Ecology, 87(10), 2006, pp. 2411–2417
? 2006 by the Ecological Society of America
CONSUMER–RESOURCE BODY-SIZE RELATIONSHIPS IN
NATURAL FOOD WEBS
ULRICH BROSE,1,2,20TOMAS JONSSON,3ERIC L. BERLOW,1,2,4PHILIP WARREN,5CAROLIN BANASEK-RICHTER,1
LOUIS-FE´LIX BERSIER,6JULIA L. BLANCHARD,7THOMAS BREY,8STEPHEN R. CARPENTER,9
MARIE-FRANCE CATTIN BLANDENIER,10LARA CUSHING,2HASSAN ALI DAWAH,11TONY DELL,12FRANCOIS EDWARDS,13
SARAH HARPER-SMITH,14UTE JACOB,8MARK E. LEDGER,13NEO D. MARTINEZ,2JANE MEMMOTT,15
KATJA MINTENBECK,8JOHN K. PINNEGAR,7BJO¨RN C. RALL,1THOMAS S. RAYNER,12DANIEL C. REUMAN,16
LILIANE RUESS,17WERNER ULRICH,18RICHARD J. WILLIAMS,2,21GUY WOODWARD,19AND JOEL E. COHEN16
1Department of Biology, Darmstadt University of Technology, Darmstadt, Germany
2Pacific Ecoinformatics and Computational Ecology Lab, Berkeley, California 94703 USA
3Systems Biology Group, School of Life Sciences, University of Sko¨vde, Sko¨vde, Sweden
4University of California, Merced, Sierra Nevada Research Institute, Yosemite National Park, California 95389 USA
5Department of Animal and Plant Sciences, University of Sheffield, Sheffield, UK
6Department of Biology, Unit of Ecology and Evolution, Fribourg, Switzerland
7The Centre for Environment, Fisheries and Aquaculture Science (CEFAS), Suffolk, UK
8Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany
9Center for Limnology, University of Wisconsin, Madison, Wisconsin 53706 USA
10Zoological Institute, C.P. 2, Neuchatel, Switzerland
11King Khalid University, College of Science, Department of Biology, Abha, Saudi Arabia
12Department of Zoology and Tropical Ecology, James Cook University, Townsville, Australia
13School of Geography, Earth and Environmental Sciences, University of Birmingham, UK
14Department of Biology, Western Washington University, Bellingham, USA
15School of Biological Sciences, Woodland Road, Bristol, UK
16Laboratory of Populations, Rockefeller and Columbia Universities, New York, New York, 10021 USA
17Institute of Soil Science, University of Hohenheim, Stuttgart, Germany
18Department of Animal Ecology, Nicolaus Copernicus University, Torun, Poland
19School of Biological and Chemical Sciences, Queen Mary University of London, UK
resource species may have important implications for interaction strengths, population
dynamics, and eventually food web structure, function, and evolution. Still, the general
distribution of consumer–resource body-size ratios in real ecosystems, and whether they vary
systematically among habitats or broad taxonomic groups, is poorly understood. Using a
unique global database on consumer and resource body sizes, we show that the mean body-
size ratios of aquatic herbivorous and detritivorous consumers are several orders of magnitude
larger than those of carnivorous predators. Carnivorous predator–prey body-size ratios vary
across different habitats and predator and prey types (invertebrates, ectotherm, and
endotherm vertebrates). Predator–prey body-size ratios are on average significantly higher
(1) in freshwater habitats than in marine or terrestrial habitats, (2) for vertebrate than for
invertebrate predators, and (3) for invertebrate than for ectotherm vertebrate prey. If recent
studies that relate body-size ratios to interaction strengths are general, our results suggest that
mean consumer–resource interaction strengths may vary systematically across different
habitat categories and consumer types.
It has been suggested that differences in body size between consumer and
allometry; body length; body mass; body-size ratio; food webs; parasitoid–host; predation;
Body size, one of the most fundamental character-
istics of an organism, is linked to physical activities, such
as locomotion, dispersal, and space use (Peters 1983,
Jetz et al. 2004), to biological rates such as growth,
Manuscript received 1 February 2006; revised 8 May 2006;
accepted 9 May 2006. Corresponding Editor: H. Hillebrand.
