The R Book, 2nd Edition

Chapter 28

Simulation Models

Simulation modelling is an enormous topic, and all I intend here is to demonstrate a few very simple temporal and spatial simulation techniques that give the flavour of what is possible in R.

Simulation models are used for investigating dynamics in time, in space, or in both space and time together. 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).

For spatial dynamics, we might use simulation models to study:

• metapopulation dynamics (where local extinction and recolonization of patches characterize the long-term behaviour, with constant turnover of occupied patches);
• neighbour relations (in spatially explicit systems where the performance of individuals is determined by the identity and attributes of their immediate neighbours);
• pattern generation (dynamical processes that lead to the generation of emergent, but more or less coherent patterns).

28.1 Temporal dynamics: 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 ...