6. Cooling of the Ocean Plates (Lithosphere) William Wilcock
Lan\'s Presentation at the Ocean Sciences Meeting 2010
description
Transcript of Lan\'s Presentation at the Ocean Sciences Meeting 2010
Ocean Sciences Meeting, Feb. 22-26, 2010 S. Lan Smith
Apparent KN
O3 (μm
ol L-1)
Optimality-based modeling of phytoplankton: Implications for predictive modeling, interpreting data
and designing experiments S. Lan Smith
EBCRP, RIGC, JAMSTEC, Yokohama, Japan
Constraints fromFundamental Processes
Physical Environment
Optimally AdaptedOrganisms
Adaptive Change
Natural Selection
Ocean Sciences Meeting, Feb. 22-26, 2010 S. Lan Smith p. 2
A result of Natural Selection, subject to Constraints
Plankton are ideal subjects: short generation times long evolutionary history
Therefore we expect them to at least approach Optimality, which suggests that this conceptshould be useful for interpreting & modeling their behavior.
Optimality
Constraints fromFundamental Processes
Physical Environment
Optimally AdaptedOrganisms
Adaptive Change
Natural Selection
Ocean Sciences Meeting, Feb. 22-26, 2010 S. Lan Smith p. 3
Optimality-Based Ideas for Modeling PhytoplanktonRoughly in the Space of Fundamental Processes Considered in Trade-offs
Nutrient Uptake
Light Aquisition
Resistance to Predators
Photoacclimation
Wirtz & Pahlow (MEPS, 2010)
Pahlow (MEPS, 2005) Armstrong (DSRII, 2006)
Armstrong (L&O, 1999)
Wirtz (J. Biotech., 2002)Smith & Yamanaka (L&O, 2007)Smith et al. (MEPS, 2009)
Merico et al. (Ecol. Modelling, 2009)
Selected Examples
Bruggemann & Kooijman (L&O, 2007)
Ocean Sciences Meeting, Feb. 22-26, 2010 S. Lan Smith p. 4
Michaelis-Menten Equation
vMM = Vmax S Ks + S
Ks is called the Half-Saturation “constant”.
But it varies with: Nutrient Concentration Species Temperature
Affinity & Ks are related:
A = Vmax Ks
A is also called a (Healey. Micrbial Ecol., 1980)
Equations for Rate of Nutrient UptakeOptimal Uptake (Pahlow, MEPS, 2005)
vOU = V0 S V0 + 2√V0 S + S A0 A0
This is like a MM equation with:
Ks = V0 + 2√V0 S A0 A0
This predicts that Ks values (as fit to the MM eqn.) should increase with nutrient concentration.
Can this explain the observed pattern?
Ocean Sciences Meeting, Feb. 22-26, 2010 S. Lan Smith p. 5Low Nutrient Conc. High Nutrient Conc.
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
1 + √A0Sa/V0
Ks = √V0 Sa A0
It’s all based on a physiological trade-off:
This agrees with the observed pattern for KNO3 from ship-board expts. (Smith et al. 2009).
This agrees with observations by Kudela & Dugdale (DSRII 47, 2000), but it needs further testing.
What do short-term uptake experiments measure?
Sa is ambient nutrient concentration, to which phytoplankton were pre-acclimated before the short-term expts.
Ocean Sciences Meeting, Feb. 22-26, 2010 S. Lan Smith p. 6
Growth rates increase exponentially with T (Eppley. Fish. Bull. 1972; Bissinger et al. L&O 2008).
For uptake or growth, Vmax is usually assumed to be independent of nutrient concentration: Michaelis-Menten (MM) kinetics.
However, Optimal Upake (OU) kinetics predictsthat Vmax (from short-term expts.) should increase hyperbolically with nutrient conc. (Smith et al. MEPS 2009).
In the ocean, T and Nutrient Conc. are strongly (negatively) correlated.
Field expts. observe the combined (net) effects.
Assumptions about Uptake Kinetics impact the interpretation of observations.
Combined Effects of T & Nutrient Concentrations
V max
Nutrient Conc.
Temperature
Nutrient Conc.