21Present address: Microsoft Research Ltd., Cambridge
CB3 0FB UK.
respiration, reproduction, and mortality (Peters 1983,
Brown et al. 2004), to evolutionary patterns (Loeuille
and Loreau 2005), and to population characteristics
such as abundance and trophic height in a food web
(Jennings et al. 2001, Cohen et al. 2003). These
relationships have stimulated theories about how species
population dynamics, interaction strengths, and food
web structure could depend on consumer–resource
body-size ratios (Yodzis and Innes 1992, Jonsson and
Ebenman 1998, Emmerson and Raffaelli 2004, Brose et
al. 2005a, Reuman and Cohen 2005, Woodward et al.
2005, Wootton and Emmerson 2005). Since the distri-
bution of trophic links and interaction strengths in a
community may reflect size constraints on who eats
whom, the ratio of body sizes between predators and
their prey may play an important role in explaining
regularities in food web structure (Warren and Lawton
1987, Cohen et al. 1993) and stability (De Ruiter et al.
1995, Neutel et al. 2002).
Empirically, predators (excluding pathogens, para-
sites and parasitoids) tend to be larger than their prey
(Warren and Lawton 1987, Cohen et al. 1993, Memmott
et al. 2000), but it remains open whether the body-size
ratios vary systematically among ecosystems or con-
sumers types. For instance, if size constraints on feeding
are related to habitat structure, the consumer-resource
body-size ratios could differ between terrestrial and
pelagic ecosystems. Here, we analyze the largest global
database on consumer and resource body sizes compiled
so far (Brose et al. 2005b). We present data on body-size
ratios for predators, parasitoids, herbivores, and detri-
tivores. Using data of carnivorous predators, we test for
significant differences in predator-prey body-size ratios
depending on habitat categories and the predator types.
We use average body masses (g; empirical measure-
ments of mass [n ¼ 13085] or allometric estimates of
mass based on empirical measurements of length [n ¼
3778]) of 16863 consumer–resource links in a global
data set (Brose et al. 2005b). The body sizes were
measured for the individuals engaged in the trophic
interactions: sometimes these individuals are adults,
sometimes larvae. If possible, predator life stages with
different feeding interactions are separated in these data.
Individual consumer species are included several times
when linked to different resource species and vice versa.
Here, ‘‘consumer’’ is used as a collective term that
includes predators (consumers that kill living animal
prey and subsequently consume all or most of it),
parasitoids (consumers that live in or on and consume a
living individual animal that is killed simultaneously or
subsequently when the larval development ends and the
consumers emerge), parasites (consumers that eat part
of an individual animal without directly killing it),
herbivores (consumers of living plants), and detritivores
(consumers that eat dead plant and animal material).
Our data include different consumer and resource types
(invertebrates, ectotherm and endotherm vertebrates)
across different habitat categories (terrestrial, lake,
stream, and marine ecosystems; see Brose et al. [2005b]
for an overview of the ecosystems studied). The Grand
Caricaie food web has been sampled twice (spring and
fall) under two treatments (mown and unmown) at two
different locations (Brose et al. 2005b). To avoid pseudo-
replication, we use just one of these samples: the fall
sample of the mown treatment of the Scirpus lacustris-
dominated locality (ScMown 2). To our knowledge this
sample does not systematically deviate from the other
samples. We did not include data of parasitic consumers
due to the low number of cases (n¼2), or of consumers
with unknown habitat types. The remaining data include
predatory (n ¼ 5156), parasitoid (n ¼ 215), herbivorous
(n ¼ 930), and detritivorous (n ¼ 218) consumers (i.e.,
four feeding types) from terrestrial (n ¼ 2245), lake (n ¼
1214), stream (n ¼ 736), and marine ecosystems (n ¼
2324). For these 6519 interactions, we calculated the
base-10 logarithm of the ratio of the body masses of
consumers (MC) to resources (MR), hereafter called
log10body-mass ratios (i.e., log10(MC/MR)). These log10
body-mass ratios were analyzed for significant differ-
ences among the feeding types (ANOVA).
The data for herbivorous and detritivorous feeding
interactions were sampled in aquatic habitats only,
whereas all data for parasitoid interactions come from
terrestrial habitats. Only the predator–prey data
spanned all habitat categories. Therefore, to explore
differences in consumer–resource body-mass patterns
among habitat categories and consumer types, we
restricted the analysis to predator–prey interactions
(see Plate 1). We excluded 53 outliers in the original
data set with residuals that deviate more than three
standard deviations from the residual mean (residuals .
