1. The strength of the trophic link between any given pair of species in a food web is likely to depend on the presence and/or densities of other species in the community. How these trophic interaction modifications (TIMs) interact with one another to produce a net modifying effect is an important but under-explored issue.
2. We review several specific types of TIMs that are well understood to address whether the magnitude of the net modification changes with the number of modifiers, and whether modifiers usually increase or decrease each other’s effects.
3. Modifications of interactions are generally not independent. It is likely that TIMs interact antagonistically in the majority of cases; the magnitudes of TIMs decrease as more modifiers are added, or new TIMs reduce the magnitudes of modifications that are already present.
4. Individual modifications are likely to have a smaller effect in many-species systems than expected from independent combination of modifications measured in systems with relatively few species. Thus, models that lack explicit TIMs may in some cases yield adequate predictions for species-level perturbations, provided that the net effects of TIMs are implicitly included in measured interaction strengths.
5. Many types of TIMs share structural similarities. Nevertheless, a complete understanding of their effects may require theory that distinguishes different ‘functional groups’ of modifiers and addresses how these are structured according to trophic relationships.
Models of natural communities, both mathematical and verbal, have usually focused on the transfer of energy and nutrients; i.e. trophic interactions. It has long been clear that there are many important ecological interactions that are not captured by such a framework. This has prompted calls for general frameworks capable of considering both trophic and non-trophic interactions (e.g. Agrawal et al. 2007; Ings et al. 2009; Olff et al. 2009). Many non-trophic interactions arise because species alter the strengths of trophic links in which they are neither predator nor prey. Examples include alternative prey that increase predator handling times, plants that afford cover to predators and/or prey, and dangerous higher-level predators that inhibit foraging. These phenomena have been described by a wide variety of terms: interaction modifications (IMs), trait-mediated indirect interactions (TMIIs), non-consumptive predator effects (NCEs), behaviourally mediated indirect interactions (BMIIs), higher-order interactions (HOIs) and rheagogies, among others. ‘Interaction modification’ appears to be the most general and self-explanatory term for such effects. Because we focus on modifications of trophic interactions, we use the more specific term ‘trophic interaction modification’, which has an easily remembered acronym (TIM). Suggestions that TIMs should be common go back several decades (Charnov, Orians & Hyatt 1976; Abrams 1983, 1984). Trophic interaction modifications are now commonly regarded as widespread and have been shown experimentally to have large quantitative effects on the dynamics of simple communities; this is evidenced by several recent special features (Schmitz, Adler & Agrawal 2003; Preisser & Bolnick 2008; Beckerman, Petchey & Morin 2010), reviews (e.g. Wootton 2002; Abrams 2010b) and meta-analyses (Preisser, Bolnick & Bernard 2005; Preisser, Orrock & Schmitz 2007). Other recent articles address the challenges of detecting and measuring TIMs in natural communities (e.g. Billick & Case 1994; Wootton 1994a,b; Peacor & Werner 2004; Dambacher & Ramos-Jiliberto 2007; Okuyama & Bolker 2007; Abrams 2008; Novak & Wootton 2008).
Because most large food web models only include direct trophic interactions, the frequent demonstrations of large magnitude TIMs raise questions about the relevance of the large body of both theoretical and empirical work that ignores such interactions. It also poses an empirical problem for those wanting to develop quantitative models of large food webs that are known or suspected to include interaction modifications. Suggestions that community ecology is too difficult to be worth pursuing have been made without even considering interaction modification (e.g. Lawton 1999). Because the number of potential TIMs increases with species richness much more quickly than does the potential number of direct trophic links, community ecology is likely to face great difficulty in developing predictive models if all potential modifier effects have to be quantified. Nevertheless, both theory and experiments on small communities suggest that modifications cannot be ignored in predicting community responses to perturbations.
We begin by reviewing some of the assumptions and results of previous approaches to incorporating many types of TIMs into large food web models. We then review several common and well-understood TIM-generating mechanisms and ask whether these mechanisms reveal general features of how multiple TIMs combine to change a predator–prey link. We focus on interactions between similar TIMs, caused by species whose roles as modifiers are qualitatively similar to one another. This is a convenient starting point for studying the net effects of multiple TIMs. We explore whether TIMs generated by each mechanism strengthen or weaken trophic links, and how position in the food web is likely to determine these effects. Most importantly, we assess whether the TIMs produced by each mechanism are as follows: (i) independent, (ii) synergistic (such that co-occurring modifiers increase the magnitudes of one another’s effects) or (iii) antagonistic (such that co-occurring modifiers reduce the magnitude of one another’s effects; Fig. 1). We argue that antagonism is the most common and independence the least common.
