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Dimensionality of consumer seach space drives tropic interaction strengths


Dimensionality of consumer seach space drives tropic interaction strengths

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Trophic interactions govern biomass fluxes in ecosystems, and stability in food webs. Knowledge of how trophic interaction strengths are affected by differences among habitats is crucial for understanding variation in ecological systems. Here we show how substantial variation in consumption-rate data, and hence trophic interaction strengths, arises because consumers tend to encounter resources more frequently in three dimensions (3D) (for example, arboreal and pelagic zones) than two dimensions (2D) (for example, terrestrial and benthic zones). By combining new theory with extensive data (376 species, with body masses ranging from 5.24 × 10(-14) kg to 800 kg), we find that consumption rates scale sublinearly with consumer body mass (exponent of approximately 0.85) for 2D interactions, but superlinearly (exponent of approximately 1.06) for 3D interactions. These results contradict the currently widespread assumption of a single exponent (of approximately 0.75) in consumer-resource and food-web research. Further analysis of 2,929 consumer-resource interactions shows that dimensionality of consumer search space is probably a major driver of species coexistence, and the stability and abundance of populations.
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ARTICLE doi:10.1038/nature11131
Dimensionality of consumer search space
drives trophic interaction strengths
Samraat Pawar
, Anthony I. Dell
& Van M. Savage
Trophic interactions govern biomass fluxes in ecosystems, and stability in food webs. Knowledge of how trophic
interaction strengths are affected by differences among habitats is crucial for understanding variation in ecological
systems. Here we show how substantial variation in consumption-rate data, and hence trophic interaction strengths,
arises because consumers tend to encounter resources more frequently in three dimensions (3D) (for example, arboreal
and pelagic zones) than two dimensions (2D) (for example, terrestrial and benthic zones). By combining new theory with
extensive data (376 species, with body masses ranging from 5.24 310
kg to 800 kg), we find that consumption rates
scale sublinearly with consumer body mass (exponent of approximately 0.85) for 2D interactions, but superlinearly
(exponent of approximately 1.06) for 3D interactions. These results contradict the currently widespread assumption of a
single exponent (of approximately 0.75) in consumer–resource and food-web research. Further analysis of 2,929
consumer–resource interactions shows that dimensionality of consumer search space is probably a major driver of
species coexistence, and the stability and abundance of populations.
Understanding how physical differences between habitats, such as dif-
ferences in precipitation, temperature and spatial dimensionality, affect
trophic interactions is key to predicting stability and diversity in eco-
logical systems
. By assuming a simple relationship between con-
sumption rate (energy acquisition) and metabolic rate (energy use),
most studies assume that per-capita consumptionrates scale with con-
sumer body size (m) to an exponent of approximately 0.75, irrespective
of taxon, environment or dimensionality
. Consequently, mass-
specific production rates
scale as m
, including biomass flow rate
and per-link trophic interaction strengths in food webs
Deviations from quarter-power scaling can arise for at least two reasons.
First, foraging is constrained by traits, such as length of locomotory
appendages or visual acuity, that do not scale directly with metabolic
. Second,species interactions in the fielddo not occur under the
idealized conditions at which metabolic and ingestion rates are usually
measured, in which individuals are not foraging, growing or repro-
. Therefore, consumption-rate scaling may be more closely
tied to field or maximal metabolic rate (exponent greater than 0.85),
rather than resting metabolic rate (exponent of approximately 0.75)
From a biomechanical perspective, both non-metabolic and
metabolic constraints on consumption rate should depend on the
habitat’s spatial dimensionality because it strongly influences the
energetic costs of locomotion (for example, to overcome gravity)
and the probability either of a consumer detecting a resource or vice
. Indeed, over two decades ago, habitat dimensionality was
proposed as a major factor driving food-web structure and ecosystem
. Subsequent studies have further elucidated the effects
of habitat dimensionality
. Notably, previous models suggest
that grazers (one type of consumer; Fig. 1 and Supplementary Fig. 1)
are constrained by how resources are distributed in space
. These
studies are foundational, but do not apply to the full diversity of
foraging strategies and interactions in natural communities.
Here we show that shifting focus from dimensionality of the
to the dimensionality of each trophic interaction yields
a new, mechanistic theory for trophic interaction strengths (Figs 1
and 2). Our approach allows both 2D and 3D interactions within the
same habitat to be considered, and can be applied to the wide range of
foraging strategies found in nature (Fig. 1 and Supplementary Fig. 1).
