Presented at AMEMR 2008, Plymouth, UK

S. Lan Smith, FRCGC, JAMSTEC AMEMR Symposium, June, 2008

MULTI-ELEMENT ECOSYSTEM DYNAMICS IN THE SERIES IRON-ENRICHMENT EXPERIMENT: COMPARING OPTIMAL UPTAKE KINETICS TO MICHAELIS-MENTEN

S. Lan Smith1, Naoki Yoshie

2, Yasuhiro Yamanaka

1

1 Ecosystem Change Research Program, FRCGC, JAMSTEC, Yokohama, Japan2 Tohoku National Fisheries Res. Inst., Shiogama, Japan

OutlineIntroduction to SERIES Model IntroductionBrief Review of Nutrient Uptake kinetics Results & Conclusions

S. Lan Smith, FRCGC ECRP

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[Si(OH)4][NO3

-]

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(B)

(C)

Time (days)

Iron-fertilization Expt. in the NE subarctic Pacific

Takeda et al (2006, DSR II 53) modeled it using a modifiedversion of the NEMURO model

NEMURO assumes fixed ratios e.g., N:Si, C:N

They applied two Si:N ratios for diatoms Fe-replete: Si:N = 1 Fe-stress: Si:N = 3

Switching was based on

degree of Nutrient limitation

=> Added 2 parameters to NEMURO

SpecificGrowth

Rate (d−1)

NutrientDrawdown

(μmol L−1 d−1)

Si: NDrawdown

Ratio(mol: mol)

Fe Stress

SERIES Expt. Changes in Growth Rate & Si:N ratio


Iron Fertilization

Si:N Uptake Rates Decrease because of Faster DIN uptake Franck et al. (DSRII 47, 2000), Franck et al. (MEPS 252, 2003)

Iron Limitation

Even Moderate Iron Stress can Increase Si:N Uptake Ratio, e.g., in ship-board expts., Southern Ocean: Si:N uptake increased for DFe < 0.5 nM, even though KsFe < 0.2 nM Franck et al. (DSRII 47, 2000)

in SERIES

Around the transition from Iron-replete to Iron-limiting, BSi-specific Si Uptake Rate increased & Si:N Uptake Ratio increased, but NOT because of a decrease in DIN uptake, as in bottle expts. Boyd et al. (L&O 50, 2005)

Si:N Uptake ratios and Iron Fertilization

S. Lan Smith, FRCGC, JAMSTEC June, 2008

Detr. DOM

ZP

ZLZS

PS PL

DSiFeDINUptake

Excretion

Grazing

Sloppy Feeding

Decay/remineralization

Mortality

Egestion

PS = non-diatoms N quota only

PL = diatoms N, Fe & Si quotas

ZS, ZL & ZP fixed C:N, Fe:N ratios only N biomass calc'd N-based growth eff.

Similar to the model of Smithet al. J. Mar. Sys. 64, 2007

Variable Composition Ecosystem Model: QeNEMURO


µ

Q

q0i

0

Growth Rate, µ = µinf L min (1 − q0i )

i

Qi

Qi is cell quota of nutrient i for diatoms: i = N, Si, FeParameters: µinf = Growth Rate at Infinite Cell Quota q0i = minimum or "subsistence" cell quota for nutrient i

Light Limitation: L = (1 − e−αI / µinf )

α depends on Fe: α = α0 (1 − q0Fe )

QFe

i.e., iron limitation reduces α, similar to Chai et al (GBC 21, 2007), based on iron-fertilization expts. (Lindley et al, DSRII 42, 1995; Lindley and Barber, DSRII 45, 1998).

Nutrient Limitation: Droop's Quota model + Fe-limited α


Fig. 3A from Takeda et al (DSRII 53, 2006)

0 5 10 15 20 25 Time (Days)

A fixed time-series of dissolved iron was applied, as fit to the data by Takeda et al (2005).

Unknown Losses of Fe(e.g., scavenging & sinking)

=>

This is preferable toa prognostic equation for iron.

