14 - Perspectives and open problems

Summary

The flavor of foraging research

The physics of foraging is exciting because so little is known and so many questions remain. Biological foraging and random searching are relatively new fields, and considerable effort is still being made to establish theoretical foundations and reliable and general methods of data collection and analysis. Many challenges are still to be overcome, most of them related to technical issues and interpretation of findings.

In this final chapter, we put the major open problems into perspective. One reason for the skepticism about anomalous diffusion and Lévy flights is the lack of obvious biological mechanisms for generating superdiffusive random walks. We will also discuss the issue of free will and the existence and uniqueness of globally optimum strategies. We begin with two problems currently being studied by researchers.

Foraging on the edge of extinction

In mass extinctions and smaller-scale extinctions, the density of organisms becomes zero (if extinction is total) or very low (if recovery eventually takes place). We saw in Chapter 13 that as the density of targets lowers, the importance of superdiffusion increases. How does organism movement change during extinction events? Is there any change in the selection pressure on how organisms move? Such questions remain relatively unexplored at the present time.

Lévy searches on small-world networks

We saw in Chapter 10 that Lévy motion can confer advantages to search processes not only in Euclidean spaces but also in discrete analogues (large-world networks), but what happens in the environment of small-world networks?