Download Coexistence of two stage-structured intraguild predators

Journal of Theoretical Biology 308 (2012) 36–44
Contents lists available at SciVerse ScienceDirect
Journal of Theoretical Biology
journal homepage: www.elsevier.com/locate/yjtbi
Coexistence of two stage-structured intraguild predators
Tim Schellekens a,n, Tobias van Kooten b
a
b
IMARES, P.O. Box 77, 4400 AB Yerseke, The Netherlands
IMARES, P.O. Box 68, 1976 CP Ijmuiden, The Netherlands
H I G H L I G H T S
c
c
c
We model two stage-structured intraguild predator populations with life-history omnivory.
We examine the consequences of distinct adult diets for coexistence of these predators.
Coexistence is enabled because one is forced to act as a predator and the other to act as a consumer.
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 16 January 2012
Received in revised form
26 April 2012
Accepted 14 May 2012
Available online 31 May 2012
An organism can be defined as omnivorous if it feeds on more than one trophic level. Omnivory is
present in many ecosystems and multiple omnivorous species can coexist in the same ecosystem. How
coexisting omnivores are able to avoid competitive exclusion is very much an open question. In this
paper we analyze a model of a community consisting of two omnivorous predators and a basal
resource. The population of both predators is explicitly structured into juveniles and adults, of which
juveniles only feed on basal resource and adults feed on a varied proportion of basal resource and
juveniles of the other population. We thereby separate the omnivorous roles (competitor for basal
resource and predator of competitors) over life history. We show in this study that persistence of
multiple omnivorous predators is possible when predators differ in adult diets. In this case, coexistence
occurs because community dynamics force one of the model species to act as a predator and the other
to act as a consumer. We conclude that separation of omnivorous roles over life history not only offers
an explanation on why systems with omnivory can persist, but also how multiple omnivores can
coexist at the same trophic levels of those systems.
& 2012 Elsevier Ltd. All rights reserved.
Keywords:
Ontogenetic diet shifts
Life-history omnivory
Niche widening
Tritrophic food chain
Reciprocal predation
1. Introduction
Pimm and Lawton (1978) defined omnivory as the feeding on
different trophic levels, which allows an intraguild predator species
to simultaneously prey on and compete with another species
(named the intraguild prey). The basic form of this type of interaction is also referred to as intraguild predation (IGP: Holt and Polis,
1997; Polis et al., 1989). IGP is shown to be common in natural
communities (Arim and Marquet, 2004; Polis, 1991; Polis et al.,
1996). Theoretical models predict, however, limited possibilities for
coexistence of intraguild predators and intraguild prey (Diehl and
Feissel, 2000; Holt and Polis, 1997; Mylius et al., 2001). These
models have led to two generic insights: reduced scope for coexistence compared to tritrophic food chains and the possibility of
alternative stable states with community shifts along productivity
n
Corresponding author. Tel.: þ31317 480954; fax: þ 31317 487359.
E-mail addresses: [email protected] (T. Schellekens),
[email protected] (T. van Kooten).
0022-5193/$ - see front matter & 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.jtbi.2012.05.017
gradients (Holt and Polis, 1997, Diehl and Feissel, 2000, Mylius et al.,
2001). Coexistence between intraguild predator and prey in models
is only possible, according to Holt and Polis, 1997, if two essential
conditions are met. Firstly, the intraguild prey should be superior in
resource competition, and secondly, productivity levels should be
intermediate. Given the commonness of omnivory in nature also
beyond these essential conditions, studies have since focused on
possible mechanisms that promote coexistence of intraguild prey
and predators. Mechanisms that have been found to promote
coexistence are age-restricted predation or prey life stages invulnerable to predation (Borer, 2002; Mylius et al., 2001; Rudolf and
Armstrong, 2008), adaptive foraging behavior by intraguild predators (Krivan, 2000; Krivan and Diehl, 2005), spatial or temporal
refuges for the intraguild prey (Amarasekare, 2008; Finke and
Denno, 2006; Janssen et al., 2007; Okuyama, 2008), additional
resources for intraguild prey (Holt and Huxel, 2007) and cannibalism (Rudolf, 2007). The mechanisms proposed may enhance coexistence of consumers and predators by extending the conditions
under which competition and predation are balanced. Borer (2006)
questioned that the effect of these mechanisms is actually present in
T. Schellekens, T. van Kooten / Journal of Theoretical Biology 308 (2012) 36–44
nature, however, because it was marginal in an empirically parameterized IGP model.
As species grow during their life, resource availability and
exploitation rate change over ontogeny (Peters, 1983; Werner
and Gilliam, 1984). Species may therefore feed on different
resources in different life stages, a phenomenon referred to as
life-history omnivory (Pimm and Rice, 1987). As a result, adult life
history omnivores for instance prey on consumers, while juveniles compete with them for a shared resource.
The impact of life-history omnivory on the dynamics of IGP
has only been studied to a limited extent (Hin et al., 2011; Mylius
et al., 2001; van de Wolfshaar et al., 2006). Nevertheless, Hin et al.
(2011) showed that life-history omnivory is a form of intraguild
predation that permits coexistence of predator and prey over
more than just intermediate resource productivities and no longer
requires the prey to be the better competitor for resource. This
occurs because Hin et al., 2011 assumed that the adult intraguild
predator feeds only on intraguild prey and hence cannot persist in
its absence. Rudolf (2007) and van de Wolfshaar et al. (2006)
modeled life-history omnivory as an ‘ontogenetic niche widening’
instead of an ontogenetic niche shift, which assumes that additional resources become available when intraguild predators
grow in size. The intraguild predator that undergoes an ontogenetic niche widening is still able to exclude the intraguild prey at
high resource productivity, when adult predators can exclusively
forage on resource (van de Wolfshaar et al., 2006).
Given the commonness of omnivory in nature, it is not surprising
that several omnivorous species regularly coexist in the same
habitat (Arim and Marquet, 2004; Polis, 1991; Polis et al., 1996).
Woodward and Hildrew, 2002 assessed the importance of body size
in relation to intraguild predation and niche overlap between
predators in the food web of Broadstone Stream (UK) and found
that mutual predation between intraguild predators was frequent.