Modeling Dissolved Iron


1V(S) = [ (As S)−1 + (Vmax)−1 ]

More generalReduces to MM as a special case

Affinity-based Equation (Aksnes & Egge, MEPS, 1991)

Optimal Uptake (OU) Equation (Pahlow, MEPS, 2005)

Uptake Sites more sites => Greater Affinity, A (lower Ks)Internal Enzymes more enzymes => Greater Vmax

Both are mostly protein& containlots of N.

US

Michaelis-Menten (MM) Equation

Uptake Rate, U(S) = [ Ks + S ]Vmax S

Rate Expressions for Nutrient Uptake

fA = fractional allocation of internal N: A = A0 fA Vmax= V0 (1 − fA)

Acclimation

NutrientIons

Ion Channels= Uptake Sites

Cell

Internal Enzymes

Low Nutrient Conc. High Nutrient Conc.


Assume a fixed total amount of internal N for Uptake Hardware

Phytoplankton maximize uptake of the growth-limiting nutrient, without reference to concentrations of non-limiting nutrients.

They allocate N for uptake hardware in the same proportion for all nutrients based only on the concentration of the growth-limiting nutrient.

Low Nutrient Concentration High Nutrient Concentration

Many uptake sites, few enzymes Few uptake sites, many enzymes

for twonutrients, & ,each withits own set ofuptake sites& enzymes

Cell

EnzymesNutrientIons

Uptake SitesCell

Essence of the SPONGE: Dynamic Physiology for Efficient Nutrient Uptake

S. Lan Smith, ECRP, FRCGC AMEMR, June, 2008

Simple Phytoplankton Optimal Nutrient Gathering Equations (SPONGE)

Optimize only for Limiting nutrient, L with conc. SL Pahlow's single-nutrient Optimal Uptake Equations:

VLim = 1

fA = 1

[(1−fA)V0, L ]−1 + [fAA0, LSL]

−1 (A0, LSL)1/2 + 1 V0, L

for any Non-Limiting Nutrient, n with conc. Sn

=> Sub-optimal uptake of Non-limiting nutrients

Vnon= 1 fA = same as above

[(1−fA)V0, n

]−1 + [fAA0, nSn]−1

NOTE: Limiting Nutrient is determined by the Quota model, NOT directly by uptake parameters.

Vnon = f (Sn, SL)


Reducing the SPONGE to MM Kinetics

for Limiting nutrient, L with conc. SL Pahlow's single-nutrient Optimal Uptake Equations:

VLim = 1

fA = 1

[(1−fA)V0, L ]−1 + [fAA0, LSL]

−1 (A0, LSL)1/2 + 1 V0, L

for any Non-Limiting Nutrient, n with conc. Sn

Vnon= 1 fA = same as above

[(1−fA)V0, n

]−1 + [fAA0, nSn]−1

Vnon = f (Sn, SL)

Set fA = constant

(NO Acclimation)

Affinity-based kineticswith constant params.is the same as MM. (Aksnes & Egge, 1991)


1. Two versions of the model: SPONGE & MM uptake kinetics Fit each to all data INSIDE Iron-fertilized patch: 2. Compare fits & modeled material flows, composition

Growth Rate (at infinite cell quotas) 1Nutrient Uptake Rate Parameters 9Grazing Rate (Zoo grazing diatoms) 1

total no. 10

Fitting Method

Parameters Varied (determined by fitting)chosen iteratively, based on Assimilations & Sensitivity Analyses

Markov Chain Monte Carlo (MCMC)as applied by Smith et al. (J. Mar. Sys. 64, 2007), Smith and Yamanaka (L&O 54, 2007; Ecol. Model., 2007), Hargreaves and Annan (Climate Dynamics 19, 2002)

+ Penalty (added to cost function) for Unrealistic N:C cell quotas > 0.25


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Nitrate

NH4

Chl

SiOH4

µM

µM

µg/L

Fits are verysimilar.

Slightdifferencesfor Growth Rates.

With SPONGE, sudden changeswhen limitingnutrient switches.

Two versions of the model, identical except for uptake kinetics:

The model is 0-D (Mixed-layer only).

Vertical bars are Std. Deviationsas assumed for weights in the fitting.

Data areassumed to be averages over the mixed-layer.

