Multiple time scale optimization explains functional trait responses to leaf water potential

Plant response to water stress involves multiple timescales. In the short term, stomatal adjustments optimize some fitness function commonly related to carbon uptake, while in the long term, traits including xylem resilience are adjusted. These optimizations are usually considered independently, the former involving stomatal aperture and the latter carbon allocation. However, short- and long-term adjustments are interdependent, as 'optimal' in the short term depends on traits set in the longer term. An economics framework is used to optimize long-term traits that impact short-term stomatal behavior. Two traits analyzed here are the resilience of xylem and the resilience of nonstomatal limitations (NSLs) to photosynthesis at low-water potentials. Results show that optimality requires xylem resilience to increase with climatic aridity. Results also suggest that the point at which xylem reach 50% conductance and the point at which NSLs reach 50% capacity are constrained to approximately a 2 : 1 linear ratio; however, this awaits further experimental verification. The model demonstrates how trait coordination arises mathematically, and it can be extended to many other traits that cross timescales. With further verification, these results could be used in plant modelling when information on plant traits is limited.