Seifert and Seifert (1976) provided one of the earliest field tests of the community matrix using insects in the water-filled bracts of Heliconia flowers in Central America (Fig. 7.5). The insects included larvae of chrysomelid beetles and syrphid flies, all of which were potential competitors.

Seifert and Seifert combined experimental manipulations with a multiple regression method which allowed them to estimate the magnitude and signs of the interaction coefficients from a generalized Lotka-Volterra model. This meant that statistical significance could be attached to each of the coefficients. The experiment involved emergent buds of Heliconia being enclosed in plastic bags to restrict immigration and oviposition. After a certain amount of growth, water was added and varying numbers of four species of insects were introduced. Following this the per-capita change in numbers with time was determined using a linearized version of equation 7.1, calculated as the change from initial density divided by the number of days over which the change took place. The initial densities of each species were used as the explanatory

Fig. 7.5 Stylized view of Heliconia wagneriana showing the dissected bract with common insect inhabitants. The species include Gillisius located on the dissected bract just above the water, Quichuana located at the base of the flower below Gillisius, Copestylum located just inside the flower and Beebeomyia located at the base of the seed. From Seifert and Seifert (1976).

Fig. 7.5 Stylized view of Heliconia wagneriana showing the dissected bract with common insect inhabitants. The species include Gillisius located on the dissected bract just above the water, Quichuana located at the base of the flower below Gillisius, Copestylum located just inside the flower and Beebeomyia located at the base of the seed. From Seifert and Seifert (1976).

variables to calculate the partial regression coefficients of the per capita rates of change against all species; that is, this gave r and aij. (Note that the rates of change were not estimated from equilibrium as assumed by the community matrix.) A negative value of the regression coefficient indicated competition while a positive value indicated mutualism (the possibility of predation was ignored given the choice of insect species). From Table 7.2 we see that nine of the inter-specific interactions were not significant and therefore were set to zero. Of the significant ones, two were negative (competitors) and one was positive (mutualism).

The equilibrium densities estimated from the model by N* = A^1ri are shown in Table 7.3 compared with those observed in the field. The fact that there are two negative (unrealistic) densities for H. wagneriana suggests that the observed mean densities either are not equilibrium densities or are results of processes not dependent on species interactions, or that the model is inappropriate.

The eigenvalues of the community matrix were determined to examine the stability of the community. The four values were -0.0221, 0.052, -0.042 and -0.239. The positive eigenvalue indicated an unstable community. Seifert and Seifert's conclusion was that H. wagneriana insect communities were indeed unstable and that migration, oviposition and local extinction processes may be important in structuring these communities. In other words it is probably not correct to model these communities in isolation. The effects of migration and local extinction are the subject of Chapter 8.

Table 7.2 Interaction matrix for Heliconia wagneriana. Non-significant coefficients are set to zero (Seifert & Seifert 1976).

Quichuana

Gillisius

Copestylum

Beebeomyia

Quichuana Gillisius Copestylum Beebeomyia

0.001

0.027

Table 7.3 Equilibrium densities predicted from the model compared with mean densities observed in the field (Seifert & Seifert 1976).

Mean densities in Estimated species unmanipulated examples equilibrium densities

Quichuana 51.00 -112

Gillisius 7.56 -23.2

Copestylum 8.78 4.09

Subsequent studies of the community matrix have covered a wide range of species. Wilson and Roxburgh (1992) provided examples of the application of the community matrix to plant species mixtures. They predicted that initially unstable six-species mixtures will, by selective deletion (following Tregonning & Roberts 1979), drop down to stable four-species mixtures. A study of the persistence of chironomid communities in the River Danube demonstrated differences in return times of perturbed communities at different sites (Schmid 1992). An analysis of local and global stability in six small mammal communities showed that all the community matrices were locally and globally stable, due to a reduction in connectance with increasing number of species (Hallett 1991).

The above examples show that it is possible to parameterize community matrix models using field data (with or without manipulations) and make testable predictions about stability, structure and return times after perturbation. Such predictions can be related to species richness and connectance. However, we need to be cautious as analysis of the community matrix is in the neighbourhood of an assumed equilibrium. For many applications we are likely to be interested in communities away from equilibrium or where non-equilibrium processes such as physical disturbance or pollution may be important. Local extinction and colonization processes may also mean that equilibrium has to be judged at larger spatial scales (Chapter 8).

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