Feb. 23, 2012S. Lan Smith

Optimality-based modeling of plankton for use in Earth-system modeling S. Lan Smith1, Markus Pahlow2,

Agostino Merico3, Kai W. Wirtz4, Andreas Oschlies2

1Japan Agency for Marine-Earth Science & Technology (JAMSTEC), Yokohama2Leibniz Institute of Marine Sciences at Kiel University (IFM-GEOMAR)

3Leibniz Center for Tropical Marine Ecology (ZMT), Bremen4Helmholtz Center for Materials & Coastal Research, Geesthacht

Ocean Sciences Meeting 2012 Salt Lake City

Feb. 23, 2012S. Lan Smith p. 2

Assumptions

Natural Selection produces optimally adapted organisms

Fitness = Growth Rate Goal-oriented

Considerable success over the past decade

Recent Developments: models of optimal foraging & Primary Production

Major Challenge

Dynamic models consistent with Evolutionarily Stable Strategy (ESS) ESS formulated in terms of steady state (John Maynard Smith)

i.e., how to describe short-term dynamics, e.g., acclimation, consistent with evolutionary adaptation of the very ability to acclimate.

from the review by Smith et al. (Limnology & Oceanography 56, 2011)

Optimality-based models of plankton

Feb. 23, 2012S. Lan Smith p. 3

Acclimation vs. Adaptation

Acclimation short-term changes e.g., seasonal change of a dog’s coat of hair

Adaptation long-term changes evolution (genetic changes in a species) species succession (changes in community composition)

The same approaches can be used to model both. e.g., Wirtz and Eckhardt (Ecol. Mod., 1996), Merico et al. (Ecol. Mod., 2009)

Feb. 23, 2012S. Lan Smith p. 4

Optimality at different levels of organization

Nutrient uptake, e.g., Optimal Uptake

as in Smith et al. (2009)

N used for other enzymes

(max. rate)

N used for uptake

sites(affinity)

nutrient uptake

Autotrophic growth, e.g., iron-light-nitrogen

colimitation as in Armstrong (1999)

phytoplankton

iron used for light

harvesting

iron used for N

assimilation

N uptakelight

phytoplankton

nutrients zooplankton

defenseuptake

Community dynamics, e.g., grazers and phytoplankton

as in Merico et al. (2009)

Maximal net growth rate

Maximal specific growth rate

Maximal uptake rate

Quantity being

optimized

trade-off

(Smith et al. L&O 2011, fig. 2)

Feb. 23, 2012S. Lan Smith p. 5

Trade-offs as ‘Hyper-Parameterizations’

‘Hyper-Parameters’ in hierarchical Bayesian modeling specify prior distributions of model parameters (e.g.,Gelmanetal.Bayesian Data Analysis,2ndedition,2004)

Trade-offs specify how the shapes of functional relationships may change, rather than fixing their shapes. Optimal Uptake kinetics

log NO3 (in seawater)

log K N

O3

-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)

V max

KNO3

Trade-off

Feb. 23, 2012S. Lan Smith p. 6

Shape-shifting of the Growth vs. Irradiance curve

RubiscoCHLa CarotPigments

Q Q0

?

f R

DIN

loss

f θ

1-f θ-f R

lossCO2

C-uptake

N-uptake

PONPOC

Gro

wth

Rat

e

Max

. Gro

wth

Rat

e

Light

Flexible Response

Wirtz & Pahlow (MEPS 2010)

Optimal Resource Allocation subject to Trade-offs

Feb. 23, 2012S. Lan Smith p. 7

New interpretations from optimality-based modeling

1. Instead of ‘Inhibition of NO3 uptake by NH4‘ -> co-limitation by Fe, light and nitrogen (Armstrong L&O 1999)

2. Instead of either multiplicative models or Liebig’s Law of the min. -> co-limitation by N, P and light (Pahlow & Oschlies MEPS 2009)

3. Instead of fixed Droop-type quota equation -> saturating response from optimization (Wirtz & Pahlow MEPS 2010)

4. Instead of Q10 ~ 2 for phytoplankton -> Q10 ~ 3 for N uptake inferred from field obs. (Smith JGR 2011)

These have implications for ecology & Earth-System Modeling.

