S. Lan Smith


S. Lan Smith

Marine Ecosystem Dynamics Research Group
Senior Scientist


Japan Agency for Marine-Earth Science and Technology (JAMSTEC)
Yokohama Institute for Earth Sciences (YES)
3173-25 Showa-machi, Kanazawa-ku, Yokohama City, Kanagawa, 236-0001, Japan


  • Ph.D., Water Resources Program, 1998 Civil Engineering, Princeton University
  • B.S., Chemical Engineering, 1992 California Institute of Technology (Caltech)

Research theme :
Interpreting observations and developing better models of plankton based on the concept of Optimality (as a result of natural selection)

Phytoplankton size-diversity mediates an emergent trade-off in ecosystem functioning for rare versus frequent disturbances
S. Lan Smith, Sergio M. Vallina & Agostino Merico

Scientific Reports, vol. 6, 17 October, 2016

In environments with less frequent disturbance, phytoplankton communities with less diversity tend to be slightly more productive (left). On the contrary, when disturbances are more frequent, more diverse communities tend to be more productive.

Developing a new marine ecosystem model to represent the adaptive capacity of plankton in the N. Pacific

CREST (Core Research for Evolutional Science and Technology) Project funded by JST (Japan Science and Technology Agency), FY2012 to FY2017

We intend to develop the new ecosystem model based on the 'adaptive dynamics' approach, using trade-offs to constrain the adaptive response.

Introduction to Optimality-based modeling

Natural selection tends to produce organisms optimally adapted to their environments.
Optimality can be considered a guiding concept.

Particularly for plankton:
  • long evolutionary history
  • short generation times
  • easy to use in experiments
Many studies have made progress by assuming:

Adaptation (species) & Acclimation (organisms) both tend to maximize growth rate.

  • Simpler models,
  • Models of greater generality.
  • New, different interpretations of observations.

Solve the Problem faced by organisms:

How to make the best use of limited resources, to maximize fitness*, subject to trade-offs in a variable environment?

*For asexually reproducing plankton, we equate fitness with growth rate.

Successful applications at various levels of organization.

Ideally, net growth rate should be optimized, but this is only possible for simple systems.

However, for many natural systems, this is not practical because it requires modeling the entire ecosystem, including predators and all other losses, which are not well known.

Nevertheless, the optimality concept has been applied successfully to model lower levels of organization, e.g., the cellular level or specific processes such as uptake.

This makes sense for sub-processes which are vital for growth.

Red arrows show the Trade-offs, linked to the quantity optimized (above).

Selected Examples

Optimal Uptake (OU) kinetics

1. agrees better with observations of nutrient uptake by phytoplankton and bacteria, compared to the widely applied Michaelis-Menten (MM) equation (Smith & Yamanaka 2007a; Smith et al. 2009, 2011),

2. reproduces observed changes in Si and N uptake during the SERIES iron-enrichment expt. (Smith et al. 2010), and

3. provides a more consistent interpretation of the combined effects of temperature and concentration on nitrate uptake as observed on oceanic cruises, and implications for the C cycle (Smith 2010, 2011).

Photoacclimation models

  • 4. agree better with observations over wider ranges of environmental conditions, compared to previous models, despite having fewer parameters (Pahlow 2005; Smith & Yamanaka 2007b; Pahlow & Oschlies 2009; Wirtz & Pahlow 2010),
  • 5. provide a new and more general interpretation of co-limitation of phytoplankton by N and P (Pahlow and Oschlies 2009), and
  • 6. reproduce the shape of the often observed “Droop curve” for growth rate from basic principles, i.e., without specifying a particular functional form (Wirtz and Pahlow 2010).

Selected Results

Selected results from 1.

Lab Expts. at extreme N:P supply ratios

Selected results from 3.

With OU kinetics, Vmax (as measured by short-term expts.) depends on ambient [NO3] as well as on T. This results in greater inferred T sensitivity, compared to the standard assumption of T dependence only (as applied with Michaelis-Menten kinetics).

Compared to MM kinetics, with OU kinetics greater T sensitivity is required to reproduce the same field data, because as T increases [NO3] tends to decrease (right).

For a data set for nitrate uptake from the N. Atlantic, Smith (2011) found

Q10 ~ 3 based on OU kinetics

as great as for heterotrophic bacteria


Q10 ~ 2 based on MM kinetics

lower than for heterotrophic bacteria

Because T and [NO3] are negatively related in the near-surface ocean (as shown above for the data set of Harrison et al. (1996) from the N. Atlantic, the effects of T and concentration tend to counteract one another for Vmax.
Because T and [NO3] are negatively related in the near-surface ocean (as shown above for the data set of Harrison et al. (1996) from the N. Atlantic, the effects of T and concentration tend to counteract one another for Vmax.

