Download How does global change affect the strength of trophic interactions?

ARTICLE IN PRESS
Basic and Applied Ecology 5 (2004) 505—514
www.elsevier.de/baae
How does global change affect the strength of
trophic interactions?
Mark Emmersona,, T. Martijn Bezemerb,1, MarkD. Hunterc,
T. Hefin Jonesd, GregoryJ. Masterse, Nicole M. Van Damb
a
Department of Zoology, Ecology and Plant Sciences, University College Cork, Lee Maltings, Prospect Row, Cork, Ireland
Netherlands Institute of Ecology (NIOO-KNAW), P.O. Box 40, 6666 ZG Heteren, The Netherlands
c
Institute of Ecology, University of Georgia, Ecology Building, Athens, GA 30602-2202, USA
d
Cardiff School of Biosciences, Cardiff University, P.O. Box 915, Cardiff CF10 3TL, UK
e
Ecological Applications, CABI Bioscience, Bakeham Lane, Egham, Surrey, TW20 9TY, UK
b
Received 4 July 2004; accepted 4 September 2004
KEYWORDS
Community;
Ecosystems;
Food webs;
Herbivore;
Plant;
Predators;
Prey;
Stability
Summary
Recent research has generally shown that a small change in the number of species in a
food web can have consequences both for community structure and ecosystem processes.
However ‘change’ is not limited to just the number of species in a community, but might
include an alteration to such properties as precipitation, nutrient cycling and
temperature, all of which are correlated with productivity. Here we argue that predicted
scenarios of global change will result in increased plant productivity. We model three
scenarios of change using simple Lotka–Volterra dynamics, which explore how a global
change in productivity might affect the strength of local species interactions and detail
the consequences for community and ecosystem level stability. Our results indicate that
(i) at local scales the average population size of consumers may decline because of poor
quality food resources, (ii) that the strength of species interactions at equilibrium may
become weaker because of reduced population size, and (iii) that species populations
may become more variable and may take longer to recover from environmental or
anthropogenic disturbances. At local scales interaction strengths encompass such
properties as feeding rates and assimilation efficiencies, and encapsulate functionally
important information with regard to ecosystem processes. Interaction strengths
represent the pathways and transfer of energy through an ecosystem. We examine how
such local patterns might be affected given various scenarios of ‘global change’ and
discuss the consequences for community stability and ecosystem functioning.
& 2004 Elsevier GmbH. All rights reserved.
Corresponding author. Tel.: +353 21 490 4190; fax: +353 21 427 0562.
E-mail address: [email protected] (M. Emmerson).
Present address: Nature Conservation and Plant Ecology Group, Wageningen University and Research Centre, Bornsesteeg 69,
6708 PD Wageningen, The Netherlands.
1
1439-1791/$ - see front matter & 2004 Elsevier GmbH. All rights reserved.
doi:10.1016/j.baae.2004.09.001
ARTICLE IN PRESS
506
M. Emmerson et al.
Zusammenfassung
Die neuere Forschung hat im Allgemeinen gezeigt, dass eine kleine Veränderung in der Zahl
der Arten in einem Nahrungsnetz sowohl Konsequenzen für die Gemeinschaftsstruktur als
auch für die Ökosystemprozesse haben kann. Wandel‘‘ist jedoch nicht nur auf die Anzahl
’’
der Arten in einer Gemeinschaft beschränkt, sondern kann auch Veränderungen von
Eigenschaften wie Niederschlag, Nährstoffkreisläufe und Temperatur beinhalten, die alle
mit der Produktivität korreliert sind. Hier argumentieren wir, dass vorhergesagte Szenarios
des globalen Wandels in einer erhöhten Pflanzenproduktivität resultieren werden. Wir
modellieren drei Szenarien des Wandels unter der Verwendung einfacher Lotka–Volterra–Dynamiken, die erkunden, wie ein globaler Wandel in der Produktivität die Stärke von
lokalen Arteninteraktionen beeinflusst, und wir beschreiben detailliert die Konsequenzen
für die Gemeinschaft und die Stabilität des Ökosystemlevels. Unsere Ergebnisse deuten
darauf hin, (i) dass auf einer lokalen Skala die durchschnittliche PopulationsgröXe der
Konsumenten aufgrund der geringen Qualität der Nahrungsressourcen abnehmen könnte,
(ii) dass die Stärke der Arteninteraktionen im Gleichgewicht aufgrund der reduzierten
PopulationsgröXe schwächer werden könnte und (iii) dass die Populationen der Arten
variabler werden und länger brauchen könnten, um sich von umweltbedingten oder
anthropogenen Störungen zu erholen. Auf lokalen Skalen umfassen Interaktionsstärken
Eigenschaften wie FraXraten und Assimilationseffizienzen und enthalten wichtige
funktionelle Information in Bezug auf Ökosystemprozesse. Interaktionsstärken repräsentieren die Energiewege und den Energietransfer in einem Ökosystem. Wir untersuchen, wie
solche lokalen Muster unter der Voraussetzung verschiedener gegebener Szenarios des
globalen Wandels‘‘beeinflusst werden könnten und diskutieren die Konsequenzen für die
’’
Gemeinschaftsstabilität und Ökosystemfunktion.
