Download - Wiley Online Library

Journal of Animal Ecology 2011, 80, 1097–1108
doi: 10.1111/j.1365-2656.2011.01852.x
Modifying modifiers: what happens when interspecific
interactions interact?
Antonio J. Golubski*† and Peter A. Abrams
Department of Ecology & Evolutionary Biology, University of Toronto, 25 Harbord St., Toronto, ON M5S 3G5, Canada
Summary
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.
Key-words: behaviour, diversity, food webs, foraging, indirect interactions, interaction modifications, IM, nontrophic interactions, trait-mediated indirect interactions, TMII
Introduction
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:
*Correspondence author. E-mail: [email protected]
†Present address: Department of Ecology & Evolutionary Biology,
University of Michigan, 2041 Kraus Natural Science Building,
830 N University Ave, Ann Arbor, MI 48109-1048, USA.
interaction modifications (IMs), trait-mediated indirect interactions (TMIIs), non-consumptive predator effects (NCEs),
behaviourally mediated indirect interactions (BMIIs), higherorder 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 metaanalyses (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 &
2011 The Authors. Journal of Animal Ecology 2011 British Ecological Society
1098 A. J. Golubski & P. A. Abrams
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.
Our current understanding of the mechanisms underlying
TIM allows predictions about whether and when interaction
modifications make a difference for system-level properties of
large food webs. Although population dynamical theory on
several specific TIM-generating phenomena is well developed, in general that theory has not isolated a ‘modification’
effect or examined how that effect changes with the addition
of other modifier species. Many models focus on small systems (e.g. Abrams 1992, 2010a; Abrams & Matsuda 1993;
Matsuda, Hori & Abrams 1994; Fryxell & Lundberg 1998;
McCann, Hastings & Huxel 1998; Bolker et al. 2003; Křivan
& Schmitz 2004), where the maximum potential number of
modifications per trophic link is low. Most works exploring
larger systems focus on TIMs arising from one or a small
number of closely related mechanisms at a time (e.g. Matsuda, Hori & Abrams 1996; Pelletier 2000; Kondoh 2003, 2007;
Drossel, McKane & Quince 2004; Uchida, Drossel & Brose
2007; Kondoh & Ninomiya 2009) and again do not specifically address how additional modifications affect the strength
of those that are already present. This focus on isolated modifications limits our ability to understand how TIMs interact
with one another when affecting a common trophic link. The
nature of these interactions is clearly critical for predicting
the emergent system-level effects of TIMs in large communities. Two recent works that have not restricted the TIMs they
model to a small number of mechanisms have assumed that
TIMs have random signs and per capita magnitudes, and
that the TIMs affecting a particular species do not interact
with one another (Arditi, Michalski & Hirzel 2005; Goudard
& Loreau 2008).
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
Fig. 1. Illustration of trophic interaction modifications, terminology
used to describe them here, and ways in which they might possibly
combine (independently, synergistically or antagonistically). The
likely prevalence of each of the latter three possibilities is the focus of
this paper.
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
2011 The Authors. Journal of Animal Ecology 2011 British Ecological Society, Journal of Animal Ecology, 80, 1097–1108
Modifying modifiers 1099
terminology. Let aij 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 a¢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 a¢ij > aij) or weakening it (helping
make a¢ij < aij). 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:
( "
a0ij
¼ aij M0ij
¼ aij max 0; 1 þ
X
#)
Mijk
eqn 1
k
The maximum function in eqn (1) prevented feeding relationships from reversing directions. Goudard & Loreau
(2008) assumed that all Mijk combine multiplicatively according to:
a0ij ¼ aij M0ij ¼ aij Y
Mijk
eqn 2
k
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 (sensu Sih, 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).
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
2011 The Authors. Journal of Animal Ecology 2011 British Ecological Society, Journal of Animal Ecology, 80, 1097–1108
1100 A. J. Golubski & P. A. Abrams
Fig. 2. General directions of trophic interaction modifications (TIMs) produced by various mechanisms, along with trophic relationships
between modifiers and links being modified that each mechanism suggests. Thick dashed grey arrows indicate links being modified, grey circles
indicate modifier species, and thin dotted grey arrows indicate modifications. Each mechanism suggests that multiple modifiers with similar trophic positions often interact in their effects on a given link (left column of diagrams), and that multiple links with similar trophic positions are
often affected similarly by a given modifier (right column of diagrams). Note that the mechanisms listed do not necessarily represent the full suite
of TIMs that may result from a given adaptive behaviour, or that may be possible for a given arrangement of trophic links. Most non-adaptive
mechanisms (other than shared predator satiation) are not included because of greater potential diversity in the trophic relationships between
modifiers and links being modified.