Implications for the carbon cycle


The concept of optimality is quite valuable for modeling plankton.

Still, important challenges remain, including:

  • Practical:
    Obtaining observations of sufficient quality and quantity to rigorously test competing theoretical models.
  • Theoretical:
    How to develop useful dynamic models based on optimality that are also consistent with the theory of the Evolutionarily Stable Strategy (ESS, by John Maynard Smith), which is formulated in terms of steady state?


  • Journal of Plankton Research
    Flexible phytoplankton functional type (FlexPFT) model: size-scaling of traits and optimal growth
    S. Lan Smith, Markus Pahlow, Agostino Merico, Esteban Acevedo-Trejos, Yoshikazu Sasai, Chisato Yoshikawa, Kosei Sasaoka, Tetsuichi Fujiki, Kazuhiko Matsumoto and Makio C. Honda
    J. Plankton Res. (2015) doi: 10.1093/plankt/fbv038 First published online: June 3, 2015

  • Journal of Plankton Research
    Leaving misleading legacies behind in plankton ecosystem modelling 
    S. Lan Smith; Agostino Merico; Kai W. Wirtz; Markus Pahlow
    Journal of Plankton Research 2014; doi: 10.1093/plankt/fbu011

  • Armstrong, RA (1999) An optimization-based model of iron–light–ammonium colimitation of nitrate uptake. Limnology & Oceanography 44, p. 1436–1446
  • Collos Y, A Vaquer and P Souchu (2005) Acclimation of nitrate uptake by phytoplankton to high substrate levels. Journal of Phycology 41, p. 466-478
  • Harrison, GW, LR Harris, and DB Irwin (1996), The kinetics of nitrogen utilization in the oceanic mixed layer: Nitrate and ammonium interactions at nanomolar concentrations. Limnology & Oceanography 41, p. 16–32
  • Merico A, J Bruggeman and K Wirtz (2009) A trait-based approach for downscaling complexity in plankton ecosystem models. Ecological Modelling 220, p. 3001-3010
  • Pahlow M (2005) Linking chlorophyll-nutrient dynamics to the Redfield N:C ratio with a model of optimal phytoplankton growth. Marine Ecology Progress Series 287, p. 33-43
  • Pahlow M and A Oschlies (2009) Chain model of phytoplankton P, N and light colimitation. Marine Ecology Prog. Ser. 376, p. 69-83
  • Rhee, G-Y (1974) Phosphate uptake under nitrate limitation by Scenedesmus sp. and its ecological implications. Journal of Phycology 10, p. 470–475
  • Smith SL (2010) Untangling the uncertainties about the combined effects of temperature and concentration on nitrate uptake in the ocean. Geophysical Research Letters 37 L11603, doi:10.1029/2010GL043617
  • Smith SL (2011) Consistently modeling the combined effects of temperature and concentration on nitrate uptake in the ocean. J. Geophysical Research--Biogeosciences 116, G04020, doi:10.1029/2011JG001681
  • Smith SL, M Pahlow, A Merico and KW Wirtz (2011) Optimality-based modelling of planktonic organisms. Limnology & Oceanography 56 Review paper, p. 2080-2094
  • Smith SL and Y Yamanaka (2007a) Optimization-based model of multinutrient uptake kinetics. Limnology & Oceanography 52, p. 1545-1558
  • Smith SL and Y Yamanaka (2007b) Quantitative comparison of photoacclimation models for marine phytoplankton. Ecological Modelling 201, p. 547-552
  • Smith SL, Y Yamanaka, M Pahlow and A Oschlies (2009) Optimal Uptake Kinetics: Physiological acclimation explains the observed pattern of nitrate uptake by phytoplankton in the ocean. Marine Ecology Progress Series 384 Feature Article, p. 1-12
  • Smith SL, N Yoshie and Y Yamanaka (2010) Physiological acclimation by phytoplankton explains observed changes in Si and N uptake rates during the SERIES iron-enrichment expt. Deep Sea Res. I 57, p. 394-408
  • Wirtz, KW and M Pahlow (2010) Dynamic chlorophyll and nitrogen:carbon regulation in algae optimizes instantaneous growth rate. Marine Ecology Progress Series 402, p. 81-96