An optimal strategy of stomatal control during a drought period in plants adapted to a humid climate is derived by maximizing the photosynthetic production during the expected duration of drought. This is worked out from the probability that rain occurs during a certain time interval, which is assumed constant. The plant model describes photosynthetic production and the consumption of water from the soil, with a given initial soil water content. Water is consumed through transpiration at a rate depending on water vapour deficit and stomatal conductance, and carbon is assimilated at a rate depending on light intensity and stomatal
conductance. The resulting optimal stomatal control consists of two processes with different time constants: (1) daily variation depending on the driving variables, and (2) a declining trend as a function of the initial soil water content and the probability of rain. The result allows for a physical interpretation of the so-called "cost of water" used in similar optimization studies. An approximate model is derived from the optimal solution, such that the "cost of water" is a function of the soil water content, and consequently, daily transpiration is a function of the soil water content and the probability of rain.
The model was applied to data on photosynthesis and transpiration in Scots pine during a 22-day drought period. There was a clear decrease in photosynthesis and transpiration during that period. The agreement between model and data was good. The residuals of photosynthesis were not systematic with respect to temperature, irradiance or water vapour deficit, but there was a slight systematic trend in the residuals of transpiration. The model provided a somewhat better fit for photosynthesis than for transpiration. The results seem to suggest that there was no decrease in photosynthetic capacity during the period, but a decrease in stomatal conductance was responsible for the changes in photosynthesis and transpiration.
Key words: transpiration, photosynthesis, drought, optimal control model, Pinus sylvestris.
Correspondence: Frank Berninger, Department of Forest Ecology, P.O. Box 24 (Unioninkatu 40), FIN-00014 University of Helsinki, Finland
Telefax: +358-0-1917605
E-mail: frank.berninger@helsinki.fi