A Model of Photosynthetic Acclimation as a Special Case of Reaction Norms

A mathematical model for photosynthetic acclimation is presented. Photosynthetic acclimation is the ability of plants to change the temperature optimum for the rate of photosynthesis in response to the growth temperature. The model is presented in a stationary version and in a dynamic version. The stationary model describes the behaviour of the plant when it is fully acclimated to a certain growth temperature. The underlying assumption of the model is that the behaviour of a plant is described by one long-term response curve and one independent short-term response curve. Both curves are for simplicity assumed to be parabolas. The stationary model shows that the empirical observation that plants normally do not acclimate fully to the growth temperature, can be explained as the optimal strategy whereby the plant maximizes its carbon uptake. The dynamic version of the model relies on the additional assumption that the rate of change of acclimation is proportional to the deviation from full acclimation. The model gives a complete description of the system when the temperature is allowed to vary with time and shows how several methodological problems connected with a stationary view of the acclimation process can be overcome using a dynamic approach.