MM version SPONGE version best costs: 44.7 44.1

Comparing Best-fits to IN-Patch Data

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Specific Growth Rate of diatoms

0 10 20Time (days)


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Diatoms as a fractionof total phytoplankton (N)

Growth Rate & Si:N drawdown ratio

Neither version of the model can reproduce the change in Growth Rate.

Both versions reproduce the steep change in Si:N, through changing the proportion of diatoms. An NPZD model (only diatoms) could NOT.

Steep, Synchronous Changes

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(day

-1)

Specific Growth Rate

Si:N

(m

ol:m

ol)

N FeLimitingNutrient

Data for drawdown ratio from Takeda et al (1996)were corrected for Patch dilution, but model was not.

MM version SPONGE version



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Time (Days)5 15 　 25Switch from N- to Fe- limitation in models:

MM: day 16-17 SPONGE: day 12-13 Boyd et al. (L&O 50, 2005) estimated day 12 from Observations

mol

(m

ol B

Si d

)−1

BSi-Specific Si Uptake Rate

SPONGE yields an increase at the transition to Fe-limiation. MM kinetics predicts a decrease.

Both models overestimate the observed rates, but SPONGE agrees with the trend.

Time Means of modeled rates:

Obs. from Boyd et al. (L&O 50, 2005)


Increase in Si Uptake Rate at onset of Iron Limitation



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Compared to Michaelis-Menten, SPONGE takes up growth-limiting nutrient faster non-limiting nutrients slower

Uptake rates of ALL nutrients depend on the conc. of growth-limiting nutrient.

Si uptake rates change sharply, even though it never becomes growth-limiting.

Switch from N- to Fe- limitation in models: MM: day 16-17 SPONGE: day 12-13 Boyd et al. (L&O 50, 2005) estimated day 12 from Observations

mol

(m

ol C

d)−1

µmol

(m

ol C

d)−1

Si

N

Fe


C-specific Rates of Nutrient Uptake (per mol C biomass)



MM kinetics predicts a much higher peak Fe : C ratio.

SPONGE suppresses uptake of non-limiting nutrients. (Smith & Yamanaka, L&O 52, 2007)

Differences in N : C ratio of diatoms cause differences in Zooplankton biomass: food quality effect Mitra et al. (L&O 52, 2007)

Grazing is based on C biomassof prey as suggested by Mitra et al. (L&O 52, 2007)

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µmol

(m

ol)−1

µm

ol (

mol

)−1

nm

ol (

mol

)−1Si

:C

N

:C

Fe:

C


Modeled Cell Quotas of Nutrients for Diatoms


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0.00.010.020.030.04


µmol

N L

−1

µmol

N L

−1

µm

ol N

L−1

Great Differences in Small and Large Zoo. ZL are the main grazers of diatoms. ZP also graze diatoms.

Results from different N : C quotas of diatomswith SPONGE vs. OU kinetics.

ZS

ZL

ZP


Modeled Biomass of Zooplankton


Conclusions

The model reproduces the steep change in Si:N drawdown ratio mostly through changing the proportion of diatoms. using either MM or SPONGE utpake kinetics, even without an increase in Si:N uptake ratio (MM version). Takada et al (2006) did say this "floristic shift could not be ruled out".

SPONGE yields different dynamics than MM: Sharp changes in uptake rates when the limiting nutrient changes,

Si uptake Rate increases, which agrees with observations, (whereas MM does not). Sudden, yet small, changes in Growth Rates. Large Differences in phy. cell quotas & Zooplankton Biomass.

Yet neither version of the model can reproduce the steep change in Growth Rate.

A Simpler NPZDD-quota model could not, either. So, what is missing ? ... other energetic requirments (e.g., for Chl) ?


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15

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Steep Changeswith SPONGEbecause ofoptimization with respect togrowth-limitingnutrient,

which causesteep changes in Uptake Ratio.

Fe

N

Si

µm

ol L

−1 d

−1

10−1

2 m

ol L

−1 d

−1MM version SPONGE version

Modeled Rates of Nutrient Uptake by Diatoms (per L water)

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Si : N Uptake Ratioof diatoms

0 10 20 Time (days)

(mol

:mol

)

Presented at AMEMR 2008, Plymouth, UK

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