3 sigma). These outliers include trophic interactions
between (1) trout and zooplankton (copepods or water-
fleas), (2) seals and nematodes, and (3) whales and
zooplankton (see Discussion).
We carried out three regressions in the remaining data
set (n ¼ 5103): ordinary linear least-squares regressions
of (1) log10predator mass as a function of log10prey
mass, (2) log10prey mass as a function of log10predator
mass, and (3) a major axis regression (type II regression)
that treats the two variables symmetrically. For regres-
sion 1, normality of the residuals was rejected (Lilliefors
test) but linearity and homoscedasticity were accepted,
whereas for regression 2, all three assumptions of the
linear regression method were rejected. Normality
assumptions of the statistical model underlying regres-
sion 3 were also violated by data (Jarque-Bera and
Lilliefors tests). All standard error estimates and P
values for regressions were therefore produced by re-
sampling ten thousand times, with replacement, 5103
data points from the data set and computing the
parameters each time.
Because the body-mass ratios are log-transformed,
‘‘mean body-mass ratios’’ that we report below for
ULRICH BROSE ET AL.2412 Ecology, Vol. 87, No. 10
different habitat categories and predator and prey types
are geometric means. Due to the absence of data on
endotherm vertebrate predators from lakes and streams
and the unequal number of replicates per cell, we used a
type VI ANOVA with sigma-restricted parameteriza-
tion. Our analyses focused on the characteristic body-
mass ratios of trophic links, but because some species
were engaged in more than a single trophic link, not all
data points were strictly independent (see Discussion on
caveats). To test the robustness of our results, we
constructed a randomly sampled reduced data set, in
which species occurred only once.
Consumer–resource log10 body-mass ratios differ
substantially among the feeding types (F3,6515¼ 3525,
P , 0.001). The consumer could be smaller than its
resource (log10body-mass ratio , 0), equally sized (log10
body-mass ratio¼0), or larger (log10body-mass ratio .
0). Predators are on geometric average about 42 times
larger than their prey (log10body-mass ratio ¼ 1.62 6
0.03 [mean 6 SE], n ¼ 5156), whereas parasitoids are
about three-quarters of the body size of their hosts (log10
body-mass ratio ¼?0.12 6 0.03, n ¼ 215). The average
log10 body-mass ratios of aquatic herbivores (8.99 6
0.15, n¼930) and aquatic detritivores (13.41 6 0.18, n¼
218) are several orders of magnitude higher than those
of aquatic predators (1.82 6 0.04, n ¼ 3126).
Across all habitat categories and predator types, the
predator mass and the prey mass increase together (Fig.
1). Both linear least-squares regressions yielded slopes
significantly smaller than unity (regression 1, log10
predator mass ¼ 0.79 3 log10 prey mass þ 1.26;
regression 2, log10prey mass ¼ 0.64 3 log10predator
mass – 1.53; standard error of slope 1 ¼ 0.01, standard
error of slope 2¼0.02, r2¼0.51, P , 0.0001, n¼5103).
The major axis regression has a slope of 1.16 6 0.01
when log10predator mass is plotted against log10prey
mass (Fig. 1). This coefficient suggests that the relative
size difference (the log10 body-mass ratio) between
predators and prey increases with increasing size of the
species when data are pooled across all habitat
categories and predator types. Three other regression
methods symmetric in the variables (Babu and Feigelson
1992) also gave slopes significantly greater than 1.
There was a significant interaction between predator
type and habitat category when explaining variance in
the log10 predator–prey body-mass ratios (F4,5093 ¼
29.542, P , 0.001; Fig. 2). Relative size differences
between predators and prey according to predator type
are generally higher in freshwater habitats than in
terrestrial or marine habitats, and habitat-specific differ-
ences exist for vertebrates but not for invertebrates (Fig.
