Vandermeer (1969) reported on a quantitative study of a community of four competing ciliate protozoan populations. The model he fitted to his observations (see previous post) indicated that three of the six pairs of interactions between the competitors were positive-negative (figure 1). One would expect this of predator-prey relations, not of competitive interactions Were these interactions actually predator-prey? Indeed, were those pairs with negative-negative interactions actually competitors? How can the values Vandermeer derived be understood and related to the actual ecological relationships among the protozoan populations?

Figure 1. Community interactions reported by Vandermeer (1969). PA = Paramecium aurelia, PB = Paramecium bursaria, PC = Paramecium caudatum, BL = Blepharisma sp.

An obvious response might be that Vandermeer’s model was inappropriate or inadequate, so let me examine this first. The inter-population interaction values he derived for his four protozoan species came from fitting the observed population trajectories to a model of the following form:

Model 1: Generalized Lotka-Volterra (GLV)

Per capita rate of change of population X =

Intrinsic growth rate for X +

Self-interaction within the X’s +

Sum of interactions of the other populations on X;

where the first term is a constant, the second is a constant times the size of population X, and the inter-population terms are constants times the sizes of the other populations.

He estimated the intrinsic growth term and self-interaction term from isolated population growth experiments, and his inter-population interaction terms from two-population experiments. Contrary to the widely held opinion that the GLV is a poor ecological model, the fit for Vandermeer’s four-population microcosms was fairly good and gave qualitatively correct predictions about coexistence of populations (Vandermeer 1981).** **

Given that Vandermeer’s model fits his observations well, one needs to look further to explain the anomalous (- +) interaction values between the competing protozoans. First note that Vandermeer’s equations did not specify all the components of the community. Each day during his experiment he removed a sample from his experimental tubes and added an equal volume of culture medium with bacteria. The bacterial populations were alive and able to grow until consumed by the protozoa. They had dynamics of their own not referred to in the equation above. In fact, it is possible that the protozoan populations were affecting each other only through these shared bacterial prey. If all the fitted interactions had indicated competition, the unspecified components might not have caused me any concern—the protozoan populations could be described as exploitative competitors. Yet the interactions were not all competitive.

Notice that the observed behavior of the protozoan sub-community—the full community minus the bacteria—was fitted with a model containing interactions only within the sub-community. Because there was no direct reference to the relationships with the hidden part of the community, the fitted interaction values had to incorporate these other indirect relationships, if they existed. Let me call the fitted interactions *apparent* interactions and use this term whenever ecologists attempt to specify the ecological dynamics of a sub-community without explicit reference to the dynamics of the community from which it has been elevated. In practice, fitted interaction values might always be apparent interactions, because there will be components the ecologists do not know about or have no data on—for example, larval and adult life stages will be lumped together, or decomposers or other components in the food web will be omitted.

The critical question is whether the distinction between direct and apparent interactions matters. Do apparent interactions deviate significantly from direct observations of interactions or from ecologists’ intuition about plausible interactions among populations? Ecologists tends to think that the protozoan populations should be competitors because they share a food resource, but Vandermeer’s study counters that idea. Can a more general conclusion be derived? This question is addressed in Taylor (2005, Chapter 1B). The next post compares different formulations of the idea of apparent interactions.

Adapted from Taylor, P.J. (2005) Unruly Complexity: Ecology, Interpretation, Engagement (U. Chicago Press).

**References**

Vandermeer, J. H. (1969). “The competitive structure of communities: An experimental approach with protozoa.” Ecology 50: 362-371.

—— (1981). “A further note on community models.” American Naturalist 117: 379-380.

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