The allometry of prey preferences.

Abstract

The distribution of weak and strong non-linear feeding interactions (i.e., functional responses) across the links of complex food webs is critically important for their stability. While empirical advances have unravelled constraints on single-prey functional responses, their validity in the context of complex food webs where most predators have multiple prey remain uncertain. In this study, we present conceptual evidence for the invalidity of strictly density-dependent consumption as the null model in multi-prey experiments. Instead, we employ two-prey functional responses parameterised with allometric scaling relationships of the functional response parameters that were derived from a previous single-prey functional response study as novel null models. Our experiments included predators of different sizes from two taxonomical groups (wolf spiders and ground beetles) simultaneously preying on one small and one large prey species. We define compliance with the null model predictions (based on two independent single-prey functional responses) as passive preferences or passive switching, and deviations from the null model as active preferences or active switching. Our results indicate active and passive preferences for the larger prey by predators that are at least twice the size of the larger prey. Moreover, our approach revealed that active preferences increased significantly with the predator-prey body-mass ratio. Together with prior allometric scaling relationships of functional response parameters, this preference allometry may allow estimating the distribution of functional response parameters across the myriads of interactions in natural ecosystems.

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The Allometry of Prey Preferences
Gregor Kalinkat1,2*, Bjo ¨rn Christian Rall2, Olivera Vucic-Pestic1, Ulrich Brose2
1Department of Biology, Darmstadt University of Technology, Darmstadt, Germany, 2J.F. Blumenbach Institute of Zoology and Anthropology, University of Go ¨ttingen,
Go ¨ttingen, Germany
Abstract
The distribution of weak and strong non-linear feeding interactions (i.e., functional responses) across the links of complex
food webs is critically important for their stability. While empirical advances have unravelled constraints on single-prey
functional responses, their validity in the context of complex food webs where most predators have multiple prey remain
uncertain. In this study, we present conceptual evidence for the invalidity of strictly density-dependent consumption as the
null model in multi-prey experiments. Instead, we employ two-prey functional responses parameterised with allometric
scaling relationships of the functional response parameters that were derived from a previous single-prey functional
response study as novel null models. Our experiments included predators of different sizes from two taxonomical groups
(wolf spiders and ground beetles) simultaneously preying on one small and one large prey species. We define compliance
with the null model predictions (based on two independent single-prey functional responses) as passive preferences or
passive switching, and deviations from the null model as active preferences or active switching. Our results indicate active
and passive preferences for the larger prey by predators that are at least twice the size of the larger prey. Moreover, our
approach revealed that active preferences increased significantly with the predator-prey body-mass ratio. Together with
prior allometric scaling relationships of functional response parameters, this preference allometry may allow estimating the
distribution of functional response parameters across the myriads of interactions in natural ecosystems.
Citation: Kalinkat G, Rall BC, Vucic-Pestic O, Brose U (2011) The Allometry of Prey Preferences. PLoS ONE 6(10): e25937. doi:10.1371/journal.pone.0025937
Editor: Andre ´ Chiaradia, Phillip Island Nature Parks, Australia
Received April 20, 2011; Accepted September 14, 2011; Published October 5, 2011
Copyright: ? 2011 Kalinkat et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: Funding has been provided by the German Research Foundation (BR 2315/6, BR 2315/13). The funders had no role in study design, data collection and
analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: kalinkat@bio.tu-darmstadt.de
Introduction
Despite decades of ecological research on species interactions, the
vast complexity of most natural communities still challenges our
understanding of population and community stability [1,2]. The
myriadsofpredator-preyinteractionsincomplexfoodwebscontrast
negative complexity-stability relationships in random interaction
networks [3]. As a general null expectation, they suggest that
complex natural food webs should be unstable unless they possess
non-random structures. Interestingly, theoretical research has
demonstrated how the distribution of weak and strong interactions
across complex food webs determines the community-level stability
[2,4–7]. In particular, research on body-mass constraints on
interaction strengths and adaptive foraging has provided major
mechanistic insights in these patterns [8–17]. Empirically, however,
progress has been hampered by the lack of approaches that can be
generalized acrossthemyriadsofinteractionsincomplex food webs.