2). These results are confirmed in the reduced data set, in
which all species occur only once (predator type 3
habitat F4,536¼ 4.6, P , 0.01). The average log10body-
mass ratios of invertebrate predators are generally
smaller than those of ectotherm vertebrate and endo-
therm vertebrate predators (Table 1). A Scheffe ´ post hoc
test indicates no significant differences in average log10
body-mass ratios among (1) invertebrate predators in
the different habitats, (2) lake and stream ectotherm
vertebrates, and (3) terrestrial endotherm vertebrates
and marine ecto- and endotherm vertebrates. All other
groups are significantly different (P , 0.05). The log10
body-mass ratios also depend on the prey type. They are
higher when invertebrates are consumed than when
ectotherm vertebrates are eaten, for invertebrate pred-
ators (invertebrate prey, 0.66 6 0.03, n ¼ 2880 vs.
ectotherm vertebrate prey, ?0.46 6 0.29, n ¼ 35),
0.0001, n¼5103) explains 86% of the variance in log10predator mass. The other lines indicate the ordinary least-squares regressions
of regression 1 (log10predator mass vs. log10prey mass; thin solid line) and regression 2 (log10prey mass vs. log10predator mass;
dashed line, plotted with axes exchanged).
Predator mass vs. prey mass. The major axis regression (heavy solid line, slope ¼ 1.16 6 0.01, intercept ¼ 1.801, P ,
October 2006 2413CONSUMER–RESOURCE BODY-SIZE RELATIONSHIPS
ectotherm (3.37 6 0.05, n ¼ 959 vs. 1.55 6 0.05, n ¼
493), and for endotherm vertebrate predators (3.54 6
0.07, n ¼ 401 vs. 2.15 6 0.08, n ¼ 298).
We analyzed a large global database on the body
masses of consumers and their trophic resources (Brose
et al. 2005b). This database includes data from some
previous studies of consumer-resource body-size pat-
terns (Warren and Lawton 1987, Memmott et al. 2000),
but adds recently published data, such as those of the
Benguela system and Tuesday Lake, as well as
previously unpublished data. In the following, we
discuss our results for consumer-resource and preda-
tor-prey body-mass ratios, caveats and implications for
food web structure and dynamics.
Consumer–resource body-mass ratios
Consistent with previous studies (Cohen et al. 1993,
Memmott et al. 2000), our results show that predators
are on average larger than their prey, whereas para-
sitoids are more similar in size to their hosts (Cohen et
al. 2005). Furthermore, herbivores and detritivores from
freshwater and marine habitats have body-mass ratios
that exceed those of other consumers by several orders
of magnitude. These links might differ in their dynam-
ical behavior from predator-prey links, but the data
available are limited (Brose et al. 2005b). In aquatic
systems, many herbivores and detritivores are gape
limited and ingest whole particles (e.g., fine particulate
matter, unicellular algae). In contrast, terrestrial plants
are sessile and their herbivores are free from size
constraints on resource handling. It is thus likely that
most terrestrial herbivores are much smaller than their
plant resources since these herbivores are primarily
invertebrates and these plants are primarily vascular.
Additionally, the body size of basal species determines
their intrinsic growth rates, and terrestrial producers are
often large and have long generation times, whereas
aquatic producers are generally small and have short
generation times. This difference could affect the
dynamics of the communities. Our database lacks
terrestrial herbivore–plant and detritivore–detritus in-
teractions, and to understand the structural and
dynamic characteristics of terrestrial food webs, it would
be useful to fill this gap.
Ect, ectotherm vertebrates; Env, endotherm vertebrates). The dashed line indicates log10body-size ratios of zero, which implies
equally sized species. Data above and below the dashed line indicate predators that are larger and smaller than their prey,
Predator–prey body-size ratios (mean, SE, and SD) across the habitat categories and predator types (Inv, invertebrates;
ratio (log10(C/R)), the log10predator-mass (log10C), and the
log10prey mass (log10R) of the habitat and predator types.
Mean and standard error of the log10body-mass
and habitat log10(C/R) log10Clog10Rn
0.6 6 0.03 –2.64 6 0.02 –3.24 6 0.02 1263
0.96 6 0.05 –1.93 6 0.05 –2.89 6 0.08
0.91 6 0.1–3.20 6 0.07 –4.11 6 0.07
0.37 6 0.090.05 6 0.06 –0.31 6 0.09
2.08 6 0.06
4.15 6 0.18
3.82 6 0.14
2.57 6 0.06
1.66 6 0.05 –0.42 6 0.07
2.79 6 0.16 –1.36 6 0.23
1.12 6 0.09 –2.69 6 0.14
2.66 6 0.04
783 0.09 6 0.07
2.91 6 0.07
2.86 6 0.1
2.61 6 0.05
4.07 6 0.1
–0.3 6 0.09
1.21 6 0.12
ULRICH BROSE ET AL.2414 Ecology, Vol. 87, No. 10
Predator–prey body-mass ratios
Confirming previous analyses (Cohen et al. 1993), our
results suggest that (1) most predators (80%) are larger
than their prey, and (2) predator size and prey size
increase together. Our ordinary least-squares regression
with predator size as the dependent variable had a slope
significantly smaller than unity, suggesting that the size
difference between predators and prey (the body-mass
ratio) decreases with increasing prey size, as Cohen et al.
