TL;DR: The proportion of change due to indirect effects was constant with web species richness, indicating that strong direct interactions and indirect effects produce roughly the same level of alteration of community structure regardless of the level of web complexity.
Abstract: To determine the patterns of occurrence and importance of indirect effects relative to direct effects in natural communities, I analyzed experimentally based studies from 23 rocky intertidal habitats. The vehicle of analysis was the construction of interaction webs, or the subset of species in food webs involved in strong interactions. The analysis focused on indirect effects involving changes in abundance, or interaction chains, since little information was available on other types of indirect effects (behavioral, chemical response, environmental). As expected, number of direct (= strong) interactions, indirect effects, interaction sequences producing indirect effects, and types of indirect effects (e.g., keystone predation, apparent competition, etc.) all increased with web species richness. Less expected, when these measures were adjusted to a per species basis, positive relationships with species richness were still observed for all measures but the number of types. In other words, with increasing web diversity, each species interacted strongly with more species, was involved in more indirect effects, and was part of more interaction pathways. The analysis identified 83 subtypes of indirect effect, including the seven previously identified types. Many of the 76 additional types could be reclassified into the seven types if the original definitions of these "classic" types were expanded to include interactions having similar effects but differing in the specific mechanism (e.g., both interference competition and inhibition of recruitment [preemption] have negative effects involving a spatial resource). Two new types of indirect effect, termed "apparent predation" and "indirect defense" were also identified, producing a total of 9 general types of indirect effect divided among 565 specific indirect effects. Of these, keystone predation (35%) and apparent competition (25%) were most common and exploitation competition (2.8%) was least common in these webs. Two methods of analysis suggested that indirect effects accounted for °40% of the change in community structure resulting from manipulations, with a range of 24—61%. The proportion of change due to indirect effects was constant with web species richness, indicating that strong direct interactions and indirect effects produce roughly the same level of alteration of community structure regardless of the level of web complexity. Several potential artifacts and biases were evaluated. Most importantly, neither variation in level of taxonomic resolution nor intensity of experimentation varied significantly with web size (species richness). Despite a bias toward manipulation of consumers over manipulation of basal species, some predator—initiated indirect effect types were scarce while some basal species—initiated types were common. While the frequency of exploitation competition may have been underestimated, it is unlikely that the frequency of this indirect effect would change dramatically: changes due to this effect should have been detected in many of the studies and reported; and the most intensively studied individual webs did not report frequencies differing much from the average. This analysis suggests investigators effectively identified and first manipulated those species responsible for most indirect effects and that more experiments added decreasing numbers of indirect effects. Moreover, the frequencies and importance of indirect effects may be more predictable than expected on the basis of theory.
TL;DR: It is shown that what is often taken as an indirect effect can in fact be further decomposed into a "pure" indirect effect and a mediated interactive effect, thus yielding a three-way decomposition of a total effect (direct, indirect, and interactive).
Abstract: Recent theory in causal inference has provided concepts for mediation analysis and effect decomposition that allow one to decompose a total effect into a direct and an indirect effect. Here, it is shown that what is often taken as an indirect effect can in fact be further decomposed into a "pure" indirect effect and a mediated interactive effect, thus yielding a three-way decomposition of a total effect (direct, indirect, and interactive). This three-way decomposition applies to difference scales and also to additive ratio scales and additive hazard scales. Assumptions needed for the identification of each of these three effects are discussed and simple formulae are given for each when regression models allowing for interaction are used. The three-way decomposition is illustrated by examples from genetic and perinatal epidemiology, and discussion is given to what is gained over the traditional two-way decomposition into a direct and an indirect effect.
TL;DR: There are two distinct pH-related mechanisms driving prokaryotic community structures, the direct effect and “spillover effects” of pH (indirect effects).
Abstract: pH is frequently reported as the main driver for prokaryotic community structure in soils. However, pH changes are also linked to “spillover effects” on other chemical parameters (e.g., availability of Al, Fe, Mn, Zn, and Cu) and plant growth, but these indirect effects on the microbial communities are rarely investigated. Usually, pH also co-varies with some confounding factors, such as land use, soil management (e.g., tillage and chemical inputs), plant cover, and/or edapho-climatic conditions. So, a more comprehensive analysis of the direct and indirect effects of pH brings a better understanding of the mechanisms driving prokaryotic (archaeal and bacterial) community structures. We evaluated an agricultural soil pH gradient (from 4 to 6, the typical range for tropical farms), in a liming gradient with confounding factors minimized, investigating relationships between prokaryotic communities (16S rRNA) and physical–chemical parameters (indirect effects). Correlations, hierarchical modeling of species communities (HMSC), and random forest (RF) modeling indicated that both direct and indirect effects of the pH gradient affected the prokaryotic communities. Some OTUs were more affected by the pH changes (e.g., some Actinobacteria), while others were more affected by the indirect pH effects (e.g., some Proteobacteria). HMSC detected a phylogenetic signal related to the effects. Both HMSC and RF indicated that the main indirect effect was the pH changes on the availability of some elements (e.g., Al, Fe, and Cu), and secondarily, effects on plant growth and nutrient cycling also affected the OTUs. Additionally, we found that some of the OTUs that responded to pH also correlated with CO2, CH4, and N2O greenhouse gas fluxes. Our results indicate that there are two distinct pH-related mechanisms driving prokaryotic community structures, the direct effect and “spillover effects” of pH (indirect effects). Moreover, the indirect effects are highly relevant for some OTUs and consequently for the community structure; therefore, it is a mechanism that should be further investigated in microbial ecology.
TL;DR: Empirical results suggest that, despite incomplete knowledge of indirect effects, community dynamics may be more predictable than expected in manipulative studies of community regulation.
Abstract: To evaluate the hypothesis that indirect effects generally take much longer to become evident in manipulative studies of community regulation than do direct effects and thus may often be missed, I studied the effect of experiment duration in a survey of marine intertidal interaction webs. Contrary to expectation, indirect effects appeared either simultaneously with direct effects or shortly after direct effects were evident. While experiment durations varied greatly, on average most direct and indirect effects became statistically significant within the first 20%–40% of the total experiment duration. Further, the duration of most experiments appeared sufficient so that most indirect effects that would be generated by the manipulation could be observed. On average, a period of “constancy” (i.e., of no further change) lasting roughly 20%–60% of the total experiment duration occurred after the last indirect effect was observed. Experiment duration did not vary with web species richness, which sugges...
TL;DR: It is argued that natural direct and indirect effects on the exposed are of intrinsic interest in various applications and coincide with the corresponding population natural direct or indirect effects when the exposure is randomly assigned, and are of relevance for assessing populationnatural direct andirect effects in the presence of exposure-induced mediator-outcome confounding.
Abstract: We define natural direct and indirect effects on the exposed. We show that these allow for effect decomposition under weaker identification conditions than population natural direct and indirect effects. When no confounders of the mediator-outcome association are affected by the exposure, identification is possible under essentially the same conditions as for controlled direct effects. Otherwise, identification is still possible with additional knowledge on a nonidentifiable selection-bias function which measures the dependence of the mediator effect on the observed exposure within confounder levels, and which evaluates to zero in a large class of realistic data-generating mechanisms. We argue that natural direct and indirect effects on the exposed are of intrinsic interest in various applications. We moreover show that they coincide with the corresponding population natural direct and indirect effects when the exposure is randomly assigned. In such settings, our results are thus also of relevance for assessing population natural direct and indirect effects in the presence of exposure-induced mediator-outcome confounding, which existing methodology has not been able to address.