Movement behavior driven by optimal foraging
If the prediction of the optimal foraging theory holds for the studied diatoms, one intuitive corollary is that the observed “circular run-and-reversal” movement mode can provide a statistical property that can maximize foraging efficiency. Indeed, our model analyses together with experimental data lend support to this speculation.
In the model setting with homogeneously distributed forage targets (Fig. 4A), our simulation analyses (see Materials and Methods ) show that the amount of resource remaining in the environment decays in an exponential manner over time (Fig. 4B). We thus use the exponent of the exponential decay as a straightforward indicator of foraging efficiency, estimated by the regression slope of unconsumed resource on logarithmic scale over time. A larger exponent (\(\tau\)) means that more resource targets can be found per unit time, hence indicating a higher foraging efficiency. However, this indicator cannot not be feasibly derived from the analytic model. Instead, we used effective diffusivity as a measure of foraging efficiency. In both analytic models and simulations, we consistently found optima of foraging efficiency at rotational diffusivity \(D_{\theta}\) around 0.1 (Fig. 4C, E). A striking finding is that this optimal point is very close to the experimentally observed values of \(D_{\theta}\). This is especially true for the simulations (there is only 9% deviation between the model and experiments, Fig. 4C) with a more realistic measure of foraging efficiency. The larger discrepancy between the analytical model and experimental data might be explained by the fact that the theoretically derived diffusion coefficient, although being strongly correlated, is insufficiently reflective of actual foraging efficiency under specific conditions (37). In our model, foraging efficiency does not show any peak with changing reversal rate (\(\nu\)) (Fig. 4D, F). However, the experimentally observed values of \(\nu\) are consistently located within the ranges presenting maximum foraging efficiency. The consistency between the experimental observations and model results remains robust if we plot the data and modeled foraging efficiency in two-dimensional parameter space (\(D_{\theta},\nu\)), clearly showing that the experimental points fall within the optimal strategy regions (yellow regions in Fig. 5A, B).
Unlike the rotational diffusivity, the lack of optimum in foraging efficiency as a function of reversal rate \(\nu\) in our random-environment model suggests that a relatively wide range of\(\nu\) can have maximized foraging efficiency. This seems somewhat counterintuitive, and contrasts with our experimental observation presenting a rather narrow range of \(\nu\). We infer there should be other benefit to obtain from the reversal behavior, such as self-organized biofilm formation, whereas a substantial experimental evidence is still lack.
Taken together, the experimentally observed movement parameters (both\(\nu\) and \(D_{\theta}\)) are consistently found in the vicinity of theoretically predicted optimal foraging efficiency. This suggests the plausibility that the movement pattern of the diatom is in line with the optimal foraging theory.