& 2004 Elsevier GmbH. All rights reserved.
Introduction
Ecological systems that are more species rich have
more interspecific pathways along which energy
can flow. These pathways can be depicted graphically as food web diagrams, and energy flow may be
characterised by the trophic interactions that take
place amongst species within the food web. The
biological strength of these interactions details the
conversion of abundance or biomass from one
trophic level to another, and provides a direct link
between the diversity and ecosystem functioning of
a community and its ecological stability (Duffy,
2002). To understand how communities might
respond to global change, we identify the basic
patterning of species interaction strengths in
communities (here patterning refers to the arrangement and relative strength of interactions
amongst species and trophic links) and investigate
how a change to that patterning might affect
ecological systems.
May (1973) found that in randomly constructed
food webs increased species richness tended to
decrease the stability of model communities. Pimm
and Lawton (1977, 1978) subsequently showed that
the patterning of species interactions (that is the
presence or absence of omnivorous links and
therefore food web structure alone) could have
dramatic effects on the stability of such systems.
They showed that omnivory (and hence the
arrangement of species interactions) would alter
the probability of stability in randomly parameterised food webs. Yodzis (1981) working with a
compiled set of 40 real, as opposed to model food
webs, found that the patterning of species interaction strengths was essential for food web
stability. He searched at random through parameter space to find stable versions of these 40
webs. He then permuted the interaction coefficients, maintaining predator–prey pairs and the
sign of each interaction (to maintain food web
structure), but randomising the original stable
pattern of interactions. Many of the resulting webs
were no longer locally stable, the detailed patterning of interaction strengths was disrupted and the
resulting webs were, on average, less stable. Pimm
(1982, p. 191) later went on to describe how food
web structure might impact three ecosystem
functions: Resilience, Nutrient cycling and Resistance. In this context the ability of a food web to
return to a pre-disturbance state can be considered
a measure of ecosystem functioning (albeit, difficult to measure in the field). These classic studies
(May, 1973; Pimm & Lawton, 1977, 1978; Yodzis,
1981) all used Lotka–Volterra dynamics:
!
n
X
dX i
¼ X i ri þ
aij X i
for i ¼ 1; 2; 3 . . . n; (1)
dt
i¼j
ARTICLE IN PRESS
Global change and interaction strength
where X i represents the population density of
species i, and r i is the intrinsic growth rate of
species i. The intrinsic growth rate is positive for
species at the base of food webs (primary producers
sequestering energy from the sun and having no
resources below them in the food web to exploit)
and negative for consumers (representing a death
rate for consumers). These classic theoretical
studies made use of linear stability analyses and
the Jacobian matrix for the determination of food
web stability. There are two quantities that emerge
as characterising the interactions amongst species,
the interaction coefficient between pairs of species
(aij ) and the elements of the Jacobian matrix at
equilibrium (aij X i ). The value aij is a per capita
effect and a constant coefficient of the model,
whilst aij X i will be dependent on the density of
species i (X i ). The elements of the Jacobian matrix
at equilibrium are the partial derivatives of the
growth equations and describe the dynamic forces
acting around the equilibrium point.
The empirical study of species’ interaction
strengths typically requires that a predator or
consumer be removed from a community and the
numerical response of its prey and predators be
quantified (although there are other ways to
empirically measure interaction strength, e.g.
consumption from gut content analysis). Measuring
interaction strength is difficult and only a small
number of studies have quantified the strength and
distribution of species interactions (Paine, 1992,
Fagan & Hurd, 1994, de Ruiter, Neutel, & Moore,
1995, Raffaelli & Hall, 1996, Wootton, 1997). In
these studies, the pattern of predominantly weak
interaction coefficients and few strong interactions
is consistent across a range of different habitat
types (both aquatic and terrestrial). Some studies,
however, report differing patterns determined by
species body size, for example Sala and Graham
(2002) working with eight marine herbivores reported a bimodal distribution of interaction
strengths that was well explained by the body size
of each consumer.
Using a non-linear modelling approach McCann,
Hastings, and Huxel (1998) showed that this
empirical pattern of weak interactions could
stabilize community dynamics when typically destabilising links (for example, omnivorous links) are
weak. Neutel, Heesterbeek, and De Ruiter (2002)
obtained a similar result using linear stability
analyses and showed that the stability of a food
web was intimately associated with the strength of
Jacobian elements in omnivorous food web loops.
