biomass
nutrient
+
+
nutrient harvesting
Trait 2: investment in nutrient harvesting
Physical setting
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General Ocean Turbulence Model (GOTM)
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1D water column
depth- and time-dependent turbulent diffusivity, k-ε turbulence model
Scenario: Bermuda Atlantic Time-series Study (BATS)
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surface forcing from ERA-40 dataset
initial state: observed depth profiles temperature/salinity
Result: trait distribution characteristics
Intermezzo: simpler trait distributions
1.
Before: “brute-force”
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2.
2 traits  25 x 25 grid = 625 ‘species’ state variables
flexible: any distribution shape possible, e.g. multimodality
high computational cost
Now: simplify via assumptions on distribution shape
characterize trait distribution by moments: mean, (co)variance, …
2. express higher moments in terms of first moments = moment closure
3. evolve first moments
E.g. 2 traits  2 x (mean, variance) + covariance = 5 state variables
1.
New state variables
variance of light harvesting investment
mean light harvesting investment
nitrogen
biomass
covariance of investments
mean nutrient harvesting investment
variance of nutrient harvesting investment
Quality of approximation
variable
deviation (%)
biomass
1.2 ± 1.9
mean light harvesting
mean nutrient harvesting
5.1 ± 4.0
8.3 ± 6.7
variance light harvesting
variance nutrient harvesting
covariance light & nutrient harv.
11.3 ± 7.7
12.7 ± 9.2
7.1 ± 5.9
Test case 2: mixotrophy
Trait 1: investment in light harvesting
nutrient
maintenance
+
light harvesting
nutrient
structural biomass
+
+
organic matter harvesting
organic matter
+
Trait 2: investment in organic matter harvesting
death
organic matter
Result: mass variables
Result: autotrophy & heterotrophy
Result: generalists vs. specialists
Conclusion
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Phytoplankton + diversity
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Moment-based approximation
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Light-driven succession in space (shade flora)
Nutrient-driven succession in time (Margalef’s Mandala)
Multiple traits, potentially correlated
Formulated as tracers that advect and diffuse normally
Deviations of 1%, 6%, 12% for biomass, mean, variance, respectively
Mixotroph + biodiversity
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Spring bloom of autotrophs, and autumn bloom of mixotrophs
Mixotrophy near surface, pure autotrophy and heterotrophy in deep
Discussion: variance dynamics matter!
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Variance determines trait flexibility
Example: simulated phytoplankton size at NABE site
Where does diversity come from?
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Without external source of variance
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Quick fixes
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variance → 0
mean → constant
despite spatial & temporal heterogeneity
lateral input (assumes heterogenity in horizontal plane)
input from below (assumes high biodiversity in the deep)
constant variance
Long-term generic solution needed!
Outlook
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Short-term
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Upcoming: paper on phytoplankton diversity in 1D (L&O)
Study (co)variance of bivariate trait distributions in 0D
Write up mixotrophy in 1D
Long-term
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Traits for stoichiometry
Physiologically-structured population models (intraspecific and
interspecific variation in size)