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Mediation analysis is widely used to test and inform theory and debate about the mechanism(s) by which causal effects operate, quantitatively operationalized as an indirect effect in a mediation model. Most effects operate through multiple mechanisms simultaneously, and a mediation model is likely to be more realistic when it is specified to capture multiple mechanisms at the same time with the inclusion of more than one mediator in the model. This also allows an investigator to compare indirect effects to each other. After an overview of the mechanics of mediation analysis, we advocate formally comparing indirect effects in models that include more than one mediator, focusing on the important distinction between questions and claims about value (i.e., are two indirect effects the same number?) versus magnitude (i.e., are two indirect effects equidistant from zero or the same in strength?). After discussing the shortcomings of the conventional method for comparing two indirect effects in a multiple mediator model—which only answers a question about magnitude in some circumstances—we introduce several methods that, unlike the conventional approach, always answer questions about difference in magnitude. We illustrate the use of these methods and provide code that implements them in popular software. We end by summarizing simulation findings and recommending which method(s) to prefer when comparing like- and opposite-signed indirect effects.

1. Introduced species disrupt native communities and biodiversity worldwide. Parasitic infections (and at times, their absence) are thought to be a key component in the success and impact of biological invasions by plants and animals. They can facilitate or limit invasions, and positively or negatively impact native species. 2. Parasites have not only direct effects on their hosts, but also indirect effects on the species with which their hosts interact. Indirect effects include density-mediated effects (resulting from parasite-induced reduction in host reproduction and survival) as well as trait-mediated indirect effects (resulting from parasite-induced changes in host phenotype, behaviour or life history). These effects are not mutually exclusive but often interact. 3. The importance of these indirect interactions for invasion success, and the extent to which these effects ramify throughout communities and influence ecosystems undergoing biological invasion provide the focus of our review. Examples from the animal and plant literature illustrate the importance of parasites in mediating both competitive and consumer—resource interactions between native and invasive species. 4. Parasites are involved in indirect interactions at all trophic levels. Furthermore, the indirect effects of parasitic infection are important at a range of biological scales from within a host to the whole ecosystem in determining invasion success and impact. 5. To understand the importance of parasitic infection in invasion success and in the outcomes for invaded communities requires an interdisciplinary approach by ecologists and parasitologists, across animal and plant systems. Future research should develop a framework integrating community ecology, evolution and immunology to better understand and manage the spread of invasive species and their diseases.

We consider causal mediation analysis when exposures and mediators vary over time. We give non-parametric identification results, discuss parametric implementation and also provide a weighting approach to direct and indirect effects based on combining the results of two marginal structural models. We also discuss how our results give rise to a causal interpretation of the effect estimates produced from longitudinal structural equation models. When there are time varying confounders affected by prior exposure and a mediator, natural direct and indirect effects are not identified. However, we define a randomized interventional analogue of natural direct and indirect effects that are identified in this setting. The formula that identifies these effects we refer to as the 'mediational g-formula'. When there is no mediation, the mediational g-formula reduces to Robins's regular g-formula for longitudinal data. When there are no time varying confounders affected by prior exposure and mediator values, then the mediational g-formula reduces to a longitudinal version of Pearl's mediation formula. However, the mediational g-formula itself can accommodate both mediation and time varying confounders and constitutes a general approach to mediation analysis with time varying exposures and mediators.

