*4.6. Response Function*

The response function was derived and integrated following four steps: (1) fit beta-function for all treatments, (2) run FSP model to obtain perceived BPFD of internodes for each treatment, (3) derive response function across all treatments for internode length in dependence of simulated perceived BPFD and (4) integrate the derived response function into the model for all treatments.

Based on the experimental observations, the parameters for the beta-function were derived for each light treatment. Based on these parameters, the FSP model of soybean dynamically simulated the plant architecture over time under each of the six light treatments.

At this stage, the growth of the internodes stopped at a final length according to the measurements. During the simulations, BPFD perceived by the internodes was recorded for each hour. The simulated perceived BPFD was used to fit a response function to the internode length observed under the different BPFD treatments:

$$\text{Internode length} = \text{L}\_{\text{min}} \left( \mathbf{1} + \left( BPFD\_{\text{min}} - BPFD\_{\text{per}} \right) \mathbf{a} \right) \text{ BPFD}\_{\text{min}} - BPFD\_{\text{per}} > \mathbf{0} \tag{5}$$

where *Lmin* is the minimum possible length of the internode, *BPFDmin* is the lowest BPFD giving *Lmin*, *BPFDper* is the average perceived BPFD of the internode during the first four days of growth and *a* is the slope of the response to *BPFDper*. The first four days of growth were used due to a very rapid growth inhibiting effect of blue light [59] and according to the results of Kahlen and Stützel [46] who found four successive days starting one week before reaching maximum growth rate to be particularly sensitive to changes in PPFD.

The found BPFD response function was integrated in the FSP model to determine *Lmax* of the beta-function and the final internode length. They were hereby simulated in dependence of the perceived BPFD during the simulations and at this stage no longer determined by experimental measurements. Internode two until nine elongated according to the integrated response function, with *Lmin*, and *t<sup>m</sup>* set for each internode according to the found parameter values for the treatment

B310 (baseline scenario with shortest internodes). Because the first internode (hypocotyl) grew before thinning and beginning of experimental measurements, its length was set to grow to the final average length of all treatments.
