Mathematical approach to effects of repeated treatments in the study of very low fluence, low fluence and high fluence germination responses

Theoretical calculation of the germination response induced by repeated treatments, separated by a dark period long enough to enable fixation of the effect of the preceding treatment, is possible when defining the percentage germination induced by the first treatment as the responding proportion (p) of the total treated seed population. Consequently the germination response induced by a second treatment should be relative to the proportion (q) of the seed population not responding to the first treatment (q = 1 - p).
The fitting of these calculations with experimental data for the Very Low Fluence Response (VLFR) for germination of seeds of Kalanchoë blossfeldiana Poelln. cv. Vesuv, induced by repeated light pulses, suggests the independency of the effect of each treatment, i.e. the effect of the second treatment is neither positively nor negatively influenced by the first treatment.
This hypothesis is not valid for calculation of the Low Fluence Response (LFR) for germination of Kalanchoë seeds induced by repeated light pulses, since the first light pulse does not result in a germination response. At least two irradiations are needed for an LFR while the third and following pulses increase the response much more than calculated with the proposed equation. It is suggested that the LFR in Kalanchoë , in contrast to the VLFR, includes the involvement of some pre-existing far-red absorbing form of phytochrome (P_fr) and the involvement of dark reactions are to be considered.
The effect of long irradiation times (up to 2xl0⁵ s) resulting in a (defined in this paper) high fluence response (HFR) for germination of Kalanchoë seeds is also discussed in terms of independently responding seed population fractions.