The detection and significance of higher order interactions (HOis) between species has been a matter of debate and experimentation in community ecology for several decades. HOis are considered potentially significant because their presence is assumed to mean that the dynamic behavior of a full community of species is unpredictable based on observations of interactions between subsets of the species within the community. Despite such attention, the causal mechanisms that produce HOis have been inadequately discussed. We discuss three different usages of the term HOis and provide insight as to why HOis might be found within a given community. HOis may be detected for three reasons: inappropriate assumptions made concerning species interactions that influence statistical tests, unmeasured parameters and variables, and interaction modifications (i.e., a functional change in the interaction of two species caused by a third species).This confusion concerning the defining attributes of HOis has made their detection problematic. While the statistical tests being used in the ecological experiments to detect HOis are described in detail in most papers, the dynamic models underlying these tests are often not made explicit. Additionally, we demonstrate the equivalency of three different statistical tests: the Case and Bender (1981) test, analysis of variance, and a multiplicative test (Wootton 1994). However, the choice of a response variable (i.e., population densities, population growth rates, per-capita growth rates, etc.) and different data transformations applied to these response variables alter the underlying dynamics model that is being tested. The result is that the statistical test applied does not always perform the intended comparison but instead tests a different and sometimes unjustified or even inappropriate dynamic model.Finally, we review the relationship between indirect effects and HOis. Whereas some researchers have lumped HOis and indirect effects, we argue that the two represent completely unique and separate phenomena. Additionally, indirect effects can complicate detection of HOis, and we review several methods by which to separate the two processes.

Summary1. In ecological webs, net indirect interactions between species are composed of interactions that vary in sign and magnitude. Most studies have focused on negative component interactions (e.g. predation, herbivory) without considering the relative importance of positive interactions (e.g. mutualism, facilitation) for determining net indirect effects. 2. In plant ⁄ arthropod communities, ants have multiple top-down effects via mutualisms with honeydew-producing herbivores and harassment of and predation on other herbivores; these ant effects provide opportunities for testing the relative importance of positive and negative interspecific interactions. We manipulated the presence of ants, honeydew-producing membracids and leaf-chewing beetles on perennial host plants in field experiments in Colorado to quantify the relative strength of these different types of interactions and their impact on the ant's net indirect effect on plants.3. In 2007, we demonstrated that ants simultaneously had a positive effect on membracids and a negative effect on beetles, resulting in less beetle damage on plants hosting the mutualism. 4. In 2008, we used structural equation modelling to describe interaction strengths through the entire insect herbivore community on plants with and without ants. The ant's mutualism with membracids was the sole strong interaction contributing to the net indirect effect of ants on plants. Predation, herbivory and facilitation were weak, and the net effect of ants reduced plant reproduction. This net indirect effect was also partially because of behavioural changes of herbivores in the presence of ants. An additional membracid manipulation showed that the membracid's effect on ant activity was largely responsible for the ant's net effect on plants; ant workers were nearly ten times as abundant on plants with mutualists, and effects on other herbivores were similar to those in the ant manipulation experiment. 5. These results demonstrate that mutualisms can be strong relative to negative direct interspecific interactions and that positive interactions deserve attention as important components of ecological webs.

We explored the relative importance of temporal vs. spatial variability to the conditionality of a mutualism between the treehopper Publilia modesta and the ant Formica obscuripes. The effect of the ants on the membracids varied considerably among years. When the effect of the ants on the membracids was estimated in five sites spread over 5 km there was mixed evidence for spatial conditionality in the mutualism. Using repeated surveys of nymph number we found that the effect of the ants on nymph number varied among sites through time. When total new adult production was examined, however, no such interaction between ants and location was evident. Aggregations displayed strong negative density‐dependent adult production. Thus, while in some sites ants had a greater positive effect on nymph survivorship, aggregations at those sites produced proportionately fewer adults because of negative density dependence. Density dependence reduced or eliminated spatial differences in the effect of the ants on the membracids. Differences among sites did not explain spatial variation in the effect of ants on nymphs or new adult production. We conclude that temporal variability is much more important than spatial variability in generating conditionality in the mutualism. Corresponding Editor: P. Nonacs

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