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.

• 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

Specific ecological target: mechanistic models ofgeographic distributions

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 , , and , the hydraulic conductivities , , and , and the stomatal conductance .

• Stomatal conductance determines conductance from atmosphere to chloroplast () 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

1

;

; ;

; ;

Min , ; Min ,

S S R R

NR CS

R s

R NR C s CS N

N NC R

dS dRQ M Q M

dt dt

U R U S

M R M S

Q U Q U

U Q

Balance equations

Fluxes

; ; c CS SU Q

Tree toy model equations (V1 morph)

Toy Model DynamicsRoot and Shoot biomasses

Log

(bio

mas

ses)

shoot

root

• Initially one player supports growth of the other

• 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”?Rate of loss of unutilized carbon

Porp

ortio

n w

aste

d

• “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”Root and shoot biomass

Log

(bio

mas

s)

• 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