SUPPLEMENTARY MATERIALS

Text S1. Theoretical derivation for the expected value of MSD and diffusivity.

Fig. S1. Distribution and trajectories of experimental \(D_{\theta}\).

Fig. S2. Trajectories at three different values of \(D_{\theta}\).

Fig. S3. Behaviors of mean squared displacement (MSD) at different values of \(D_{\theta}\).

Fig. S4. The efficiency without scaling to the maximal foraging efficiency.

Movie S1. Typical trajectories of swimming diatoms in real experiments on diatom movement behaviors.

Movie S2. Typical trajectories of swimming diatoms in theoretical simulations of Eqs. (1).