Applications of Search in Biology: Some Open Problems - Search Theory: A Game Theoretic Perspective - page 284

served to make small local random movements interspersed with rare long-distance
jumps. When the probability distribution for the step size follows a power law the
resulting process is called a Lévy walk. Theory borrowed from theoretical physics
has been used to infer optimality of such super-diffusive movement strategies for
sparse patchily distributed prey. Careful analyses of theory, computation, and infer-
ence from data have cast doubt on any such global assertion of optimality [ 16 , 17 ].
Nevertheless, search theories should be freed from the constraints of the diffusive
paradigm.
Environments Are Interesting
Biological environments are seldom, if ever, homogeneous, isotropic, and static.
Complex and dynamic structure is visible at scales ranging from the sub-cellular to
the ecological. The consequences of this complexity are intimately related to those
concerning modelling movement as simple random walks versus sub- or super-
diffusive processes outlined above, and there are mathematical analogies in their
methods of solution. Ecology involves, by definition, interactions between life and
environment, and so very often the feedbacks between searcher and search arena
will dictate behaviour.
One exciting direction is to escape Euclidean space in favour of environments
described by graphs; a collection of locations connected by weighted edges. Inter-
actions between biology and complex environments can be captured succinctly and
elegantly in this way (see, for example, Durham et al. [ 11 , 12 ]) and the expand-
ing theory of search on networks (Chap. 2 of this volume) has great potential to
be applied. Linking such individual-based studies to larger-scale properties at the
population level (sensu [ 18 ]) is an important and tractable challenge.
Some Princesses Are Monsters
It is tempting to transfer theories directly between disciplines, for example by taking
the classic Princess and Monster game [ 14 ] and identifying the Princess as “prey”
and the Monster as “predator”. However, even a princess must eat, and only the
rarest and most savage monster can safely consider itself invulnerable to attack.
In other words, the actors in biological systems may be motivated by factors not
considered by the modeller, either by choice or through ignorance.
Conversely, observing a particular behaviour in nature and attributing this to op-
timisation of some externally imagined metric could be misleading - ambiguities
between pattern and process are common in the literature. It may be possible to
show compelling statistical differences between the movement of male and female