Aggregated distributions

A more subtle, but more generally applicable path to the coexistence of a superior and an inferior competitor on a patchy and ephemeral resource is based on the idea that the two species may have independent, aggregated (i.e. clumped) distributions over the available patches. This would mean that the powers of the superior competitor were mostly directed against members of its own species (in the high-density clumps), but that this aggregated superior competitor would be absent from many patches - within which the inferior competitor could escape competition. An inferior competitor may then be able to coexist with a superior competitor that would rapidly exclude it paradox of the plankton a clumped superior competitor adversely affects itself and leaves gaps for its inferior

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k of the negative binomial

Figure 8.12 When two species compete on a continuously distributed resource, one species would exclude the other in approximately 10 generations (as indicated by the arrow). However, with these same species on a patchy and ephemeral resource, the number of generations of coexistence increases with the degree of aggregation of the competitors, as measured by the parameter k of the 'negative binomial' distribution. Values above 5 are effectively random distributions; values below 5 represent increasingly aggregated distributions. (After Atkinson & Shorrocks, 1981.)

k of the negative binomial

Figure 8.12 When two species compete on a continuously distributed resource, one species would exclude the other in approximately 10 generations (as indicated by the arrow). However, with these same species on a patchy and ephemeral resource, the number of generations of coexistence increases with the degree of aggregation of the competitors, as measured by the parameter k of the 'negative binomial' distribution. Values above 5 are effectively random distributions; values below 5 represent increasingly aggregated distributions. (After Atkinson & Shorrocks, 1981.)

from a continuous, homogeneous environment. Certainly it can do so in models (see, for example, Atkinson & Shorrocks, 1981; Kreitman et al., 1992; Dieckmann et al., 2000). For instance, a simulation model (Figure 8.12) shows that the persistence of such coexistence between competitors increases with the degree of aggregation (as measured by the parameter k of the 'negative binomial' distribution) until, at high levels of aggregation, coexistence is apparently permanent, although this has nothing to do with any niche differentiation. Since many species have aggregated distributions in nature, these results may be applicable widely.

Note, however, that whilst such coexistence of competitors has nothing to do with niche differentiation, it is linked to it by a common theme - that of species competing more frequently and intensively intraspecifically than they do interspecifically. Niche differentiation is one means by which this can occur, but temporary aggregations can give rise to the same phenomenon - even for the inferior competitor.

In seeking to justify the applicability of these models to the real world, however, one question in particular needs to be answered: are two similar species really likely to have independent distributions over available patches of resource? The question has been addressed through an examination of a large number of data sets from Diptera, especially drosophilid flies - where eggs are laid, and larvae develop, in ephemeral patches (fruits, fungi, flowers, etc.). In fact, there was little evidence for independence in the aggregations of coexisting species (Shorrocks et al., 1990; see also Worthen & McGuire, 1988). However, computer simulations suggest that whilst a positive association between species (i.e. a tendency to aggregate in the same patches) does make coexistence more difficult, the level of association and aggregation actually found would still generally lead to coexistence, whereas there would be exclusion in a homogeneous environment (Shorrocks & Rosewell, 1987).

The importance of aggregation for coexistence has been further supported by another spatially explicit model based on a two-dimensional lattice of cells (see Section 8.5.1), each of which could be occupied by one of five species of grass: Agrostis stolonifera, Cynosurus cristatus, Holcus lanatus, Lolium perenne and Poa trivialis (Silvertown et al., 1992). The model was a 'cellular automaton', in which each cell can exist in a limited number of discrete states (in this case, which species was in occupancy), with the state of each cell determined at each time step by a set of rules. In this case, the rules were based on the cell's current state, the state of the neighboring cells and the probability that a species in a neighboring cell would replace its current occupant. These replacement rates of each species by each other species were themselves based on field observations (Thorhallsdottir, 1990).

If the initial arrangement of the species over the grid was random (no aggregation), the three competitively inferior species were quickly driven to extinction, and of the survivors, Agrostis (greater than 80% cell occupancy) rapidly dominated Holcus. If, however, the initial arrangement was five equally broad single-species bands across the landscape, the outcome changed dramatically: (i) competitive exclusion was markedly delayed even for the worst competitors (Cynosurus and Lolium); (ii) Holcus sometimes occupied more than 60% of the cells, at a time (600 time steps) where, with an initially random arrangement, it would have been close to extinction; and (iii) the outcome itself depended largely on which species started next to each other, and hence, initially competed with each other.

