First, I briefly review of selected recent studies which have improved our understanding of phytoplankton through the concept of optimality. Then, I present my most recent study of the combined effects of temperature and nutrient concentrations on the rates of nutrient uptake by phytoplankton. The point is that our assumptions about the fundamental dependencies affect our interpretation of the patterns observed in field experiments.

1. Optimality-based modeling of phytoplankton:
Implications for predictive modeling, interpreting data
and designing experiments
S. Lan Smith
EBCRP, RIGC, JAMSTEC, Yokohama, Japan
Constraints from
Fundamental Processes
Natural Selection
Adaptive Change
Apparent KNO3 (μmol L-1)
Optimally Adapted
Organisms
Physical Environment
S. Lan Smith Ocean Sciences Meeting, Feb. 22-26, 2010

2. Optimality
A result of Natural Selection,
subject to Constraints
Plankton are ideal subjects: Constraints from
short generation times Fundamental Processes
long evolutionary history
Therefore we expect them to Natural Selection
at least approach Optimality, Adaptive Change
which suggests that this concept
should be useful for interpreting
Optimally Adapted
& modeling their behavior. Organisms
Physical Environment
S. Lan Smith p. 2 Ocean Sciences Meeting, Feb. 22-26, 2010

3. Optimality-Based Ideas for Modeling Phytoplankton
Selected Examples Roughly in the Space of Fundamental Processes
Considered in Trade-offs
Light
Photoacclimation
Aquisition
Wirtz & Pahlow (MEPS, 2010)
Pahlow (MEPS, 2005)
Armstrong (DSRII, 2006)
Armstrong (L&O, 1999)
Bruggemann & Kooijman Wirtz (J. Biotech., 2002)
(L&O, 2007) Smith & Yamanaka (L&O, 2007)
Smith et al. (MEPS, 2009)
Nutrient
Uptake
Resistance Merico et al. (Ecol. Modelling, 2009)
to Predators
S. Lan Smith p. 3 Ocean Sciences Meeting, Feb. 22-26, 2010

4. Equations for Rate of Nutrient Uptake
Optimal Uptake (Pahlow, MEPS, 2005) Michaelis-Menten Equation
V0 S Vmax S
vOU = vMM =
Ks + S
A0 √
V0 + 2 V0 S + S
A0 Ks is called the
This is like a MM equation with: Half-Saturation “constant”.
But it varies with:
Nutrient Concentration
A0 √
Ks = V0 + 2 V0 S
A0 Species
Temperature
This predicts that Ks values (as fit to
the MM eqn.) should increase with Affinity & Ks are related:
nutrient concentration. Vmax
A=
Can this explain Ks
the observed pattern?
A is also called a
(Healey. Micrbial Ecol., 1980)
S. Lan Smith p. 4 Ocean Sciences Meeting, Feb. 22-26, 2010

5. What do short-term uptake experiments measure?
If phytoplankton do not have time to acclimate during expts.,
Optimal Uptake (OU) kinetics predicts (Smith et al. MEPS, 2009) for
apparent values of Michaelis-Menten “constants”:
Vmax = √A0Sa/V0 V0
This agrees with observations by
Kudela & Dugdale (DSRII 47, 2000),
1 + √A0Sa/V0
but it needs further testing.
V0 Sa
Ks = √
A0
This agrees with the observed pattern for KNO3
from ship-board expts. (Smith et al. 2009).
It’s all based on a physiological trade-off:
Sa is ambient nutrient
concentration, to which
phytoplankton were
pre-acclimated before
the short-term expts.
Low Nutrient Conc. High Nutrient Conc.
S. Lan Smith p. 5 Ocean Sciences Meeting, Feb. 22-26, 2010

6. Combined Effects of T & Nutrient Concentrations
Growth rates increase exponentially with T
(Eppley. Fish. Bull. 1972; Bissinger et al. L&O 2008).
Max. Uptake Rate, Vmax
For uptake or growth, Vmax is usually assumed
to be independent of nutrient concentration: Temperature
Michaelis-Menten (MM) kinetics.
However, Optimal Upake (OU) kinetics predicts
that Vmax (from short-term expts.) should MM
increase hyperbolically with nutrient conc. OU
(Smith et al. MEPS 2009). Nutrient Conc.
Nutrient Conc.
In the ocean, T and Nutrient Conc. are strongly
(negatively) correlated.
Vmax
Field expts. observe the combined (net) effects.
Assumptions about Uptake Kinetics impact
the interpretation of observations. Temperature
S. Lan Smith p. 6 Ocean Sciences Meeting, Feb. 22-26, 2010

7. Correlation of T & [NO3] in the Surface Ocean
Negative Correlation in General
(e.g., Silio-Calzada et al. Remote Sens. Environ.112, 2008)
Up-welling brings cold, nutrient-rich water
While phytoplankton grow, nutrients are depleted
& at the same time, water is warmed
Here for the data of
Harrison et al (L&O 1996)
*Thanks to G. W. Harrison for
providing the complete data set.
The regression line was
fitted for log [NO3] vs. log T
S. Lan Smith p. 7 Ocean Sciences Meeting, Feb. 22-26, 2010

