1. DEB Modeling of Tree Performance Roger Nisbet 1, Glenn Ledder 2, Sabrina Russo 2, Megan Bartlett 3, Caroline Farrior 4, V. Couvreur 5, Erik Muller 1, Angie Peace 4, Loorens Poorter 6, Lauren Sack 3, Frank Sterck 6, Danielle Way 7, Elke Zimmer 8. 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.

2. 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 of geographic distributions Sound like NicheMapper?

3. 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.

4. 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.

5. “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

6. 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 Sack 1 Storage: Core DEB concept 1. Osborne, C. P. and L. Sack. 2012. Philosophical Transactions of the Royal Society B-Biological Sciences 367:583-600.

7. Existing model – DEB3

8. Why not adopt DEB3 model? “too complicated” (scary) too many parameters Unstudied and challenging qualitative dynamics

9. 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

10. Simplification? one N and one C reserve for whole tree STILL MANY KAPPAS – AND ISSUES ABOUT RECYCLING

11. Hydraulic Submodel Osborne & Sack 2012

12. Alternative approach to the problem of kappa proliferation: Sharing the surplus ERIK MULLER TALK!

13. “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) U CS = photosynthate production rate U NR = nitrogen assimilation rate by roots Q S, Q R = biomass production rates M S, M R = maintenance rates  N,  C = rejection fluxes from Sus  = ratio of N:C ratios in shoots vs roots

14. Tree toy model equations (V1 morph)

15. Toy Model Dynamics Root and Shoot biomasses Log (biomasses) 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.

16. Why is surplus sharing “optimal”? Rate of loss of unutilized carbon Porportion wasted “Waste” C or N is utilized by neither root nor shoot No C is wasted in balanced growth Similar result (not shown) for N

17. Surplus sharing not always “optimal” Root and shoot biomass Log (biomass) Previous runs had lower C:N ratio in shoots than roots With low-N leaves, there is oscillatory growth pattern (overcompensation)

18. 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

19. More realistic synthesizing unit Low C:NHigh C:N Waste (“dissipation”) implies control – but slower growth

20. Take home messages for DEBologists Great scope for DEB-inspired approaches to plant ecology Keep it simple – but not too simple Understand dynamical mechanis ms