To test our predictions, we compiled a data set that contains a per-
capita consumption rate of 255 consumer–resource interactions
covering 230 species, 12 orders of magnitude in body size, and aquatic
(189 interactions) as well as terrestrial (66 interactions) habitats
Department of Biomathematics, David Geffen School of Medicine, University of California, Los Angeles, California 90095-1766, USA.
School of Marine and Tropical Biology, James Cook University,
Townsville QLD 4811, Australia.
Department of Ecology & Evolutionary Biology, University of California, Los Angeles, California 90095, USA.
Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico
87501, USA.
Figure 1
Consumer–resource interactions can be classified by
dimensionality. If the consumer searches for resources (by flying, swimming,
or sitting and waiting) on habitat surfaces (for example, on the water surface,
benthos or in grassland), the interaction is 2D, and if it searches habitat volume,
the interaction is 3D. A consumer or resource may be involved in both 2D and
3D interactions, corresponding to different consumer–resource combinations
and foraging strategies.
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Empirical patterns
Using our comprehensive data set, we first demonstrate strong
empirical differences between 2D and 3D interactions in the scaling
of search and consumption rate with consumer body size (Fig. 3).
When resources are scarce, more closely resembling field conditions,
the observed scaling exponent for consumption rate in 3D interac-
tions (1.06 60.06 (95% confidence intervals)) is significantly higher
than in 2D (0.85 60.05) (likelihood ratio test, P,0.001) (Fig. 3a, c).
These scaling exponents are significantly higher than the currently
used exponent of 0.75 (one-sample F-test P,0.01). Furthermore,
apart from organisms that are much smaller than a honeybee (weigh-
ing less than 3 310
kg, where 2D and 3D scaling lines would
intersect), 3D consumption rates are higher than in 2D (Fig. 3a, b).
For a 1-kg organism, 3D consumption rate is ten times higher than in
2D (6.30 63.01 versus 0.63 60.24 mg s
) (Fig. 3a, b).
When resources are abundant, typical of laboratory conditions,
consumption rates still scale more steeply (1.00 60.06 versus
0.85 60.05) and show higher baseline values in 3D than 2D
(19.95 611.00 versus 3.16 61.30 mg s
for a 1-kg organism)
(Fig. 3c, d). Thus, even at high resource densities at which searching
for resources is expected to be less constraining, dimensionality
remains important. The canonical 0.75 scaling exponent for con-
sumption rate is excluded from the 95% confidence intervals of the
observed scaling exponents under all conditions (Fig. 3).
We also analysed the scaling of search rates. The rate at which a
consumer searches for a resource limits consumption rates when
resources are scarce (Figs 1, 2 and 3e, f). For active-capture and
grazing foragers, search rate (area/time or volume/time) is the speed
at which a consumer moves through the landscape to find food,
whereas for sit-and-wait foragers, it is the speed at which resources
move through the consumer’s attack space (Figs 1 and 2). We find
that search rates have a scaling exponent of 1.05 60.08 in 3D
and 0.68 60.12 in 2D (Fig. 3e, f), indicating that differences in
consumption-rate scaling are primarily driven by differences in
search rate. This result is a key validation of our model below.