Decapods, for instance, appear capable of preying on heterospecific
juveniles while feeding on the same basal resources as heterospecifics (League-Pike and Shulman, 2009; Ojeda and Dearborn, 1991;
Ropes, 1969; Rossong et al., 2006; Williams et al., 2006). The same
holds true for spider communities (Balfour et al., 2003; Rypstra and
Samu, 2005). Interestingly, all these studies show that the occurrence of the intraguild predatory interaction is size-dependent;
Small individuals of the intraguild predator compete for resources
with the intraguild prey, whereas larger individuals feed on them.
Although coexistence of multiple intraguild predators is commonly observed in nature, it is only studied to a limited extent
using models. General consensus among these theoretical studies
is that possibilities for coexistence of multiple omnivores on the
same trophic level at the same time are limited.
Feeding relationships in ecological communities are generally
conceptualized as networks of nodes representing taxa linked by
feeding interactions, the strength of which is based on assumptions about body size (Brose et al., 2006; Woodward et al., 2005).
In these networks, trophic position of species is fixed. Size
spectrum models, in contrast, describe the community as a
continuous size distribution, and diets are determined by some
criterion, often related to gape size. This means that as organisms
grow, ontogenetic niche widening occurs and they move up the
trophic hierarchy (e.g. Hartvig et al., 2011; Law et al., 2009;
Williams and Martinez, 2000). As a result, size spectrum models
generally predict food webs with a higher degree of omnivory at
larger body size. Because species with a similar size-range will
have similar diets and hence strong niche overlap, all but one of
these species will generally be outcompeted in resulting food
webs. According to size spectrum models, coexistence of multiple
omnivores is therefore only possible between species which start
off at and/or ultimately reach different body sizes and thus attain
sufficient niche segregation.
37
Using a simple population dynamical model, HilleRisLambers
and Dieckmann (2003) varied the diet of two unstructured
intraguild populations by defining a trade-off between feeding
on heterospecifics and resource. In their model, coexistence was
only possible when omnivores were ‘punished’ with lower combined maximum intake rates compared to specialized predators
or consumers. In essence, coexistence was only possible if both
species were a priori set to be more efficient as either a predator
or a consumer. When omnivores profited from feeding on more
than one trophic level, or their combined intake did was not differ
from the intake of specialized predators or consumers, coexistence was highly unlikely. The authors disregarded, however, the
fact that omnivory results from changes in body size over
ontogeny (Polis et al., 1989) and assumed unstructured populations. Thereby, they overlooked possible mechanisms for coexistence that may arise from population dynamical feedbacks of
population structure as presented by Hin et al. (2011).
In this paper, we include population structure and study the
possibilities for coexistence of two intraguild predators with linear
trade-offs between feeding on heterospecifics and resource. We
assume, following studies on natural occurrences of coexisting
omnivores, that predation only takes place when individuals get
large enough (adult) and that juveniles feed on shared resource only.
For one of the populations at a time, we vary the diet of adults in a
linear trade-off. At one extreme this population only feeds on
resource throughout its entire life and no predation on heterospecifics takes place. At the other extreme the adults exclusively prey
on juvenile heterospecifics. We show, in contrast to predictions from
size spectrum models (e.g. Hartvig et al., 2011; Law et al., 2009;
Williams and Martinez, 2000) and HilleRisLambers and Dieckmann
(2003), that coexistence of two intraguild predators is stable if either
of these extremes in the varied population is approached. These two
extremes result in two different community settings. In the first
setting just one intraguild population preys on the other, resulting in
community dynamics that resemble classic intraguild predation
schemes in which coexistence is limited to intermediate resource
productivities. In the second setting predation takes place between
the two populations reciprocally, but community dynamics reflect
that of a tritrophic food chain. This setting results in coexistence
possibilities beyond intermediate resource productivities.
2. Materials and methods
Dynamics are modeled using the bioenergetics approach of Yodzis
and Innes (1992) with a stage-structured extension as formulated by
De Roos et al. (2008) for the two intraguild predators. Five ordinary
differential equations (ODEs) keep track of biomass changes of
resource R, and two intraguild predators: P, the fixed population,
and G, the varied population (juveniles Pj and Gj and adults Pa and Ga,
see Table 1, subscripts j and a are used throughout the text to indicate
juveniles and adults, respectively).
Resource follows semi-chemostat dynamics in absence of P
and G, with turnover rate d and maximum resource density Rmax.
We have explicitly avoided the use of logistic growth of resource
to avoid problems in mass-balance (Kooi et al., 1998). Resource
biomass decreases through feeding by P and G.
Both intraguild predators are structured into a juvenile and an
adult stage which potentially feeds on juveniles of the other
predator and/or resource biomass. Because much of the descriptions
for both intraguild predators are the same, we will use subscript i in
these descriptions to indicate either of the populations G or P.
Juvenile predator biomass decreases through predation by
intraguild predators and through background mortality mb
(Table 1). Juvenile net biomass production, nij, is used for
growth of juveniles and maturation, which is represented by the
38
T. Schellekens, T. van Kooten / Journal of Theoretical Biology 308 (2012) 36–44
mass-specific rate gi. Net biomass production of adults, nia, is only
used for reproduction. Intraguild predators therefore do not grow
after entering the adult stage. Adult biomass only decreases
through background mortality, mb.
The mass-specific maturation rate is derived in De Roos et al.
(2007):
gi ¼
nij mi
will vary FG to investigate the consequences of this linear tradeoff between feeding on heterospecifics and resource. At first we
assume adults of the fixed intraguild predator, Pa, always feed on
both resource and juvenile competitors (Gj) equally (FP ¼0.5).
Later on, we will fix FG and vary FP. Hence mass-specific net
biomass production rates for both populations’ juvenile stages Pj
and Gj become:
ð1Þ
1z1mi =nij
nij ðRÞ ¼ sMi
Maturation depends on net biomass production of juveniles,
nij, juvenile predator mortality mi and the ratio of predator body
size at birth and at maturation, represented by the parameter z
(De Roos et al., 2007). Eq. (1) captures the growth and survival of
juvenile individuals from the size at birth to the size at maturation in such a way that the stage-structured biomass model in
equilibrium is exactly identical to a physiologically structured
population model (PSPM) accounting for a continuous sizedistribution of juvenile predators (De Roos, 2008).