Previous general models of interacting TIMs
To facilitate discussion of previous models, as well as some results of the current work, we first introduce some terminology. Let αij represent the unmodified link between predator species j and prey species i, measured as the instantaneous consumption rate of prey by an average predator individual divided by prey density. This is equivalent to the interaction coefficient (Laska & Wootton 1998) in a Lotka-Volterra model with linear functional and numerical responses. Because this measure does not convert nonlinear links into linear approximations, it avoids criticisms of scalar measures of interaction strength (e.g. Abrams 2001). We use α′ij to represent the link after all modifications; M′ij represents the combined effect of all modifications of that link, and Mijk represents the modification of that link attributable to species k (Fig. 1).
Two recent articles have incorporated multiple TIMs into large assembly-based food web models (Arditi, Michalski & Hirzel 2005; Goudard & Loreau 2008). Both assume that TIMs are independent, so that each Mijk is only a function of the population density of the modifier species, k, and is independent of the number and the values of other modifying terms affecting the link. Each model also assumes that there is an equal probability of any Mijk strengthening a link (i.e. contributing to making α′ij> αij) or weakening it (helping make α′ij< αij). Both models assign TIMs randomly so that the presence, direction and magnitude of any TIM is independent of the positions of the modifier and the link being modified in the web relative to one another. Arditi, Michalski & Hirzel (2005) assumed that the individual modifications Mijk could be positive or negative (with equal mean magnitudes), and that they combined additively:
The maximum function in eqn (1) prevented feeding relationships from reversing directions. Goudard & Loreau (2008) assumed that all Mijk combine multiplicatively according to:
Here, the Mijk was assumed to be positive with an expected geometric mean of 1.
The assumptions in both Arditi, Michalski & Hirzel (2005) and Goudard & Loreau (2008) imply ever-increasing average trophic link strength with either community size or frequency of modifications. This arises from the presence of a minimum of 0 and no upper limit for M′ij. Goudard & Loreau (2008, p. 102) suggest that many of their results were because of these increases. The assumptions in both articles are clearly extreme simplifications, and without more mechanistic approaches, their associated errors and biases remain unclear. If interactions between TIMs are sufficiently ubiquitous, strong and structured, neglecting these interactions is likely to bias our understanding of food web structure and dynamics.
Classification of mechanisms producing TIMs, and some general principles of TIM interaction
The following sections review several commonly discussed types of TIMs, generated via different mechanisms. Each suggests that the net modification of a given link is often contributed to by several similar modifier species, usually with similar trophic positions relative to that link (Fig. 2). We focus on interactions between those sets of similar modifiers. A short section discussing interactions between more dissimilar TIMs is also included.
Most of the TIMs explored here involve adaptively plastic traits that species adjust in response to trade-offs between two or more interactions. Such traits have been classified as affecting general or specific types of foraging or defence (Abrams 2010b). Each of these categories produces characteristic TIMs, which interact in ways that can usually be deduced.
For many of the mechanisms reviewed, groups of species are substitutable (sensuSih, Englund & Wooster 1998) in their roles as modifiers: their effects may differ quantitatively a great deal, but are qualitatively redundant. Substitutability of modifiers that affect a species’ general foraging and/or defensive effort is inherently implied by the generality of the response evoked. Some mutualisms in which one partner benefits though increased uptake of resources (referred to here as ‘resource mutualisms’ for simplicity) or reduced consumption by predators (‘protection mutualism’) involve TIMs very similar to those resulting from adaptive foraging and defensive traits. Substitutability of modifiers in these mutualisms is suggested by the similarity of benefits provided by each of a diverse set of partners. Empirical work also suggests that substitutability is common among modifiers that generate TIMs unrelated to foraging and defensive trade-offs, including TIMs associated with important forms of facilitation (Table 1 A, B).
