The central idea underlying theoretical studies of the movement of organisms is that they need to encounter their targets. The targets can be other organisms of the same species (e.g., mates) or of a different species (e.g., prey) or, more generally, anything else sought (e.g., nesting sites). In the context of reactiondiffusion processes, the reactions (e.g., eating and mating) only take place when the relevant organisms successfully diffuse toward each other and meet. We next discuss a general theoretical approach to the study of encounter rates.
A general theory of searchers and targets
We classify the two interacting reactive-diffusive species (i.e., organisms) as either searcher (e.g., predator, forager, parasite, pollinator, male) or target (e.g., prey, food, female). Both searchers and targets move stochastically. We can now include most of the interactions in real ecosystems in this general framework , including the classical predator-prey interactions where an organism eats (usually smaller) organisms. It also includes diverse other interactions, such as osmotrophs looking for substrates and nutrients; parasites (including viruses) infecting organisms much larger than themselves (classical host-parasite interactions); organisms looking for aggregates (mixtures of amorphous organic matter, micro-organisms and/or inorganic particles), swarms, wakes, etc., also larger than themselves; and even mating encounters in which both male and female may have similar sizes (although sexual dimorphism is common) .
According to the theory of optimal foraging [128, 364], evolution through natural selection has led over time to highly efficient – even optimal – strategies.
From the previous chapters, we see that (1) superdiffusion optimizes search efficiencies under specific (but common) circumstances and that (2) many animals move superdiffusively. Assuming these two facts, does it follow that there is a causal relation between them? Lévy strategies indeed optimize random searches, but does it necessarily follow that selective pressures systematically forced organism adaptation toward this optimal solution?
This is an important question because an adaptive pathway toward an optimal solution can prematurely stop at some suboptimal point that decreases the selection pressure on this particular feature to a level below the selective pressures on other issues . Biology and physiology are replete with suboptimal solutions. The classic example is the structure of the human retina, which has blood vessels on the wrong side of the photosensitive layer . Compromise solutions arise because adaptation (1) includes a stochastic component, (2) has to build on preexisting designs, and (3) occurs in a complex field where other pressures may be present and may possibly be stronger.
Dolphins, in the context of (mammalian) swimming adaptations, perform well, but how can we know whether or not their shape represents an optimal design? Some species of shark may have an even better hydrodynamic shape. Also, why did dolphins return to the ocean when selective pressures were pushing for improved terrestrial adaptation? The complex evolutionary history of real organisms contains many such contingent situations, such as changing selective pressures, genetic drift, low-number bottlenecks, and rare catastrophic events.
Do good theories always come from good data?
According to conventional wisdom concerning the scientific method, good theories come from good experimental data, and bad theories from bad experimental data. Yet the history of the physics of foraging is a remarkable counterexample. To illustrate this, we briefly recount one of the important scientific investigations in the field, published in Nature in 1996. The original study of wandering albatrosses  inspired dozens of other studies, yet later required correction due to its spurious data.
Lévy flights of the wandering albatross
The albatross can fly great distances, at exceptional speeds. There are significant differences among species of albatross . Wandering albatrosses in southern Georgia can sustain a speed in excess of 100 km/h by taking advantage of the local wind field . They frequently fly 500 km per day, with an upper limit in the range 750–950 km per day. Phillips et al.  report that one gray-headed albatross circumnavigated the Southern Ocean in only 46 days. Because of their great mobility and large size, we decided to focus on the albatross (instead of, e.g., the sparrow) in our original study. The foraging strategy of the wandering albatross  stands apart from that of other seabirds . Weimerskirch et al.  studied the distribution of prey encounters for wandering albatrosses and reported results that strongly suggest a foraging strategy that differs from those of most seabirds.
The classic paradigm of simple diffusion is used to describe a wide range of phenomena, ranging from how the original humans migrated and dispersed out of Africa to the spread of pollen. Until the twentieth century, Fick's laws were thought to be universally valid for describing diffusion. The physiologist Adolf Fick introduced the idea that diffusion is proportional to the gradient of concentration. For practical as well as for historical reasons, normal diffusion is commonly assumed for transport processes. For example, Fourier's law for heat flow is analogous to Fick's laws of diffusion, with temperature gradients playing the role of concentration gradients.
Like Gaussian statistics, normal diffusion is ubiquitous because of the wide applicability of the central limit theorem. Standard methods in spatial ecology traditionally have tended to assume Brownian motion and Fickian diffusion as two basic properties of animal movement in the long time limit, i.e., at large spatial scales and long temporal scales. We refer the reader to the seminal book by Berg  on random walks in biology.
Fickian or normal diffusion assumes that animal movements can be modeled, in the long-term limit, as uncorrelated random walks [21, 35, 265]. In many cases, normal diffusion describes experimentally observed phenomena. The classic study by Skellam  of the colonization of Europe by muskrats assumed normal diffusion, for example (Figure 5.1).
Email your librarian or administrator to recommend adding this to your organisation's collection.