A mechanistic model for search rate
Our empirical analysis reveals that search- and consumption-rate
scaling vary systematically with the dimensionality of search space
(that is, interaction dimensionality). We now present a model that
predicts these empirical patterns by focusing on three key compo-
nents of search rate: relative velocity, reaction distance and handling
(Fig. 2). Relative velocity (v
) is the rate at which consumer–
resource pairs converge across the landscape, and it is the root-mean-
square of their body velocities. A potential encounter occurs when
either the resource or consumer comes within the distance (d)at
which one can detect and react to the other. Because each individual
moving through the landscape maintains a search space enclosed by a
surface with radius d, we can derive (Supplementary Information)
that the search rate (a) increases with dimensionality (D):
where s
52 in 2D and pin 3D. Based on biomechanical principles,
we obtained predictions for the scaling exponents p
and p
(of v
d, respectively; Fig. 2), and validated them empirically using another,
independent data set that we compiled (Table 1 and Supplementary
Information). Using these, we predict:
where m
is consumer body mass. For active foraging, the constant
a0is 2v0d0in 2D and pv0d2
0in 3D. The function f(k
) isolates
dependence of aon consumer–resource size ratio k
(that is,
(where m
is resource body mass)) from its direct dependence
on consumer mass. Both a
and f(k
) vary weakly with foraging
strategy (Supplementary Information). To relate equation (2) directly
to previous studies by expressing it solely in terms of consumer mass,
we determine how k
scales with consumer mass using our con-
sumption-rate data set. Substituting this scaling together with values
for p
and p
(Table 1) into equation (2) gives:
log10(Consumer mass)
log10(Consumption rate)
0.75 power
log10(Search rate)
b Scarce resources
c Abundant resources d Abundant resources
y = 0.85x – 6.2
R2 = 0.84
y = 1.06x – 5.2
R2 = 0.85
e Scarce resources f Scarce resources
a Scarce resources
2D 3D
y = 0.85x – 5.5
R2 = 0.86
y = 1.00x – 4.7
R2 = 0.84
y = 0.68x – 3.08
R2 = 0.60
y = 1.05x – 1.77
R2 = 0.77
–8 –6 –4 –2 0 2 –8 –6 –4 –2 0 2
Figure 3
Effect of interaction dimensionality on scaling of search and
consumption rate. ad, Scaling of per-capita consumption rate (kg s
consumer body mass (kg) at different resource densities. e,f, Scaling of search
rate (m
in 2D, and m
in 3D). See Table 1 for sample sizes. Solid black
lines were fitted using OLS regression (see Methods). Exponents in all panels
except eare significantly different from the canonical 0.75 value (dotted line).
Consumption-rate scaling shows less variance than search rate, possibly
because consumers choose resources that maximize biomass consumption rate
(product of search rate, resource density and resource mass; equation (4)),thus
minimizing scatter.
Capture and
mR, mC = Resource (R) and consumer (C) body masses
kRC = mR/mC = Body mass ratio
β = Exponent for handling time (th)
pv = Exponent for consumer or resource velocity (vR,vC)
pd = Exponent for consumer–resource reaction distance (d)
Scaling parameters
D = Interaction dimensionality (2 or 3)
d (mRmC)
th mC
vR,vC mC
D = 2
vC > 0
vR > 0
Figure 2
Model for scaling of search and consumption rate with body size.
This model (2D active capture isshown here) can also be used to predict search
and consumption rates for grazing and sit-and-wait foraging strategies
(Supplementary Information).
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Cin 2D
Cin 3D ð3Þ
where a
and a
are dimension-specific constants. These exponents
match our empirical results extremely well (Fig. 3e, f and Table 1).
Even if the weak contribution of f(k
) (Supplementary Information)
to the scaling is ignored, the predicted search rate exponents (p
(D–1)) would be 0.68 in 2D and 1.06 in 3D. These exponents are
extremely close to the empirical estimates of 0.68 60.12 in 2D and
1.05 60.08 in 3D (Table 1; Fig. 3).
Predictions for consumption rate
The product of search rate, a, and resource density, x
(individuals per
area or volume), yields encounter rate. Consumption rate is con-
strained by this encounter rate and by handling time; that is, the
duration of time to pursue, subdue and ingest each resource
(Fig. 2). Together, these components give a saturating per-capita bio-
mass consumption rate (c) (Holling’s type II functional response
terms of spatial dimension (D):
Here, m
is the average mass of the resource, x
is resource biomass
density, and t
is conventional handling time divided by resource
mass (Supplementary Information 1.4). The constant s9
includes a
roughly constant attack success probability. Our results are robust to
changes in this probability for resource items common in the con-
sumer’s diet (Supplementary Information).
With scarce resources (x
) the second term in the denom-
inator of equation (4) becomes much smaller than 1, and thus c<
. Substituting the scaling for a(equation (2)) gives:
To convert this into a scaling relationship solely with consumer mass,
we use our functional response data set (Supplementary Information)
to quantify the scaling of x
and m
with consumer mass (Table 1).