(1993) found. Our ordinary least-squares regression with
prey size as the dependent variable also had a slope
smaller than unity suggesting that the body-mass ratio
increases with increasing predator size. These results are
mutually exclusive. However, they should both be
discarded because standard linear models assume that
the predictor variables were measured without error and
that the distributions of residuals are normal, both
tenuous assumptions for the data of this study. The
major axis regression demonstrates that with increasing
body sizes the size difference between predators and prey
increases, in contrast to results of Cohen et al. (1993)
based on ordinary linear regression. Woodward et al.
(2005) show that the maximum prey size increases more
strongly with predator size than the minimum prey size,
so large predators feed on a larger size range of prey
species and are less similar in size to their average prey
size, as found here.
The geometric mean predator–prey body-mass ratio is
substantially higher for vertebrate predators than for
invertebrate predators, and it is lower for ectotherm
vertebrate prey than for invertebrate prey. Do the body-
mass ratios primarily depend on the predator type or on
the prey type? Our data are too scarce for some
combinations of predator and prey types (such as
invertebrate predators and ectotherm vertebrate prey)
to allow a full factorial analyses of this questions. Still,
they suggest the predator type dominates: vertebrate
predators have body-mass ratios to their prey that are
more than two orders of magnitude larger than
invertebrate predators for every prey type. Moreover,
invertebrate predators have small body-mass ratios
though they consume almost exclusively invertebrate
prey, whereas vertebrate predators have high body-mass
ratios even when they consume vertebrate prey. There-
fore, we will subsequently focus on the predator types
when discussing our results.
The body-mass ratios are higher for (1) vertebrate
predators than invertebrate predators, and (2) ectotherm
vertebrate predators in freshwater habitats than in
terrestrial or marine habitats. As predator size increases
1.16 times as fast as prey size in our pooled data, higher
ratios could reflect higher prey body-masses. The
average prey size of invertebrates is roughly three and
four orders of magnitude smaller than those of
ectotherm and endotherm vertebrates, respectively.
While this difference in prey size may account for an
increase in body-mass ratios of 0.48 (330.16, ectotherm
vertebrates) and 0.64 (4 3 0.16, endotherm vertebrates),
the actual differences in body-ratios between the
B. C. Rall.
Predator–prey interaction between the lycosid spider Pisaura mirabilis and the cricket Gryllus assimilis. Photo credit:
October 2006 2415CONSUMER–RESOURCE BODY-SIZE RELATIONSHIPS
predator types are more than two orders of magnitude.
Moreover, the average prey size of ectotherm vertebrate
predators is larger in terrestrial and marine habitats than
in freshwater ecosystems, whereas their body-mass
ratios are higher in the freshwater ecosystems. Differ-
ences in prey size can thus maximally account for a
fourth of the differences in body-mass ratios between the
predator types, and it is unlikely that they explain the
observed differences between the habitat types.
Prey that are much smaller than the predator may
contain too little energy to be worth the energetic costs
of prey capture and consumption unless the prey can be
harvested very efficiently by, for example, filter feeders
such as baleen whales. Two of the groups of outliers that
were removed (seal–nematode and whale–zooplankton
interactions) represent this feeding strategy. By remov-
ing these links from the analysis we are not suggesting
that these interactions are biologically unimportant.
Rather these interactions represent a feeding strategy
that is biologically interesting but cannot be described
by the same body mass relationship as other predator–
prey interactions. The large body-mass ratios of
vertebrate predators indicate that they have optimized
their ability to efficiently consume small bodied prey
(vertebrate and invertebrate). At the other end of the
scale, prey species that are very large relative to the
predator will be difficult to capture and handle. Our
results suggest that some invertebrate predators have
optimized their morphology and physiology to allow
effective handling of large bodied prey species (mainly
invertebrates). For instance, the use of toxins and
external digestion allows spiders to consume prey species
of almost equal body size. Also, many invertebrate
predators are suctorial (e.g., Hemiptera, some Diptera
larvae, triclads, some leeches), which allows them to
handle large prey.