Allometric functional responses predicting consumption rates by
predator and prey body masses [18–22] and environmental
temperature [23,24] provide a critically important first step towards
such generality. However, they focus on single-prey interactions
while ignoring the complexity of natural communities, where
predators are exposed to multiple prey. Here, we present an
approach to generalize allometric interaction strengths from single-
prey to multi-prey experiments.
One of the standard measures of interaction strength in food
webs [25] is provided by predator-prey functional responses
[26,27] describing the per capita consumption rate of a predator,
F, depending on prey density:
F~
aN
1zaThN
ð1Þ
where N is prey abundance, This the handling time needed to kill,
ingest and digest an individual of the prey and a is the attack rate
(hereafter: ‘‘capture rate’’ sensu [28]). This type II functional
response with a constant capture rate can be modified to account
for capture rates that vary with prey density, a=bNq[15,29,30],
which yields type III functional responses:
F~
bNqz1
1zbThNqz1
ð2Þ
where b is a capture coefficient (sometimes also referred to as
search coefficient), and q is a scaling exponent that converts
hyperbolic type II (q=0) into sigmoid type III (q.0) functional
responses (see Fig. 1a; note that some authors refer to intermediate
or modified type II functional responses for values 0,q,1; e.g.,
[30]). The Hill exponent, h, used in some prior studies (e.g., [29]) is
equivalent to q (h=q+1). Interestingly, the plethora of functional
response studies concentrate on single-predator – single-prey
studies (see refs [31–33] for an overview). Nevertheless, the
question remains if these findings hold when predator and prey are
embedded in the complex network of a natural community, where
most predators have multiple prey.
To overcome this deficit we increased the complexity of the
experimental setting by the comparisons of single-prey functional
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Figure 1. Conceptual illustrations of (a) type II and type III (single-prey) functional responses and the implications of variance in the scaling exponent
q as well as consequences for absolute prey consumption and (b–e) preferences and switching in two-prey (here: j and k) experiments: b)
‘‘Traditional’’ preference plot with relative consumption depending on relative density of prey j: Consumption is strictly density-dependent (the
diagonal solid line), or exhibits preferences for prey j (upper, long-dashed line) or switching behaviour (sigmoid, dotted line). c–e) Novel null model
based on two-prey functional responses (Equation 3) with varying capture rate ratios (bij/bikwith 0.01,bij,10 and bik=1) for the two prey in c) type II
(qij=qik=0) and d) type III functional responses (qij=qik=1). e) Gradual conversion of type II to type III functional responses when both prey are
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responses from a prior study [18] with two-prey experiments
under identical experimental conditions, an experimental design
rarely found in the literature (but see refs [34–36] for examples).
Traditionally, however, most two-prey experiments that were
designed as to investigate preference and switching behaviour have
simplified this approach by (1) skipping the single-prey functional
response experiments, and (2) varying the relative densities of both
prey while keeping a constant total prey density [37–40]. These
approaches are illustrated in Figure 1. The diagonal representing
strictly density dependent consumption has often been used as the
null model (Fig. 1b, solid line), and deviations from it were
interpreted as preference for one prey (Fig. 1b, dashed line) or prey
switching (Fig. 1b, dotted line) as an indicator of adaptive foraging
behaviour [37–39,41,42]. Historically, the quest for switching and
adaptive foraging behaviour has been fuelled by its stabilizing
effect on population dynamics [15,30,43,44]. One crucially
important question remaining is whether strict density dependence
(i.e., the diagonal in Fig. 1b) is a reasonable null model and
consistent with predictions of the two single-prey functional
responses. The functional response concept can be extended to a
two-prey version:
Fij~
bijN
?
qijz1
?
??
j
1zbijThijN
qijz1
j
zbikThikN
qikz1
ð
k
Þ
ð3Þ
where the per capita consumption of predator i on prey j depends
also on the interaction between predator i and prey k [28,44,45].