Mass-specific net biomass production of juveniles and adults,
denoted by nij and nia, respectively, equals the difference between
mass-specific ingestion and mass-specific maintenance Ti. Ingestion follows a type II functional response with maximum ingestion rate Mi, half-saturation constant Hi and conversion efficiency
s. Parameter FG models the extent of ontogenetic diet shift
between juveniles and adults of predator G. ^G can be interpreted
as the relative time spent by adults feeding on a particular prey
species and can be varied in a linear trade-off. At ^G ¼1, no diet
shift occurs and both stages of G feed on the resource R. When
FG o1, however, individuals broaden their diet after maturation
and start feeding on juvenile heterospecifics (Pj). At FG ¼0.5,
adults spend half their time feeding on resource and half on
juvenile heterospecifics. At FG ¼0, the varied population G
experiences a full diet shift over ontogeny: juveniles feed on the
resource only and adults feed on juvenile heterospecifics only. We
Table 1
Ordinary differential equations.
dR
R
FP R
¼ dðRmax RÞM p
P M p
Pa
dt
HþR j
H þ FP R þ ð1FP ÞGj
R
FG R
G M g
M g
Ga
HþR j
H þ FG R þ ð1FG ÞPj
dGj
¼ nga ðR,Gj ÞGa þ ngj ðRÞGj gg ðngj ðRÞÞGj mgj ðP a ÞGj
dt
dGa
¼ gg ðngj ðRÞÞGj mg Ga
dt
dP j
¼ npa ðR,Gj ÞP a þ npj ðRÞPj gp ðnpj ðRÞÞP j mpj ðGa ÞPj
dt
dP a
¼ gp ðnpj ðRÞÞP j mb P a
dt
R
T i
H þR
The mass-specific net biomass production rates for adults Ga
and Pa become:
nga ðR,Pj Þ ¼ sMg
FG Rþ ð1FG ÞPj
T g
H þ FG R þ ð1FG ÞPj
npa ðR,Gj Þ ¼ sMp
FP R þ ð1FP ÞGj
T p
H þ FP R þð1FP ÞGj
With corresponding mortality rates for the juvenile stages:
mpj ðGa Þ ¼ mb þ
ð1FG ÞGa M p
H þ FG R þð1FG ÞP j
mgj ðPa Þ ¼ ma þ
ð1FP ÞP a Mp
H þ FP R þ ð1FP ÞGj
2.1. Model parameterization
The model is parameterized to describe the dynamics of
herring using similar rates as in Van Leeuwen et al. (2008).
Furthermore, we assume that all parameters, except F are the
same in both populations. This way we can isolate the effects of
changing F on community dynamics from effects of other
differences between populations. The stage-structured biomass
model and its parameterization as used here, is such that the
results presented in this report are more generally applicable to
interactions between all sorts of organisms (for justification of
this statement see De Roos et al., 2007; De Roos et al., 2008;
Schellekens et al., 2010). Model parameters and their default
values are summarized in Table 2.
Maximum ingestion (M) and maintenance (T) are both massspecific rates (expressed in unit biomass per unit biomass per unit
time), whereas the mortality parameter (m) represents a per
capita rate.
The maximum resource density Rmax and half-saturation
density H are expressed as gram biomass per unit volume and
therefore the only parameters containing the unit of volume. H
can be set to 1 without loss of generality, as this merely implies a
scaling of the unit of the total system volume. Maximum resource
density Rmax is then expressed as multiples of the half-saturation
density. A conversion efficiency of 0.5 is used for conversion of
both resource and consumer biomass (Peters, 1983).
Table 2
Parameters and parameter values.
Parameter
Resource
Rmax
Varied
0.1
d
s
M
T
mb
H
F
z
Predator G and P
Description
0.5
0.23
0.032
0.001
1
Varied
0.035
Resource maximum biomass density
Resource turn-over rate
Assimilation efficiency
Maximum ingestion rate (mass specific)
Maintenance rate (mass specific)
Background mortality rate
Half-saturation constant
Adult time spent feeding on either juvenile heterospecifics or R
Newborn-adult predator size ratio
T. Schellekens, T. van Kooten / Journal of Theoretical Biology 308 (2012) 36–44
39
Model predictions are analyzed for different values of Rmax and
F. Productivity of a semi-chemostat system is given by d Rmax, so
varying maximum resource density Rmax corresponds to varying
the productivity, and we use maximum resource density and
resource productivity as synonyms throughout the rest of this
study. We used Content, a numerical bifurcation software package (Kuznetsov et al., 1996), to calculate equilibrium densities as
a function of Rmax and FG and to assess equilibrium stability.
3. Results
3.1. FG ¼1, consumer and intraguild predator
This configuration lets population G feed on resource R
throughout its life (Fig. 1a). Therefore, the interaction between
the varied and fixed population (G and P) is one that is similar to a
classic intraguild predation scheme, like the one presented by
Mylius et al. (2001). There, the intraguild predator (equivalent to
the fixed population P) is an inferior resource competitor compared to the intraguild consumer (equivalent to the varied
population G), but instead is able to feed on the consumer.
