Applications of Search in Biology: Some Open Problems - Search Theory: A Game Theoretic Perspective - page 283

reasoning are bright. Importantly, any such insight would emerge from rigorous
theory, where the assumptions are transparent and the model ingredients precisely
defined (even if they do not perfectly mimic biological reality). This is a useful
counter to the fashion for ever-larger supercomputer simulations of biological sys-
tems, which can be visually compelling but which are prone to statistical misinter-
pretation, hidden parameter assumptions, and errors in computational implementa-
tion. There is room, and need, for both flavours of research.
In this brief article I first try to identify where the existing theories of search
and rendezvous may need rethinking when challenged by the uncomfortably dirty
realities of real-world biology. These are not criticisms. Indeed, many of the issues
raised are readily tackled within the context of existing theory. Where modifications
are needed, there is every chance that these are both tractable and intellectually
satisfying for those with large enough brains.
Finally, three open problems are described. In stark similarity to the “blind”
and “stupid” foragers considered below, these are constrained by the author's lo-
cal knowledge of the mathematical and biological research environment, and biased
heavily by those with whom he is fortunate to collaborate. Solving these problems
will confer uncertain intellectual fitness benefits within the complex and stochas-
tic research landscape, but is likely to provide avenues into still richer problems
emerging from the flood of technology-driven data.
18.2 Biological Complications Relating to Search
and Rendezvous
Individuals Move in Interesting Ways
Movement in biology was traditionally modelled using biased random walks; the
animal (or cell, or chemical) takes randomly oriented steps of a constant size, and
its location is described via a diffusive process with a Gaussian probability density.
Variations of this paradigm have been applied with much success [ 8 ]. However,
where random walks fail, this is likely to be for interesting reasons.
Firstly, organisms can sense their local environment directly, they can make
changes to this local environment, and they may gain more global knowledge via
visual or chemical cues. Global information will always, however, be uncertain
relative to local knowledge [ 6 ]. Such elaborations can be built into search theo-
ries; strategies employing 'tokens' (see Kiniwa et al., Chap. 8 , and Chalopin et al.,
Chap. 12 , for games that involve tokens), and the ideas of reinforced random walks,
have been usefully explored. Behaviour also depends on state; a hungry solitary lion
moves differently to a well-fed member of a pride. Again, existing theories can be
adapted (Broom, Chap. 15 )or[ 1 , 15 ].
Simple random walks are challenged by recent literature synthesising the data
and theory behind Lévy walks. Individuals across a broad range of species are ob-