EMPIRICAL APPROACHES TO QUANTIFYING INTERACTION INTENSITY: COMPETITION AND FACILITATION ALONG PRODUCTIVITY GRADIENTS

Quantitative synthesis across studies requires consistent measures of effect size among studies. In community ecology, these measures of effect size will often be some measure of the strength of interactions between taxa. However, indices of interaction strength vary greatly among both theoretical and empirical studies, and the connection between hypotheses about interaction strength and the metrics that are used to test these hypotheses are often not explicit. We describe criteria for choosing appropriate metrics and methods for comparing them among studies at three stages of designing a meta-analysis to test hypotheses about variation in interaction intensity: (1) the choice of response variable; (2) how effect size is calculated using the response in two treatments; and (3) whether there is a consistent quantitative effect across all taxa and systems studied or only qualitatively similar effects within each taxon–system combination. The consequences of different choices at each of these stages are illustrated with a meta-analysis to examine the relationship between competition/facilitation intensity and productivity in plants. The analysis used a database of 296 cases in 14 studies. The results were unexpected and largely inconsistent with existing theory: competition intensity often significantly declined (rather than increased) with productivity, and facilitation was sometimes restricted to more productive (rather than less productive) sites. However, there was considerable variation in the pattern among response variables and measures of effect size. For example, on average, competitive effects on final biomass and survival decreased with standing crop, but competitive effects on growth rate did not. On the other hand, facilitative interactions were more common at low standing crop for final biomass and growth rate, but more common at high standing crop for survival. Results were more likely to be significant using the log response ratio (ln[removal/control]) as the effect size than using the relative competition intensity ([removal − control]/removal), although the trends for these conceptually similar indices did not differ. When all studies were grouped in a single meta-regression of interaction intensity on standing crop to test quantitative similarity among studies, survival showed the clearest negative relationship. However, when the same regressions were done for each unique combination of taxon and site within each study to test for qualitative similarity among studies, the slopes averaged over studies tended to be negative for biomass and growth rate, but not different from zero for survival. These results are subject to a number of caveats because of the limitations of the available data—most notably, the extension of effects of interactions on individual growth or survival to effects on population distribution and abundance or community structure is highly problematic. Nevertheless, the fact that none of the meta-analyses demonstrated a significant positive relationship between competition and standing crop but that we frequently found negative relationships is an important pattern that has not been apparent from qualitative surveys of individual studies, and it demonstrates the potential power of meta-analysis in ecology. We conclude with recommendations to overcome some of the limitations of the currently available data and meta-analytical procedures.