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.