*4.4. Statistical Design and Analysis*

Measurements of growth dynamics of internodes, petioles and leaflets of each phytomer were used to fit the beta-function (Equation (3)) [51]:

$$L(t) = L\_{\max} \left( 1 + \frac{t\_\ell - t}{t\_\ell - t\_m} \right) \left( \frac{t}{t\_\ell} \right)^{\frac{t\_\ell}{t\_\ell - t\_m}} \ 0 \le t\_m < t\_\ell \tag{3}$$

$$L(t > t\_\ell \ ) \ = L\_{\max}$$

where *L(t)* is the size at day *t*, *Lmax* is the final size, *t<sup>e</sup>* is the day when the final size is reached and *t<sup>m</sup>* is the day on which the growth rate peaks. The parameters *Lmax*, *t<sup>e</sup>* and *t<sup>m</sup>* were estimated with the nls-function in the R-package stats [52].

To determine the plants used for the destructive measurements during each experiment, randomizations were performed within two blocks (plant location). The first block comprised the first and last row and the second block the two center rows (Figure 7).

The six light treatments of the experiment were performed with two replicates. Given three LED chambers, three out of the six light treatments could be tested in the same run, i.e., each replicate comprised two runs, resulting in four runs in total (Supplementary Materials, S1). For the arrangement of treatments within the LED chambers over time and space, an α-design with two replicates and a block (time) size of two was used. The effect of BPFD on biomass, morphology, leaf physiology and parameters of the beta-function was tested. The second and mostly third phytomer (hypocotyl counted as first phytomer) were chosen for specific analysis, because they comprised the most comprehensive measurements from beginning to end of growth. According to the experimental design, the following mixed model was used to analyze the data in the SAS® software (SAS Institute, Inc., Cary, NC, USA):

$$y\_{iklmu} = \mu + b\_k + i\_{kl} + p\_{klm} + \tau\_{klmn} + \tau\_i + e\_{iklmn} \tag{4}$$

where µ is the intercept, *b<sup>k</sup>* is the fixed effect of the *k* th complete replicate, *ikl* is the random effect of the *l* th incomplete block (time) within the *k* th replicate, *pklm* is the random effect of the *m*th chamber within the *l* th run, *rklmn* is the random effect of the *n* th block (plant location) within the *m*th chamber of the *l* th run and the *k* th replicate, τ*<sup>i</sup>* is the main effect of the *i* th light treatment, and *eiklmn* is the error effect of observation *yiklmn* with homogeneous variance. Residuals were checked graphically for normal distribution and homogeneous variance. After finding significant effects via F-test, a multiple t-test to compare least square means was used to create a letter display [53]. Note that least square means are presented in the results section as data was not balanced, because only three out of six light treatments were tested within each run. Least square means are based on model (Equation (4)) to adjust for block effects.

**Figure 7.** Illustration of the randomization for the plants used for the destructive measurements within the first (light blue square) and second (dark blue square) block (plant location). The numbers exemplarily show the day of the destructive measurements the plants were used for.
