Empirical approaches to quantifying interaction intensity: competition and facilitation along productivity gradients - Meta-Analysis in Ecology

Ecology, June, 1999 by Deborah E. Goldberg, Tara Rajaniemi, Jessica Gurevitch, Allan Stewart-Oaten

INTRODUCTION

Testing hypotheses in community ecology often requires quantification of the magnitude of interactions between species so that these magnitudes can be compared among groups of taxa or of environments. For example, a number of models predict how the magnitude of competition varies along gradients of environmental favorability (e.g., Miller 1967, Grime 1973, Newman 1973, Connell 1975, Rosenzweig and Abramsky 1986, Menge and Sutherland 1987, Tilman 1988) or among taxa (e.g., Grime 1977, Tilman 1988). While many of these models have been tested empirically in individual studies, examining their generality requires synthesis of results across many studies. To date, such synthesis has largely been based on narrative reviews or counts of significant/nonsignificant effects (e.g., Connell 1983, Schoener 1983, Sih et al. 1985, Goldberg and Barton 1992, but see Gurevitch et al. 1992). Instead of these qualitative summaries, quantitative synthesis that compares actual measures of the intensity of interactions across studies using meta-analytic procedures may provide a more powerful approach to test these models and evaluate their applicability. However, quantitative synthesis requires consistent indices of interaction intensity among studies.

Recently, attention has been drawn to the importance of deriving measures of interaction intensity from particular ecological models (Laska and Wootton 1998, Osenberg et al. 1999). This approach requires an explicit, appropriate model, as well as assumptions about factors such as equilibrial status of a population or the time scale of interactions (Laska and Wootton 1998). However, in many cases, this will not be possible and, therefore, it will be necessary to use more empirical considerations to choose appropriate indices of interaction intensity. Such empirically derived indices of interaction intensity are not suitable for parameterizing models or for testing quantitative predictions (Osenberg et al. 1999) but yield valuable information on patterns in the consequences of interactions to test qualitative predictions and generate new hypotheses.

In this paper, we provide guidance both on choosing appropriate indices and on using these indices in meta-analyses to test hypotheses about variation in the consequences of interactions, especially competition and facilitation (see Navarrete and Menge [1996], Osenberg et al. [1997], and Wootton [1997] for recent discussions of predator-prey interaction strength). We then illustrate these issues using data on competition and facilitation along productivity gradients for plants. Whether competition is more important at high productivity (Grime 1973, 1977) or similarly important regardless of productivity (Newman 1973, Tilman 1988) has been a very controversial area in plant ecology. While numerous relevant experiments have been performed (e.g., Wilson and Tilman 1991, 1995, Reader et al. 1994, Twolan-Strutt and Keddy 1996), there has not yet been a quantitative synthesis.

AN EMPIRICAL APPROACH TO CHOOSING METRICS OF INTERACTION INTENSITY

Testing hypotheses about variation in interaction intensity involves choices at three stages of quantification: (1) the response variable that is actually measured on the targets in each treatment, (2) how the change in the response variable between treatments is quantified (e.g., using absolute or relative differences), and (3) how this effect size is compared among taxa or environments. In this section, we describe general criteria for choices at each stage. Most previous discussions of interaction intensity have focused on the second of these stages; as we illustrate in the following section, results of synthesizing interaction intensity can also depend on the choices at the first and third stages.

We first define some terminology to facilitate clear definitions of different kinds of metrics of interaction intensity. The individual or taxon whose response is being measured is referred to as the "target" and the organisms causing any suppressive or facilitative effect as the "associates" (cf. Goldberg and Scheiner 1993). For most organisms, the most common type of field experiment on interactions includes only two treatments that differ in abundance of the associates: presence of the associate at its natural abundance (control treatment) vs. its complete absence (removal treatment). In plants (and sessile animals), where the limiting resources tend to be similar among taxa within a community, the associate is most commonly all vegetation other than the target (Goldberg and Barton 1992). The descriptions of indices below assume this kind of experiment, although they can easily be used for other types of data.

Response variable

The response variable is what is actually measured or estimated about the targets in each abundance treatment. For each taxon of targets, this could be an individual-level measure (e.g., a behavioral descriptor or a component of individual fitness such as growth rate, survival, reproduction) or a population-level measure (e.g., population size or growth rate, relative abundance). For parameterizing population-dynamic models or testing hypotheses about the effect of competition on distribution and abundances, population-level responses should be measured (e.g., Paine 1992). However, data on population abundances and, especially, population dynamics in response to competition are relatively rare for large or long-lived organisms (Sih et al. 1985, Goldberg and Barton 1992). Instead, various logistical constraints dictate that most experiments on the consequences of competition quantify effects on components of individual fitness. Therefore the challenge is to use individual-level data to infer something about populations. One approach is to integrate effects of interactions throughout the life history by parameterizing a demographically based model of population growth (Gurevitch 1986, McPeek and Peckarsky 1998). When the entire life cycle cannot be followed, inferences from individuals to populations can still be made if the chosen individual-level response variable strongly influences population dynamics. This has usually been implicitly assumed rather than explicitly justified in experimental studies, but it may be possible to make non-arbitrary choices of individual response variables based on attempts to categorize organisms by the life-cycle stages most important for population growth (e.g., for plants: Silvertown et al. 1993, Franco and Silvertown 1996). The choice of response variable is not trivial - a number of studies have quantified interactions for different demographic parameters or at different life-history stages and found that both the overall magnitude of interactions (and even their sign) and the relative competitive abilities of different taxa depend on the response variable (e.g., DeSteven 1991a, b, Howard 1998, and see Example: . . ., below). McPeek and Peckarsky (1998) showed that even strong effects on several components of individual fitness could translate into minimal effects on population growth rate.