However, like in van de Wolfshaar et al. (2006) the adults of the
fixed population P have widened their niche compared to juveniles, feeding on both resource and juveniles of the varied
population (Gj). Just like in the unstructured IGP system (Mylius
et al., 2001), four equilibrium types at FG ¼1 occur: (1) a
resource-only equilibrium; (2) a consumer-resource equilibrium;
(3) a coexistence equilibrium with resource, consumers and
intraguild predators and (4) a predator-resource equilibrium
(Fig. 2, right panel). The resource-only equilibrium is stable when
there is not enough basal resource to sustain either populations G
and P. The varied population G has lower resource requirements
than the fixed (i.e. Rng oRnp, see Tilman, 1982). Therefore the varied
population G can invade the resource-only equilibrium when
there is still too little basal resource for the fixed population P
Fig. 2. Diet proportion of adults of population G (FG) over resource productivity
Rmax. Changing positions of the productivity thresholds changing FG from 1 to 0.5
(G is better competitor, but weaker predator than P; Ga relies mostly on basal
resource). Gray lines: single population invasion thresholds (solid: invasion
threshold of G, dashed: invasion threshold of P). Black lines: coexistence thresholds (dashed: Eg, solid: Ip).
to sustain. In the resulting stable G-resource equilibrium, resource
density stays constant at Rng while biomass G increases with
increasing Rmax. Invasion of the fixed population (P) in the
G-resource equilibrium becomes possible when net biomass
production of the fixed population becomes high enough to
overcome their background mortality and the life time reproduction equals unity. This productivity threshold is denoted as the
invasion point of the fixed population P (Ip; Fig. 3, right panel).
Following (De Roos, 2008) we express this invasion threshold as:
npa mpj =npj 1
z
¼1
mb
ð2Þ
Increasing productivity in the coexistence equilibrium
(P þG þR) increases equilibrium biomass of predator P and
resource biomass and decreases the biomass of G. Above a certain
resource productivity (the G-exclusion point (Eg), in Fig. 3), the
varied population is excluded by the fixed population and only
the P-resource equilibrium is stable.
3.2. 0.5 o FG o1, two intraguild predators, G the most efficient
competitor
Fig. 1. (a) Community structure at FG ¼ 1 (population G is a consumer of basal
resource only), (b): Community structure at FG ¼0.5 (adults of population G feed
on resource and juvenile heterospecifics equally, similar to population P),
(c): Community structure at FG ¼ 0.0 (adults of population G feed on juvenile
heterospecifics only).
Decreasing FG decreases the ability of population G to use the
basal resource. It requires higher resource productivity in order to be
able to persist in the system in absence of the fixed population P. In
other words, the minimum resource productivity needed for the
single population invasion threshold increases with decreasing FG
(visible in Fig. 4 as the solid gray line). Until FG ¼0.5, however, the
minimum resource requirements of G remain below that of P (Fig. 2).
Decreasing FG simultaneously enables the adults of the varied
population G to feed on heterospecific juveniles Pj. As a result, the
fixed population P now suffers higher mortality. Furthermore, the
invasion threshold of P (Ip, Eq. (2)) is only satisfied at higher Rmax
when decreasing FG. Because of the increasing predation on Pj, P
needs ever more resource productivity to compensate for those
losses, even though the competitive difference between G and P for
resource becomes smaller with decreasing FG. At a certain value of
FG the invasion point of P (Ip) crosses the exclusion point of
population G (Eg), resulting in a single threshold Ip. This makes
invasion of the fixed population and therefore coexistence
40
T. Schellekens, T. van Kooten / Journal of Theoretical Biology 308 (2012) 36–44
Fig. 4. Diet proportion of adults of population G (FG) over resource productivity
Rmax. Changing positions of the productivity thresholds changing FG from 0.5 to
0.0 (G is worse competitor, but stronger predator than P; Ga relies mostly on
predation of Pj). Gray lines: single population invasion thresholds (solid: invasion
threshold of G, dashed: invasion threshold of P). Black lines: coexistence thresholds (solid: Ig, dashed: Eg, dotted: start of limit cycles).
parameter combination for which life-time reproduction in
absence of predation equals 1 for varied population G:
nga mgj =ngj 1
z
¼1
mb
Fig. 3. Biomass equilibria of P, G and R over Rmax (from top to bottom panels
reflecting trophic position) at two values of diet proportion; FG ¼ 0.8 at the left and
FG ¼ 1 at the right panels (G is better competitor, but weaker predator than P; Ga
relies mostly on basal resource). Dotted equilibria: unstable. Solid equilibria:
stable (green: resource only equilibria, gray: single population equilibria, black:
coexistence equilibria). Green vertical lines: single population invasion thresholds
(solid: lowest threshold (G), dashed: highest threshold). Black vertical lines:
coexistence thresholds (solid: Ip, dashed: Eg). (For interpretation of the references
to colour in this figure legend, the reader is referred to the web version of this
article.)
unstable (Fig. 3, left panel dotted lines). As a consequence, from Ip
onwards the fixed population P eliminates G through predation
without the possibility for coexistence.
If FG ¼0.5, as in Fig. 1b, both intraguild predator populations
have equal feeding and production rates and hence all invasion
thresholds collapse into a single higher-order bifurcation point
(see Figs. 2 and 4). This represents a biologically unlikely situation
which we do not discuss further.
3.3. FG o0.5, two intraguild predators, G the more efficient predator
When FG o0.5, population G will be a more efficient predator
but a poorer resource competitor than population P (Fig. 4, note
the (trophic) position of P and G); when FG o0.5: Rng 4Rnp and
population P becomes the more efficient resource consumer. At
low resource productivity population P will be able to exclude
population G by resource competition. Increasing productivity at
low enough FG (below 0.34 in this case, Fig. 4) will enable
population G to invade, because G will depend to a lesser extent
on the resource, and instead feeds on Pj. Furthermore, this results
in a new productivity threshold: Ig, which, like Eq. (2), is the
ð3Þ
When productivity is increased further, population G can
exclude P, but an alternative stable state emerges. When FG is
nearly zero, adults of population G require Pj to sustain, such that
P can no longer be excluded.
As shown in Fig. 4, decreasing the value of FG towards zero
shifts the position of Ig toward higher Rmax values, while the
productivity threshold from where coexistence is possible (Eg)
changes less rapid over Rmax. Ultimately this results in the
equilibrium configuration as illustrated in Fig. 5 (right panel) for
FG ¼0. In coexistence the community at FG ¼0 consists of two
distinct types of intraguild predators: a life history omnivore (G)
and an ontogenetic niche widener (see Fig. 1c). Ga now solely
feeds on juvenile heterospecifics (Pj), while Gj only forages on the
resource. Pj also feeds on resource only whereas Pa feeds on both
resource and juvenile heterospecifics (Gj).
