1. PHOTO BY S. MANZONI Eco-hydrological optimality to link water use and carbon gains by plants Manzoni S. 1,2, G. Vico 2, S. Palmroth 3, G. Katul 3,4, and A. Porporato 3,4 1 Physical Geography and Quaternary Geology, Stockholm Univ. 2 Crop Production Ecology and Ecology Dept., SLU, Uppsala 3 Nicholas School of the Environment, Duke Univ., USA 4 Civil and Environmental Engineering, Duke Univ., USA

2. PHOTO BY S. MANZONI Carbon uptake Soil carbon Respiration Food, fiber, biofuels… Respiration

3. Soil moisture PHOTO BY S. MANZONI E A Transpiration Carbon uptake Rainfall Stomatal conductance as a “compromise between the need to provide a passage for assimilation and the prevention of excessive transpiration” (Cowan and Troughton, 1971, Planta)

4. How do plants respond to altered climatic conditions? Can we optimize agro- ecosystem management to balance productivity and resource use? Can we breed crops towards more efficient resource use?

5. Regulation of water transport Stomatal closure limits evaporation from the leaves Lens (2011), New Phytologist Plant xylem limits transport of liquid water to the leaves Manzoni et al. (2013) Adv. Water Res. -ψP-ψP gcgc -ψP-ψP gPgP E LAI g c (  P )

6. Water use strategies involve tradeoffs 1)High transpiration allows plants to grow faster → competitive advantage (Eagleson, 2002, Rodriguez-Iturbe and Porporato 2004) BUT: high transpiration lowers soil moisture faster → earlier water stress? 2)Stomatal closure reduces desiccation risk (Cowan, 1982) BUT: lower stomatal conductance decreases C uptake → carbon starvation?

7. Tradeoffs require ‘balanced’ solutions Hypothesis: Water use strategies are optimal in a given environment (idea pioneered by Givnish, Cowan and Farquhar) Process-based optimal control problem 1)Objective: maximize photosynthesis (A) 2)Control: stomatal conductance to CO 2 (g C ) 3)Constraint: soil water is limited

8. Optimality at different time scales 1) Sub-daily, at ~constant soil moisture 2) One dry-down (days-weeks) 3) Several years and longer: stochastic soil moisture Water use strategies vary with the temporal scale of interest, because environmental drivers fluctuate at different scales Data from Fazenda Tamandua, Brazil R

9. The water flux is driven by the atmospheric evaporative demand The CO 2 flux is driven by the gradient between atmospheric and internal CO 2 concentrations Stomatal controls on transpiration and photosynthesis Biochemical C fixation wawa caca wiwi cici gcgc EA C fixation From the xylem Stomatal cavity Guard cells

10. The water flux is driven by the atmospheric evaporative demand The CO 2 flux is driven by the gradient between atmospheric and internal CO 2 concentrations Stomatal controls on transpiration and photosynthesis Biochemical C fixation A(g c ) gcgc Downward concavity! E(g c )

11. 1) Sub-daily time scale Objective: maximize Soil moisture changes slowly compared to light and VPD  Soil moisture is assumed constant Marginal water use efficiency Optimal stomatal conductance λ is constant, but undetermined! (classical solution by Cowan and Farquhar; Hari and Mäkelä)

12. λ = constant at given soil moisture Correct scaling g c and E vs. vapor pressure deficit D Katul et al., 2009, PCE Proportionality of g c and A (see also Hari et al., 2000, Aus. J. Plant Phys.) Palmroth et al., 1999, Oecologia

13. 2) Dry-down time scale (days to weeks) Objective: maximize RE Subject to the constraint L ZrZr Q Marginal water use efficiency Optimal stomatal conductance λ is defined by the boundary conditions of the optimization (Manzoni et al. 2013, AWR) with time

14. λ increases with decreasing water availability λ increases as drought progresses across species, ecosystems, and climates (Manzoni et al., 2011, Functional Ecol) ΨΨ λ/λ ww -ψ-ψ λ λ ww -ψ-ψ gcgc Time

15. 3) Optimal water use in stochastic environments Ψ 90,s -ψP-ψP gcgc -ψP-ψP gPgP ψ 50 s E Transpiration – moisture curve depends on plant hydraulic traits Constraint: Stochastic rainfall → p(s) depends on the E(s) curve and hence also on plant hydraulic traits LAI g c SPAC model

16. Objective: maximize Constraint: 3) Optimal water use in stochastic environments → Focus on stomatal and xylem conductances: What is the optimal shape of g c (  P ) and g P (  P )? → p(s) depends on the E(s) curve and hence also on plant hydraulic traits → Plant strategies optimize the long-term mean C uptake

17. Optimal water use explains plant trait coordination Observations are consistent with prediction of coordinated stomatal closure and cavitation occurrence -ψP-ψP gcgc Ψ 90,s -ψP-ψP gPgP ψ 50 <A><A> LAI g c

18. Conclusions 1.Sub-daily time scale: optimization explains stomatal responses to air humidity and photosynthesis-transpiration relations 2.Dry-down time scale: plants optimally down-regulate water losses as soils dry 3.Long term: coordination among plant hydraulic traits emerges as an optimal evolutionary strategy