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
2011 The Authors. Journal of Animal Ecology 2011 British Ecological Society, Journal of Animal Ecology, 80, 1097–1108
Modifying modifiers 1101
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)
Observation
TIM-generating mechanism
Modifiers
References
(A) Redundancy among modifier
species
Associational refuge ⁄
susceptibility
Plant neighbours
Epibionts
Sessile algae & invertebrates
Shrubs
Non-host plant leaves
McNaughton (1978)
Wahl, Hay & Enderlein (1997)
Stachowicz & Hay (2000)
Baraza, Zamora & Hódar (2006)
Tahvanainen & Root (1972)
Bushes
Macrophytes
Vegetation
Woody vegetation
Jaksić & Fuentes (1980)
Crowder & Cooper (1982)
Groner & Ayal (2001)
Hopcraft, Sinclair & Packer
(2005)
Radke & Gaupisch (2005)
Power (1987); Steinmetz, Soluk &
Kohler (2008)
Dill & Fraser (1984)
Peacor & Werner (2001)
Relyea (2003)
(B) Redundancy among modifier
species implied by
conceptually grouping
multiple species together
Effects of non-prey on
foraging success
Effects of non-prey on
foraging success
Antipredator defences
(C) Saturating effects of modifier
density
(D) Saturating responses to
predator density
(E) Saturating effects of modifier
diversity
(F) Prioritization of responses to
multiple species
Antipredator defences
Protection mutualism
Antipredator defences
Resource mutualism
Predator-specific defences
Diet choice
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 addi-
Phytoplankton
Wading ⁄ diving & swimming
predators
Trout model
Dragonfly larvae
Beetle larvae, water bugs,
dragonfly larvae
Dragonfly larvae
Beetle larvae
Ants
Ciliate
Stickleback
Nudibranch cue
Arbuscular mycorrhizal
fungi
Bass vs. crayfish
Snakes vs. owls
Fish vs. stoneflies
Weasels vs. kestrels
Beetle larvae, water bugs,
dragonfly larvae
Crayfish, sunfish &
waterbugs
Birds vs. bass
Assorted references
Relyea (2004)
Schoeppner & Relyea (2008)
Ness, Morris & Bronstein (2006)
Wiackowski & Starońska (1999)
Teplitsky, Plénet & Joly (2005)
Harvell (1990)
van der Heijden et al. (1998)
Rahel & Stein (1988)
Kotler, Blaustein & Brown (1992)
Soluk (1993)
Korpimäki, Koivunen & Hakkarainen (1996)
Relyea (2003)
Hoverman & Relyea (2007)
Steinmetz, Soluk & Kohler (2008)
Stephens & Krebs (1986)
(pp. 187-194)
tion 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:
aij
1 þ aij hij Ni þ akj hkj Nk
eqn 3
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 (aij) 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):
2011 The Authors. Journal of Animal Ecology 2011 British Ecological Society, Journal of Animal Ecology, 80, 1097–1108
1102 A. J. Golubski & P. A. Abrams
aij
¼
1 þ aij hij Ni þ akj hkj Nk
aij
1 þ aij hij Ni
Mijk
eqn 4
where
eqn 8b
Mijk ¼
1 þ aij hij Ni
1 þ aij hij Ni þ akj hkj Nk
eqn 5
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:
aij
1 þ aij hij Ni þ akj hkj Nk þ agj hgj Ng
aij
Mijg
¼
eqn 6
1 þ aij hij Ni þ akj hkj Nk
where
Mijg ¼
1 þ aij hij Ni þ akj hkj Nk
1 þ aij hij Ni þ akj hkj Nk þ agj hgj Ng
1 þ aij hij Ni
1 þ aij hij Ni þ akj hkj Nk þ agj hgj Ng
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.
eqn 7a
Defensive reduction in generalized foraging
effort
The total modification of the i–j link in the presence of k
and g is:
M0ij ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
!
