So far we have just considered single-species population dynamics. However, in nature organisms do not generally exist in isolated populations but they live alongside organisms from many other species. Whilst a large number of these species will be unaffected by the presence or absence of one another, in some cases two or more species will interact competitively. Such competition may either be for common resources that are in short supply, such as food or space, or it may be that organisms from different species attack each other directly.

Now there is considerable evidence to suggest that species population stability is typically greater in communities with many interacting species than in simple ones. For example, it has been noted that simple laboratory predator–prey populations characteristically undergo violent oscillations; cultivated land and orchards have shown themselves to be fairly unstable; whilst the rain forest, a highly complex structure, appears to be very stable. On closer examination, however, the issue clouds over since species integration in a complex community is a highly non-linear affair, and quite remarkable instabilities can ensue from the introduction or removal of a single species (May, 1971b). We shall therefore ignore the difficult world of three or more interacting populations and concentrate on just two (an extremely important field of study in its own right).

Before we begin it is worthwhile repeating Park's (1954) warning that the functional existence of inter-species competition may be inferred from a body of data even when no such inter-species dependence exists.