Throughout this book I have emphasized how simple rules followed by individual animals and humans can produce surprisingly complex patterns. It is this observation, combined with the idea that we can use mathematical models to predict these patterns, upon which the idea of self-organization is founded (Camazine et al. 2001; Nicolis & Prigogine 1977). Indeed, it is common to hear these “complex systems” contrasted with “complicated systems.” The former term is associated with systems in which complexity emerges from simple interactions, while the latter is associated with systems where large numbers of different components, each with its own particular role, interact to produce an output. The contrast is best illustrated by examples from physics. An example of a physicist’s complex system is a sandpile. When grains of sand are dropped from above onto a particular position, a pile builds up and sand moves down the outside of the pile. The movement of sand on the outside of the pile is difficult to predict and occurs on scales ranging from small local toppling to large avalanches. Removing one or two grains of sand will not change this overall pattern. A car or an airplane, on the other hand, can be thought of as complicated. It consists of lots of parts that are carefully put together to drive from A to B. Removing certain components can completely change the car’s capability of completing its journey.
Are animal groups sandpiles or cars? Up until now, I have emphasized the former analogy. However it is often the second analogy that is more appropriate when studying animal interactions. For example, individual honeybees are known to use at least 17 different communication signals, the most famous of which is the waggle dance, and adjust their behavior in response to at least 34 different cues (Seeley 1998). The bees take different behavioral roles at different times during their life. Furthermore, there are certain components, such as the queen, which are essential to the smooth functioning of the colony.
In general, when building mathematical models the question of whether a system is complex or complicated is not a particularly useful one to ask. Rather, the question is whether there is a level of description at which