Due to the competitive advantage of P, the P-resource equilibrium is stable for all Rmax values (visible at FG ¼0 in Fig. 5 as
the solid gray line). Like Hin et al. (2011) described for their
system with one intraguild predator and prey, the introduction of
predator G in our system is hampered by a juvenile bottleneck
created by the competitive advantage of P. As an alternative
outcome of dynamics a stable coexistence state exists alongside
the P-resource equilibrium. Since sustenance of Ga is (largely)
dependent on Pj when FG is small, P cannot be excluded from the
coexistence equilibrium by G. Therefore, at low FG values the
only productivity threshold present is Eg, marking the lower limit
of Rmax for which the intraguild predator G can persist in
coexistence (Fig. 5, right panel). Increasing productivity in this
coexistence state increases biomass of G and the predatory
control of G over P. Biomass of P therefore stays constant with
changing productivity, releasing top-down control of resource
biomass. In this coexistence state, predation by Ga acts as the
main structuring force. Its predatory control over population P
decreases competition between juvenile heterospecifics Gj and Pj,
increases food availability for Gj and enables their coexistence
T. Schellekens, T. van Kooten / Journal of Theoretical Biology 308 (2012) 36–44
41
Fig. 6. Diet proportion of adults of population P (FP) over resource productivity
Rmax when FG ¼0.0. Changing positions of the coexistence productivity thresholds
changing FP from 0.5 to 0.0 (G is worse competitor, but stronger predator than P;
Ga relies mostly on predation of Pj). Coexistence thresholds (dashed: Eg, dotted:
start of limit cycles). Note the logarithmic x-axis.
(dashed line Fig. 6). Although the invasion boundary of population
G moves to higher Rmax when FP is reduced, coexistence remains
possible if the adult diets of the two omnivores remain different.
4. Discussion
Fig. 5. Biomass equilibria of G, P and R over Rmax (from top to bottom panels
reflecting trophic position) at two values of diet proportion; FG ¼0.2 at the left and
FG ¼ 0.0 at the right panels (G is worse competitor, but stronger predator than P;
Ga relies mostly on predation of Pj). Dotted equilibria: unstable. Solid equilibria:
stable (green: resource only equilibria, gray: single population equilibria, black:
coexistence equilibria). Green vertical lines: single population invasion thresholds
(solid: lowest threshold (P), dashed: highest threshold). Black vertical lines:
coexistence thresholds (solid: Ig, dashed: Eg). (For interpretation of the references
to colour in this figure legend, the reader is referred to the web version of this
article.)
with population P. The equilibrium patterns in this stable coexistence state therefore largely resemble those of a three-species
linear food chain (Oksanen et al., 1981). In an alternative stable
state without predatory control of G over P unbalanced competition for resources between juvenile heterospecifics Gj and Pj
creates a juvenile competitive bottleneck in population G. The
bottleneck, in turn, restricts formation of adults and thereby
decreases predatory control of G over P even further. In this
alternative stable state, therefore, unbalanced interspecific competition structures the community leading to exclusion of population G.
We show that the equilibrium pattern when FG is close to zero
remains when the ‘fixed’ predator is also allowed to increase the
proportion of heterospecific juveniles in the diet of adults in
Fig. 6. For this purpose we vary FP from 0.5 (as it was fixed in
previously) to 0. When adults of population P proportionally have
a more predacious diet, they release the top-down control of
resource but increase the mortality of juvenile heterospecifics.
Given certain resource productivity the change in RnP with the
decrease in FP is slower than the increase in mortality rate of
juvenile heterospecifics mgj. Therefore, introduction of population
G requires more resource productivity to balance these rates
We have shown that even though both populations could prey
on the other and both consume resource (in a linear trade-off),
coexistence of two intraguild predators is enabled because the
effect on community dynamics of either of these interactions is
minimized through a change in population stage-structure. The
change in stage-structure is an emergent effect of the community
configuration (such as depicted in Fig. 1); the more efficient
predator (and therefore the least efficient consumer) reduces
juveniles of the other species and so decreases the competition
among juveniles. The model predicts extended coexistence possibilities when the community consists of a niche widener and a
life history omnivore. Stable coexistence only occurs, however,
when community dynamics are shaped primarily by predation
with competitive interactions playing only a marginal role. As a
result, community dynamics in stable coexistence largely resemble those of a three-species linear food chain. Community
dynamics may also be governed by strong competition, leading
to an alternative stable state in which the better juvenile
competitor outcompetes the other species by means of a juvenile
bottleneck.
When the varied population G is a pure resource consumer
(FG ¼1) an increase in resource productivity can enable a small
biomass of the intraguild predator to invade the system. The
presented dynamics of the system at FG ¼1 is qualitatively
equivalent to that of models with unstructured populations, but
also resembles that of structured population models presented by
Mylius et al. (2001) and van de Wolfshaar et al. (2006). In contrast
to the situation at FG ¼1, establishment after an invasion of small
biomass is impossible when adults of the varied population feed
exclusively on juveniles of the fixed population P (at FG ¼0). In
that case, the equilibrium with only the most efficient resource
consumer present (P-resource equilibrium) is stable at all levels of
resource productivity large enough for P to persist in the system.
