*3.3. BPFD Response Function*

A linear function described well the response to BPFD and was applied for the simulations. Kahlen and Stützel [46] also applied a linear response to PPFD and red to far-red ratio for modeling the response of cucumber to light environment. Other studies found a non-linear response function to BPFD for stem length of soybean [17–19]. This can be due to lower BPFD levels in these studies (BPFD levels < 5%) based on which a non-linear function could be fitted [19]. A continuation of the function in the present study below a BPFD ratio of 15% could evolve non-linear, but in the context of speed breeding this low BPFD levels are not important as this would result in tall plants. For the speed breeding system, it was important to determine the point of a saturated response to BPFD to reach short plants and reduce the BPFD to reduce energy consumption. A saturated response to emitted BPFD was reached under treatments between 210 and 310 µmol m−<sup>2</sup> s −1 in the experimental setup. Two earlier studies on soybean found a saturated response already under 30–50 µmol m−<sup>2</sup> s −1 BPFD [17,18], whereas one study also found an effect from higher BPFD (130 µmol m−<sup>2</sup> s −1 ) [19],

indicating interactions with other factors resulting in these discrepancies. One aspect could be the light spectrum, as earlier studies used broader spectra containing green and far-red light [17–19] and additionally included UV-A light in the BPFD [19]. Green light can influence cryptochrome antagonistic to blue light and especially under high PPFD [47]. The addition of green light to a red and blue spectrum increased plant height of soybean under a PPFD of 200 µmol m−<sup>2</sup> s <sup>−</sup><sup>1</sup> but had no influence under 500 µmol m−<sup>2</sup> s −1 [48]. Far-red light can lead to an increase in plant height by reducing the red to far-red ratio perceived by phytochrome as shown for soybean by adding far-red light to a broad light spectrum [12]. In addition, a broader spectrum within the blue range can influence the magnitude of the blue light effect on cryptochrome. For hypocotyl elongation of *Arabidopsis thaliana* (L.) Heynh., the action spectrum of cryptochrome to monochromatic light did not change within the range 390–530 nm, but an increased stability of CRY2 protein was observed under monochromatic light compared to a broader blue spectrum [49]. These differences in the reactions under narrow peaks compared to the reactions during the response to high PPFD, here imitated with high BPFD, indicated that a broader spectrum within the blue range could affect the BPFD level necessary to avoid an elongation response.

In the experiments, the elongation response of the third internode to low BPFD was slightly stronger than at the second internode, and a higher BPFD level was necessary to achieve the minimum length of the third internode. Simulations indicated that this was due to self-shading, which was larger at the third than the second internode. Based on the simulated *BPFDper*, a common response function was found for the second and third internode. This emphasizes the importance of knowing the perceived light environment at organ-level, e.g., as in this study by means of simulations with an FSP model, as it enables a better evaluation of the influence from the light microclimate than relating the response directly to the light emitted from the light source [46].

The parameters *t<sup>e</sup>* and *t<sup>m</sup>* of the beta-function were in most cases not significantly different between treatments and no trend was present, which indicated that a common parameter could be used for all levels of BPFD only changing *Lmax* according to the *BPFDper*. This was confirmed by the accurate simulations of internode length at all BPFD levels based on *t<sup>e</sup>* and *t<sup>m</sup>* found under B310. Importantly, the small difference in height between B310 and B260 were well simulated, showing that the model was very useful to determine the necessary BPFD to reach the minimum height.