Inserting the parameters of the two single-prey functional
responses (i-j and i-k) in this model yields predictions of relative
consumption within a two-prey experiment (Fig. 1c–e). If both
single-prey functional responses are type II (i.e. qij=qik=0),
variance in the capture rates bijand bik(while Thij=Thik) can result
in substantial variation in the predicted relative feeding rates of the
two-prey experiment (Fig. 1c). Strictly density dependent con-
sumption (i.e. the highlighted diagonal solid line in Fig. 1c) only
emerges if bijand bikare identical. If both single-prey functional
responses are of type III, sigmoid feeding curves are predicted for
all combinations of capture rates, and the diagonal indicating
density-dependent consumption does not occur on the predicted
consumption plane (Fig. 1d). Thus, even if the two single-prey
functional responses are characterised by the same handling and
capture parameters (i.e., bij=bik and Thij=Thik) strictly density
dependent consumption in the two-prey experiment is only
predicted for pure type II functional responses (qij=qik=0, Fig. 1e).
Together, these conceptual patterns have shown that strictly
density-dependent consumption (i.e., the diagonal line in Fig. 1b)
can only be used as the null model in two-prey experiments in the
unlikely situation that both prey are consumed with exactly the
same type II functional response. In all other cases, deviation from
strictly density-dependent consumption can simply be a conse-
quence of inherent characteristics of the predator-prey relationship
(e.g. physiological or morphological constraints like limitations of
the digestive system or gape-size limitation) manifested in different
capture rates (and/or handling times as well as scaling exponents).
Thus, the separation of active switching (i.e. switching behaviour
deviating from single-prey based predictions) from passive
switching (i.e. switching behaviour complying with single-prey
based predictions) has been proposed [46]. We propose to further
expand this concept by also separating active preferences (i.e.
preference or avoidance behaviour deviating from single-prey
based predictions) from passive preferences (i.e. preference or
avoidance behaviour complying with single-prey based predic-
tions).
Ecology has profited tremendously from replacing linear with
non-linear null models in biodiversity research (i.e., neutral theory
[47] or mid-domain models of biodiversity [48]). In the same vein,
we propose that the wide-spread linear null model of strictly
density dependent consumption is lacking realism and should be
replaced by non-linear multi-prey functional responses. At the cost
of increased complexity, they introduce more ecological plausibil-
ity and provide a deeper mechanistic understanding of predator-
prey interactions. Subsequently, we will illustrate the use and
potential of these non-linear null models in consumption
experiments with terrestrial predators.
In the tradition of metabolic scaling models [49,50], several
studies dealing with a wide range of organisms revealed how
capture rates (sometimes referred to as capture coefficients e.g.,
[51]) and handling time depend on body masses. In these
relationships, handling times increase with increasing prey mass
but decrease with increasing predator mass [18,52–55], while
capture rates follow hump-shaped relationships with predator-prey
body-mass ratios [18–21,52,54]. Regarding the allometry of the
scaling factor q we are not aware of any other study but the one by
Vucic-Pestic and colleagues [18].
Here, we used allometric single-prey functional response models
from a previous study [18] to predict the per capita feeding rates in
two-prey experiments (Eqn. 3) using parameters from Vucic-Pestic
and colleagues [18] to predict our two-prey experiments (see
Methods section for details). We hypothesised that allometric
functional response parameters should predict the consumption
rates in the two-prey experiments thus resulting in ‘‘passive
preferences’’ or ‘‘passive switching’’. Alternatively, we aimed at
explaining deviations from the multi-prey functional responses,
equivalent to ‘‘active preferences’’ or ‘‘active switching’’, by
predator-prey body mass ratios.
Materials and Methods
Allometric single-prey functional responses
In their study, Vucic-Pestic and colleagues [18] addressed
systematic effects of predator and prey body masses on the
functional response parameters handling time, Th, capture rate, a,
and the scaling exponent q in experiments with 13 predator species
comprising ground beetles and wolf spiders. The allometric
dependence of handling time was estimated as:
log10Th~plog10MPznlog10MNzlog10Th 0 ð Þ
ð4Þ
with MPas predator mass, MNas prey mass, and p, n, Th(0)as
constants. Furthermore, a hump-shaped relation for the capture
coefficient b was defined as:
log10bR
ð Þz1
??~A
exp e W{log10Rz1
ð
1zexp be W{log10Rz1
ð
ðÞÞðÞ
ðÞÞðÞ
ð5Þ
consumed with the same capture rate (bij=bik=1). Constant handling time is used in figures c–e (Thij=Thik=0.1). Note that the diagonal of strictly
density-dependent consumption as the traditional null model (panel b) only emerges if both prey are consumed with exactly the same type II
functional response (solid black lines in figures c and e).