There is no suggestion, of course, that natural communities of grasses exist as broad single-species bands - but, neither are we likely to find communities with species mixed at random, such that there is no spatial organization to be taken into account. The model emphasizes the dangers of ignoring aggregations (because they shift the balance towards intra- rather than interspecific competition, and hence promote coexistence), but also the dangers of ignoring the juxtaposition of aggregations, since these too may serve to keep competitive subordinates away from their superiors.

Despite a rich body of theory and models, there are few experimental studies that directly address the impact of spatial patterns on population dynamics. Stoll and Prati (2001) performed experiments with real plants in a study that had much in common with Silvertown's grasses in a cellular automaton plants in a field experiment

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theoretical treatment. They tested the hypothesis that intraspecific aggregation can promote coexistence and thus maintain high species richness in experimental communities of four annual terrestrial plants: Capsella bursa-pastoris, Cardamine hirsuta, Poa annua and Stellaria media. Stellaria is known to be the superior competitor among these species. Replicate three- and four-species mixtures were sown at high density, and the seeds were either placed completely at random or seeds of each species were aggregated in subplots within the experimental areas. Intraspecific aggregation decreased the performance of the superior Stellaria in the mixtures, whereas in all but one case aggregation improved the performance of the three inferior competitors (Figure 8.13).

More generally, the success of 'neighborhood' approaches (Pacala, 1997) in the study of plant competition, where the focus is on the competition experienced by individuals in local patches, rather than densities averaged out over whole populations, argues again in favor of the importance of acknowledging spatial heterogeneity. Coomes et al. (2002), for example, investigated competition between two species of sand-dune plant, Aira praecox and Erodium cicutarium, in northwest England. The smaller plant, Aira, tended to be aggregated even at the smallest spatial scales, whereas Erodium was moderately aggregated in patches of 30 and 50 mm radius but, if anything, was evenly spaced within 10 mm radius patches (Figure 8.14a). The two species, though, were negatively associated with one another at the smallest spatial scale (Figure 8.14b), indicating that Aira tended to occur in small, single-species clumps. Aira was therefore much less liable to competition from Erodium than would be the case if they were distributed at random, justifying the application by Coomes et al. of simulation models of competition where local responses were explicitly incorporated.

Repeatedly in this section, then, the heterogeneity often heterogeneous nature of the environ- stabilizes ment can be seen to have fostered coexistence without there being a marked differentiation of niches. A realistic view of interspecific competition, therefore, must acknowledge that it often proceeds not in isolation, but under the influence of, and within the constraints of, a patchy, impermanent or unpredictable world. Furthermore, the heterogeneity need not be in the temporal or spatial dimensions that we have discussed so far. Individual variation in competitive ability

Figure 8.13 (left) The effect of intraspecific aggregation on above-ground biomass (mean ± SE) of four plant species grown for 6 weeks in three- and four-species mixtures (four replicates of each). The normally competitively superior Stellaria media (Sm) did consistently less well when seeds were aggregated than when they were placed at random. In contrast, the three competitively inferior species - Capsella bursa-pastoris (Cbp), Cardamine hirsuta (Ch) and Poa annua (Pa) - almost always performed better when the seeds had been aggregated. Note the different scales on the vertical axes. (From Stoll & Prati, 2001.)

(a) Aira Erodium

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(a) Aira Erodium

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Figure 8.14 (a) Spatial distribution of two sand-dune species, Aira praecox and Erodium cicutarium at a site in northwest England. An aggregation index of 1 indicates a random distribution. Indices greater than 1 indicate aggregation (clumping) within patches with the radius as specified; values less than 1 indicate a regular distribution. Bars represent 95% confidence intervals. (b) The association between Aira and Erodium in each of the 3 years. An association index greater than 1 indicates that the two species tended to be found together more than would be expected by chance alone in patches with the radius as specified; values less than 1 indicate a tendency to find one species or the other. Bars represent 95% confidence intervals. (After Coomes et al., 2002.)

within species can also foster stable coexistence in cases where a superior nonvariable competitor would otherwise exclude an inferior nonvariable species (Begon & Wall, 1987). This reinforces a point that recurs throughout this text: heterogeneity (spatial, temporal or individual) can have a stabilizing influence on ecological interactions.

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