'Gaps' of unoccupied space occur unpredictably in many environments. Fires, landslips and lightning can create gaps in woodlands; storm-force seas can create gaps on the shore; and voracious predators can create gaps almost anywhere. Invariably, these gaps are recolonized. But the first species to do so is not necessarily the one that is best able to exclude other species in the long term. Thus, so long as gaps are created at the appropriate frequency, it is possible for a 'fugitive' species and a highly competitive species to coexist. The fugitive species tends to be the first to colonize gaps; it establishes itself, and it reproduces. The other species tends to be slower to invade the gaps, but having begun to do so, it outcompetes and eventually excludes the fugitive from that particular gap.
This outline sketch has been given some quantitative substance in a simulation model in which the 'fugitive' species is thought of as an annual plant and the superior competitor as a perennial (Crawley & May, 1987). The model is one of a growing number that combine temporal and spatial dynamics by having interactions occur within individual cells of a two-dimensional lattice, but also having movement between cells (see also Inghe, 1989; Dytham, 1994; Bolker et al., 2003). In this model, each cell can either be empty or occupied by either a single individual of the annual or a single ramet of the perennial. Each 'generation', the perennial can invade cells adjacent to those it already occupies, and it does so irrespective of whether those cells support an annual (a reflection of the perennial's competitive superiority), but individual ramets of the perennial may also die. The annual, however, can colonize any empty cell, which it does through the deposition of randomly dispersed 'seed', the quantity of which reflects the annual's abundance. Putting details aside, the annual can coexist with its superior competitor, providing the product (cE*) of the annual's fecundity (c) and the equilibrium proportion of empty cells (E*) is sufficiently great (Figure 8.10), i.e. as long as the annual is a sufficiently good colonizer and there are sufficient opportunities for it to do so. Indeed, the greater cE*, the more the balance in the equilibrium mixture shifts towards the annual (Figure 8.10).
An example is provided by the coexistence of the sea palm Postelsia palmaeformis (a brown alga) and the mussel Mytilus californianus on the coast of Washington (Paine, 1979). Postelsia is an annual that must re-establish itself each year in order to persist at a site. It does so by attaching to the bare rock, usually in gaps in the mussel bed created by wave action. However, the mussels themselves slowly encroach on these gaps, gradually filling them and precluding colonization by
Figure 8.10 In a spatial lattice, a model fugitive annual plant can coexist with a competitively superior perennial provided cE* > 1 (where c is the annual's fecundity and E* the equilibrium proportion of empty cells in the lattice). For larger values, the fraction of cells occupied by the annual increases with cE*. (After Crawley & May, 1987.)
Postelsia. Paine found that these species coexisted only at sites in which there was a relatively high average rate of gap formation (about 7% of surface area per year), and in which this rate was approximately the same each year. Where the average rate was lower, or where it varied considerably from year to year, there was (either regularly or occasionally) a lack of bare rock for colonization. This led to the overall exclusion of Postelsia. At the sites of coexistence, on the other hand, although Postelsia was eventually excluded from each gap, these were created with sufficient frequency and regularity for there to be coexistence in the site as a whole.
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