The varied population G is then excluded by resource competition
42
T. Schellekens, T. van Kooten / Journal of Theoretical Biology 308 (2012) 36–44
because juveniles Gj are not only preyed on by Pa but also
experience a developmental bottleneck because resource is
depleted. Invasion of the varied population (G) is only possible
if maturation of juveniles is possible. Maturation only takes place
if resource is sufficiently abundant. In other words, successful
invasion is possible if Ga can inflict enough mortality on heterospecifics (Pj) such that resource is raised above the minimum
required for Gj to mature. These invasion requirements are similar
to what was found by Hin et al. (2011) for a life-history omnivore
(like the varied population G at FG 0) invading a community of a
consumer feeding on a basal resource. We, on the other hand,
considered invasion in a community of basal resource fed upon by
a population that also preys on heterospecifics. Compared to Hin
et al. (2011) we hence introduce extra juvenile mortality in the
intraguild predator. The main conclusion of the analysis of Hin
et al. (2011) was that because the life-history omnivore has split
its roles over its lifetime (a predator as adult and competitor as
juvenile) the effect of these roles on community dynamics is split
as well. Either the omnivore acts as a competitor or it acts as a
predator. In the latter case, community dynamics follow simple
trophic interactions with three trophic levels. Invasion of the life
history omnivore (G) in this paper has similar dynamical results,
which shows that the life history omnivore creates community
dynamics that force it to primarily act as a predator and force
heterospecifics (P) to primarily act as consumer of the basal
resource, even though it preys on life history omnivores (G) as
well. Both this study and that of Hin et al. (2011) offer an
explanation as to why intraguild systems in nature often behave
as three-species linear food chains (Oksanen et al., 1981) if life
history omnivory is involved in the ontogeny of intraguild predators (Persson and De Roos, 2012). We furthermore show that
this emergent community pattern is robust against extra juvenile
mortality in both intraguild predators (when FG ¼0), through
mutual predation and cannibalism, as long as dependency on
predation exists and diets of omnivores are different. In addition,
we show that like a niche shift (i.e. when the adult diet differs
from the juvenile diet, F ¼0), niche widening (i.e. when adult diet
is wider than that of juveniles so that F a0) also enables these
community patterns.
The coexistence of intraguild predators can be compared to that
of competitors that feed on the same resources, but undergo extra
(in this case juvenile) mortality in presence of the other competitor.
In regard to interspecific competition and coexistence of populations
with ontogenetic niche shifts, theory has focused on the interactions
with populations exhibiting ontogenetic habitat shifts (Haefner and
Edson, 1984; Loreau and Ebenhoh, 1994; Moll and Brown, 2008;
Mougi and Nishimura, 2005). Some studies even represented
competitive interactions as negative density dependence, affecting
reproduction and maturation instead of explicitly representing
competition for resources (Haefner and Edson, 1984; Moll and
Brown, 2008; Mougi and Nishimura, 2005). This emphasizes the
focus of these studies on the effect of habitat segregation on
competition instead of the effect of differences in resource use.
Loreau and Ebenhoh (1994) have studied the competitive interactions between two populations exhibiting ontogenetic habitat shifts
during their lifetime. For coexistence to occur, each population
should be most resource limited in the habitat where the other
population was most efficient in resource use (Loreau and Ebenhoh,
1994). Also McCann (1998) analyzed a model describing competition between two consumers, both of which had ontogenetic niche
shifts, without assuming an explicit change in habitat but a distinct
resource for juvenile competitors from that of adults, excluding
competition between the life stages. This resource segregation
between life-history stages is conceptually identical to the habitat
segregation between stages assumed in other studies (Haefner and
Edson, 1984; Loreau and Ebenhoh, 1994; Mougi and Nishimura,
2005; Moll and Brown, 2008). Consequently, the type of coexistence
occurs under the same conditions as coexistence in studies with
explicit habitat segregation, namely, that a competitive advantage at
one life stage has to be balanced by a disadvantage at another life
stage. In contrast, competition in our model between stages was
separated only when F ¼0. Furthermore, we did not a priori assume
that individuals ever changed their competitive ability during their
lifetimes. Instead, the changes in competitive abilities of the
population and the resulting community dynamics were a property
emerging from the life history omnivory itself.
Coexistence of intraguild predators is clearly possible in nature
(Polis, 1991, Polis and Strong 1996, Arim and Marquet, 2004), but
this observation has been hard to reconcile with insights from
theory. Intraguild predation theory shows that coexistence
between predator and prey is limited to intermediate resource
productivity because only there a balance is possible between
competition and predation, such that prey do not undergo too
much mortality and predators not too much competition.
Coexistence possibilities of more than one intraguild predator
have scarcely been investigated theoretically. From more complex
food web models we learn that large sized species are likely to
engage in omnivory, but few of these species are predicted to
persist in food webs because of large overlap in resource use (e.g.
Law et al., 2009). In size spectrum-based food web models, large
species do not only engage in (intraguild) predation but can also
engage in cannibalism. Cannibalism in both intraguild predator
and prey has shown to facilitate and stabilize coexistence in IGPmodules (Rudolf, 2007). We have investigated the consequences
of enabling cannibalism in both of the intraguild predator
populations when either or both undergo a strong ontogenetic
niche shift (FG ¼0) and find no qualitative changes (details of
implementation and results shown in supplement) with respect
to the results presented in this paper, other than stabilization of
coexistence takes place at high rates of cannibalism in accordance
with predictions from Rudolf (2007).
Using a simple population dynamic model HilleRisLambers
and Dieckmann (2003) show that in a system of two unstructured
intraguild predators, coexistence occurs only when one is forced
to play the role of consumer, profiting mostly from feeding on
resource, while the other is forced to play the role of predator and
relies on feeding on the consumer. Compared to the standard case
with one intraguild predator and a consumer, HilleRisLambers
and Dieckmann (2003) predict that coexistence between two
intraguild predators occurs in a narrower range of productivities.
HilleRisLambers and Dieckmann (2003) varied the diet of the
unstructured populations by defining a trade-off between feeding
on heterospecifics and resource. They then investigated the
consequences of the strength of trade-offs on community structure and came to the conclusion that medium to strong trade-offs
(when intraguild predators are punished compared to specialist
consumers and predators) maximize coexistence possibilities.
