The R Book, 3rd Edition

23Simulation Models

Simulation modelling is an enormous topic, and all we will do here is to demonstrate a few very simple temporal and spatial simulation techniques that give the flavour of what is possible in , which has very powerful simulation capabilities. Simulation models are typically used for investigating dynamics in time, in space, or in both space and time together.

23.1 Temporal dynamics

For temporal dynamics, we might be interested in:

• the transient dynamics (the behaviour after the start but before equilibrium is attained – if indeed equilibrium is ever attained);
• equilibrium behaviour (after the transients have damped away);
• chaos (random‐looking, but actually deterministic temporal dynamics that are extremely sensitive to initial conditions).

23.1.1 Chaotic dynamics in population size

Biological populations typically increase exponentially when they are small, but individuals perform less well as population density rises, because of competition, predation, or disease. In aggregate, these effects on birth and death rates are called density‐dependent processes, and it is the nature of the density‐dependent processes that determine the temporal pattern of population dynamics. The simplest density‐dependent model of population dynamics is known as the quadratic map. It is a first‐order non‐linear difference equation:

where is the population size at time ...