Comparison of Two Shoot--Root Partitioning Models with Respect to Substrate Utilization and Functional Balance

A transport resistance model for shoot—root partitioningby Thornley and a more aggregated partitioning model by Reynoldsand Thornley are compared. Three functional forms of substrateutilization are applied, corresponding to different assumptionson the ability of carbon and nitrogen to compensate one anotherin promoting structural growth. On the basis of simulationsat balanced exponential growth, it is shown that the Reynoldsand Thornley model (in optimal form) is embedded in the Thornleymodel. Davidson's functional balance is studied as a functionof the degree of carbon-nitrogen compensation. The applicabilityof the models and the utilization functions is discussed. Model, shoot-root partitioning, substrate utilization, functional balance     

Optimal Control of Gas Exchange during Drought: Empirical Evidence

The optimal regulation model by Mäkelä, Berningerand Hari (Annals of Botany 77: 461–467, 1996) was appliedto data for photosynthesis and transpiration of Scots pine duringa 22-d drought period. There was a clear decrease in photosynthesisand transpiration during that period. The agreement betweenmodel and photosynthesis data was good. The residuals of photosynthesiswere not systematic with respect to temperature, irradianceor water vapour deficit. However, the model initially overestimatedtranspiration by 50%, although there was a clear linear relationshipbetween measured and estimated values. The results suggest thatthere was no decrease in photosynthetic capacity during theperiod, but a decrease in stomatal conductance was responsiblefor the changes in photosynthesis and transpiration. The observationsare similar to results in the literature. Transpiration; photosynthesis; stomatal conductance; drought; Pinus sylvestris     

Optimal Control of Gas Exchange during Drought: Theoretical Analysis

An optimal strategy of stomatal control during a drought period,in plants adapted to a humid climate, is derived by maximizingthe photosynthetic production during the expected duration ofdrought. The expected duration of drought is calculated fromthe probability that rain occurs during a certain period, whichis assumed constant. The underlying plant model describes photosyntheticproduction and the consumption of water from the soil, witha given initial soil water content. Water is consumed throughtranspiration at a rate dependent on water vapour deficit, temperatureand stomatal conductance and carbon is assimilated at a ratedependent on light intensity and stomatal conductance. The optimizationproblem is solved with driving variables and the probabilityof rain corresponding to a Fenno-Scandian climate. The resultingoptimal stomatal control consists of two processes with differenttime constants: (1) daily variation depending on the drivingvariables, and (2) a declining trend as a function of the initialsoil water content and the probability of rain. The result allowsfor a physical interpretation of the so-called ‘cost ofwater’ used in similar optimization studies. An approximatemodel is derived from the optimal solution, such that the ‘costof water’ is a function of the soil water content. Photosynthesis; transpiration; stomatal conductance; soil water content; probability of rain; optimal control; drought; model