Numerical simulations
The parameters of the simulation correspond to Fig. 2D and E, Fig. 3C. For each parameters \(D_{\theta}\) and \(\nu\), 1000 trajectories of 600 sec were simulated using a time-step \(\delta t=0.1\ \)sec with the parameter values \(V_{0}=17\ \mu m/s\), \(D_{r}=0\ \mu m^{2}/s\),\(\omega=\pi/36\) rad/s. In Fig. 4C, \(\nu=0.02\ s^{-1}\), in Fig. 4D, \(D_{\theta}=0.0054\ rad/s\).
We start by analyzing an active cell with a sensing radius \(r_{c}\), blindly searching for 4000 nutrient resource (targets) in an environment with a homogeneous topography (47). As a diatom cruises throughout the searching space, it continuously captures nutrients that come within a capture radius \(r_{c}\) from the cells center. At each step, the ‘nutrients’ that come within a capture radius \(r_{c}\) from the cell center will be removed. We evaluate the individual search efficiency by calculating the leftover nutrients \(n\) in the searching space. The amount of leftover nutrients \(n\) in each run shows a monotonous decline as a function of the area swept by the active cell. Here, we assume that all cells use the same strategy of reversal and rotational diffusivity for the simulations. Fig. 4B plots the average amount of leftover nutrients \(n\), obtained from 1,000 simulated trajectories as a function of various rotational diffusivity, so that the decay rate\(\tau\) of the exponential fitted is defined as the foraging efficiency.
For the evolutionarily stable strategy analysis, up to 1000 cells are simulated with various prescribed rotational diffusivities\(D_{\theta}\). Fitness is given by the product of survival probability and division rate. We assumed that survival probability is proportional to the foraging efficiency in the ESS analysis. A mutant strategy with a relative fitness value larger than the resident population will invade and potentially take over them. For any combination of resident and mutant movement strategy, the relative fitness of the mutants is depicted in a pairwise invasibility plot (Fig. 6).