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 [19], 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) [19].

According to the theory of optimal foraging [128, 364], evolution through natural selection has led over time to highly efficient – even optimal – strategies.