DEB Modeling of Tree Performance
Roger Nisbet1, Glenn Ledder2, Sabrina Russo2, Megan Bartlett3,
Caroline Farrior4, V. Couvreur5, Erik Muller1, Angie Peace4, Loorens
Poorter6, Lauren Sack3, Frank Sterck6, Danielle Way7, Elke Zimmer8.
Working group at National Institute for Mathematical
and Biological Synthesis (NIMBioS) – Knoxville, TN, USA
1: University of California, Santa Barbara, USA; 2: University of Nebraska, Lincoln,
USA; 3: University of California, Los Angeles, USA; 4: National Institute for
Mathematical and Biological Synthesis, USA; 5: University of California, Davis, USA; 6:
Wageningen University, The Netherlands; 7: University of Western Ontario, Canada; 8:
Belgian Nuclear Research Institute, Belgium.
Specific ecological target: mechanistic models of
geographic distributions
• Need for distribution models that are mechanistic –
based on the fundamental niche
• Take as environmental parameters as inputs and use
physiological process-models integrating functional
trait values to predict the probability of occurrence,
given the environment
• Represent physiological potential to occupy
environmental space
• Predict multidimensional trait space that enables
occupation of a given environment
Sound like NicheMapper?
Initial objectives for working group
• To use a DEB-based model (or models) to identify
combinations of functional and biomass- and
nutrient-allocation traits that maximize net
photosynthetic carbon gain (C-gain) and survival at
the level of the whole tree.
• To test/modify the model(s) by comparing predicted
trends in functional traits, growth, and survival
along resource availability gradients with data for
Bornean and Bolivian tree species.
Initial objectives for working group
• To use a DEB-based model (or models) to identify
combinations of functional and biomass- and
nutrient-allocation traits that maximize net
photosynthetic carbon gain (C-gain) and survival at
the level of the whole tree.
• To test/modify the model(s) by comparing predicted
trends in functional traits, growth, and survival
along resource availability gradients with data for
Bornean and Bolivian tree species.
“Pre-DEB” statement of trade-offs
• Allocation: Larger investment in leaves vs. roots →
more light capture, but reduced nutrient & water uptake
• Photosynthesis: Lower C:N ratio in leaves →
more C-assimilation, but higher leaf turnover &
respiratory maintenance costs
• Hydraulics: Greater water conductivity 
more C-assimilation, but greater cavitation vulnerability
• Storage Higher reserve density →slower growth, but
better stress response
Modeling trade-offs
• Allocation:
Core DEB model concept
• Photosynthesis: Many options (DEB-based or not).
Plant physiologists like Farquhar model. Must link to
a hydraulic model
• Hydraulics:
Good model by Osborne and Sack1
• Storage:
Core DEB concept
1. Osborne, C. P. and L. Sack. 2012. Philosophical Transactions of the Royal Society
B-Biological Sciences 367:583-600.
Existing model – DEB3
Why not adopt DEB3 model?
• “too complicated” (scary)
• too many parameters
• Unstudied and challenging qualitative dynamics
Why not adopt DEB3 model?
• “too complicated” (scary)
Model can be written in non-intimidating way
• too many parameters Serious issue, especially the
number of “kappas”. Should we allow the use of
optimization criteria for parameter estimation?
All “DEB instincts” suggest answer is no.
• Unstudied and challenging qualitative dynamics
Understanding the dynamic properties of the
model (esp. how homeostasis would play out)
would be a major project
Simplification? one N and one C
reserve for whole tree
STILL MANY KAPPAS – AND ISSUES ABOUT RECYCLING
Hydraulic Submodel
• Hydraulic submodel consists of 7 algebraic
equations to determine the water potentials
𝜓𝐿 , 𝜓𝑆 , and 𝜓𝑅 , the hydraulic conductivities
𝐾𝐿 , 𝐾𝑆 , and 𝐾𝑅 , and the stomatal conductance
𝑔𝑠 .
• Stomatal conductance determines
conductance from atmosphere to chloroplast
(𝑔𝑡 ) for the photosynthesis submodel.
Osborne & Sack 2012
Alternative approach to the
problem of kappa proliferation:
Sharing the surplus
ERIK MULLER TALK!
“Dynamical Mechanism”
“Toy model” of sharing the surplus
Black fluxes
- biomass
Red fluxes
- carbon
Green fluxes - nitrogen
R = root biomass
S = shoot biomass
• = synthesizing unit (SU)
UCS = photosynthate production rate
UNR = nitrogen assimilation rate by roots
QS, QR = biomass production rates
MS, MR = maintenance rates
rN, rC = rejection fluxes from Sus
q = ratio of N:C ratios in shoots vs roots
Tree toy model equations (V1 morph)
Balance equations
dS
dR
 QS  M S ;
 QR  M R
dt
dt
Fluxes
U NR   R;
U CS   S ;
M R   R;
M s  S;
QR  Min U NR , rC  ;
Qs  Min U CS , q 1 r N 
r N  U NC  QR ;
rc  U CS  QS ;
Toy Model Dynamics
Root and Shoot biomasses
• Initially one player
supports growth of
the other
Log (biomasses)
root
shoot
• Then “balanced
growth”
• Consistent with
evolutionary theory
if applied to
superorganism*
Iwasa, Y. and J. Roughgarden. 1984. Theoretical Population Biology 25:78-105.
Why is surplus sharing “optimal”?
Porportion wasted
Rate of loss of unutilized
carbon
• “Waste” C or N is
utilized by neither
root nor shoot
• No C is wasted in
balanced growth
• Similar result (not
shown) for N
Surplus sharing not always “optimal”
Log (biomass)
Root and shoot biomass
• Previous runs had
lower C:N ratio in
shoots than roots
• With low-N leaves,
there is oscillatory
growth pattern
(overcompensation)
Tentative conclusion
• If at least one organ needs a higher proportion
than its partner of the element it cannot obtain
directly, then surplus sharing leads to balanced
growth at the optimal rate.
• Otherwise there is wasteful overcompensation
and hysteresis
More realistic synthesizing unit
Low C:N
High C:N
Waste (“dissipation”) implies control – but slower growth
Take home messages for DEBologists
• Great scope for DEB-inspired
approaches to plant ecology
• Keep it simple – but not too simple
• Understand dynamical mechanisms