Substituting these along with the previously determined scaling of size
ratio (k
) in equation (5) gives:
Cin 2D
Cin 3D ð6Þ
where c
and c
are dimension-specific constants. Equation (6)
predicts the steeper and superlinear scaling that is empirically
observed in 3D for consumption rate (Fig. 3a, b and Table 1). Note
that the scaling of consumption rate, c, closely matches the scaling of
search rate, a(compare equations (3) and (6)). The existing small
difference arises because of the weak scaling of the product (x
of resource density and mass with consumer mass (Table 1 and
Supplementary Information).
When resources are unlimited (x
R), the term s0DvrdD{1xRmR
dominates both the numerator and denominator of equation (4),
resulting in a value of 1. Consequently, search and detection become
instantaneous, and consumption rate depends only on mass-specific
handling rate (1/t
) (Fig. 2):
where bis the scaling exponent of the consumer’s whole-body
metabolic rate and t
is a body-temperature and metabolic-state-
dependent constant. We find that mass-specific handling time, t
scales as 1.1 60.07 in 3D and 1.02 60.08 in 2D (Supplementary
Information). However, the observed consumption-rate scaling in 2D
is 0.85 60.05, and is 1.00 60.06 in 3D, both closer to predictions for
scarce rather than unlimited resources (Table 1). Therefore, even
when functional responses seem to saturate and resources are
considered abundant, consumption rate does not scale like handling
time, and must therefore continue to be constrained by search
dimensionality. This also explains why most previous studies have
reported 0.75 power scaling of consumption rate
. The data in
these previous studies are actually maximal ingestion rates collected
from sedentary individuals that are provided with unlimited
. Our data, for both scarce and abundant resources, are
more representative of field conditions because they are extracted
from functional response data.
Although our theory predicts that a
and c
are larger than a
and c
, respectively (Supplementary Information), the magnitude of
the observed difference is much larger than predicted (Fig. 3). One
explanation is that most 3D interactions are aquatic, and most 2D
interactions are terrestrial. The energetic cost for swimming is about
ten times lower than for running
, probably increasing encounter
rates for non-directed movement. This difference could elevate the
intercept (but not exponent), contributing to the observed ten times
larger baseline consumption rates in 3D. Nevertheless, 2D aquatic and
2D terrestrial interactions scale similarly (Fig. 3a–c), indicating other
differences between pelagic (3D) and benthic (2D) aquatic zones, and
highlighting the need for further study.
Dimensionality and trophic interaction strengths
By deriving the scaling of search rate (a), a fundamental parameter in
consumer–resource and food-web models, we have provided a mech-
anistic basis for linking interaction dimensionality with trophic inter-
action strengths, which are proportional to ax
(refs 11, 13, 15,
16, 28, 29). In contrast to current theories, our results show that
scaling of trophic interaction strength can deviate substantially from
C. Specifically, if resource size (m
) and resource density (x
are decoupled from consumer size, consumption rate scales like
search rate (equation (3)), and thus interaction strength scales as
Cin 2D, and m0:05
Cin 3D. Even when m
and x
scale with consumer mass (Table 1 and Supplementary Fig. 2), trophic
interaction strengths scale as m{0:15
C(2D) or m0:06
C(3D) when
resources are scarce, and as m{0:15
C(2D) or m0
C(3D) when resources
are abundant. This variation in the scaling of trophic interaction
strengths implies that consumer–resource dynamics are likely to be
constrained by interaction dimensionality.
Implications for population dynamics
By incorporating our scaling equations for a(equation (3)) into a
population dynamics model (Methods), we now show that dimen-
sionality can affect populations in three fundamental ways. First, 3D
interactions allow a larger range of viable consumer–resource body-size
Table 1
Empirical and predicted scaling exponents of consumption rate and its components with interaction dimensionality (D)
DSearch and consumption rate (n 5255) Consumption-rate components
Search rate
(scarce resources)
Consumption rate Relative velocity
Reaction distance
Handling time
Resource mass
Resource density
Scarce resources Abundant resources
2D 0.68 60.12*(0.63) 0.85 60.05 (0.78) 0.85 60.05 (0.78) 0.26 60.04*(0.27) 0.21 60.08 (0.3 3) 21.0260.08 (20.75) 0.73 60.10 20.79 60.08
3D 1.05 60.08*(1.03) 1.06 60.06 (1.16) 1.00 60.06 (1.16) 0.26 60.04*(0.27) 0.20 60.06 (0.3 3) 21.1 60.07 (20.75) 0.92 60.08 20.86 60.07
For search and consumption rate, if the 3D exponent is significantly larger than 2D as predicted (likelihood ratio test), both are shown in bold. There are no predicted exponents for resource mass and resource
density scaling because they depend upon experimental design (Supplementary Information). Steeper than predicted exponents of handling time may arise because pursuit and subjugation scale with maximal
rather than resting metabolic rate
*Empirical exponent is statistically indistinguishable (P50.05 for all significance tests) from the predicted value (in parentheses).
