Abstract Bartumeus

Based on a one-dimensional comparative analysis we show a mechanism by which, at random, a searcher can optimize the encounter with close and distant targets. The mechanism consists of combining an optimal diffusivity (optimally enhanced diffusion) with a minimal diffusion constant. In such a way the search dynamics adequately balances the tension between finding close and distant targets, while, at the same time, shifts the optimal balance towards relatively larger close-to-distant target encounter ratios. We find that introducing a hierarchical multiscale set of reorientations ensures both a thorough local space exploration without oversampling and a fast spreading dynamics at the large scale. More recent works show that, if partial knowledge exists about target relative distances the best alternative (in terms of search efficiency) to a random search is an informed combination of only two walk scales (related to the exploitative and explorative scales, respectively).

Ref.: Vicenc Mendez, Daniel Campos, Frederic Bartumeus, Stochastic foundations of movement ecology (Springer, Berlin, 2013)