Kuijper, Kooi, Zonneveld, and Kooijman (2003) also
explored the consequences of increased productivity for the dynamics of simple food webs featuring
507
intraguild predation (using non-linear functional
responses). They found that over a gradient of
nutrient enrichment intraguild predation acted to
stabilise food chains, eliminated chaotic dynamics
and was favoured in systems with low turnover
rates, where the intraguild predator had a low
interaction strength and a low yield on the basal
resource. Theoretical studies suggest therefore
that, within food webs, it is the specific arrangement of weak interactions that promotes food web
stability. How might the arrangement, and hence
patterning of species interactions be affected by
predicted changes to the global biosphere? Would a
change to the patterning of species interaction
strengths caused by such predicted changes be
sufficient to cause instabilities in community
dynamics? We now consider a global change
scenario and examine how this scenario might
affect the strength and patterning of species
interactions.
Defining change
To make our task somewhat more manageable, we
limit our discussion to scenarios of global change
associated with increasing concentrations of atmospheric CO2. Predictions suggest that by the end of
the century atmospheric CO2 levels will rise from
approximately 350 ppm to about 700 ppm (Intergovernmental Panel on Climate Change (IPCC),
2001). Associated with this increase in CO2 levels
there are (i) direct effects of atmospheric carbon
on plant photosynthesis and primary production,
(ii) increases in average global temperature (global
average surface temperatures have already increased by 0.6 1C during the 20th century, IPCC,
2001), and (iii) changing patterns of precipitation.
Coupled atmosphere–ocean general circulation
models provide the best predictions, on how
patterns of temperature and precipitation will
change as CO2 levels rise (IPCC, 2001). Most
terrestrial regions will experience an increase in
mean annual temperature between 3 and 10 1C. In
contrast, rates of precipitation could either decrease or increase (by up to 2 mm per day),
depending on region.
It is generally accepted that photosynthetic rates
are limited primarily by carbon (Drake, Gonzalez–Meler, & Long, 1997). Hence, most models predict
that net primary production will increase, as
atmospheric concentrations of CO2 increase. For
most plant species, increased rates of primary
production are associated with increases in relative
growth rate (Saxe, Ellsworth, & Heath, 1998). The
ARTICLE IN PRESS
508
effects of concomitant changes in temperature and
precipitation are harder to predict. Our ability to
make predictions is also limited, because models
that include multiple interactive effects of global
change are still relatively rare. A recent metaanalysis of available studies, suggests that ecosystem warming should increase plant productivity by
an average of 19%, with a 95% confidence interval
of 15–23% (Rustad et al., 2001). If true, then this
may imply that the effects of global warming on
productivity will operate in the same direction as
the direct effects of CO2 on productivity. In the
early 1970s Rosenzweig (1971) showed that increasing nutrient or energy supply would serve to
destroy steady-state systems. He provided a warning against the enrichment of ecosystems because
of the destabilising effects this would have on
productivity.
While the predicted increases in primary production may appear to favour herbivore populations,
many empirical studies suggest that plant quality
(important for consumers) will decline as CO2 levels
rise (Bezemer & Jones, 1998). In nearly every case
examined to date, foliar nitrogen concentrations
decline under elevated CO2, and when present,
foliar concentrations of condensed tannins increase
(e.g. Lincoln, Fajer, & Johnson, 1993; Lindroth,
Arteel, & Kinney, 1995). We hypothesise, that
herbivores confronted with low-quality plant tissue, would compensate by eating more. This
prediction usually holds true, particularly for
chewing and mining insects (Lincoln et al., 1993;
Lindroth et al., 1995; Bezemer & Jones, 1998).
Non-chewing insects have been less well studied
and general patterns are yet to emerge (Bezemer,
Knight, Newington, & Jones, 1999). As well as
separating quality and quantity effects, it is also
crucial that we distinguish between overall levels
of defoliation and per capita consumption by
insects. Increases in plant productivity, and nitrogen-mediated declines in insect density, can result
in lower levels of defoliation on plants, despite
increases in per capita consumption rates by
herbivores (Stiling et al., 2003).
While there is little information on how primary
consumers (herbivores) respond in the longer term
to changes in temperature and atmospheric CO2
concentrations, there is even less information on
the effects of climate change on secondary
consumers (parasitoids and predators). Using mathematical models Hassell, May, Pacala, and Chesson
(1991) showed that host–parasitoid relationships
might be altered by environmental change. Temperature elevation, for example, may differentially
affect developmental rates of hosts and parasitoids. Such differences can potentially result in the
M. Emmerson et al.
breakdown of synchronisation between the two
populations, which in turn may have major effects
on population dynamics.
Simulating the effects of change
The use of Lotka–Volterra dynamics ((1) above) is
commonly criticised because they incorporate
linear functional responses of predators on prey.