Feb. 23, 2012S. Lan Smith p. 8

T sensitivity for phytoplankton

CO2

Inorganic C Organic C

sinking & exportNo Net Effect on Uptake or Export

CO2

Inorganic C Organic C

sinking & exportwarming

CO2

Inorganic C Organic C

sinking & exportLess Uptake & Less Export

CO2

Inorganic C Organic C

sinking & exportwarming

Standard Assumption: Degradation has greater T sensitivity than Production

However, if Production has the same T sensitivity as Degradation

Common view: Bacteria are more T sensitivity than Phytoplankton. Q10 ~ 2 to 3 (Pomeroy and Wiebe. Aquat. Microb. Ecol. 2001)

OU kinetics applied to field obs. implies: Q10 ~ 3 for nutrient uptake (Smith. GRL 2010, JGR 2011), rather than Q10 ~ 2 (Eppley. 1972).

Feb. 23, 2012S. Lan Smith p. 9

Differences between species: Large-scale patterns of dominanceLitchman et al. (Ecology Letters 10, 2007) “Thesetrade-offs,arisingfromfundamentalrelationssuchascellularscaling lawsandenzymekinetics,definecontrastingecologicalstrategies...[which]can explainthedistributionpatternsofmajorfunctionalgroupsandsizeclasses alongnutrientavailabilitygradients.”

Applications in 3-D models (Follows et al. Science, 2007) & the MIT group.

Monteiroetal.(GBC,2011)‘environmentselects’forN2fixers But how to model more

detailed (finely resolved) & realistic biodiversity?& account for the adaptive capacity of each species?

Feb. 23, 2012S. Lan Smith p. 10

Trait x should change in proportion to its effect on fitness, F:

dx = dx∂F(x,E)

dt ∂x dx: flexibility ~ diversity (trait distribution) E: Environment (light, temperature, etc.)

For plankton F = Growth; dx/dt depends on E (Smithetal.L&O,2011)

Acclimation Rates depend on: 1. possible range of trait values (adaptive capacity), 2. environmental variability 3. current distribution of trait values

Remaining Challenge: modelled diversity tends to collapse immigration required to maintain diversity (Bruggeman & Kooijman L&O 2007)

‘Adaptive Dynamics’: evolutionary changes McGill and Brown (An. Rev. Ecol. Evol. Syst. 2007), Litchman et al. (PNAS 2009) ‘adaptive dynamics’: species succession, communities Wirtz & Eckhardt (Ecol. Modell. 1996), Wirtz (J. Biotech. 2002), Abrams (J. Evol. Biol. 2005)

‘adaptive dynamics’: modelling how fast traits change

Also allows modeling the dist. of x, without discretely resoving it.

Feb. 23, 2012S. Lan Smith p. 11

Different Postulates about the Nature of Life

1. Life is tough and flexible because organisms and species had to be so in order to survive throughout billions of years of evolution (for bacteria & plankton). Pro: Basis for more general understanding New interpretations of obs.

Con: Risk: may over-estimate the ‘Adaptive Capacity of Life’, which does have limits; i.e., may miss some real threats. Humans have driven some species extinct.

2. Life is fragile and inflexible so that any change in environmental conditions might cause Scary Disasters! despite the fact that life evolved experiencing changes in climate & geography. Pro: May identify real threats & risks. Many opportunities for sensational papers (e.g., in Nature), which advance scientists’ careers. Con: Risk: loss of credibility, if predicted Disasters do not occur. No basis for understanding or modeling ‘Adaptive Capacity of Life’.

vs.

Feb. 23, 2012S. Lan Smith p. 12

Conclusions

Life is tough and flexible, to a non-neglible extent.

Earth-System Models should account for ‘Adaptive Capacity of Life’.

Optimality-based models are one means to do this using trade-offs as ‘Hyper-Parameterizations’ to constrain adaptive responses.

We need observations to keep this realistic.