9 - Spatial population dynamics

Summary

The geographic distribution of a species over its range of habitats, and the associated dynamics of population growth, are inseparably related, a fact which no complete study of population development can afford to ignore (see Levin, 1974). Thus whilst the assumption that populations develop at a single location is ideal for mathematical purposes, in real life we must accept that individuals seldom mix homogeneously over the whole region available to them but develop instead within separate sub-regions. Indeed, this is precisely the reason why we extended the non-spatial predator–prey process (Chapter 6) to allow individuals of either species to migrate between separate sites (Chapter 7). Having shown that spatial and non-spatial predator–prey behaviour can be very different, we clearly need to extend our spatial framework to cover more general population processes.

Most species attempt to migrate for a variety of both individual and population reasons, including: search for food; territorial extension for increasing population needs; widening the available gene pool; and minimizing the probability of extinction. Migration can range from being purely local, e.g. aquatic life in a small pond, to extensive migration patterns covering a fair part of the Earth's surface, e.g. birds, locusts, salmon, caribou, and viruses. Moreover, migration can occur either between distinct sites, such as neighbouring valleys or islands in an archipaelego, or else it can occur within continuous media such as the air or sea.