Table 1. Examples of empirical observations supporting the expectation that similar trophic interaction modifications affecting a common link will interact antagonistically. Saturating responses to predator density that are not clearly linked to resource uptake (such as changes in body shape; D) are categorized separately from those (such as changes in activity level) that are (C)
Substitutability of modifiers implies that multiple TIMs should combine into a common functional form having the same shape as the relationship of a single TIM to the density of a single modifier species. This allows a straightforward deduction of how their effects combine into a net TIM. When TIMs are produced by plastic traits (including behaviour), limits on that plasticity translate into limits on the maximum aggregate magnitude of TIMs; thus, distinct TIMs affecting the same trait(s) in the same direction will interact antagonistically given a moderate to high total density of the set of substitutable species producing the TIMs. Ultimately, a given predator–prey link is restricted to a finite range of values in all systems: weakening modifications cannot produce negative attack rates, and strengthening modifications cannot make the forager eat faster than some physiologically determined maximum rate. Such limitation is only possible when there is ultimately diminution of the per capita effect of each modifier as the number of modifier species or their density increases; thus, TIMs must combine antagonistically in the limit of an extremely rich community. Empirical work on natural and laboratory systems (Table 1 C, D) also supports the expectation that TIMs because of similar modifiers often interact antagonistically.
Modifiers that occupy similar trophic positions do not always constitute a substitutable group. This is often the case when TIMs are caused by specialized foraging or defensive traits. In these cases, the same constraints that commonly lead to trade-offs among interactions (e.g. if foraging for one type of prey comes at the expense of foraging for other types) imply a prioritization of species’ responses to modifiers. This imparts a hierarchical nature to TIMs and again suggests that antagonistic interactions will be prevalent.
The following sections illustrate how the biology of each of several TIM-generating mechanisms contributes to the general expectations outlined above. These expectations also hold for several additional related mechanisms that we omit for the sake of conciseness. The analysis begins with a more technical section that shows how individual and net TIMs can be quantified. This section uses the well-understood TIM produced by alternative prey when there is a fixed handling time for each (shared predator satiation); satiation is often assumed to reflect a constraint rather than adaptive trait plasticity.
Shared predator satiation
Predators require time to handle prey items they catch, and this interferes with capturing additional prey. Thus, when two or more prey species share a common predator, an increase in the abundance of any prey species reduces the strength of the trophic links between all other species and that predator. This is one of the earliest TIM-generating phenomena to be explored in the theoretical ecology literature and is implicit in a multi-species type II functional response. Given the ubiquity of satiation in measured functional responses (Jeschke, Kopp & Tollrian 2004), these TIMs are likely to be among the most common types in real food webs. However, satiation is omitted from models that assume linear functional responses, as many large food web models do. This example is used to illustrate how TIMs and their interaction may be quantified. Modifications are assumed to combine multiplicatively, but each modification may have a different, and possibly complicated functional form. We examine the modification produced by the addition of a finite number of individuals of a new modifier species at the original set of densities of the species already present. This is appropriate for the period of time immediately following addition of a significant number of individuals of a new species.
A multi-species type II functional response is the most common method of representing satiation; here, the predation rate per prey by an individual of species j on species i (i.e. the link strength) in the presence of a second prey species k is:
where aij is the attack rate of predator j on prey i, and hij is its corresponding handling time.
The single prey (i) version of the link strength (αij) is given by eqn (3) without the term involving Nk in the denominator. Thus, the addition of species k clearly decreases the strength of the link between i and j. Equation 3 may be rewritten to separate out the unmodified i–j link from k’s modification (Mijk):
In this case, Mijk ranges from values close to one (when species k only slightly weakens the i–j link) to values close to 0 (when species k greatly weakens the original link). We can compare eqn (3) to the equivalent expression after another prey species (g) is added and similarly isolate the further modification because of g:
The total modification of the i–j link in the presence of k and g is:
The modifier terms [eqns (5) and (7a,b)] depend on the population sizes of all prey species in the system. In particular, Mijg is a function of the density of the previous modifier, k. All else being equal, species g weakens the interaction between i and j by a larger amount in the absence of species k than in its presence. Thus, modifications of a predator’s interaction with a prey species because of satiation by shared prey combine antagonistically. The interaction between prey i and predator j is decreased by successively smaller amounts by each additional prey. Equation (7b) also highlights the fact that these modifications share a common functional form (all modifiers’ contributions are summed in the denominator).