8. Dependence of Uptake Rate, v, on T & Nutrients
for maximum uptake rate, Vmax as determined by short-term expts.
Assuming Multiplicative Effects
This widely-applied equation is
Michaelis-Menten (MM)
from Goldman and Carpenter
-Ea/RT [NO ] (Limnol. Oceanogr. 19, 1974).
v = Vmax e 3
Ks + [NO3]
Optimal Uptake (OU)
v = V0√[NO3]aA0/V0 e a
-E /RT [NO3]
1 + √[NO3]aA0/V0 √[NO3]aV0/A0 + [NO3]
This ratio determines how Vmax The apparent value of Ks
depends on ambient nutrient depends on ambient nutrient
concentration, [NO3]a. concentration, before
It can be determined separately sampling for expts.
from fits to data: Ks vs. [NO3]a. (Smith et al. MEPS, 2009).
S. Lan Smith p. 8 Ocean Sciences Meeting, Feb. 22-26, 2010

9. Dependence of Vmax on T & Nutrients
for maximum uptake rate, Vmax, as determined by short-term expts,
assuming Multiplicative Effects
Michaelis-Menten (MM) Optimal Uptake (OU)
-Ea/RT √[NO3]aA0/V0 V e-Ea/RT
Vmax = V0 e Vmax = 0
1 + √[NO3]aA0/V0
2 parameters were fitted by regression
to data sets for Vmax, [NO3]a & T,
for each eq., respectively. This ratio was determined
separately, from fits to
V0 potential maximum of Vmax
data for Ks vs. [NO3] as in
Ea Energy of Activation
Smith et al. (MEPS 2009).
S. Lan Smith p. 9 Ocean Sciences Meeting, Feb. 22-26, 2010

10. data of Harrison et al. (L&O 1996) MM OU
T- dependent model 100.0 N &T- dependent model
50
Fits of Arrhenius T- using fit of T vs. [NO3]
50.0
only T- dependent model
Chl-Specific Max. NO3 Uptake Rate (nmol h-1(μg)-1)
dependence, with the Q10 = 1.7 Q10 = 3.4
10
MM- and OU-based as- 5.0
10.0
5.0
sumptions, respectively,
for Vmax 1.0 data 1.0
0.5 fits with obs. 0.5
Data: Chl-specific max.
T & [NO3]
[NO3] uptake rate.
275 285 295 275 285 295
Inferred Q10 is nearly T(K)
100.0
twice as high with the 50
50.0
OU-based assumption.
10 10.0
Residual Square Error: 5.0 5.0
MM OU
9.3 8.5 1.0 T- dependent model 1.0
constant Vmax
0.5 0.5
Fitted values of Ea sig. N &T- dependent model
only N- dependent model
diff. from 0 for both. 10 1 0.1 0.01 0.001 10 1 0.1 0.01 0.001
[NO3] (μmol L-1)
S. Lan Smith p. 10 Ocean Sciences Meeting, Feb. 22-26, 2010

11. data of Kanda et al. (L&O 1985) MM OU
1.0 1.0
Q10 = 1.5 Q10 = 2.7
Chl-Specific Max. NO3 Uptake Rate (nmol h-1 (μg chl)-1 )
Fits of Arrhenius T- depen-
dence, with the MM- and 0.5 0.5
OU-based assumptions, re-
spectively, for Vmax
Data: Chl-specific max. N &T- dependent model
0.1 0.1
T- dependent model
[NO3] uptake rate. using fit of T vs. [NO3]
using fit of [NO3] vs. T
only T- dependent model
Inferred Q10 is nearly 285 290 295 300 285 290 295 300
T(K)
twice as high with the OU-
1.0 1.0
based assumption.
Residual Square Error: 0.5 0.5
MM OU
0.82 0.34
Fitted values of Ea sig. diff. data
0.1 fits with obs. 0.1 N &T- dependent model
from 0 for both. T & [NO3]
using fit of T vs. [NO3]
only N- dependent model
0.1 0.01 0.001 0.1 0.01 0.001
[NO3] (μmol L-1)
S. Lan Smith p. 11 Ocean Sciences Meeting, Feb. 22-26, 2010

12. Conclusions
Optimality-based ideas imply different Interpretations of Observations.
Specifically for Combined Effects of T & Concentration on Uptake
Estimated Q10’s are 2X greater assuming OU vs. MM kinetics.
Caveat: The observed Vmax were Chl-specific
Chl:N ratios tend to be greater under nutrient-rich conditions,
which should under-estimate N-specific rates at high N (low T)
Therefore my analysis probably over-estimates Q10’s
for both MM- and OU- kinetics
Yet even with biomass-specific Vmax, OU would yield higher Q10’s
because of the strong negative correlation of T & [NO3}
Significant Uncertainties remain about T-dependence & uptake kinetics
We need more controlled experiments &
field observations of biomass-specific rates
S. Lan Smith p. 12 Ocean Sciences Meeting, Feb. 22-26, 2010