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combinations than in 2D, primarily because 3D consumption rates
scale more steeply and have higher baseline values. Depending upon
baseline carrying capacity (K
, defined as maximal biomass density for
a 1 kg organism; Supplementary Information), the majority of 2,929
species pairs from seven communities fall within our predicted
coexistence domains (Fig. 4a), with upper and lower limits of observed
size ratios closely matching predicted extinction boundaries. In 2D,
when K
ranges from 0.01 to 1 (kg
) the predicted coexistence
domains contain 88.8% to 99.8% of the empirical data. In 3D, when K
ranges from 3 to 300 (kg
), 74.3% to 99.8% of the data are within
the predicted domain (we explain below why carrying capacity is
typically higher in 3D than 2D). Thus, interaction dimensionality
may explain why consumer–resource interactions with larger size
ratios (for example, filter feeding
) and larger consumers are more
common in pelagic environments compared to benthic or terrestrial
(Fig. 4a).
Second, because strong trophic interactions can destabilize com-
15,16, 28,29
, communities dominated by 3D interactions (for
example, pelagic or aerial habitats) may be inherently unstable. Indeed,
we find that persistent consumer–resource boom–bust dynamics are
more likely in 3D than in 2D (Fig. 4b and Supplementary Fig. 3). In
nature, these instabilities may be partly offset by larger regions of
coexistence that are possible in 3D (Fig. 4a) or by negative consumer
density dependence
. Nevertheless, our results are consistent with
empirical observations that pelagic communities appear less stable
than terrestrial communities
. They also suggest that 3D aquatic eco-
systems may experience more frequent top-down regulation than 2D
terrestrial ecosystems
Third, we predict that population densities across consumer–
resource pairs scale with body size more steeply in 3D (exponent of
–1.12) than 2D (exponent of –0.76) (Fig. 4c). Only 2D scaling matches
Damuth’s 20.75 rule, which was derived from data on terrestrial
mammals (that is, 2D consumers)
. Thus, for a given carrying
capacity (maximal abundance of resources), steeper size–abundance
scaling of consumers in 3D habitats relative to 2D habitats should be
expected, and this helps to explain deviations from Damuth’s rule in
local communities
In our population model, we assume resource carrying capacities
scale with a 0.75 exponent (Supplementary Information), as expected
when food supply to resources is unlimited (equation (7))
. For
example, maximal abundance of primary producers in 2D (for
example, terrestrial plants) and 3D (for example, pelagic phytoplankton)
should scale as metabolic rate (that is, Damuth’s rule) irrespective of
dimensionality, which is well supported empirically
. Future studies
should incorporate potential differences in scaling of carrying capacity
across trophic levels. We also assume higher baseline carrying capacities
2–3 orders of magnitude higher turnover rates than terrestrial plants and
form a less variable and more nutritious autotroph base than plants in
2D terrestrial ecosystems such as grasslands
. This is an important
difference between habitats because it helps to explain the potential
advantage of 3D interactions. If resources had the same numbers
(but not densities) in 2D and 3D habitats (for example, 1 kg m
), resources would probably be too sparse for a 3D search space
to be advantageous.
The consequences of interaction dimensionality for population
dynamics may also be mediated by other abiotic differences between
aquatic and terrestrial habitats. For example, 2D habitats such as
benthic zones may have a greater potential for prey refuges than 3D
habitats such as pelagic zones. Structural complexity reduces con-
sumer search rates, potentially resulting in type III functional res-
ponses instead of type I or II (refs 30, 40). We find no significant
propensity for type III functional responses in 2D relative to 3D in our
data set (Supplementary Information), probably because laboratory
experiments typically use habitats that are simpler than real habitats.
