1. Ocean Sciences Meeting 2012 Salt Lake City
Optimality-based modeling of plankton
for use in Earth-system modeling
S. Lan Smith1, Markus Pahlow2,
Agostino Merico3, Kai W. Wirtz4, Andreas Oschlies2
1 Japan Agency for Marine-Earth Science & Technology (JAMSTEC), Yokohama
2 Leibniz Institute of Marine Sciences at Kiel University (IFM-GEOMAR)
3 Leibniz Center for Tropical Marine Ecology (ZMT), Bremen
4 Helmholtz Center for Materials & Coastal Research, Geesthacht
S. Lan Smith Feb. 23, 2012

2. Optimality-based models of plankton
Assumptions
Natural Selection produces optimally adapted organisms
Fitness = Growth Rate Goal-oriented
Considerable success over the past decade
Recent Developments:
models of optimal foraging & Primary Production
Major Challenge
Dynamic models consistent with Evolutionarily Stable Strategy (ESS)
ESS formulated in terms of steady state (John Maynard Smith)
i.e., how to describe short-term dynamics, e.g., acclimation,
consistent with evolutionary adaptation of the very ability to acclimate.
from the review by Smith et al. (Limnology & Oceanography 56, 2011)
S. Lan Smith p. 2 Feb. 23, 2012

3. Acclimation vs. Adaptation
Acclimation
short-term changes
e.g., seasonal change of a dog’s coat of hair
Adaptation
long-term changes
evolution (genetic changes in a species)
species succession (changes in community composition)
The same approaches can be used to model both.
e.g., Wirtz and Eckhardt (Ecol. Mod., 1996), Merico et al. (Ecol. Mod., 2009)
S. Lan Smith p. 3 Feb. 23, 2012

4. Optimality at different levels of organization
Maximal net growth rate
Quantity Maximal specific growth rate
being
optimized
Maximal uptake rate
nutrients zooplankton light nutrient
N uptake uptake
uptake defense
N used N used
trade-off iron iron
for other for uptake
used for light used for N
harvesting assimilation enzymes sites
phytoplankton (max. rate) (affinity)
phytoplankton
Community dynamics, Autotrophic growth, Nutrient uptake,
e.g., grazers and phytoplankton e.g., iron-light-nitrogen e.g., Optimal Uptake
as in Merico et al. (2009) colimitation as in Armstrong (1999) as in Smith et al. (2009)
(Smith et al. L&O 2011, fig. 2)
S. Lan Smith p. 4 Feb. 23, 2012

5. Trade-offs as ‘Hyper-Parameterizations’
‘Hyper-Parameters’ in hierarchical Bayesian modeling
specify prior distributions of model parameters
(e.g., Gelman et al. Bayesian Data Analysis, 2nd edition, 2004)
Trade-offs specify how the shapes of functional relationships
may change, rather than fixing their shapes.
Optimal Uptake kinetics
Trade-off Adaptive Response
1.0
Uptake
0.8
Rate
0.6
0.4
Vmax
0.2
0.0
0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000
NO3 in incubation expts.
KNO3
0
log KNO3
-1
-2
n = 61 data pts.
-3
-2.5 -1.0 0.0
Smith et al. (MEPS 2009) log NO3 (in seawater)
S. Lan Smith p. 5 Feb. 23, 2012

6. Shape-shifting of the Growth vs. Irradiance curve
Optimal Resource Allocation Flexible Response
subject to Trade-offs
Max. Growth Rate
CO 2
C-uptake loss
Pigments Rubisco
CHLa Carot
fθ fR
POC PON Q0
Q
1-f θ-f R
Growth Rate
?
loss
N-uptake
DIN
Wirtz & Pahlow (MEPS 2010) Light
S. Lan Smith p. 6 Feb. 23, 2012

7. New interpretations from optimality-based modeling
1. Instead of ‘Inhibition of NO3 uptake by NH4‘
-> co-limitation by Fe, light and nitrogen (Armstrong L&O 1999)
2. Instead of either multiplicative models or Liebig’s Law of the min.
-> co-limitation by N, P and light (Pahlow & Oschlies MEPS 2009)
3. Instead of fixed Droop-type quota equation
-> saturating response from optimization (Wirtz & Pahlow MEPS 2010)
4. Instead of Q10 ~ 2 for phytoplankton
-> Q10 ~ 3 for N uptake inferred from field obs. (Smith JGR 2011)
These have implications for ecology & Earth-System Modeling.
S. Lan Smith p. 7 Feb. 23, 2012