We use Lotka–Volterra dynamics for their simplicity
(relatively they are easier to parameterise) and as
a heuristic tool to explore the qualitative response
of local community interactions to various global
scenarios of change. Our aim has not been to make
quantitative predictions regarding the likely
changes in species population size resulting from
increased productivity, but rather to make qualitative forecasts using existing modelling frameworks.
The use of Type II or III functional responses might
well change the qualitative patterns we observe in
this study, we have not explored the robustness of
our findings to these alternative scenarios
(although see Kuijper et al. (2003) for likely
results). For further simplicity, we use a discrete
time version of the Lotka–Volterra framework ((1)
above) to explore the effects of ‘change’ (here
defined as an increase in productivity) on interaction strength. In discrete time (1) above becomes:
!
n
X
X i;tþ1 ¼ X i;t þ X i;t r i þ
aij X j;t ;
(2)
i¼j
where X i;t is the population density of species i at
time t, and basal species population growth is
logistic. We defined a simple three species food
chain in which the third species (i.e. the secondary
consumer is an omnivorous predator) is capable of
feeding on both the primary consumer (herbivore)
and the basal resource (plant) (see Fig. 1). A
gradient of productivity was established by incrementing the intrinsic rate of increase (r i ) of the
basal species in the food chain. We explored three
different scenarios to investigate how the persistence (stability) of this simple three species food
chain might be affected given an increase in basal
species productivity. To summarise, these differing
scenarios represent situations where:
(i) Consumer–resource interactions (aij ) and intraspecific competitive interactions (aii ) for
the non-basal species are considered constant,
i.e. there is no concomitant change in plant
quality. This scenario serves as a baseline against which to compare subsequent
scenarios.
ARTICLE IN PRESS
Global change and interaction strength
509
3
Secondary
r
consumer
a
Non-basal
23
A =
a
32
Primary
consumer
−0.5
−0.05
0.05
−0.1
−0.3
0.0005
0.03
−0.1
K
a
13
2
a
31
a
21
a
12
1
Primary
Basal
producer
Figure 1. Simple omnivorous food web used to simulate the effects of increased productivity on the strength of species
interactions. The basic parameter values used in simulations are depicted in the matrix A. Birth and death processes
have slightly different meanings for different trophic levels. For the basal species population growth is logistic so that
the per capita birth rate=r1/K1, r1 being the intrinsic rate of increase of Species 1 and K1 the carrying capacity which is
set equal to 1. For the consumers, r2 and r3 define the negative per capita death rates of Species 2 and 3, set at –0.01
and –0.001, respectively. The biological justification for this being that death rate declines with an increase in body size
and trophic height. Similarly, intraspecific competition terms have different meanings for the different species present
in the system. For the basal species a11 ¼ r 1 =K 1 ; whilst for non-basal species intraspecific competition is set equal to
0.1 (a22 and a33 ). Therefore as r1 increases, the strength of basal species intraspecific competition increases relative
to non-basal species intraspecific competition.
(ii) As the intrinsic rate (growth rate) of a plant
population increases, plant quality declines. To
compensate for this an herbivore must ingest
more plant material to fulfil its nutritional
requirements. Therefore in the second scenario as the basal species’ intrinsic population
growth rate (r i ) increases so too will the
herbivores per capita effects (aij ) on plants.
In this way the interaction coefficient asymptotes as the intrinsic rate of the basal species
increases. Essentially, as primary productivity
increases, there is a concomitant reduction in
the quality of plant material.
(iii) At low levels of productivity, plant quality
should be high and consequently consumers
would not need to ingest much plant material
to satisfy their nutritional requirements.
Therefore, when the intrinsic growth rates of
primary producers are low, the per capita
effects of primary consumers on prey are
small. However, the benefits to consumers
should be large, because plant quality is high.
It is difficult to represent this if it is assumed
that the ecological efficiency of the consumer
remains constant. Typically the positive per
capita effects of the resource on the consumer
are defined by aji ¼ aij e; where, e, is an
ecological efficiency, normally set to 0.1. In
the third scenario, to simulate an increase in
plant quality at low levels of plant productivity, we assume that the ecological efficiency of
a consumer is also a function of the primary
producers intrinsic growth rate, decreasing
asymptotically as intrinsic rate increases.
Simply, as productivity increases, there are
concomitant changes in both plant quality
(which declines) and a consumer’s ecological
efficiency (which also declines).