1. Classic theory holds that the main interaction within the herbivore guild is competition, based on research focused on co-occurring, similarly sized species that reduce the quantity of shared plant resources. However, plant quality may also be crucial in mediating herbivore interspecific interactions. This is especially true when competition occurs between distantly related herbivore species, given that small terrestrial herbivores (e.g., insect herbivores) appear to be more sensitive to alterations of plant quality than plant quantity. 2. In this study, we first tested in the field whether large vertebrate herbivores (cattle Bos taurus) exerted a negative effect on smaller insect herbivores (grasshopper Euchorthippus unicolor) through their overlapping foraging preferences for a dominant grass Leymus chinensis. We measured changes in grass quantity, grass quality, and microclimatic conditions in response to vertebrate grazing and conducted additional manipulative studies in the field and the laboratory to identify potential mechanisms underlying the interaction. 3. Our results showed that grazing by large herbivores caused a significant decline in grasshopper population density and individual performance (survival, size, and weight of both female and male E. unicolor), despite a 38% increase in grass nitrogen (N) content in grazed plots. Experiments manipulating N levels of L. chinensis in the field and the laboratory confirmed that enriching plant N had a negative effect on grasshopper individual performance and population size. Therefore, enhanced quality (N content) of plant resources appears to be an important driver in mediating the negative effect of vertebrate grazing on grasshoppers.a 4. Synthesis. We document that phylogenetic relatedness and trait similarity can be poor predictors of interaction strength in some cases, since distantly related herbivores of disparate size can interact indirectly via changes in plant quality. Counter-intuitively, the observed negative effect of cattle on grasshoppers was mediated, at least in part, by an increase in plant quality in cattle grazed areas. The implication is that light to moderate grazing, a common management strategy, may contribute to suppression of grasshoppers in the Eurasian steppe grassland system by altering plant nutrient supplies.

Indirect species interactions are ubiquitous in nature, often outnumbering direct species interactions. Yet despite evidence that indirect interactions have strong ecological effects, relatively little is known about whether they can shape adaptive evolution by altering the strength and/or direction of natural selection. We tested whether indirect interactions affect the strength and direction of pollinator-mediated selection on floral traits of the bumble-bee pollinated wildflower Lobelia siphilitica. We estimated the indirect effects of two pollinator predators with contrasting hunting modes: dragonflies (Aeshnidae and Corduliidae) and ambush bugs (Phymata americana, Reduviidae). Because dragonflies are active pursuit predators, we hypothesized that they would strengthen pollinator-mediated selection by weakening plant–pollinator interactions (i.e., a density-mediated indirect effect). In contrast, because ambush bugs are sit-and-wait predators, we hypothesized that they would weaken or reverse the direction of pollinator-mediated selection by altering pollinator foraging behavior (i.e., a trait-mediated indirect effect). Specifically, if ambush bugs hunt from plants with traits that attract pollinators (i.e., prey), then pollinators will spend less time visiting those plants, weakening or reversing the direction of selection on attractive floral traits. We did not find evidence that high dragonfly abundance strengthened selection on floral traits via a density-mediated indirect effect: neither pollen limitation (a proxy for the strength of plant–pollinator interactions) nor directional selection on floral traits of L. siphilitica differed significantly between high- and low-dragonfly abundance treatments. In contrast, we did find evidence that ambush bug presence affected selection on floral traits via a trait-mediated indirect effect: ambush bugs hunted from L. siphilitica plants with larger daily floral displays, reversing the direction of pollinator-mediated selection on daily display size. These results suggest that indirect species interactions have the potential to shape adaptive evolution by altering natural selection.

Trophic interactions and ecosystem engineering are ubiquitous and powerful forces structuring ecosystems, yet how these processes interact to shape natural systems is poorly understood. Moreover, trophic effects can be driven by both density- and trait-mediated interactions. Microcosm studies demonstrate that trait-mediated interactions may be as strong as density-mediated interactions, but the relative importance of these pathways at natural spatial and temporal scales is underexplored. Here, we integrate large-scale field experiments and microcosms to examine the effects of ecosystem engineering on trophic interactions while also exploring how ecological scale influences density- and trait-mediated interaction pathways. We demonstrate that (i) ecosystem engineering can shift the balance between top-down and bottom-up interactions, (ii) such effects can be driven by cryptic trait-mediated interactions, and (iii) the relative importance of density- versus trait-mediated interaction pathways can be scale dependent. Our findings reveal the complex interplay between ecosystem engineering, trophic interactions, and ecological scale in structuring natural systems.