1þaij hij Ni
akj hkj Nk
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Mijk ¼
1þaij hij Ni þakj hkj Nk þagj hgj Ng
agj hgj Ng akj hkj Nk
eqn 7b
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:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
!
1þaij hij Ni
agj hgj Ng
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Mijg ¼
1þaij hij Ni þakj hkj Nk þagj hgj Ng
agj hgj Ng akj hkj Nk
eqn 8a
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
2011 The Authors. Journal of Animal Ecology 2011 British Ecological Society, Journal of Animal Ecology, 80, 1097–1108
Modifying modifiers 1103
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 foragingpredation 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 pre-
dators 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.
Predator-specific defences
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.
2011 The Authors. Journal of Animal Ecology 2011 British Ecological Society, Journal of Animal Ecology, 80, 1097–1108
1104 A. J. Golubski & P. A. Abrams
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.
Diet choice
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;
2011 The Authors. Journal of Animal Ecology 2011 British Ecological Society, Journal of Animal Ecology, 80, 1097–1108
Modifying modifiers 1105
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 fourlevel 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.
Discussion
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
2011 The Authors. Journal of Animal Ecology 2011 British Ecological Society, Journal of Animal Ecology, 80, 1097–1108
1106 A. J. Golubski & P. A. Abrams
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).
Acknowledgements
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.
2011 The Authors. Journal of Animal Ecology 2011 British Ecological Society, Journal of Animal Ecology, 80, 1097–1108
Modifying modifiers 1107
References
Abrams, P.A. (1983) Arguments in favor of higher order interactions. American
Naturalist, 121, 887–891.
Abrams, P.A. (1984) Foraging time optimization and interactions in food webs.
American Naturalist, 124, 80.
Abrams, P.A. (1987) The functional responses of adaptive consumers of two
resources. Theoretical Population Biology, 32, 262.
Abrams, P.A. (1992) Predators that benefit prey and prey that harm predators:
unusual effects of interacting foraging adaptations. American Naturalist,
140, 573–600.
Abrams, P.A. (1995) Implications for dynamically variable traits for identifying, classifying, and measuring direct and indirect effects in ecological communities. American Naturalist, 146, 112–134.
Abrams, P.A. (2001) Describing and quantifying interspecific interactions: a
commentary on recent approaches. Oikos, 94, 209–218.
Abrams, P.A. (2008) Measuring the impact of dynamic antipredator traits on
predator-prey-resource interactions. Ecology, 89, 1640–1649.
Abrams, P.A. (2010a) Quantitative descriptions of resource choice in ecological
models. Population Ecology, 52, 47–58.
Abrams, P.A. (2010b) Implications of flexible foraging for interspecific interactions: lessons from simple models. Functional Ecology, 24, 7–17.
Abrams, P.A. & Matsuda, H. (1993) Effects of adaptive predatory and antipredator behavior in a two prey – one predator system. Evolutionary Ecology, 7, 312–326.
Agrawal, A.A., Ackerly, D.D., Adler, F., Arnold, A.E., Cáceres, C., Doak,
D.F., Post, E., Hudson, P.J., Maron, J., Mooney, K.A., Power, M.,
Schemske, D., Stachowicz, J., Strauss, S., Turner, M.G. & Werner, E. (2007)
Filling key gaps in population and community ecology. Frontiers in Ecology
and the Environment, 5, 145–152.
Arditi, R., Michalski, J. & Hirzel, A.H. (2005) Rheagogies: modelling non-trophic effects in food webs. Ecological Complexity, 2, 249–258.
Baraza, E., Zamora, R. & Hódar, J.A. (2006) Conditional outcomes in plantherbivore interactions: neighbors matter. Oikos, 113, 148–156.
Beckerman, A., Petchey, O.L. & Morin, P. (2010) Adaptive foragers and community ecology: linking individuals to communities and ecosystems. Functional Ecology, 24, 1–6.
Billick, I. & Case, T.J. (1994) Higher order interactions in ecological communities: what are they and how can they be detected? Ecology, 75, 1530–1543.
Bolker, B., Holyoak, M., Křivan, V., Rowe, L. & Schmitz, O. (2003) Connecting theoretical and empirical studies of trait-mediated interactions. Ecology,
84, 1101–1114.
