a simple size-based model of phytoplankton communities reveals size-scaling of phytoplankton growth...

AMEMR Symposium June 30, 2014S. Lan Smith

S. Lan Smith1,2, Markus Pahlow3, Chisato Yoshikawa4 + Agostino Merico5,6, Esteban Acevedo-Trejos5,6, Yoshikazu Sasai1,

Kosei Sasaoka7, Tetsuichi Fujiki1, and Kazuhiko Matsumoto8

1 Marine Ecosystem Dynamics Research Group, RCGC, JAMSTEC, Yokohama, Japan2 CREST, Japan Science and Technology Agency, Tokyo, Japan

3 GEOMAR, Helmholtz Centre for Ocean Research, Kiel, Germany 4 Institute of Biogeosciences, JAMSTEC

5,6 Systems Ecology, ZMT and Jacobs University, Bremen, Germany 7 Global Chemical and Physical Oceanography Group, JAMSTEC

8 Development of Environmental Geochemical Cycle Research, JAMSTEC

A simple size-based model of phytoplankton communities

reveals size-scaling of phytoplankton growth traits

in terms of observed allometries Combining traits & trade-offs (Smith et al. JPR Horizons 2014)

Sunlight

Nutrient Supply

αVmax

μmax

chl

α

Vmax

μmax

chl

AMEMR Symposium June 30, 2014S. Lan Smith p. 2

‘Leaving mis-leading legacies behind in plankton ecosystem modelling’ Smith, Merico, Wirtz and Pahlow (J. Plankton Res. 2014)

Typical small cell adapted to high-light, low-nutrients

Typical large cell adapted to low-light, high-nutrients

Overall Approach to Modelling Adaptive Response

Combine Traits and Trade-offs

We encourage combining traits with trade-offs based on fundamental principles, more exploratory modelling studies.


Combining Traits with a Trade-off for Nutrient Uptake Recent theoretical models of nutrient uptake kinetics (Aksnes & Cao, MEPS 2011; Fiksen et. al. L&O 2013) account explicitly for combined effects of: 1. phytoplankton cell size 2. extra-celleluar diffusion * but not for adaptive response

Optimal Uptake kinetics (Smith et al. MEPS 2009) accounts for adaptive response

* but not for cell size, nor diffusion log NO3 (in seawater)

log

K NO

3

-2.5 -1.0 0.0

-3

-2

-1

0

n = 61 data pts.

0 200 400 600 800 1000

0.0

0.2

0.4

0.6

0.8

1.0

0 200 400 600 800 1000 0 200 400 600 800 1000

Upt

ake

Rat

e

NO3 in incubation expts.

Adaptive Response

Smith et al. (MEPS 2009)

Trade-off

V max

α

�L�o�w��N�u�t�r�i�e�n�t��C�o�n�c�.��H�i�g�h��N�u�t�r�i�e�n�t��C�o�n�c�. New model explains: 1. overall pattern observed by ship-board expts., 2. variability, in terms of size.

data from ship-board expts.Collos et al. (2005)Harrison et al. (1996)McCarthy et al. (1999)

r = 100 μm

r = 20 μm

r = 2 μm

r = 0.2 μm

r = 100 μm

r = 20 μm

r = 2 μm

r = 0.2 μm

New modelSize-only model

K NO

3 (m

icro

mol

L-1

)

NO3 (micromol L-1)

0.001

0.01

0.1

1

10

0.001 0.01 0.1 1.0 10

�N�u�t�r�i�e�n�t��u�p�t�a�k�e��k�i�n�e�t�i�c�s��b�a�s�e�d��o�n��c�e�l�l��s�i�z�e��a�n�d��t�r�a�d�e�-�o�f�f�

Smith et al. MEPS (in press)

These concepts are indeed compatible!


�B�a�l�a�n�c�e�d� �G�r�o�w�t�h� �A�s�s�u�m�p�t�i�o�n� �(�B�u�r�m�a�s�t�e�r� �A�m�.� �N�a�t�.� �1�9�7�9�)

V� �=� μQ

�A� �s�i�n�g�l�e�,� �e�x�p�l�i�c�i�t� �e�q�u�a�t�i�o�n�:� μ� �=� �f�(�N�,� �I�)

�i�n�c�l�u�d�i�n�g� �a�d�a�p�t�i�v�e� �r�e�s�p�o�n�s�e�* �*�a�s�s�u�m�i�n�g� �i�n�s�t�a�n�t�a�n�e�o�u�s� �o�p�t�i�m�a�l� � � �r�e�s�o�u�r�c�e� �a�l�l�o�c�a�t�i�o�n

Vmax

α

�O�p�t�i�m�a�l� �U�p�t�a�k�e� �k�i�n�e�t�i�c�s� �(�P�a�h�l�o�w�.� �M�E�P�S�,� �2�0�0�5�;� �S�m�i�t�h� �e�t� �a�l�.� �M�E�P�S�,� �2�0�0�9�)�a�f�f�i�n�i�t�y� �(α�)� � �v�s�.� �m�a�x�.� �u�p�t�a�k�e� �r�a�t�e� �(Vmax�)

� � ∝ fA� � � � � �v�s�.� � � � � � � � � � � � � � � � � � � � ∝ �(1 − fA�)� � � � � � � � � � �.

