Of all areas of ecology, population biology is perhaps the most mathematically developed, and has involved a long history of mathematicians fascinated by problems associated with the dynamics of population development. Interest was induced by early studies of small mammals and laboratory controlled organisms, since these easily lent themselves to a mathematical formulation. A great deal of more recent research is concerned with modelling multi-species and spatial population growth, though it is not clear just how effective these models are for predicting behaviour outside the laboratory. There is general uncertainty regarding whether populations in the natural environment are mostly regulated from within by density-dependent factors, or whether the main influence is due to external density-independent factors. Theoretical developments have generally followed the former route, primarily because there is much less information on external factors due to their complexity and variability (see Gross, 1986).

Throughout most of this text we shall therefore disregard the (generally unknown) external influences on population growth, and develop the ideas of density-dependence. Moreover, since even apparently minor modifications to simple biological models can lead to difficult, if not intractable, mathematics, we shall begin by investigating the simplest possible forms of model structure (Chapter 2). In these, members of a population are assumed to develop independently from each other, for then the resulting mathematical analyses are sufficiently transparent to enable useful biological conclusions to be drawn.