## Optimun model for stomatal control

As nature has not provided plants with a membrane permeable to CO2 but impermeable to water vapour, the energy gain for plants in the form of carbon always involves a cost in terms of a loss of water. This phenomenon, together with ideas of natural selection, has lead to the hypothesis of optimal stomatal opening which, simulataneously, maximizes the carbon gain and minimizes the loss of water (Cowan, 1977; Guehl and Aussenac, 1987). The optimum model by Hari et al. (1986) and its further developments (e.g. Mäkelä et al. 1996; Hari et al. 2000) fall into this genre of models combining gas exchange and stomatal control. The model has been parameterised using extensive data from chamber measurements in the field, and it has been tested against independent data (Hari et al. 1993; 2009). A recent study has shown that the model derived from the optimum approach is mathematically equivalent with the more conventional semi-empirical models (Medlyn et al. 2011).

In order to compare the carbon gain with the loss of water in the optimisation problem, the model utilises a parameter called “the cost of water”. While the cost of water can be assumed approximately constant when water is readily available, it is expected to increase during a prolonged drought period. Finding the optimal time course for the “cost of water” during a drought period provides an additional optimisation problem which involves the optimal use of water available during a drought period. Mäkelä et al. (1996) and Berninger et al. (1996) studied optimal strategies of drought response using this approach and assuming that the plants were adapted to the expected duration of drought. The expected duration of drought period was calculated from the probability that rain occurs during a certain time period.

**References:**

**Berninger, F., Mäkelä, A. & Hari, P.** 1996. Optimal control of gas exchange during drought: Empirical evidence. Annals of Botany 77, 469-476.

**Cowan I. R.** 1977. Stomatal behavior and the environment. Advances in Botanical Research 4, 117-227.

**Guehl J. M. and Aussenac G.** 1987. Photosynthesis decrease and stomatal control of gas exchange in Abies alba Mill. in response to vapour pressure difference. Plant Physiology 83, 316-322.

**Hari, P., Hänninen, H., Berninger, F., Kolari, P., Nikinmaa, E. & Mäkelä-Carter, A.** 2009. Predicting boreal conifer photosynthesis in field conditions. Boreal Environment Research 14, (suppl. A), 19-28.

**Hari, P., Mäkelä, A., Korpilahti, E. & Holmberg, M.** 1986. Optimal control of gas exchange. Tree Physiology 2, 169-175.

**Hari, P., Mäkelä, A. & Pohja, T.** 2000. Surprising implications of the optimality hypothesis of stomatal regulation gain support in a field test. Australian Journal of Plant Physiology 27, 77-80.

**Medlyn, B. E., Duursma, R. A., Eamus, D., Ellsworth, D. S., Prentice, I. C., Barton, C. V. M., Crous, K. Y., De Angelis, P., Freeman, M. and Wingate, L.** 2011. Reconciling the optimal and empirical approaches to modelling stomatal conductance. Global Change Biology 17, 2134-2144.

**Mäkelä, A., Berninger, F. & Hari, P.** 1996. Optimal control of gas exchange during drought: Theoretical analysis. Annals of Botany 77, 461-467.

**Vesala, T., Kulmala, M., Lushnikov A. A. and Hari, P.** 1993. A model for gas exchange through stomata. The Fifth Finnish National Aerosol Symposium. Helsinki 1.-3.6.1993. Finnish Association for Aerosol Research, Report Series in Aerosol Science 23, 48-53.