1 fA 0

�O�p�t�i�m�a�l� �G�r�o�w�t�h� �m�o�d�e�l� �(�P�a�h�l�o�w� �a�n�d� �O�s�c�h�l�i�e�s�.� �M�E�P�S�,� �2�0�1�3�)

� � � � �N� �u�p�t�a�k�e� �(V�^ �)� � �v�s�.� � � � � �C� �f�i�x�a�t�i�o�n� �(μ�^ �I�)� � � � � � � � � � � � � ∝� fV ∝� �(�1� −� �

Qs� − fV�)� � QN

0.5 fV 0

New Simple, Adaptive Phytoplankton model: AdaPFT

Just 1 diff. eqn. for dynamics of C biomass.

+ can easliy calc. chl:C & N:C


Non-Adaptive vs. Adaptive models

How do changing env. conditions impact:

Overal ecosystem response to, e.g., climate change or human nutrient inputs?

Realized (modelled) biodiversity?


Different Response: Standard PFT vs. Adaptive PFT

both shown for l = 0 (ESD = 1 mm)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 10 20 30 40 50

Monod curves at different Light levels

μ (d

-1)

N (mol m-3)

AdaPFTPFT

I = 100

I = 50

I = 10

I = 1E m-2 d-1 0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 10 20 30 40 50

N = 100N = 10

N = 1

N = 0.1

mol m-3

P-I curves at different Nutrient levels

μ (d

-1)

I (E m-2 d-1)

Parameters for the PFT model were tuned to match the AdaPFT model at high I and high N.

AdaPFT: Inter-dependentm = S(I)Z(I,N)

PFT: Independent Responsem = S(I)f(N)

�O�p�t�i�m�a�l� �G�r�o�w�t�h� �t�r�a�d�e�-�o�f�f�(�P�a�h�l�o�w� �a�n�d� �O�s�c�h�l�i�e�s� �2�0�1�3�)

�r�e�s�o�u�r�c�e� �a�l�l�o�c�a�t�i�o�n�:� � � � �N� �u�p�t�a�k�e� �(V�^ �)� � �v�s�.� � � � � �C� �f�i�x�a�t�i�o�n� �(μ�^ �I�)� � � � � � � � � � � � � ∝� fV ∝� �(�1� −� �

Qs� − fV�)� � QN

0.5 fV 0

AdaPFT grows faster when either resource

becomes limiting.

Optimal use of resources subject to the trade-off


0-D (box) model of the mixed layer at stns. K2 & S1

Non-Adaptive PFT vs. AdaPFTa single PFT for each (NPD model), respectively

embedded in the same physical modelFitted to Obs. Data for NO3, chl and PP


Tim

e (d

ays)

fV

2010

201

1

201

220

10

2

011

2

012

0.5 0.4 0.3 0.2 0.1 0.0

0

200

400

600

800

1000Ti

me

(day

s)

0

200

400

600

800

1000

Tim

e (d

ays)

fV

2010

201

1

201

220

10

2

011

2

012

0.5 0.4 0.3 0.2 0.1 0.0

0

200

400

600

800

1000

Tim

e (d

ays)

0

200

400

600

800

1000

Non-Adaptive PFT vs. AdaPFT

Turn off Optimization:

constant fAconstant fV

Optimal Resource Allocation

optimize fA | N

optimize fV | N, I

stn. K2

stn. S1

stn. K2

stn. S1

more allocation to light gathering at stn. K2

=> lower fV (lower in winter)

more allocation to nutrient uptake at stn. K2 higher fV <=

(higher in summer)

Applied in a 0-D (box) model of the mixed layer for two time-series stns.


Standard PFT vs. Adaptive PFT applied to stns. K2 & S1

More Difference at N-poor stn. S1 only AdaPFT captures early bloom

Less Difference at N-rich stn. K2 Seasonal cycle of chl differs greatly

0

10

20

30

40

0

5

10

15

20

25

0.2

0.4

0.6

0.8

1.0

1.2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.5

1.0

1.5

2.0

2.5

0.07

0.08

0.09

0.10

0.11

Time (days) Time (days)

P. P

rod.

(mg

C m

-3 d

-1)

N (m

mol

L-1

)

chl (

mg

m-3

)

chl:C

(g m

ol-1

)

Bio

mas

s (m

mol

C m

-3)

Q (m

ol N

(mol

C)-1

)

stn K2

0 200 400 600 800 10000 200 400 600 800 1000

P. Production

chl

DIN

Phy C Biomass

chl:C ratio

Q (N:C ratio)

AdaPFT in colorsNon-adaptive PFT (grey) 0

2

4

6

8

10

12

0.0

0.5

1.0

1.5

0.0

0.2

0.4

0.6

0.8

0.10.20.30.40.50.60.7

0.1

0.2

0.3

0.4

0.5

0.6

0.04

0.06

0.08

0.10

Time (days) Time (days)

P. P

rod.