We use the following functions for simulating the
relationship between intrinsic rate and both herbivorous per capita effects (aij ) and ecological
efficiency in Scenario (ii) and (iii), respectively:
F ii ðr 1 Þ ¼ l þ u
r1
¼ aij
b þ r1
ðScenario ðiiÞÞ
(3)
r1
¼ e ðScenario ðiiiÞÞ:
b þ r1
(4)
and
F iii ðr 1 Þ ¼ u l
For (3), l and u are constants, defining the lower
and upper bounds of the interaction coefficient and
here were set at 0.2 and 0.8 for the primary
consumer and 0.002 and 0.008 for the secondary
consumer, respectively, b is a constant, set equal to
unity. For (4) we set l and u both at 0.3 this
provides a biologically plausible range (see Begon,
Harper, & Townsend, 1996; Jonsson & Ebenman,
1998) of 0.3 to 0.06 for the ecological efficiency
used in the herbivorous interactions of the primary
and secondary consumers (see Fig. 1 for a description of the basic parameter values used in these
simulations (scenario (i))).
ARTICLE IN PRESS
510
M. Emmerson et al.
pected given the logistic growth of the basal
species (see Figs. 2A–C for details of how fluctuations in the basal species population are reflected
in the population dynamics of the primary consumer). In the simulations detailed here, at high
values of the basal species intrinsic growth rate
(r 1 43) the basal species became extinct resulting
in the collapse of the whole food web. The
extinction of the basal species is caused by the
extreme chaotic oscillations evident in the basal
species population, these oscillations increase with
increased productivity and eventually cause the
population to crash and become extinct (notice
how oscillations become more pronounced in Figs.
To investigate the three scenarios above, we
established a gradient of productivity by incrementing the intrinsic rate of the basal species (r1)
over 0.01 intervals. For each value of the intrinsic
rate, r1, the dynamical system (2) was then
iterated for 40,000 time steps to allow the system
to arrive at either an equilibrium point or a cyclic
or chaotic attractor. We then examined each
species population for persistence and noted any
extinction that occurred. As the intrinsic rate of
the basal species increases the basal species
population moves from a stable equilibrium to a
series of limit cycles and finally falls onto a chaotic
attractor, this dynamical behaviour is not unex-
ij i
Jacobian Matrix Element
(α X *)
i
ii
C
iii
A
B
Rateof Population Increase (r )
1
B
C
i
Population
Size (X )
A
ABC
Time
Figure 2. A bifurcation diagram showing the consequences of scenarios (i), (ii) and (iii) (see text) for the magnitude of
Jacobian elements as a function of the primary producers intrinsic rate (r1) using Lotka–Volterra dynamics in discrete
time. The figure shows the effects of the primary consumer on the primary producer. The main figure shows how the
strength of a population level interaction is affected by each of the scenarios. The Jacobian elements are the
interaction coefficients (aij ; per capita effects) multiplied by the population size (X i ) of species i (aij X i ). For scenario (i)
the interactions remain weak, (ii) The interactions increase in strength (become more negative) as intrinsic rate
increases, and (iii) the population level interactions decline as intrinsic rate increases. To illustrate how these
populations behave through time, the sub-panes A–C show the dynamic behaviours of the primary consumers
population, in scenario (ii). The three panes A–C correspond to three values of r1, the intrinsic rate of the primary
producer, (A) r 1 ¼ 2; (B) r 1 ¼ 2:5; and (C) r 1 ¼ 3 (see the main figure pane).
ARTICLE IN PRESS
Global change and interaction strength
2A–C). However, at no point in the simulations
(prior to the extinction of the basal species) did
either the primary or secondary consumer become
extinct. Although there is little qualitative difference in terms of species persistence, the differing
scenarios affected consumer population sizes differently. In scenario (i) the abundance of both
primary and secondary consumer was low, being
largely unresponsive to the behaviour of basal
species population dynamics. In scenario (ii) basal
species population dynamics remained largely
unaffected. In contrast, non-basal species populations increased monotonically and coincidentally
became increasingly variable. In scenario (iii) the
population size of non-basal species both declined
substantially and became more variable as basal
species intrinsic rate increased. The decline in
average population size and coincident increase in
variability mean that the population of each
species may be more prone to random environmental disturbances as productivity increases. This
effect is especially marked, when the scenarios
that lead to a suggested increase in productivity
also predict increased occurrence of extreme
climatic events. Despite this, scenarios (ii) and
(iii) result in consumer populations, which are on
average larger than for scenario (i) where interaction coefficients and assimilation efficiencies are
not dependent on basal species productivity. A
sensitivity analysis of the parameter values for each
consumer–resource interaction coefficient (aij )
used in scenarios (i)–(iii) indicates that the qualitative results of this scenario are robust to small
changes of the parameter values (5% change).