8. T sensitivity for phytoplankton
Common view: Bacteria are more T sensitivity than Phytoplankton.
Q10 ~ 2 to 3 (Pomeroy and Wiebe. Aquat. Microb. Ecol. 2001)
OU kinetics applied to field obs. implies: Q10 ~ 3 for nutrient uptake
(Smith. GRL 2010, JGR 2011), rather than Q10 ~ 2 (Eppley. 1972).
Standard Assumption: Degradation has greater T sensitivity than Production
CO2 CO2
Inorganic C Organic C Inorganic C Organic C
warming Less Uptake &
sinking & export Less Export sinking & export
However, if Production has the same T sensitivity as Degradation
CO2 CO2
Inorganic C Organic C Inorganic C Organic C
No Net Effect on
warming
sinking & export Uptake or Export sinking & export
S. Lan Smith p. 8 Feb. 23, 2012

9. Differences between species: Large-scale patterns of dominance
Litchman et al. (Ecology Letters 10, 2007)
“These trade-offs, arising from fundamental relations such as cellular scaling
laws and enzyme kinetics, define contrasting ecological strategies ... [which] can
explain the distribution patterns of major functional groups and size classes
along nutrient availability gradients.”
Applications in 3-D models (Follows et al. Science, 2007) & the MIT group.
Monteiro et al. (GBC, 2011)
‘environment selects’ for N2 fixers
But how to model more
detailed (finely resolved)
& realistic biodiversity?
& account for the
adaptive capacity of each
species?
S. Lan Smith p. 9 Feb. 23, 2012

10. ‘adaptive dynamics’: modelling how fast traits change
Trait x should change in proportion to its effect on fitness, F:
dx = d ∂F(x,E) Also allows modeling
x
dt ∂x the dist. of x, without
discretely resoving it.
dx: flexibility ~ diversity (trait distribution)
E: Environment (light, temperature, etc.)
For plankton F = Growth; dx/dt depends on E (Smith et al. L&O, 2011)
Acclimation Rates depend on:
1. possible range of trait values (adaptive capacity),
2. environmental variability
3. current distribution of trait values
Remaining Challenge: modelled diversity tends to collapse
immigration required to maintain diversity (Bruggeman & Kooijman L&O 2007)
‘Adaptive Dynamics’: evolutionary changes
McGill and Brown (An. Rev. Ecol. Evol. Syst. 2007), Litchman et al. (PNAS 2009)
‘adaptive dynamics’: species succession, communities
Wirtz & Eckhardt (Ecol. Modell. 1996), Wirtz (J. Biotech. 2002), Abrams (J. Evol. Biol. 2005)
S. Lan Smith p. 10 Feb. 23, 2012

11. Different Postulates about the Nature of Life
1. Life is tough and flexible vs. 2. Life is fragile and inflexible
because organisms and so that any change in
species had to be so environmental conditions
in order to survive might cause Scary Disasters!
throughout billions of despite the fact that life
years of evolution (for evolved experiencing changes
bacteria & plankton). in climate & geography.
Pro: Pro:
Basis for more general understanding May identify real threats & risks.
New interpretations of obs. Many opportunities for
sensational papers (e.g., in Nature),
Con: which advance scientists’ careers.
Risk: may over-estimate the Con:
‘Adaptive Capacity of Life’,
which does have limits; Risk: loss of credibility,
i.e., may miss some real threats. if predicted Disasters do not occur.
Humans have driven some No basis for understanding or
species extinct. modeling ‘Adaptive Capacity of Life’.
S. Lan Smith p. 11 Feb. 23, 2012

12. Conclusions
Life is tough and flexible, to a non-neglible extent.
Earth-System Models should account for ‘Adaptive Capacity of Life’.
Optimality-based models are one means to do this
using trade-offs as ‘Hyper-Parameterizations’
to constrain adaptive responses.
We need observations to keep this realistic.
S. Lan Smith p. 12 Feb. 23, 2012