Fig. 5

Optimal foraging model. a shows a graphical definition of the model and b shows a simulation snapshot, illustrating a forager (large cyan circle) that has found a resource aggregate, and has switched to the slow movement mode to consume resources (small magenta circles). c shows how mean resource consumption rate \(\rho\) varies from a totally stationary searcher (\(\alpha =0\); continuous horizontal line) through a searcher following the optimal rate \({\alpha }^{\star }\) (vertical line) to a highly mobile searcher (\(\alpha \to \infty\), dashed line). In c, the dots with error bars show simulation results, whereas the lines follow the analytical prediction of \(\rho \approx {\rho }_{0}+{\epsilon }^{d}{\rho }_{1}\) (see Eq. (1)). The contour lines in d show the optimal switching rate \({\alpha }^{\star }\) as a function of the rescaled detection rate \(\gamma \beta /{\mu }^{2}\) of the searcher and the clustering level \(\lambda I\) of the targets. Error bars represent three standard errors. Parameters are shown in the Methods section