The quantification of modifications above assumes that the order of addition of prey species is known and used in determining TIMs’ magnitudes. Alternatively, proportions of the total modification could be assigned to each modifier based on the fraction of the total additional handling time that is attributable to that species. Equation (7b) may be decomposed as follows into two multiplicative components reflecting the relative sizes of each modifier’s impact on the i–j link:
The terms in parentheses apportion the effects of g and k so that the product, MijgMijk, gives the total modification, eqn (7b). Equations (8a,b) always assign greater weight to the species with the larger contribution to that total modification. Whether one uses eqns (5, 7a), eqns (8a, b), or some other scheme to decompose the total modification, the two general results noted above apply: single-species modifications combine antagonistically, and both the prey and other modifier densities enter into a new prey species’ modification of an existing predator–prey link.
Subsequent sections do not provide detailed mathematical formulas for TIMs. This is because most involve a wider range of functional forms, and the general nature of interactions between TIMs can be deduced without quantitative formulas.
Defensive reduction in generalized foraging effort
Perhaps the most frequently discussed cause of TIMs is adjustment of foraging activity or ‘effort’ to balance energetic gains against predation risk. ‘Effort’ can mean time spent foraging, speed of movement or choice of habitat (Abrams 1984). Models considering this behaviour commonly assume that both risk of predation and uptake of resources increase with effort, and that species adjust their effort to maximize their fitness (Abrams 1984, 1992, 1995; Bolker et al. 2003; Brown & Kotler 2004). Reduced activity in response to predation risk has been documented empirically across a wide array of systems (Lima 1998; Werner & Peacor 2003). In such a scenario, two potential sources of TIMs may exist: predator effects on interactions between a prey and the prey’s resources, and effects of those resources on interactions between the prey and its predators. We consider the former first. In this context, reduced foraging effort is a generalized antipredator defence, and the discussion that follows is applicable to other generalized defences, even chemical or mechanical defences of autotrophs, provided they entail a reduced uptake of resources.
The general nature of the defence means that the prey’s response to each modifier is qualitatively similar. The combined effects of TIMs should then be set by the functional form of the prey’s behavioural response to total predator density. Although results have been mixed, empirical work often shows steeper reductions in foraging activity per predator added when total predator density or amount of predator cue is low than when it is high (Table 1 C; Dill & Fraser 1984; Peacor & Werner 2001; Relyea 2003, 2004; Schoeppner & Relyea 2008). Analogously, investment into physiological defences has been shown to saturate with predator density or the amount of predator cue present (Table 1 D; Harvell 1990; Wiackowski & Starońska 1999; Teplitsky, Plénet & Joly 2005; Hoverman & Relyea 2007). This suggests a decelerating response of prey defence to predator density; predator modifications of prey activity (and thus uptake of resources) will then combine antagonistically.
Deceleration is particularly likely at high predator densities because defensive behaviours have limits. Even if foraging becomes more risky, it cannot disappear completely because assured starvation will override any finite risk of predation. Prey in greater need of food have repeatedly been shown to accept higher foraging risk (Lima 1998). Of course, synergistic combination of modifiers is possible in some systems over some ranges of total predator density. Synergism would be expected when the prey defensive response is a sigmoid (e.g. Type III) function of total predator density and current predator density is low. In such a case, the addition of more predators may increase prey’s ability to sense predator presence and may therefore produce a more than proportionate response.
Resource effects on generalized risky foraging
The preceding section discussed modifications of a prey–resource link by predators. Prey foraging effort is also likely to be affected by resource availability (Werner & Peacor 2003); resources then modify the links between those prey and their predators. These modifications may either weaken or strengthen those interactions (Abrams 1984). Decreased risky foraging in response to increased resource results from saturating benefits of additional resource intake (Werner & Anholt 1993). Conversely, greater risk-taking with greater resource abundance can occur with weakly saturating or non-saturating benefits from resource consumption. Both types of responses have been observed (Gilliam & Fraser 1987; Werner & Anholt 1993), and both types could occur within the same system, given a sigmoid curve relating fitness to resource intake. Once again, the generality of the foraging response means that the type of TIM interaction is determined by the functional form of a single-species TIM. Resource-caused modifications of predator–prey links will likely combine synergistically when prey foraging increases with total resource availability and antagonistically when foraging decreases with resource availability. Both responses are possible (Abrams 1984, 1995). However, because foraging activity always has a maximum, antagonistic interactions always occur at high enough total resource densities, while synergistic interactions may or may not occur at low resource densities, depending on the shape of the prey’s foraging-predation risk trade-off.