The predator–prey body-mass ratios of vertebrate
predators are generally higher in freshwater than in
marine or terrestrial habitats in our data. The morpho-
logical constraints determining the maximum prey size
are most important in pelagic ecosystems, where
predators are restricted by the lack of hard surfaces.
Here, most predators completely consume their prey
(gape limitation) as they must avoid having their
recently killed prey sink. This strong maximum size
constraint on the interaction yields a clear size structure
with high body-mass ratios in pelagic ecosystems, where
energy flows from small phytoplankton to large
predatory fish. Similar arguments apply to stream
communities, where predators are often engulfers as
they must prevent their prey from being swept away.
Terrestrial predators also eat prey smaller than them-
selves, but in general, size constraints on trophic
interactions are less pronounced than in aquatic
habitats. Being supported by hard surfaces, terrestrial
predators can successfully capture larger prey than their
aquatic counterparts. While this difference in the
physical structure of the environment may explain why
terrestrial predators have smaller body-mass ratios than
freshwater predators, the low body-mass ratios of
marine invertebrate predators could result from a
dominance of benthic species. Additional data from
pelagic marine ecosystems and benthic lake ecosystems
are needed to analyze systematically the possible differ-
ences between marine vs. freshwater and benthic vs.
pelagic predator–prey body-mass ratios.
Four caveats have to be recognized. First, the body
sizes are averaged over the trophically interacting
populations, but size-structured interactions may affect
our analyses. In size-structured populations, if only large
consumer individuals consume small resource individu-
als, these interactions are mischaracterized by ratios of
averaged body masses. This caveat applies particularly
to cannibalistic feeding interactions and consumers that
change diet as they grow, which might be exemplified by
one of the excluded groups of outliers (trout–copepod/
waterflea interaction). Second, the average body size of a
resource population can sometimes describe the individ-
uals that are not consumed instead of characterizing the
trophic interaction. For instance, consumers might
preferentially consume small resource individuals, thus
increasing the average body size of the resource
population. Third, under link-based approaches such
as ours, several links share a common consumer or
resource species. The data points are not independent in
a statistically strict sense, thus violating the assumptions
of sums of squares statistics (Reuman and Cohen 2004).
While the first two obstacles can only be overcome by
specific sampling procedures such as visual analyses of
individual consumption events, the third point can be
addressed by random subsamples of statistically inde-
pendent data points (Warren and Lawton 1987).
Following this approach, we have shown that our
results hold in the reduced data set. Nevertheless, the
P values in the overall data set should be regarded as
descriptive statistics, rather than probabilities (Reuman
and Cohen 2004). Fourth, our data come from many
distinct communities. The relationship between predator
size and prey size across pooled communities need not
be the same as that relationship in a given, local
community. Further research is required to analyze the
differences between a local community and an amalgam
of multiple communities with respect to the relationship
of predator and prey size.
Several data categories are absent or underrepresented
in the data analyzed here (e.g., terrestrial detritivores
and herbivores, invertebrates feeding on vertebrates). In
addition to challenging other studies to corroborate or
refute the findings reported here, we also call for new
data on these consumer categories. Recent experiments
suggest that the per capita interaction strength increases
with the consumer–resource body-mass ratio (Emmer-
ULRICH BROSE ET AL.2416Ecology, Vol. 87, No. 10
son and Raffaelli 2004). If this relationship is general, Download full-text
our results suggest that the per capita effect of vertebrate
predators on their prey could be higher on average than
the per capita effect of invertebrate predators. Similarly,
our predator–prey body-mass data suggest that per
capita interaction strengths might increase from terres-
trial to freshwater habitats and aquatic herbivores might
have the strongest per capita impacts on their resources.
These suggestions require testing.
With regret we have had to remove the late Peter Yodzis
from our list of authors. While we deeply appreciate the data
and ideas that he contributed to this paper, his passing before
having any chance to review the manuscript makes it unfair for
us to assert his approval of its content by including him as an
author. We thank Roland A. Knapp for providing data and
Stefan Scheu for comments. Financial support has been
provided to U. Brose, B. C. Rall, and C. Banasek-Richter by
the German Research Foundation (BR 2315/1-1,2) and to J. E.
Cohen and D. C. Reuman (DEB 9981552 and DMS 0443803)
and to E. L. Berlow, L. Cushing, N. D. Martinez, and R. J.
Williams (DBI-0234980 and ITR-0326460) by the United States
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