Ecology is the study of complex interactions. But what, exactly, is an ecological interaction? This and the following posts will indicate that our intuition can be misleading. When I see the Great Blue Heron standing still near the edge of the local river suddenly duck its head under the surface and come up with fish in its beak, I know that, as a three-year old on my knee once said watching a nature show, the fish won’t be going home to mummy tonight. The fish is prey; the heron is a predator. The question, however, is what ecological interaction do herons and fish have?

Adapting text from Taylor (2005):

**Interactions: Definitions and Estimation**

Interactions may be directly observed, but these are interactions between individual organisms. Alternatively, interactions between populations may be inferred from data. This either

- requires a theory that tightly links a qualitative outcome (e.g., non-coexistence of similar populations) with the interaction (e.g., competition), or
- requires quantitative data on population sizes.

Such population data may be construed in two ways:

1) as population sizes changing over time under a fixed set of conditions. The effect of population j on population i is then defined as its contribution to altering the rate of change of i. There are three major approaches to the estimation of these effects:

a. Fit the data to a model postulated to govern the interacting populations, that is, estimate the values of the parameters for which the model best fits the data;

b. Infer interactions from data on experimental perturbations from equilibrium. Bender et al. (1984) propose two procedures, “PULSE” and “PRESS,” for estimating the parameters of a Generalized Lotka-Volterra (GLV) model (model 1 in Taylor 2005, Chapter 1A). These procedures require that the populations are initially at equilibrium and that a controlled series of perturbations from that equilibrium can be performed.

c. interactions inferred from data on moving equilibria. To understand this somewhat paradoxical approach requires first the introduction of the second construal of quantitative data on population sizes:

2) moving equilibria of the population sizes under conditions that are changing, perhaps as induced experimentally.

The effect of population j on population i can be defined in terms of the co-variation of their equilibrium values—does one go up when the other goes down or do they go up and down together? Such interactions are usually limited to competition, mutualism or null interactions. This concept of interaction is not closely related to either directly observed interactions or those derived from data construed to be population sizes changing over time under a fixed set of conditions (type 1). If values for type 1 interactions (approaches a or b) are estimated, then type 2 interactions can be calculated by loop analysis (Puccia and Levins 1985). If values for type 2 interactions are estimated, then the qualitative values of type 1 interactions can sometimes be inferred by inverse loop analysis (Puccia and Levins 1985)—this constitutes approach c above.

**References**

Bender, E. A., T. J. Case and M. E. Gilpin (1984). “Perturbation experiments in community ecology: Theory and practice.” *Ecology* 65: 1-13

Puccia, C. J. and R. Levins (1985). *Qualitative Modeling of Complex Systems: An Introduction to Loop Analysis and Time Averaging*. Cambridge, MA: Harvard University Press

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

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