Predator interference via generalized defences
Predators that induce generalized defences in a shared prey species reduce the strengths of one another’s interactions with the prey. As before, defensive responses that decelerate with predator density imply that TIMs between separate predators combine antagonistically. Accelerating responses (and synergistic interactions between TIMs) seem most likely when total predator density is low, and additional predator species raise the total risk above a detection or response threshold.
Some prey defences are only effective against one or a subset of the predator types, and trade-offs may require that one defence be increased at the expense of another. Different types of refuges that are effective against different predator types produce such predator-specific defence. Soluk (1993) describes defence in grazing mayflies, which spend time on top of rocks to reduce predation risk from stoneflies and remain below rocks to reduce risk from fish. Small rodents are often more vulnerable to land-based predators under cover, but more vulnerable to avian predators in the open (e.g. Kotler, Blaustein & Brown 1992; Korpimäki, Koivunen & Hakkarainen 1996). Fish in streams often find refuge against multiple swimming predators in shallow water, and against multiple wading or diving predators in deeper water (Power 1987; Steinmetz, Soluk & Kohler 2008). In such situations, predators (modifiers) that elicit one type of defensive response diminish protection from other types of predators, thereby imposing a TIM that strengthens links between the prey and those other predators.
In one simple model where each predator species constitutes a unique type against which a unique defence is effective (Matsuda, Abrams & Hori 1993), the optimum strategy is for prey to allocate all of their defensive effort against only the deadliest predator species. Some empirical studies have found that prey faced with multiple predator species responded, behaviourally and/or morphologically, in a manner similar to when they were exposed to only the most deadly of the predators (Table 1 F). In such a scenario, link strengths will only be affected by a change that alters the identity of the most dangerous predator type, and only links involving the formerly and currently most dangerous predators will change. In a system with many predator species, an additional predator is less likely to modify existing interactions than in a system with fewer predators, because it is less likely that a given new predator will be more dangerous than any of those already present. Thus, TIMs interact antagonistically, because each species’ expected effect on links is smaller when a greater number of additional modifier species are present.
In most real world systems, prey are likely to continue to defend against all predator types to some degree, but merely skew their defensive effort based on the threat posed by each. In this situation, TIMs will again combine antagonistically because, all else being equal, a given predator introduction will alter the relationships between the relative threats posed by each type of predator by a smaller amount in a large system (where many other predators are present) than in a species-poor one.
When predator types consist of more than one species, predators of the same type will likely weaken one another’s links with prey. These effects, as well as the strengthening modifications of other types’ links described above, may accelerate with low to moderate total abundance of that predator type, particularly if some threshold relative abundance must be passed for the type to warrant defensive investment. However, if the only constraints keeping defence against a given type from being maximal are competing alternative defences, such thresholds represent the points at which TIMs caused by those alternative defences are replaced by TIMs caused by defence against the focal type. A predator type at low density only fails to produce a TIM because of the TIMs due to predator types against whom defence is a higher priority. The net result is that most interactions between TIMs remain antagonistic.
Prey may also modify one another’s links with a shared predator by altering that predator’s relative foraging effort on each of them. For example, abundant and/or high-quality prey may cause predators to ignore rare/low quality prey that they may otherwise have attacked. Some models of diet choice deal with prey species that each require a particular predator behaviour to be detected or encountered. These models predict perfect predator switching (Křivan 1997), whereby predators only attack the single prey type that currently yields the greatest net benefit per unit foraging time or effort (generally a function of relative prey density). In contrast, classical optimal foraging theory (Stephens & Krebs 1986), deals with prey that are encountered simultaneously. It predicts that predators should only include prey whose ratio of energy content (e) to handling time (h) is above some threshold determined by the abundance of prey with higher e/h ratios. Both of these frameworks involve a hierarchy among prey types in their profitability (defined differently in each model) to the predator. As with predator-specific defences, this hierarchy requires a prioritization of species’ responses to potential modifiers, which determines the nature of interactions between TIMs. Low-profitability prey that are excluded from the diet experience a weakening net TIM that reduces the strength of their link with the predator to 0 (M′ = 0). Only higher-profitability prey contribute to this net TIM. In the perfect predator switching case, net TIMs will only change if the identity of the single most profitable prey changes; even then, only the link strengths of the formerly and newly most profitable prey will be affected. In a sense, all prey species contribute to the net TIM acting on the least profitable one, but removal of any subset of superior prey will not alter that net TIM so long as at least one remains. Less extreme, but similar restrictions apply in the optimal foraging theory scenario. In either case, most species losses, additions or changes in density will not affect most net TIMs. A given species is also less likely to affect links in a large community, where it is less likely to be included among the most profitable prey. Thus, species’ contributions to net TIMs will generally be smaller than would be expected based on independent effects, and TIMs will combine antagonistically.