What, then, are the implications for the patterning of Jacobian elements and the local stability of
such a simplistic food web? Using the discrete time
dynamics detailed in the scenarios above, we have
seen that the dynamical system displays complex
non-equilibrium dynamics (discrete and continuous
time models demonstrate different behaviours). If
instead of using the discrete time dynamics, we
consider the continuous time version of the
Lotka–Volterra dynamical system (Eq. (1) above),
we might be able to explore the local stability and
hence resilience of these systems. Using the
parameter values obtained from scenarios (i)–(iii),
we examined the local stability of the resulting
Jacobian matrices in continuous time, as r1
increased (for the system to be locally stable the
real part of the dominant eigenvalue must be
negative). We calculated the return time (RT ) for
each community to assess how stability might be
affected. By evaluating the dominant eigenvalue,
which is the characteristic root of the dynamic
system, close to the equilibrium point, we can
511
calculate the return time (RT ¼ 1=Re lMax ; where
Re lMax ; is the real part (Re) of the dominant
eigenvalue (lMax )). When interaction coefficients
do not vary with respect to basal species growth
rate (r 1 ), and primary consumer population size is
small, the Jacobian elements (interaction
strengths) are weak and return times are long,
irrespective of productivity (scenario (i)). When the
interaction coefficients increase with intrinsic rate,
but assimilation efficiency remains constant, return
times decline asymptotically and Jacobian elements become stronger, that is more negative
(scenario (ii)). For scenario (iii) when both interaction coefficients and assimilation efficiency are a
function of r1, the Jacobian elements become
weaker as productivity increases and return times
increase (Figs. 2 and 3). The implication is that
when Jacobian elements are weak, the system
takes longer to recover from small perturbations
close to equilibrium. We speculate that weak
interactions might therefore delay the recovery of
food webs.
Discussion
Incorporating some additional basic assumptions
into existing Lotka–Volterra models, regarding the
possible response of plant–herbivore interactions
to different scenarios of global change, permits a
heuristic exploration of the qualitative consequences of such change, for the stability of real
communities. We find that increased herbivore
consumption associated with a decline in plant
quality leads to an overall decline in herbivore
population size. A decline in herbivore densities is
also seen in empirical studies investigating the
effects of CO2 enrichment on plant growth (Stiling
et al., 2003). Evidence for increased per capita
consumption is mixed; McNaughton, Oesterheld,
Frank, and Williams (1989) for example have shown
that there is a positive relationship between
primary production and the amount of that
productivity, which is consumed by herbivores in
grasslands. In theoretical studies there have been
contrasting viewpoints. Resource-controlled models assume no relationships between the strength of
consumer control and primary productivity, whilst
consumer controlled models predict that the
interaction strength of the highest trophic level
should increase with productivity (Chase, Leibold,
Downing, & Shurin, 2000). We have envisaged a
scenario whereby primary consumer consumption
increases as plant productivity increases because
quality declines. It could also be argued that
ARTICLE IN PRESS
512
M. Emmerson et al.
Return Time to Equilibrium
(-1/Re(λ1))
i
ii
iii
Rate of
Population Increase (r1)
Figure 3. The stability of a three species food web measured as return time ð1=Reðl1 ÞÞ to equilibrium. For the
determination of return time the model parameterisations suggested by scenarios (i), (ii) and (iii) are used to
parameterise Lotka–Volterra dynamics in continuous time. Note that there are different behaviours of discrete and
continuous time models, i.e. non-equilibrium and equilibrium dynamics for discrete (Fig. 2) and continuous time,
respectively.
secondary consumer consumption of primary consumers will increase. In insect systems, primary
consumers would be required to eat more, with the
consequence that growth is slowed, this could lead
to a higher exposure of primary consumers to their
natural enemies (slow growth–high mortality hypothesis). Such effects of global change may also
be due to altered interactions between soil and
above-ground communities (Schröter et al., 2004,
Wardle et al., 2004), which subsequently may alter
levels of secondary plant compounds and, therefore, plant quality (Van Dam et al., 2003). We have
not considered such effects in the present study.
We have used a simple food web and employed a
range of parameter values, which produced feasible communities (i.e. where all species populations
have positive densities) and have explored how
changes to these parameter values affect community feasibility. At first this might seem trivial but
feasibility is important, mathematically stable
communities could be produced which have negative densities. We explored whether possible
scenarios of environmental change might take a
community into an unfeasible region of parameter
space, where one or more species populations
would decline or become extinct. In none of these
scenarios did the consumer populations decline to
the point of extinction (consumer species loss only
occurred following extinction of the basal species).
Generally, for the three scenarios we have investigated, increased productivity does not result in
decreased community persistence. However, we
have investigated only one possible food web with
limited dynamics. There are many possible food
web scenarios and other forms of dynamics (e.g.
McCann et al., 1998, using Type II or III functional
responses), which could be investigated, including
those that feature apparent competition or more
complex scenarios of intra-guild predation (Kuijper
et al., 2003).
Our discussion of change has focused on the
effects of increased productivity on the strength of
plant–herbivore interactions. We have not considered how species might respond over evolutionary
time scales to possible environmental changes
(Hoffmeister, Vet, Biere, Holsinger, & Filser,
2004), or how spatial scales, both above ground
(Van de Koppel et al., in press) and below ground
(Hedlund et al., 2004) may alter interaction
strengths; such scenarios remain to be investigated. Here we have illustrated how existing
simplistic models can provide important heuristic
insights into the causes of documented patterns in
real communities and the types of patterns we
might expect to emerge as our environment
changes.
