The practical consequence of independent development is that individual members of a population must be able to live in virtually unrestricted environments in which no intraspecific competition can occur. Obvious potential situations are where species have been introduced into, or have invaded, isolated areas. Unfortunately, very few such cases have been extensively studied, though one that has is the invasion of Great Britain by the collared dove, Streptopelia decaocto (Hutchinson, 1978; Hengeveld, 1989). The bird spread westwards in Europe and started to breed in Britain in 1954. For the next ten years reasonably accurate censuses exist, but then the dove became sufficiently common to reduce its appeal to bird watchers and so data collection became inadequate. The rise in population growth between 1955 and 1963 (Figure 2.1) shows an almost linear relationship between the logarithm of population size and time. As we shall soon see, this is associated with independent growth during the early years; breeding birds were pioneers with no immediate neighbours. However, by the mid-1960s the dove had colonized most of Britain and competition for resource was beginning to take effect, shown by the crude 1970 estimate which is quite out of line with the values for earlier years.

If we ignore the invasive spatial element, the development of the dove population involves just two features, birth and death. Since each of these is easiest to understand in isolation, we shall first study them separately (Sections 2.1 and 2.2) before bringing them together as the simple birth–death process (Section 2.3).