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).