Brown, J.S. & Kotler, B.P. (2004) Hazardous duty pay and the foraging cost of
predation. Ecology Letters, 7, 999–1014.
Charnov, E.L., Orians, G.H. & Hyatt, K. (1976) Ecological implications of
resource depletion. American Naturalist, 110, 247–259.
Crowder, L.B. & Cooper, W.E. (1982) Habitat structural complexity and the
interaction between bluegills and their prey. Ecology, 63, 1802–1813.
Dambacher, J.M. & Ramos-Jiliberto, R. (2007) Understanding and predicting
effects of modified interactions through a qualitative analysis of community
structure. Quarterly Review of Biology, 82, 227–250.
Dill, L.M. & Fraser, A.H.G. (1984) Risk of predation and the feeding behavior
of juvenile coho salmon (Oncorhynchus kisutch). Behavioral Ecology and
Sociobiology, 16, 65–71.
Drossel, B., McKane, A.J. & Quince, C. (2004) The impact of nonlinear functional responses on the long-term evolution of food web structure. Journal of
Theoretical Biology, 229, 539–548.
Duffy, J.E. & Hay, M.E. (1991) Food and shelter as determinants of food
choice by an herbivorous marine amphipod. Ecology, 72, 1286–1298.
Fryxell, J.M. & Lundberg, P. (1998) Individual Behavior and Community
Dynamics. Chapman & Hall, London.
Gilliam, J.F. & Fraser, D. (1987) Habitat selection under predation hazard: test
of a model with foraging minnows. Ecology, 68, 1856–1862.
Goudard, A. & Loreau, M. (2008) Nontrophic interactions, biodiversity, and
ecosystem functioning: an interaction web model. American Naturalist, 171,
91–106.
Groner, E. & Ayal, Y. (2001) The interaction between bird predation and plant
cover in determining habitat occupancy of darkling beetles. Oikos, 93, 22–
31.
Harvell, C.D. (1990) The ecology and evolution of inducible defenses. Quarterly Review of Biology, 65, 323–339.
van der Heijden, M.G.A., Klironomos, J.N., Ursic, M., Moutoglis, P.,
Streitwolf-Engel, R., Boller, T., Wiemken, A. & Sanders, I.R. (1998) Mycorrhizal fungal diversity determines plant biodiversity, ecosystem variability
and productivity. Nature, 396, 69–72.
Holland, J.H., Chamberlain, S.A. & Horn, K.C. (2009) Optimal defence theory
predicts investment in extrafloral nectar resources in an ant-plant mutualism.
Journal of Ecology, 79, 89–96.
Hopcraft, J.G.C., Sinclair, A.R.E. & Packer, C. (2005) Planning for success:
Serengeti lions seek prey accessibility rather than abundance. Journal of Animal Ecology, 74, 559–566.
Hoverman, J.T. & Relyea, R.A. (2007) The rules of engagement: how to defend
against combinations of predators. Oecologia, 154, 551–560.
Ings, T.C., Montoya, J.M., Bascompte, J., Blüthgen, N., Brown, L., Dormann,
C.F., Edwards, F., Figueroa, D., Jacob, U., Jones, J.I., Lauridsen, R.B.,
Ledger, M.E., Lewis, H.M., Olesen, J.M., van Veen, F.J.F., Warren, P.H. &
Woodward, G. (2009) Ecological networks – beyond food webs. Journal of
Animal Ecology, 78, 253–269.
Jaksić, F.M. & Fuentes, E.R. (1980) Why are native herbs in the Chilean matorral more abundant beneath bushes: microclimate or grazing? Journal of Ecology, 68, 665–669.
Jeschke, J.M., Kopp, M. & Tollrian, R. (2004) Consumer-food systems: why
type I functional responses are exclusive to filter feeders. Biological Reviews,
79, 337–349.
Kondoh, M. (2003) Foraging adaptation and the relationship between foodweb complexity and stability. Science, 299, 1388–1391.
Kondoh, M. (2007) Anti-predator defence and the complexity-stability relationship of food webs. Proceedings of the Royal Society B Biological Sciences,
274, 1617–1624.
Kondoh, M. & Ninomiya, K. (2009) Food-chain length and adaptive foraging.
Proceedings of the Royal Society B Biological Sciences, 276, 3113–3121.
