# Lan\'s Presentation at the Ocean Sciences Meeting 2010

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### Transcript of Lan\'s Presentation at the Ocean Sciences Meeting 2010

- 1. Optimality-based modeling of phytoplankton: Implications for predictive modeling, interpreting data and designing experimentsS. Lan SmithEBCRP, RIGC, JAMSTEC, Yokohama, Japan Constraints from Fundamental ProcessesNatural SelectionAdaptive Change Apparent KNO3 (mol L-1)Optimally Adapted OrganismsPhysical Environment S. Lan Smith Ocean Sciences Meeting, Feb. 22-26, 2010

2. OptimalityA result of Natural Selection,subject to ConstraintsPlankton are ideal subjects:Constraints from short generation timesFundamental Processes long evolutionary historyTherefore we expect them to Natural Selectionat least approach Optimality, Adaptive Changewhich suggests that this conceptshould be useful for interpreting Optimally Adapted& modeling their behavior.OrganismsPhysical EnvironmentS. Lan Smithp. 2 Ocean Sciences Meeting, Feb. 22-26, 2010 3. Optimality-Based Ideas for Modeling PhytoplanktonSelected Examples Roughly in the Space of Fundamental ProcessesConsidered in Trade-offsLight PhotoacclimationAquisition 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 ResistanceMerico 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 EquationV0 SVmax SvOU = vMM = Ks + SA0V0 + 2 V0 S + SA0 Ks is called the This is like a MM equation with:Half-Saturation constant. But it varies with:Nutrient ConcentrationA0Ks = V0 + 2 V0 S A0 SpeciesTemperature This predicts that Ks values (as fit to the MM eqn.) should increase with Affinity & Ks are related: nutrient concentration.VmaxA= 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) forapparent values of Michaelis-Menten constants: Vmax = A0Sa/V0 V0This agrees with observations byKudela & Dugdale (DSRII 47, 2000), 1 + A0Sa/V0but it needs further testing. V0 SaKs =A0 This agrees with the observed pattern for KNO3 from ship-board expts. (Smith et al. 2009). Its all based on a physiological trade-off:Sa is ambient nutrientconcentration, to whichphytoplankton werepre-acclimated beforethe short-term expts. LowNutrientConc.HighNutrientConc. S. Lan Smith p. 5 Ocean Sciences Meeting, Feb. 22-26, 2010 6. Combined Effects of T & Nutrient ConcentrationsGrowth rates increase exponentially with T(Eppley. Fish. Bull. 1972; Bissinger et al. L&O 2008). Max. Uptake Rate, VmaxFor uptake or growth, Vmax is usually assumedto be independent of nutrient concentration:Temperature Michaelis-Menten (MM) kinetics.However, Optimal Upake (OU) kinetics predictsthat Vmax (from short-term expts.) shouldMMincrease 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.VmaxField expts. observe the combined (net) effects.Assumptions about Uptake Kinetics impactthe interpretation of observations. Temperature S. Lan Smithp. 6 Ocean Sciences Meeting, Feb. 22-26, 2010 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 waterWhile phytoplankton grow, nutrients are depleted & at the same time, water is warmedHere for the data ofHarrison et al (L&O 1996)*Thanks to G. W. Harrison forproviding the complete data set.The regression line wasfitted for log [NO3] vs. log T S. Lan Smith p. 7Ocean Sciences Meeting, Feb. 22-26, 2010 8. Dependence of Uptake Rate, v, on T & Nutrientsfor maximum uptake rate, Vmax as determined by short-term expts.Assuming Multiplicative Effects This widely-applied equation isMichaelis-Menten (MM) from Goldman and Carpenter -Ea/RT [NO ](Limnol. Oceanogr. 19, 1974).v = Vmax e3 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 Ksdepends on ambient nutrientdepends on ambient nutrientconcentration, [NO3]a. concentration, beforeIt can be determined separatelysampling for expts.from fits to data: Ks vs. [NO3]a.(Smith et al. MEPS, 2009). S. Lan Smithp. 8Ocean 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 EffectsMichaelis-Menten (MM)Optimal Uptake (OU) -Ea/RT[NO3]aA0/V0 V e-Ea/RT Vmax = V0 eVmax = 01 + [NO3]aA0/V02 parameters were fitted by regression to data sets for Vmax, [NO3]a & T, for each eq., respectively.This ratio was determinedseparately, from fits to V0 potential maximum of Vmaxdata for Ks vs. [NO3] as in Ea Energy of ActivationSmith et al. (MEPS 2009). S. Lan Smithp. 9Ocean 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 model50Fits of Arrhenius T- using fit of T vs. [NO3] 50.0only T- dependent model Chl-Specific Max. NO3 Uptake Rate (nmol h-1(g)-1)dependence, with theQ10 = 1.7Q10 = 3.4 10MM- and OU-based as-5.0 10.05.0sumptions, respectively,for Vmax 1.0 data 1.0 0.5 fits with obs. 0.5Data: Chl-specific max. T & [NO3][NO3] uptake rate.275 285 295275 285295 Inferred Q10 is nearlyT(K)100.0twice as high with the 50 50.0OU-based assumption. 1010.0Residual Square Error:5.0 5.0 MMOU 9.3 8.51.0T- dependent model 1.0 constant Vmax0.5 0.5Fitted values of Ea sig.N &T- dependent modelonly N- dependent modeldiff. from 0 for both.10 1 0.10.010.001 101 0.1 0.01 0.001[NO3] (mol L-1) S. Lan Smithp. 10Ocean Sciences Meeting, Feb. 22-26, 2010 11. data of Kanda et al. (L&O 1985)MMOU 1.0 1.0Q10 = 1.5Q10 = 2.7Chl-Specific Max. NO3 Uptake Rate (nmol h-1 (g chl)-1 ) Fits of Arrhenius T- depen- dence, with the MM- and 0.5 0.5OU-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 modelInferred Q10 is nearly285 290295 300285 290295300T(K) twice as high with the OU- 1.0 1.0 based assumption. Residual Square Error:0.5 0.5 MMOU0.820.34 Fitted values of Ea sig. diff. data 0.1fits with obs. 0.1 N &T- dependent model from 0 for both. T & [NO3] using fit of T vs. [NO3] only N- dependent model 0.10.01 0.001 0.1 0.01 0.001[NO3] (mol L-1) S. Lan Smith p. 11 Ocean Sciences Meeting, Feb. 22-26, 2010 12. ConclusionsOptimality-based ideas imply different Interpretations of Observations. Specifically for Combined Effects of T & Concentration on UptakeEstimated Q10s 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 Q10sfor both MM- and OU- kineticsYet even with biomass-specific Vmax, OU would yield higher Q10sbecause 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 ratesS. Lan Smith p. 12 Ocean Sciences Meeting, Feb. 22-26, 2010