ARTICLE IN PRESS
Global change and interaction strength
Despite the limited scope of this study, we
propose that fine-scale local species interactions
will be affected by global environmental change
(here ‘change’ is synonymous with an increase in
productivity) and that a number of far reaching
consequences might result: (1) as a consequence of
fast growing poor quality food resources, herbivorous interaction coefficients will become stronger as
grazers fulfil their dietary needs. Neutel et al.
(2002) investigating complex soil food webs have
found that the pattern of weak interactions in
omnivorous food web loops is vital for food web
stability. A change to the arrangement of such
interactions in more complex food webs than the
simplistic web we have explored here could result
in dramatic consequences for food web and
ecosystem stability. (2) The average population
size of consumers may decline because of poor
quality food resources; (3) Jacobian elements may
become weaker because of reduced population
sizes; and (4) species populations will become more
variable and may take longer to recover from
environmental or anthropogenic disturbances. Recent studies by Emmerson and Yearsley (2004)
support the conclusion that weaker interactions
will delay the recovery of ecosystems. When
omnivory is present in a food web, this work also
shows that including weak interactions increases
the probability of finding a stable parameterisation
of the food web. Increasing the probability of
finding a stable food web is not the same as
quantitatively increasing the stability of the food
web in terms of its resilience and variability of its
component populations. The last point (4) is also
important because extreme climatic effects are
predicted to increase with predicted scenarios of
global warming. The combined effect of reduced
population size, larger population variability and
extreme climatic effects will likely result in an
increased probability of extinction for such populations. In conclusion, empirical validation of our
simulations is necessary. On the basis of this study
local communities may become inherently less
stable, by this we mean less resilient, more
variable, smaller and hence more prone to extinction as they respond to predicted global environmental change.
Acknowledgements
Special thanks to John Pitchford for valuable
comments on an earlier version of this manuscript.
We also thank all those that participated in
discussion during the ‘Trophic interactions in a
513
changing world’ meeting, Texel, The Netherlands
co-subsidized by the European Science Foundation
(exploratory workshops programme).
References
Begon, M., Harper, J., & Townsend, C. (1996). Ecology:
individuals, populations and communities. UK: Blackwell Science.
Bezemer, T. M., & Jones, T. H. (1998). Plant–insect
herbivore interactions in elevated atmospheric CO2:
quantitative analyses and guild effects. Oikos, 82,
212–222.
Bezemer, T. M., Knight, K. J., Newington, J. E., & Jones,
T. H. (1999). How general are aphid responses to
elevated atmospheric CO2. Annals of the Entomological Society of America, 92, 724–730.
Chase, J. M., Leibold, M. A., Downing, A. L., & Shurin, J.
B. (2000). The effects of productivity, herbivory, and
plant species turnover in grassland food webs.
Ecology, 81, 2485–2497.
De Ruiter, P. C., Neutel, A.-M., & Moore, J. C. (1995).
Energetics, patterns of interaction strengths, and
stability in real ecosystems. Science, 269, 1257–1260.
Drake, B., Gonzalez-Meler, M., & Long, S. P. (1997). More
efficient plants: a consequence of rising atmospheric
CO2. Annual Review of Plant Physiology and Plant
Molecular Biology, 48, 607–637.
Duffy, J. E. (2002). Biodiversity and ecosystem function:
the consumer connection. Oikos, 99, 201–219.
Emmerson, M. E., & Yearsley, J. M. (2004). Weak
interactions, omnivory and emergent food web properties. Proceedings of the Royal Society, London Series
B, 271, 397–405.
Fagan, W. F., & Hurd, L. E. (1994). Hatch density
variation of a generalist arthropod predator: population consequences and community impact. Ecology,
75, 2022–2032.
Hassell, M. P., May, R. M., Pacala, S. W., & Chesson, P. L.
(1991). The persistence of host–parasitoid associations in patchy environments. 1. A general criterion.
The American Naturalist, 138, 568–583.
Hedlund, K., Griffiths, B., Christensen, S., Scheu, S.,
Setälä, H., Tscharntke, T., & Verhoef, H. (2004).
Trophic interactions in a changing world: responses of
soil food webs. Basic and Applied Ecology, 5, 495–503.
Hoffmeister, T.S., Vet, L.E.M., Biere, A., Holsinger, K., &
Filser, J. (2005). Ecological and evolutionary consequences of biological invasion and habitat fragmentation. Ecosystems, in press.
Intergovernmental Panel on Climate Change (IPCC)
(2001). Climate change 2001. New York: Cambridge
University Press.