Korpimäki, E., Koivunen, V. & Hakkarainen, H. (1996) Microhabitat use and
behavior of voles under weasel and raptor predation risk: predator facilitation? Behavioral Ecology, 7, 30–34.
Kotler, B.P., Blaustein, L. & Brown, J.S. (1992) Predator facilitation: the combined effects of snakes and owls on the foraging behavior of gerbils. Annales
Zoologici Fennici, 29, 199–206.
Křivan, V. (1997) Dynamic ideal free distribution: effects of optimal patch
choice on predator-prey dynamics. American Naturalist, 149, 164–178.
Křivan, V. & Schmitz, O.J. (2004) Trait and density mediated indirect interactions in simple food webs. Oikos, 107, 239–250.
Laska, M.S. & Wootton, J.T. (1998) Theoretical concepts and empirical
approaches to measuring interaction strength. Ecology, 79, 461–476.
Lawton, J.H. (1999) Are there general laws in ecology? Oikos, 84, 177–192.
Liere, H. & Larsen, A. (2010) Cascading trait-mediation: disruption of a traitmediated mutualism by parasite-induced behavioral modification. Oikos,
119, 1394–1400.
Lima, S.L. (1998) Stress and decision making under the risk of predation: recent
developments from behavioral, reproductive, and ecological perspectives.
Advances in the Study of Behavior, 27, 215–290.
Matsuda, H., Abrams, P.A. & Hori, M. (1993) The effect of adaptive anti-predator behavior on exploitative competition and mutualism between predators. Oikos, 68, 549–559.
Matsuda, H., Hori, M. & Abrams, P.A. (1994) Effects of predator-specific
defense on community complexity. Evolutionary Ecology, 8, 628–638.
Matsuda, H., Hori, M. & Abrams, P.A. (1996) Effects of predator-specific
defense on biodiversity and community complexity in two-trophic-level communities. Evolutionary Ecology, 10, 13–28.
McCann, K., Hastings, A. & Huxel, G.R. (1998) Weak trophic interactions
and the balance of nature. Nature, 395, 794–798.
McNaughton, S.J. (1978) Serengeti ungulates: feeding selectivity influences the
effectiveness of plant defense guilds. Science, 199, 806–807.
Ness, J.H., Morris, W.F. & Bronstein, J.L. (2006) integrating quality and quantity of mutualistic service to contrast ant species protecting Ferocactus wislizeni. Ecology, 87, 912–921.
Novak, M. & Wootton, J.T. (2008) Estimating nonlinear interaction strengths:
an observation-based method for species-rich food webs. Ecology, 89, 2083–
2089.
Okuyama, T. & Bolker, B.M. (2007) On quantitative measures of indirect interactions. Ecology Letters, 10, 264–271.
Olff, H., Alonso, D., Berg, M.P., Eriksson, B.K., Loreau, M., Piersma, T. &
Rooney, N. (2009) Parallel ecological networks in ecosystems. Philosophical
Transactions of the Royal Society B Biological Sciences, 364, 1755–1779.
Peacor, S.D. & Werner, E.E. (2001) The contribution of trait-mediated indirect
effects to the net effects of a predator. Proceedings of the National Academy
of Sciences of the United States of America, 98, 3904–3908.
Peacor, S.D. & Werner, E.E. (2004) How dependent are species-pair interaction
strengths on other species in the food web? Ecology, 85, 2754–2763.
Pelletier, J.D. (2000) Are large ecosystems more unstable? A theoretical reassessment with predator switching. Mathematical Biosciences, 163, 91–96.
2011 The Authors. Journal of Animal Ecology 2011 British Ecological Society, Journal of Animal Ecology, 80, 1097–1108
1108 A. J. Golubski & P. A. Abrams
Power, M.E. (1987) Predator avoidance by grazing fishes in temperate and
tropical streams: importance of stream depth and prey size. Predation: Direct
and Indirect Impacts on Aquatic Communities (eds W.C. Kerfoot & A. Sih).
pp. 333–351. University Press of New England, Hanover, London.
Preisser, E.L. & Bolnick, D.I. (2008) When predators don’t eat their prey: nonconsumptive predator effects on prey dynamics. Ecology, 89, 2414–2415.