Empirical work has supported some general features of each of the forms of diet choice discussed above, but predator behaviour is never exactly optimal. Predator preferences and switching are never absolute, and some low-quality prey are always consumed (Stephens & Krebs 1986; Abrams 2010a). These caveats change predicted absent links or zero effects of species additions/deletions to weak ones, but do not alter the basic features of the TIMs. In the switching scenario, prey species of a common type increase one another’s consumption, and the TIMs they impose may accelerate with total density of their prey type when that total density is low. As with specialized defences, these effects represent mitigation of TIMs caused by other types so long as foraging effort on a prey type is only constrained by effort invested on other types.
When species forage adaptively for complementary resources, the opposite of switching (‘anti-switching’) occurs because species preferentially consume the most limiting resource, which is often the least abundant (Abrams 1987). If there are many resources/prey that constitute complementary foods, each food species imposes a strengthening TIM on at least some (and maybe all) others. When there are strict trade-offs between consumption rates of different, nutritionally essential foods, the optimal condition for the consumer is colimitation by all, so that strict optimality by the predator/consumer will likely produce many TIMs (Abrams 1987). In a system with two or more nutritionally essential types of prey, nutritionally similar prey are likely to impose weakening TIMs on one another’s links to a shared predator, because of anti-switching between nutritional types. Because the essential nature of each type prevents the consumption of the type from dropping to 0, these TIMs are likely to interact antagonistically.
Diffuse resource and protection mutualisms
The benefits provided by mutualists often constitute TIMs. In ant protection mutualisms, ants reduce the strength of plant–herbivore or herbivore–predator links. Mycorrhizal fungi enhance consumption of soil nutrients by plants. Species in both of these mutualisms associate with multiple partners (modifiers) that provide qualitatively similar benefits. The saturation of benefits that has been observed to occur with increasing partner diversity (van der Heijden et al. 1998) or density (Ness, Morris & Bronstein 2006) in these mutualisms implies that TIMs describing those benefits would also likely combine antagonistically. Furthermore, (i) the modifier in each of the above mutualisms also acts as a consumer of its partner (at least when ants receive energetic rewards), (ii) each mutualism may involve modifications of multiple trophic links (protection against multiple herbivores/predators or increased uptake of multiple soil nutrient pools) and (iii) partners often seem able to adaptively regulate their mutualistic associations (e.g. Sylvia & Neal 1990; Holland, Chamberlain & Horn 2009). Because of this, TIMs in these mutualisms are structurally similar to those produced by previously discussed mechanisms (Fig. 2b,d).
Non-adaptive mechanisms for TIMs
There are additional TIMs that do not involve trade-offs associated with adaptive foraging and defensive traits. For convenience, we will refer to these as non-adaptive mechanisms, although some cases involve predator preferences or prey defensive behaviours. Non-adaptive TIMs have in general received less attention. However, this category includes several interactions of clear widespread importance, including common forms of facilitation. One example is associational defence/refuge/resistance, whereby the presence of well-defended or unpalatable species reduces consumption of less well-defended species with which they co-occur. Consumption may alternatively be enhanced by highly palatable species (associational susceptibility). Similar situations arise when structural vegetation interferes with or facilitates hunting, or when heterospecific neighbours interfere with herbivores’ abilities to locate target plants. These interactions differ from the other cases we have discussed in that modifiers often need not have any particular trophic relationship to the species whose link is being modified. Shared predator satiation (discussed earlier) is also a particularly prevalent non-adaptive TIM.