doi:10.1371/journal.pone.0025937.g001
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where A is a constant, W represents the body mass ratio at which
50% of the maximum capture coefficient is reached, e is the rate of
change in search with mass controlling the steepness of the curve,
R is the body-mass ratio (MP/MN) and b determines the
asymmetry of the curve [18]. While handling time decreased with
predator mass and increased with prey mass, capture rates
followed hump-shaped relationships with predator–prey body-
mass ratios ([18], Table 1, Figure 2). The scaling exponent, q, was
low for predator-prey pairs with low body mass ratios (i.e. spiders -
springtails and beetles – fruit flies) and high for the ones with high
body mass ratios (i.e. spiders – fruit flies and beetles – lesser
mealworm larvae) ([18], Table 1, Figure 2). These parameter
combinations yield hump-shaped functional responses as present-
ed in Figure 3 a–d.
Preference experiments
The experimental setting of our study followed the methods of
previous studies [18,21–24]: The predator individuals were kept
separate in plastic jars dispersed with water and were deprived of
food for at least 48 hours before the start of the experiments. The
experiments were performed in PerspexH arenas (20620610 cm)
covered with lids. The lids contained gauze covered holes to allow
for gas exchange. The arena floor was covered with moist plaster
of Paris (200 g dry weight) to provide constant moisture during the
experiments. Habitat structure in the arenas was provided by moss
(Polytrichum formosum, 2.35 g dry weight) that was first dried for
several days at 40uC to exclude other animals and then re–
moisturised prior to the experiments. Prey individuals were placed
in the arenas half an hour in advance of the predators to allow
them to adjust to the arenas. The experiment was run for 24 hours
with a day/night rhythm of 12/12 h dark/light and temperature
of 15uC in temperature cabinets. Initial and final prey densities
were used to calculate the number of prey eaten. Control
experiments without predators showed that prey mortality or
escape was negligible.
The predator species represent a subset of those deployed within
the previous study on allometric functional responses [18]
including three wolf spiders (Aranea: Lycosidae) and three ground
beetles (Coleoptera: Carabidae) that were weighted individually
before the experiments. Consistent with predator body masses
from the previous study [18], they were spanning a relatively wide
range of body masses (Table 1). All animals in the experiments
were either sampled by pitfall trapping outside protected areas
around Darmstadt, Germany, or they were reared in laboratory
cultures. Pitfall trapping was conducted at agricultural field sites
with acknowledgment of land owners. None of the animal species
involved are threatened of extinction nor is any one of them under
protection.
Due to logistic constraints it was impossible within the present
study to test the two-species allometric functional response model
Figure 2. Conceptual graphic showing allometric relationships in the single-prey functional response parameters capture rate,
handling time and the scaling exponent q as revealed by the previous study of Vucic-Pestic and colleagues [18].
doi:10.1371/journal.pone.0025937.g002
Table 1. Parameters of the allometric two-prey functional response model as the null model for the preference experiment (Figs. 3
and 4): N=number of replicates; MP=average predator mass [mg]; R=average predator-prey body-mass ratio; q=scaling
exponent; * parameters taken from ref [18].
NMP
R(predator:large prey)
q(large prey)*q(small prey)*
spiders2070.170.52
Trochosa terricola juvenile69 2.7661.95
Pardosa lugubris 7028.895 20.35
Trochosa terricolsa adult 68 78.87455.55
beetles145 0.020.89
Anchomenus dorsalis 48 12.1080.52
Calathus fuscipes 4965.7122.83
Harpalus rufipes 48 120.5615.18
Parameters applied in eqns. (4) and (5)u
P=20.94; n=0.83; Th(0)=0.35; A=3.69; e=0.48; W=0.45; b=47.13;
doi:10.1371/journal.pone.0025937.t001
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The Allometry of Prey Preferences
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