Jonsson, T., & Ebenman, B. (1998). Effects of predator–prey body size ratios on the stability of food chains.
Journal of Theoretical Biology, 193, 407–417.
Kuijper, L. D. J., Kooi, B. W., Zonneveld, C., & Kooijman,
S. A. L. M. (2003). Omnivory and food web dynamics.
Ecological Modelling, 163, 19–32.
ARTICLE IN PRESS
514
Lincoln, P. E., Fajer, E. D., & Johnson, R. H. (1993).
Plant–insect herbivore interactions in elevated CO2.
Trends in Ecology and Evolution, 8, 64–68.
Lindroth, R. L., Arteel, G. E., & Kinney, K. K. (1995).
Responses of three saturniid species to paper birch
grown under enriched CO2 atmospheres. Functional
Ecology, 9, 306–311.
May, R. M. (1973). Stability and complexity in model
ecosystems (2nd ed.). Princeton, NJ: Princeton University Press.
McCann, K., Hastings, A., & Huxel, G. R. (1998). Weak
trophic interactions and the balance of nature.
Nature, 395, 794–798.
McNaughton, S. J., Oesterheld, M., Frank, D. A., &
Williams, K. J. (1989). Ecosystem-level patterns of
primary productivity and herbivory in terrestrial
habitats. Nature, 341, 142–144.
Neutel, A.-M., Heesterbeek, J. A. P., & de Ruiter, P. C.
(2002). Stability in real food webs: weak links in long
loops. Science, 296, 1120–1123.
Paine, R. T. (1992). Food-web analysis through field
measurement of per capita interaction strength.
Nature, 355, 73–75.
Pimm, S. L. (1982). Food webs. Chicago: University of
Chicago Press.
Pimm, S. L., & Lawton, J. H. (1977). Number of trophic
levels in ecological communities. Nature, 268,
329–331.
Pimm, S. L., & Lawton, J. H. (1978). On feeding on more
than one trophic level. Nature, 275, 542–544.
Raffaelli, D. G., & Hall, S. J. (1996). Assessing the
relative importance of trophic links in food webs. In
Polis, G. A., & Winemiller, K. O. (Eds.), Food webs:
integration of patterns and dynamics (pp. 185–191).
New York: Chapman & Hall.
Rosenzweig, M. L. (1971). Paradox of enrichment:
destabilisation of exploitation ecosystems in ecological time. Science, 171, 385–387.
Rustad, L., Campbell, J., Marion, G., Norby, R., Mitchell,
M., Hartley, A., Cornelissen, J., & Gurevitch, J.
(2001). A meta-analysis of the response of soil
M. Emmerson et al.
respiration, net nitrogen mineralization, and aboveground plant growth to experimental ecosystem
warming. Oecologia, 126, 543–562.
Sala, E., & Graham, M. H. (2002). Community-wide
distribution of predator–prey interaction strength in
kelp forests. Proceedings of National Academy of
Sciences USA, 99, 3678–3683.
Saxe, H., Ellsworth, D. S., & Heath, J. (1998). Tansley
Review No. 98. Tree and forest functioning in an
enriched CO2 atmosphere. New Phytologist, 139,
395–436.
Schröter, D., Brussaard, L., De Deyn, G. B., Poveda, K.,
Brown, V. K., Berg, M. P., Wardle, D. A., Moore, J. C.,
& Wall, D. H. (2004). Trophic interactions in a
changing world: modelling aboveground-belowground
interactions. Basic and Applied Ecology, 5, 515–528.
Stiling, P., Moon, D. C., Hunter, M. D., Colson, J., Rossi,
A. M., Hymus, G. J., & Drake, B. G. (2003). Elevated
CO2 lowers relative and absolute herbivore density
across all species of a scrub–oak forest. Oecologia,
134, 82–87.
Van Dam, N. M., Harvey, J. A., Wäckers, F. L., Bezemer, T.
M., Van der Putten, W. H., & Vet, L. E. M. (2003).
Interactions between aboveground and belowground
induced responses against phytophages. Basic and
Applied Ecology, 4, 63–77.
Van de Koppel, J., Bardgett, R.D., Bengtsson, J.,
Rodriguez-Barrueco, C., Rietkerk, M., Wassen, M., &
Wolters, V. (2005). Trophic interactions in a
changing world: the role of spatial scale. Ecosystems,
in press.
Wardle, D. A., Bardgett, R. D., Klironomos, J. N., Setälä,
H., Van der Putten, W. H., & Wall, D. H. (2004).
Ecological linkages between aboveground and belowground biota. Science, 304, 1629–1633.
Wootton, T. (1997). Estimates and tests of per capita
interaction strength: diet, abundance, and impact of
intertidally foraging birds. Ecological Monographs, 67,
45–64.
Yodzis, P. (1981). The stability of real ecosystems.
Nature, 289, 674–676.