Most descriptions of these effects imply a certain amount of redundancy among the species providing them. This is supported by studies showing that multiple species can confer similar facilitative benefits (Tahvanainen & Root 1972; McNaughton 1978; Wahl, Hay & Enderlein 1997; Stachowicz & Hay 2000; Baraza, Zamora & Hódar 2006). Redundancy is also implied in these cases because modifying species are often grouped together, e.g. as ‘macrophytes’ or ‘phytoplankton’ affecting predation by fish (Crowder & Cooper 1982; Radke & Gaupisch 2005), ‘vegetation’ affecting predation by birds (Groner & Ayal 2001), ‘bushes’ affecting grazing by rabbits (Jaksić & Fuentes 1980) or ‘woody vegetation’ providing cover for lions (Hopcraft, Sinclair & Packer 2005). Such redundancy again implies antagonistic interaction between TIMs whenever each single TIM is a decelerating function of total modifier density. Because of the general constraints on interaction strengths discussed earlier, non-adaptive TIMs must also interact antagonistically at high total modifier density. Effects of modifiers may also saturate independently of limits on interaction strength (for example, increases in vegetation may cease to provide added benefits once cover is sufficiently abundant). Trophic interaction modifications are more likely to combine synergistically when total modifier abundance is relatively low. For example, if vegetation increases predation by providing cover for stealthy hunters, the effect may not become pronounced until that cover is sufficiently abundant that it is difficult for prey to avoid. Further empirical descriptions of how the strengths of these kinds of effects vary as functions of modifier density are much needed.
Scaling up to more complex TIM interactions
We have not considered interactions between TIMs of multiple types, or between TIMs that arise from the same mechanism but where modifiers differ in their role relative to the focal link. Both of these cases are very likely in large food webs and may also occur in small webs having a reasonably complex structure. In some cases, the implications of such interactions are straightforward. In systems with diet choice and type II functional responses, TIMs caused by shared predator satiation will be experienced by those species included in the diet. Herbivores’ diet choice may be influenced by the effects of their food plants on exposure to predation (e.g. Duffy & Hay 1991); in these cases, TIMs caused by defence and foraging may act in concert, again with a hierarchical aspect to TIM interactions. A similar scenario may result from habitat choice that is based on both predation risk and foraging opportunities. When the introduction of a higher-level predator causes lower-level predators to reduce their activity, this is turn should reduce many modifications attributable to those lower-level predators’ interactions with the rest of the community. Thus, many links experience a TIM from the newly added higher-level predator that interacts antagonistically with existing TIMs from the lower-level predators. This occurs in Abrams’ (1992) model of a four-level food chain with interacting adaptive behaviours (which was one of the earliest models of interacting TIMs, although that terminology was not used). An empirical example has recently been documented in the form of predation risk from a parasitic fly disrupting an ant-hemipteran mutualism (Liere & Larsen 2010). These types of systems are still likely to be characterized by redundancy of effects from similar members of a trophic level on some species that is located many links away in the food web. For example, if Abrams’ (1992) food chain model was extended to include multiple resources on the bottom level, it is likely that they would have TIMs on the top trophic link that have the same sign and interact antagonistically with one another.
Despite these examples, interactions between TIMs of multiple types/sources remain an understudied topic whose implications at the community scale are only beginning to be understood. Exploring what if any generalities concerning those effects can be made, and whether/how they affect the conclusions reached here, is an important next step towards better understanding the aggregate implications of TIMs.
Many studies of foraging have documented TIMs that are large in magnitude (reviews by Lima 1998; Werner & Peacor 2003; and Preisser, Bolnick & Bernard 2005; Preisser, Orrock & Schmitz 2007 among others). Given what is known about their mechanism, interactions between TIMs are inevitable for many if not all types of modifications. Despite this, applied models in fields such as conservation and fisheries almost never include TIMs, let alone their interaction. On the theoretical side, most studies of large food webs also ignore TIMs. Given that TIMs are likely to be important, it is important to construct models that include them, which is only possible if we have a better understanding of how they interact.