Coexistence, however, was negligible or non-existent if the
trade-off was weak or linear. In contrast to HilleRisLambers and
Dieckmann (2003), we considered stage-structured populations,
where juveniles had different diets from adults. Similar to
HilleRisLambers and Dieckmann (2003) we varied the proportion
of predatory feeding and resource consumption, but only in adults
and only in a linear fashion. Where HilleRisLambers and
Dieckmann (2003) investigated the consequences of the strength
of trade-offs on community structure, we investigated the dynamical causes of community structure and specifically the effect of
life history omnivory. Our model setup results in coexistence
possibilities as extensive as presented in classic intraguild predation theory or even extended beyond intermediate resource
productivities, due to the inclusion of life history omnivory
or ‘‘an ontogenetic specialist’’. This type of omnivore has not
T. Schellekens, T. van Kooten / Journal of Theoretical Biology 308 (2012) 36–44
been considered in size-spectrum models or the model of
HilleRisLambers and Dieckmann, (2003), since in those models
omnivores widen their niches. ‘Ontogenetic specialists’ have been
found to be common in nature and crucial in determining food
web stability (Rudolf and Lafferty, 2011). Like Hin et al. (2011), we
show that stable coexistence in our model occurs with life history
omnivores (ontogenetic specialists) and ontogenetic niche wideners if these can actually shape their community through predation. Rudolf and Lafferty (2011) show that these species with
sequential specialization in resource use are sensitive to resource
loss and overexploitation, leading to the loss of the life history
omnivore and changes in community structure that disable the
reintroduction of this omnivore. The generic instability of the
coexistence with life history omnivores can be a reason why food
web models that generate food web structures stochastically
(Brose et al., 2006; e.g. Hartvig et al., 2011; Law et al., 2009;
Williams and Martinez, 2000; Woodward et al., 2005) underestimate the occurrence of coexistence of intraguild predators
(with similar size ranges) and the response of ecosystems to
(anthropogenic) change (Rudolf and Lafferty, 2011).
Acknowledgments
This research has been supported by EU FP7 grant FACTS
(Forage Fish Interactions), grant agreement no. 244966.
Appendix A. Supporting information
Supplementary data associated with this article can be found in
the online version at http://dx.doi.org/10.1016/j.jtbi.2012.05.017.
References
Amarasekare, P., 2008. Coexistence of intraguild predators and prey in resourcerich environments. Ecology 89, 2786–2797.
Arim, M., Marquet, P.A., 2004. Intraguild predation: a widespread interaction
related to species biology. Ecol. Lett. 7, 557–564.
Balfour, R.A., Buddle, C.M., Rypstra, A.L., Walker, S.E., Marshall, S.D., 2003.
Ontogenetic shifts in competitive interactions and intra-guild predation
between two wolf spider species. Ecol. Entomol. 28, 25–30.
Borer, E.T., 2002. Intraguild predation in larval parasitoids: implications for
coexistence. J. Anim. Ecol. 71, 957–965.
Borer, E.T., 2006. Does adding biological detail increase coexistence in an
intraguild predation model? Ecol. Model. 196, 447–461.
Brose, U., Jonsson, T., Berlow, E.L., Warren, P., Banasek-Richter, C., Bersier, L.F.,
Blanchard, J.L., Brey, T., Carpenter, S.R., Blandenier, M.F.C., Cushing, L., Dawah, H.A.,
Dell, T., Edwards, F., Harper-Smith, S., Jacob, U., Ledger, M.E., Martinez, N.D.,
Memmott, J., Mintenbeck, K., Pinnegar, J.K., Rall, B.C., Rayner, T.S., Reuman, D.C.,
Ruess, L., Ulrich, W., Williams, R.J., Woodward, G., Cohen, J.E., 2006. Consumerresource body-size relationships in natural food webs. Ecology 87, 2411–2417.
De Roos, A.M., 2008. Demographic analysis of continuous-time life-history models.
Ecol Lett. 11, 1–15.
De Roos, A.M., Schellekens, T., van Kooten, T., van de Wolfshaar, K., Claessen, D.,
Persson, L., 2007. Food-dependent growth leads to overcompensation in stagespecific Biomass when mortality increases: The influence of maturation versus
reproduction regulation. Amer. Nat. 170, E59–E76.
De Roos, A.M., Schellekens, T., van Kooten, T., van de Wolfshaar, K., Claessen, D.,
Persson, L., 2008. Simplifying a physiologically structured population model to
a stage-structured biomass model. Theor. Pop. Biol. 73, 47–62.
Diehl, S., Feissel, M., 2000. Effects of enrichment on three-level food chains with
omnivory. Amer. Nat. 155, 200–218.
Finke, D.L., Denno, R.F., 2006. Spatial refuge from intraguild predation: implications for prey suppression and trophic cascades. Oecologia 149, 265–275.
Haefner, J.W., Edson, J.L., 1984. Community invasion by complex life cycles. J.
Theor. Biol. 108, 377–404.
Hartvig, M., Andersen, K.H., Beyer, J.E., 2011. Food web framework for sizestructured populations. J. Theor. Biol. 272, 113–122.
HilleRisLambers, R., Dieckmann, U., 2003. Competition and predation in simple
food webs: intermediately strong trade-offs maximize coexistence. Proc. Roy.
Soc. London Ser. B 270, 2591–2598.
43
Hin, V., Schellekens, T., De Roos, A.M., Persson, L., 2011. Coexistence of predators
and prey in intraguild predation systems with ontogenetic niche shifts. Amer.
Nat. 178, 701–714.
Holt, R.D., Polis, G.A., 1997. A theoretical framework for intraguild predation.
Amer. Nat. 149, 745–764.
Holt, R.D., Huxel, G.R., 2007. Alternative prey and the dynamics of intraguild
predation: Theoretical perspectives. Ecology 88, 2706–2712.
Janssen, A., Sabelis, M.W., Magalhäes, S., Montserrat, M., Van der Hammen, T, 2007.
Habitat structure affects intraguild predation. Ecology 88, 2713–2719.
Kooi, B., Boer, M., Kooijman, S., 1998. On the use of the logistic equation in models
of food chains. Bull. Math. Biol. 60, 231–246.
Krivan, V., 2000. Optimal intraguild foraging and population stability. Theor. Pop.
Biol. 58, 79–94.
Krivan, V., Diehl, S., 2005. Adaptive omnivory and species coexistence in tritrophic food webs. Theor. Pop. Biol. 67, 85–99.
Kuznetsov, Y.A., Levitin, V.V., Skovoroda, A.R., 1996. Continuation of stationary
solutions to evolution problems in content. Centre for Mathematics and
Computer Science, Amsterdam.
Law, R., Plank, M.J., James, A., Blanchard, J.L., 2009. Size-spectra dynamics from
stochastic predation and growth of individuals. Ecology 90, 802–811.