Even if type III responses are more common in 2D, results for the effects
of dimensionality on consumer–resource population dynamics remain
qualitatively unchanged (Supplementary Information). Nevertheless,
an important future direction will be to understand how habitat com-
plexity affects search and consumption rates. Synthesizing our model
with previous work on fractal dimensionality of resource disper-
should be an important step in this direction. Perception of
structural complexity also scales with body size
structurally simple for a bison, but complex for a nematode.
Our study provides new and more accurate scaling relationships for
consumer–resource interactions
, gives novel insights into con-
sumer–resource dynamics, and offers a mechanistic model that incor-
porates dimensionality and foraging strategy into food-web dynamics.
Our results help to explain why aquatic environments generally show
higher energy fluxes and lower stabilitythan terrestrial environments
why they often show inverted biomass pyramids
, and why larger
consumers have a relative advantage in pelagic (3D) versus terrestrial
(2D) environments
. Predicting strengths of pair-wise trophic inter-
actions is key to understanding higher-order effects, including indirect
interactions and polyphagy
. Our model for pairwise interactions
should provide a starting point for studying how the effects of
dimensionality propagate through entire community food-webs.
Studying communities with mixtures of 2D and 3D interactions will
3D exponent = –1.12
–10 –5 05
(Consumer mass)
(Resource mass)
(Body mass)
limit cycle
2D 3D
Resource abundance
−9 –4 1
Consumer abundance
High densityLow density
–9 –4 1–14 6
2D exponent = –0.76
Damuth's rule = –0.75
= 3
K0 = 30
K0 = 300
Figure 4
Effects of interaction dimensionality on consumer–
resource dynamics. a, Intensity map of logarithm of total consumer–resource
equilibrium densities, ranging from coexistence at high (dark) to low (yellow)
densities, or extinction (white). Black dots are real 2D (n51,627) and 3D
(n51,302) consumer–resource pairs (Supplementary Table 8). Consumer and
resource sizes are equal along the diagonal line. Lower extinction boundaries
(dashed lines) correspond to different baseline carrying capacities (K
); the
outermost boundary corresponds to empirical estimates. Predicted 2D
coexistence regions that lack observed species pairs probably represent under-
sampling of interactions for the smallest consumers (for example, micro
predators) and largest consumers (for example, large mammalian
.b, Comparison of population dynamics of two 2D (1 and 2 in
a) and two 3D (3 and 4 in a) species pairs. c, Scaling of equilibrium abundance
across all 3D (blue) and 2D (red) consumer–resource pairs plotted in a.The
variation and discreteappearance of the data arises mainly because a consumer
may feed on multiple resource species of different sizes and vice versa.
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be particularly revealing in this context. We conclude that interaction
dimensionality is a critical factor driving consumer–resource
dynamics. A better understanding of the effects of dimensionality will
lead to better predictions of food-web and ecosystem dynamics, and
how these complex systems might respond to environmental change.
Functional response data were compiled from the literature (Supplementary
Table 5). Interaction dimensionality was assigned according to consumer search
space (Fig. 1). The minimum resource density in each study was classified as
scarce, and the density corresponding to the maximum consumption rate was
classified as abundant. The search rate (a) in each functional response was cal-
culated at each scarce density by dividing the associated consumption rate (c)by
the associated density. The scaling of ais our fundamental theoretical result
(equation (2)) and is based on derived scalings for v
,dand t
. We verified
predicted scalings of these components by compiling an additional data set of
136 interactions between 157 taxa. To move from predicted scaling exponents of
a(equation (3)) to predictions for scaling exponents of c(equation (4)), we
calculated the scaling of resource number density (x
) and mass (m
) across
studies in the functional response database. All exponents were estimated using
ordinary least squares regression (OLS) of log trait value versus log body mass.
Major axis regression yields steeper exponents than OLS but does not qualita-
tively alter our results. We also tested for robustness of predictions to realistic
variation in body velocity scaling. All data were standardized to 15 uC using the
Boltzmann–Arrhenius model
. For population dynamics we used the
Rosenzweig–MacArthur model for the rate of change in time, t, for the resource
) and consumer (C5x
) biomass densities
dt~rR 1{R
Here, ris the resource’s intrinsic biomass production rate, Kis resource’s biomass
carrying capacity, zis the consumer’s biomass loss rate, eis the consumer’s
biomass conversion efficiency, and t
is the resource mass-specific handling time.