Preisser, E.L., Bolnick, D.I. & Bernard, M.F. (2005) Scared to death? The
effects of intimidation and consumption in predator-prey interactions. Ecology, 86, 501–509.
Preisser, E.L., Orrock, J.L. & Schmitz, O.J. (2007) Predator hunting mode and
habitat domain alter nonconsumptive effects in predator-prey interactions.
Ecology, 88, 2744–2751.
Radke, R.J. & Gaupisch, A. (2005) Effects of phytoplankton-induced turbidity
on predation success of piscivorous Eurasian perch (Perca fluviatilis): possible implications for fish community structure in lakes. Naturwissenschaften,
92, 91–94.
Rahel, F.J. & Stein, R.A. (1988) Complex predator-prey interactions and predator intimidation among crayfish, piscivorous fish, and small benthic fish.
Oecologia, 75, 94–98.
Relyea, R.A. (2003) How prey respond to combined predators: a review and
empirical test. Ecology, 84, 1827–1839.
Relyea, R.A. (2004) Fine-tuned phenotypes: tadpole plasticity under 16 combinations of predators and competitors. Ecology, 85, 172–179.
Schmitz, O.J., Adler, F.R. & Agrawal, A.A. (2003) Linking individual-scale
trait plasticity to community dynamics. Ecology, 84, 1081–1157.
Schoeppner, N.M. & Relyea, R.A. (2008) Detecting small environmental
differences: risk-response curves for predator-induced behavior and
morphology. Oecologia, 154, 734–754.
Sih, A., Englund, G. & Wooster, D. (1998) Emergent impacts of multiple predators on prey. Trends in Ecology & Evolution, 13, 350–355.
Soluk, D.A. (1993) Multiple predator effects: predicting combined functional
response of stream fish and vertebrate predators. Ecology, 74, 219–225.
Stachowicz, J.J. & Hay, M.E. (2000) Geographic variation in camouflage specialization by a decorator crab. American Naturalist, 156, 59–71.
Steinmetz, J., Soluk, D.A. & Kohler, S.L. (2008) Facilitation between herons
and smallmouth bass foraging on common prey. Environmental Biology of
Fishes, 81, 51–61.
Stephens, D.W. & Krebs, J.R. (1986) Foraging Theory. Princeton University
Press, Princeton.
Sylvia, D.M. & Neal, L.H. (1990) Nitrogen affects the phosphorous response
of VA mycorrhiza. New Phytologist, 115, 303–310.
Tahvanainen, J.O. & Root, R.B. (1972) The influence of vegetational diversity
on the population ecology of a specialized herbivore, Phyllotreta cruciferae
(Coleoptora: Chrysomelidae). Oecologia, 10, 321–346.
Teplitsky, C., Plénet, S. & Joly, P. (2005) Costs and limits of dosage response to
predation risk: to what extent can tadpoles invest in anti-predator morphology? Oecologia, 145, 364–370.
Uchida, S., Drossel, B. & Brose, U. (2007) The structure of food webs with
adaptive behaviour. Ecological Modelling, 206, 263–276.
Wahl, M., Hay, M.E. & Enderlein, P. (1997) Effects of epibiosis on consumerprey interactions. Hydrobiologia, 355, 49–59.
Werner, E.E. & Anholt, B.R. (1993) Ecological consequences of the trade-off
between growth and mortality rates mediated by foraging activity. American
Naturalist, 142, 242–272.
Werner, E.E. & Peacor, S.D. (2003) A review of trait-mediated indirect interactions in ecological communities. Ecology, 84, 1083–1100.
Wiackowski, K. & Starońska, A. (1999) The effect of predator and prey density
on the induced defence of a ciliate. Functional Ecology, 13, 59–65.
Wootton, J.T. (1994a) Predicting direct and indirect effects: an integrated
approach using experiments and path analysis. Ecology, 75, 151–165.
Wootton, J.T. (1994b) Putting the pieces together: testing the independence of
interactions among organisms. Ecology, 75, 1544–1551.
Wootton, J.T. (2002) Indirect effects in complex ecosystems: recent progress
and future challenges. Journal of Sea Research, 48, 157–172.
Received 12 September 2010; accepted 29 March 2011
Handling Editor: Andrew Beckerman
2011 The Authors. Journal of Animal Ecology 2011 British Ecological Society, Journal of Animal Ecology, 80, 1097–1108