Three generalizations emerge from the preceding analysis of many of the mechanisms that commonly cause TIMs. The first is that the aggregate effect of multiple modifier species differs from the independent combination of single modifier effects for all of the mechanisms reviewed; TIMs are fundamentally interdependent. Secondly, TIMs are highly structured. Multiple modifier species that are similar in their trophic relationships and/or habitat use are likely to impose similar TIMs on a given predator–prey link. Such groups include predators feeding by similar methods on one or more prey, or similar prey sharing one or more predators. Thus, TIMs are often multi-species phenomena, with modifier ‘functional groups’ that contribute to similarly comodify one or several trophic links. Random TIMs are as unlikely as random trophic connections in a multi-species community.
Thirdly, interactions between TIMs usually cause each modifier’s effects (and therefore the aggregate effect of many TIMs) to be weaker than would be expected if TIMs were independent. This is because of the prevalence of antagonistic interactions between TIMs, particularly when the net TIM is large. Interactions between TIMs should be more numerous in more speciose systems, simply because the potential number of modifications per link increases exponentially with species richness. In a very large system, the predominance of antagonistic interactions should mean that the addition or loss of any single modifier species will generally have a negligible impact on link strengths, because several similar modifiers will be expected to contribute to each net TIM. Thus, even in communities where TIMs are very common and the net TIM affecting most links is large, the TIM caused by an individual modifier on a particular link may often be weak. This suggests that individual TIMs may often be difficult to detect, but also that ignoring individual TIMs is unlikely to greatly affect quantitative predictions about the effects of small perturbations on large food webs. If empirically measured trophic links implicitly include the net effects of many TIMs, predicting the consequences of a change in the density of a single species may not require a model that explicitly represents modifier effects.
The likely predominance of antagonistic (over synergistic) interactions also suggests that the complexity introduced by TIMs is likely to be greatest in communities of intermediate diversity. Such communities are speciose enough to have many TIMs, but only a few species are likely to contribute to any given net TIM, so that net TIM strength is more likely to be sensitive to changes in the population size of any single modifier. Similarly, TIMs might be most noticeable either early in a community assembly process or late in a series of species losses, when the species that is added to or deleted from the community is most likely to be the sole representative of a modifier functional group. These possibilities provide further motivation for describing the functional forms of TIMs, and in particular whether TIMs in natural systems tend to be accelerating or decelerating functions of modifier densities.
This analysis highlights important distinctions between different types of TIMs in their structure and interactions. Particularly pronounced differences occur between TIMs that arise from traits involving general foraging or defence and those involving specialized foraging or defence. The mechanisms reviewed here represent idealized scenarios, in which each adaptive trait responds to a single trade-off. In real systems, this is likely often not the case (e.g. specialized defences may come not only at the expense of alternate defences but also foraging effort). While such considerations add complexity to TIM–TIM interactions, the constraints on traits and interactions discussed earlier suggest that antagonistic interactions between TIMs should generally still be expected. Although this analysis has lumped species that have qualitatively similar effects on a focal trophic link, it does not imply that species identity or traits are unimportant in determining the nature of interactions between TIMs. The functional diversity of species and their environment determines how many different specialized types of foraging or defence are possible, and it is likely that some species have unique traits that produce similarly unique TIMs. TIM–TIM interactions involving such unique TIMs would be a particular case of interactions between dissimilar TIMs, already highlighted as an important topic for future research.
Species interactions do not occur in a vacuum, and it is clear that the strengths of trophic links in nature depend on the densities of species in the community beyond the focal pair. Incorporating these complex phenomena into food web models is a challenging task, and the need to consider interactions between TIMs and structural details of various modification types will make it more difficult. The current results suggest that models omitting these factors in favour of randomly assigned, independent TIMs likely introduce directional biases, which may increase with system size. On a promising note, these results also suggest that the added consideration of interactions between TIMs may in some cases simplify model predictions, if antagonistic interactions make link strengths in some systems less sensitive to changes in the density of any one modifier species. More empirical studies of interactions between TIMs are necessary to gauge how often this possibility is realized in nature, and such studies will be important for progress in food web ecology. Two important tasks of future work should be to quantify the frequencies of antagonistic and synergistic interactions and to better define modifier functional groups (or more generally the degree of overlap in species’ effects as modifiers).
A. J. Golubski was supported by National Science Foundation (USA) postdoctoral fellowship OISE-0754419. P. A. Abrams was supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada.