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Supporting Information A. Isotropic and anisotropic growth.

Supporting Information B. The model.

Supporting Information C. Model implementation: an exact stochastic simulator.

Supporting Information D. Model calibration.

Fig. S1. Relationship between cluster surface area and perimeter for clusters in the trough at day 13. For all scaling relationships, the coefficient of determination (R2) was greater than 0.93 and significance (P) better than 0.0001. (a) The relationship of area versus perimeter results in an exponent between 0 and 1. Isotropic growth yields an exponent of 0.5. Increasing deviation of an exponent of 0.5 indicates an isotropic growth. Independent of the geometric shape (here circle and square) isotropic growth results in an exponent of 0.5. The example for anisotropic growth in one axis is given by ‘square’, where the doubling of one axis results in an exponent 0.83. The ‘ellipse’ is an example of anisotropic growth in both axis with the ratio of 4:1 (a:b), resulting in an exponent of 0.63.

Fig. S2. Schematic representation of one iteration of the multi-objective procedure used to calibrate model parameters. (a) Several simulations are run with different parameter sets (blue dots) chosen from broad parameter ranges (grey shading) through Latin hypercube sampling (steps 1–3 of the calibration procedure). (b) The candidate simulations are evaluated according to different objectives (blue dots); then Pareto-efficient candidates are identified (red dots); finally, top-ranked simulations (green dots) are selected (steps 4–6). After these steps, the search space is narrowed down (step 7), and the procedure is repeated until convergence (step 8). Note that the fitting procedure is portrayed here for a generic problem with two tuning parameters and two calibration objectives (e.g. minimization of the RSS's for two observed/simulated quantities).

Fig. S3. Probability density functions of daily size distributions for clusters located at the crest. Red dots: experimental data; blue circles: reference model simulation; grey dots: results from 500 model simulations with parameter values randomly selected from uniform distributions centred around the reference parameter set (±20% variations).

Fig. S4. Q-Q plot of modelled versus observed size distributions for clusters located at the crest. The closer the blue crosses to the green line (where model results are exactly equal to experimental observations), the higher the explanatory power of the model. The values of R2 have been computed as R2 = 1 − RSS/TSS, where TSS is the total sum of squares of the observations (quantiles of cluster log-sizes).

Fig. S5. Probability density functions of daily size distributions for clusters located in the trough (details as in Fig. S3).

Fig. S6. Q–Q plot of modelled versus observed size distributions for clusters located in the trough (details as in Fig. S4).

Table S1. Chlorophyll-a concentration and bacterial abundance at the crest and in the trough at day 4 and day 12 of the experiment. Given are mean values (n = 3) ± SD. Both chlorophyll-a concentration (paired t-test: tdf:5 = 2.06, P = 0.1) and bacterial abundance (paired t-test: tdf:5 = 1.13, P = 0.31) did not differ significantly between crest and trough.

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