Temperature
Max
. Upt
ake
Rat
e, V
max
MMOU
Ocean Sciences Meeting, Feb. 22-26, 2010 S. Lan Smith p. 7
Correlation of T & [NO3] in the Surface OceanNegative 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
Ocean Sciences Meeting, Feb. 22-26, 2010 S. Lan Smith p. 8
Dependence of Uptake Rate, v, on T & Nutrientsfor maximum uptake rate, Vmax as determined by short-term expts. Assuming Multiplicative Effects
Michaelis-Menten (MM)
v = Vmax e-Ea/RT
[NO3] Ks + [NO3]
Optimal Uptake (OU)
v = V0√[NO3]aA0/V0 e-Ea/RT [NO3] 1 + √[NO3]aA0/V0 √[NO3]aV0/A0 + [NO3]
This ratio determines how Vmaxdepends on ambient nutrient concentration, [NO3]a. It can be determined separately from fits to data: Ks vs. [NO3]a.
The apparent value of Ksdepends on ambient nutrientconcentration, before sampling for expts.(Smith et al. MEPS, 2009).
This widely-applied equation is from Goldman and Carpenter (Limnol. Oceanogr. 19, 1974).
Ocean Sciences Meeting, Feb. 22-26, 2010 S. Lan Smith p. 9
Dependence of Vmax on T & Nutrientsfor maximum uptake rate, Vmax, as determined by short-term expts, assuming Multiplicative Effects
Michaelis-Menten (MM) Optimal Uptake (OU)
Vmax = V0 e-Ea/RT Vmax = √[NO3]aA0/V0 V0 e-Ea/RT
1 + √[NO3]aA0/V0
2 parameters were fitted by regression to data sets for Vmax, [NO3]a & T, for each eq., respectively.
V0 potential maximum of Vmax
Ea Energy of Activation
This ratio was determined separately, from fits to data for Ks vs. [NO3] as in Smith et al. (MEPS 2009).
Ocean Sciences Meeting, Feb. 22-26, 2010 S. Lan Smith p. 10
Fits of Arrhenius T- dependence, with the MM- and OU-based as-sumptions, respectively, for Vmax
Data: Chl-specific max. [NO3] uptake rate.
Inferred Q10 is nearly twice as high with the OU-based assumption.
Residual Square Error: MM OU 9.3 8.5
Fitted values of Ea sig. diff. from 0 for both.
data of Harrison et al. (L&O 1996) MM OU
Chl
-Spe
cific
Max
. NO
3 Upt
ake
Rat
e (n
mol
h-1
(μg)
-1)
[NO3] (μmol L-1)
T- dependent model constant Vmax
T(K)
T- dependent modelusing fit of T vs. [NO3]
N &T- dependent model only N- dependent model
N &T- dependent model only T- dependent model
0.51.0
5.010.0
50.0100.0
10 1 0.1 0.01 0.001
275 285 295
0.51.0
5.010.0
50.0100.0
0.51.0
5.010
50
10 1 0.1 0.01 0.001
275 285 295
0.51.0
5.010
50
datafits with obs. T & [NO3]
Q10 = 1.7 Q10 = 3.4
Ocean Sciences Meeting, Feb. 22-26, 2010 S. Lan Smith p. 11
data of Kanda et al. (L&O 1985) MM OU
Fits of Arrhenius T- depen-dence, with the MM- and OU-based assumptions, re-spectively, for Vmax
Data: Chl-specific max. [NO3] uptake rate.
Inferred Q10 is nearly twice as high with the OU-based assumption.
Residual Square Error: MM OU 0.82 0.34
Fitted values of Ea sig. diff. from 0 for both.
[NO3] (μmol L-1)
T(K)
Chl
-Spe
cific
Max
. NO
3 Upt
ake
Rat
e (n
mol
h-1
(μg
chl)-1
) Q10 = 2.7
0.1 0.01 0.001
0.1
0.5
1.0
285 290 295 300
0.1
0.5
1.0
N &T- dependent model using fit of [NO3] vs. Tonly T- dependent model
N &T- dependent model using fit of T vs. [NO3] only N- dependent model
0.1
0.5
1.0
0.1 0.01 0.001
T- dependent modelusing fit of T vs. [NO3]
285 290 295 300
0.1
0.5
1.0Q10 = 1.5
datafits with obs. T & [NO3]
Ocean Sciences Meeting, Feb. 22-26, 2010 S. Lan Smith p. 12
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
Conclusions