The paper discusses the non-parametric identification of causal direct and indirect effects of a binary treatment based on instrumental variables. We identify the indirect effect, which operates through a mediator (i.e. intermediate variable) that is situated on the causal path between the treatment and the outcome, as well as the unmediated direct effect of the treatment by using distinct instruments for the endogenous treatment and the endogenous mediator. We examine various settings to obtain non-parametric identification of (natural) direct and indirect as well as controlled direct effects for continuous and discrete mediators and continuous and discrete instruments. We also provide a simulation study and two empirical illustrations.

Experimentation is a powerful methodology that enables scientists to establish causal claims empirically. However, one important criticism is that experiments merely provide a black box view of causality and fail to identify causal mechanisms. Specifically, critics argue that, although experiments can identify average causal effects, they cannot explain the process through which such effects come about. If true, this represents a serious limitation of experimentation, especially for social and medical science research that strives to identify causal mechanisms. We consider several experimental designs that help to identify average natural indirect effects. Some of these designs require the perfect manipulation of an intermediate variable, whereas others can be used even when only imperfect manipulation is possible. We use recent social science experiments to illustrate the key ideas that underlie each of the designs proposed.

Summary Ecological communities consist of antagonistic and mutualistic interactions that can vary in their strength. Indirect effects act among species within or across trophic levels through multiple pathways in an interaction network. Although there are many studies showing indirect effects in ecological communities, we know little about how indirect effects impact the wider community by linking other direct and indirect interactions. Herbivore‐induced indirect effects are ubiquitous and powerful forces in structuring ecological communities. In a plant‐associated network, aphids have the potential to connect multiple interactions through ant‐ and plant‐mediated indirect effects on co‐occurring and/or temporally separated species. We examined how aphids affect the interaction network on tall goldenrod, Solidago altissima, based on data of arthropod species on it with and without the aphid, Uroleucon nigrotuberculatum, using structural equation modelling (SEM) analysis. The presence of aphids greatly changed the strength of several species interactions throughout the season. In the early season, aphids had negative indirect effects on leafhoppers and moth caterpillars through ants. On the other hand, aphid‐induced leaf regrowth decreased scale insects but increased grasshoppers in the late season, when the aphid was no longer present. Moreover, the aphid‐generated interactions increased seed production of tall goldenrods, due to indirect pathways through the leaf regrowth. The aphid thus played a critical role as a network creator in determining the interaction network by generating ant‐ and plant‐mediated indirect effects. In particular, the aphid‐induced leaf regrowth contributed to interaction diversity (i.e. total number of positive/negative interactions and link density per each species) by connecting arthropod species in the early and late seasons. We disentangled the complexity of direct and indirect pathways generated by the aphid (i.e. keystone herbivore), which largely determines community structure of associated arthropods and plant reproductive success. Our study combining ant‐ and plant‐mediated indirect interactions mediated by the aphid provides a basis of better understanding of the underlying mechanisms of how the impact of the keystone herbivore can spread through plant‐based insect networks via direct and indirect pathways. A lay summary is available for this article. Lay Summary

This paper investigates the intersection of income and race in structuring access to higher education among students that participate in a national high-stakes exam in Brazil. Our objectives are (i) to estimate the probability of students coming from different income strata, racial groups, and performance levels to access higher education and (ii) to decompose income and racial effects into direct (net of educational performance) and indirect effects (through educational performance). Our data comes from a panel of high school graduates tracked between 2012 and 2017 and allow us to describe the following findings. Firstly, the probability of entering higher education is always higher among candidates from higher income strata. Second, there is a convergence in admission probabilities across the performance scale. Third, the admission curve across a performance scale is much steeper among applicants from low-income strata compared to richer students. In all of these results, students self-identified as black, brown, or indigenous (BBI) are less likely to transition to higher education than whites, even though they are in the same income and performance strata. We suggest that students from privileged socioeconomic backgrounds benefit from alternative entry strategies, such as paying tuition at less competitive private colleges. For students from low-income strata, the main alternative for entering higher education is through high academic performance. By decomposing racial effects, we show the cumulative effect of racial stratification; the gap between white and BBI students is both related to higher propensity of transitioning to higher education and higher educational performance.