League-Pike, P.E., Shulman, M.J., 2009. Intraguild Predators: Behavioral Changes
and Mortality of the Green Crab (Carcinus Maenas) during Interactions with
the American Lobster (Homarus Americanus) and Jonah Crab (Cancer Borealis). J. Crust. Biol. 29, 350–355.
Loreau, M., Ebenhoh, W., 1994. Competitive-exclusion and coexistence of species
with complex life-cycles. Theor. Pop. Biol. 46, 58–77.
McCann, K., 1998. Density-dependent coexistence in fish communities. Ecology
79, 2957–2967.
Moll, J.D., Brown, J.S., 2008. Competition and coexistence with multiple life-history
stages. Amer. Nat. 171, 839–843.
Mougi, A., Nishimura, K., 2005. Coexistence of competitive species with a stagestructured life cycle. Ecol. Res. 20, 581–589.
Mylius, S.D., Klumpers, K., de Roos, A.M., Persson, L., 2001. Impact of intraguild
predation and stage structure on simple communities along a productivity
gradient. Amer. Nat. 158, 259–276.
Ojeda, F.P., Dearborn, J.H., 1991. Feeding ecology of benthic mobile predators experimental analyses of their influence in rocky subtidal communities of the
Gulf of Maine. J. Exp. Mar. Bio. Ecol. 149, 13–44.
Oksanen, L., Fretwell, S.D., Arruda, J., Niemela, P., 1981. Exploitation ecosystems in
gradients of primary productivity. Amer. Nat. 118, 240–261.
Okuyama, T., 2008. Invited views in basic and applied ecology - Intraguild
predation with spatially structured interactions. Basic Appl. Ecol. 9, 135–144.
Persson, L., De Roos, A.M., 2012. Mixed competition-predation: potential vs.
realized interactions. J. Anim. Ecol. 81, 483–493.
Peters, R.H., 1983. The ecological implications of body size. Cambridge University
Press, Cambridge.
Pimm, S.L., Lawton, J.H., 1978. Feeding on more than one trophic level. Nature 275,
542–544.
Pimm, S.L., Rice, J.C., 1987. The Dynamics of multispecies, multi-life-stage models
of aquatic food webs. Theor. Pop. Biol. 32, 303–325.
Polis, G.A., 1991. Complex trophic interactions in deserts - an empirical critique of
food-web theory. Amer. Nat. 138, 123–155.
Polis, G.A., Strong, D.R., 1996. Food web complexity and community dynamics. Am.
Nat. 147, 813–846.
Polis, G.A., Myers, C.A., Holt, R.D., 1989. The ecology and evolution of intraguild
predation - potential competitors that eat each other. Annu. Rev. Ecol. Syst. 20,
297–330.
Polis, G.A., Holt, R.D., Menge, B.A., Winemiller, K.O., 1996. Time, space and life history:
influences on food webs. In: Polis, G.A., Winemiller, K.O. (Eds.), Food webs:
integration of patterns and dynamics. Chapman & Hall, New York, pp. 435–460.
Ropes, J.W., 1969. Feeding Habits of Green Crab, Carcinus-Maenas (L). United
States Fish and Wildlife Service Fishery Bulletin 67, 183-&.
Rossong, M.A., Williams, P.J., Comeau, M., Mitchell, S.C., Apaloo, J., 2006. Agonistic
interactions between the invasive green crab, Carcinus maenas (Linnaeus) and
juvenile American lobster, Homarus americanus (Milne Edwards). J. Exp. Mar.
Bio. Ecol. 329, 281–288.
Rudolf, V.H.W., 2007. The interaction of cannibalism and omnivory: Consequences
for community dynamics. Ecology 88, 2697–2705.
Rudolf, V.H.W., Armstrong, J., 2008. Emergent impacts of cannibalism and size
refuges in prey on intraguild predation systems. Oecologia 157, 675–686.
Rudolf, V.H.W., Lafferty, K.D., 2011. Stage structure alters how complexity affects
stability of ecological networks. Ecol. Lett. 14, 75–79.
Rypstra, A.L., Samu, F., 2005. Size dependent intraguild predation and cannibalism
in coexisting wolf spiders (Araneae, Lycosidae). J. Arachnol. 33, 390–397.
Schellekens, T., De Roos, A.M., and Persson, L., 2010. Ontogenetic diet shifts result
in niche partitioning between two consumer species irrespective of competitive abilities. American Naturalist.
Tilman, D., 1982. Resource competition and community structure. Princeton
University Press, Princeton.
van de Wolfshaar, K.E., de Roos, A.M., Persson, L., 2006. Size-dependent interactions inhibit coexistence in intraguild predation systems with life-history
omnivory. Amer. Nat. 168, 62–75.
Van Leeuwen, A., De Roos, A.M., Persson, L., 2008. How cod shapes its world. J. Sea
Res. 60, 89–104.
Werner, E.E., Gilliam, J.F., 1984. The ontogenetic niche and species interactions in
size-structured populations. Annu. Rev. Ecol. Syst. 15, 393–425.
44
T. Schellekens, T. van Kooten / Journal of Theoretical Biology 308 (2012) 36–44
Williams, P.J., Floyd, T.A., Rossong, M.A., 2006. Agonistic interactions between invasive
green crabs, Carcinus maenas (Linnaeus), and sub-adult American lobsters,
Homarus americanus (Milne Edwards). J. Exp. Mar. Bio. Ecol. 329, 66–74.
Williams, R.J., Martinez, N.D., 2000. Simple rules yield complex food webs. Nature
404, 180–183.
Woodward, G., Hildrew, A.G., 2002. Body-size determinants of niche overlap and
intraguild predation within a complex food web. J. Anim. Ecol. 71, 1063–1074.
Woodward, G., Ebenman, B., Emmerson, M., Montoya, J.M., Olesen, J.M., Valido, A.,
Warren, P.H., 2005. Body size in ecological networks. Trend Ecol. Evolut. 20,
402–409.
Yodzis, P., Innes, S., 1992. Body size and consumer-resource dynamics. Am. Nat.
139, 1151–1175.