(mg

C m

-3 d

-1)

N (m

mol

L-1

)

chl (

mg

m-3

)

chl:C

(g m

ol-1

)

Bio

mas

s (m

mol

C m

-3)

Q (m

ol N

(mol

C)-1

)

stn S1

0 200 400 600 800 10000 200 400 600 800 1000

P. Production

chl

DIN

Phy C Biomass

chl:C ratio

Q (N:C ratio)

Each model was fitted to data (red dots) using the Adaptive Metropolis algorithm (Smith JGR 2011)


New size-based PhyEFT model Size scaling of Traits (input parameters)

as in Wirtz (Mar. Biol. 2013)Dark Light

Adaptive Response to env. (light & N)

Big is better at high N

Small is better at low N

(esp. at high light)0

1

2

3

4

0.2 0.5 2 5 20 50

N = 10 mmol m-3

N = 1 mmol m-3

N = 0.1 mmol m-3

Effe

ctiv

e m

ax. (

Mon

od) g

row

th ra

te

μm

ax (d

-1)

Strong Light Limitation, S(I) = 0.2

0

1

2

3

4

0.2 0.5 2 5 20 50

Effe

ctiv

e m

ax. (

Mon

od) g

row

th ra

te μ

max

(d-1

)

Light Replete, S(I) = 1.0

empirical allometriesLitchman et al. (Ecol. Lett. 2007) Edwards et al. (L&O 2007) Marañon et al. (Ecol. Lett. 2013)


V� �=� μQ



Vmax

α�O�p�t�i�m�a�l� �U�p�t�a�k�e� �k�i�n�e�t�i�c�s�

�(�P�a�h�l�o�w�.� �M�E�P�S�,� �2�0�0�5�;� �S�m�i�t�h� �e�t� �a�l�.� �M�E�P�S�,� �2�0�0�9�)�a�f�f�i�n�i�t�y� �(α�)� � �v�s�.� �m�a�x�.� �u�p�t�a�k�e� �r�a�t�e� �(Vmax�)

� � ∝ fA� � � � � �v�s�.� � � � � � � � � � � � � � � � � � � � ∝ �(1 − fA�)� � � � � � � � � � �.

1 fA 0



Qs� − fV�)� � QN

0.5 fV 0

Cell Size (ESD, mm) Cell Size (ESD, mm)


Effective Monod (growth) params. vs. MM params.Burmaster (Am. Nat. 1979) MM kinetics (uptake) + Droop model (Growth) => Monod kinetics (growth)Similarly, we combine OU kinetics (uptake) + Optimal Growth (OG) model => Effective Monod Params.

where

or, equivalently

Now, observed size-scalings for MM & Droop parameters can be used to predict size-scalings for Monod parameters.


New size-based PhyEFT model -- with Dynamic N:C ratio

Size scaling of Traits (input parameters)

as in Wirtz (Mar. Biol. 2013)


V� �=� μQ



Vmax



� � ∝ fA� � � � � �v�s�.� � � � � � � � � � � � � � � � � � � � ∝ �(1 − fA�)� � � � � � � � � � �.

1 fA 0



Qs� − fV�)� � QN

0.5 fV 0

N:C ratio depends on

N supply (directly)

Light (inversely) High Ligh => low N:C

Cell Size (inversely) Larger => lower N:C


Size-Scaling of Traits => Size-Scaling of Growth Empirical

Size-scalingsResponse depends on both cell size and EnvironmentNew modelling

framework to relate lab. measurements to the dynamic response of phytoplankton communities.

Km < KV

(growth) (uptake)

and the size-scaling for Km depends on light and nutrient environment.


V� �=� μQ



Vmax



� � ∝ fA� � � � � �v�s�.� � � � � � � � � � � � � � � � � � � � ∝ �(1 − fA�)� � � � � � � � � � �.

1 fA 0



Qs� − fV�)� � QN

0.5 fV 0


Summary & Conclusions

Adaptive Plankton Functional Type: AdaPFT Optimization of specific growth rate subject to 2 trade-offs: 1. Optimal Uptake (OU) kinetics 2. C (energy) vs. N aquisition

AdaPFT responds quite differently vs. Non-Adaptive PFTs Variable chl & N content => more dynamic Greater variability esp. for chl (observable)

Framework for scaling from obs.-based allometries of Traits to Net Response: Growth! => Effective values of Monod parameters & their size-scalings depend on both: Traits, and Environmental Conditions (through adaptive response)

AMEMR Symposium June 30, 2014S. Lan Smith

Position Available!

Project Scientist or Postdoc@ JAMSTEC

funded for 3.5yrs. by JST

a simple size-based model of phytoplankton communities reveals size-scaling of phytoplankton growth...

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