Size scaling for aand t
were based on our results, and that for r,zand Kwere
based on previous work
. We tested robustness of our results by varying model
structure between the Rosenzweig-MacArthur model and the Lotka–Volterra
predator–prey model, and also by using a type III instead of a type II functional
Received 13 December 2011; accepted 3 April 2012.
Published online 30 May 2012.
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Supplementary Information is linked to the online version of the paper at
Acknowledgements We thank the authors who contributed data (Supplementary
Tables 5–8), and P. Amarasekare, J. H. Brown, E. Economo, A. Mikheyev, C. Estrada,
C. Johnson, M. Johnson and K. Lafferty for helpful discussions and comments. S.P.,
A.I.D. and V.M.S. were supported by University of California, Los Angeles
Biomathematics start-up funds andby the US National Science Foundation Division of
Environmental Biology award 1021010.The data reported in thispaper are available in
the Supplementary Information online.
Author ContributionsS.P., A.I.D. and V.M.S. contributed equally to this work.All authors
discussed the results and commented on the manuscript.
Author Information Reprints and permissions information is available at The authors declare no competing financial interests.
Readers are welcome to comment on the online version of this article at Correspondence and requests for materials should be
addressed to S.P. (
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Supplementary resource (1)

... Previous studies that have considered the surrounding medium have usually focused on specific aspects of predation or on specific taxa (Domenici et al., 2011), or have investigated one specific aspect of the medium such as dimensionality (Pawar et al., 2012(Pawar et al., , 2015 or habitat complexity , more rarely two factors simultaneously (Wasserman et al., 2016). But the overall role played by the surrounding medium acting on the predator-prey relationship, which drives the functional response, remains to be explored. ...
... Several studies have begun to investigate this promising avenue. For example, the dimensionality of the physical medium was shown to constrain predator-prey interactions since predators are expected to capture pelagic and flying prey more efficiently than benthic and terrestrial prey (Pawar et al., 2012). Extending this framework to predict pairwise trophic interactions in natural situations, Pawar et al. (2019) fall short of deriving the parameters of their functional response model from physical factors other than dimensionality. ...
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First derivations of the functional response were mechanistic, but subsequent uses of these functions tended to be phenomenological. Further understanding of the mechanisms underpinning predator-prey relationships might lead to novel insights into functional response in natural systems. Because recent consideration of the physical properties of the environment has improved our understanding of predator-prey interactions, we advocate the use of physics-based approaches for the derivation of the functional response from first principles. These physical factors affect the functional response by constraining the ability of both predators and prey to move according to their size. A physics-based derivation of the functional response should thus consider the movement of organisms in relation to their physical environment. One recent article presents a model along these criteria. As an initial validation of our claim, we use a slightly modified version of this model to derive the classical parameters of the functional response (i.e., attack rate and handling time) of aquatic organisms, as affected by body size, buoyancy, water density and viscosity. We compared the predictions to relevant data. Our model provided good fit for most parameters, but failed to predict handling time. Remarkably, this is the only parameter whose derivation did not rely on physical principles. Parameters in the model were not estimated from observational data. Hence, systematic discrepancies between predictions and real data point immediately to errors in the model. An added benefit to functional response derivation from physical principles is thus to provide easy ways to validate or falsify hypotheses about predator-prey relationships.
... Interactions between predator and prey in natural communities are difficult to describe quantitatively. Various mathematical models have been used to quantify prey acquisition by the predator and to investigate the nature and the strength of species interactions within food webs (Abrams et al., 1998;Baudrot et al., 2016;Chan et al., 2017;Pawar et al., 2012). Several studies have compared how a predator acquisition rate varies with prey density using statistical approaches (reviewed by Novak and Stouffer 2020), but few of them explicitly tackled the underlying mechanisms. ...
... A potential encounter occurs between the predator and a prey item i when the predator is at a distance (d i ), being defined as the maximum distance at which the predator can detect a prey item i (in 2D, detection region = 2d i ; Pawar et al., 2012). ...
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Prey handling processes are considered a dominant mechanism leading to short‐term positive indirect effects between prey that share a predator. However, a growing body of research indicates that predators are not necessarily limited by such processes in the wild. Density‐dependent changes in predator foraging behavior can also generate positive indirect effects but they are rarely included as explicit functions of prey densities in functional response models. With the aim of untangling proximate mechanisms of species interactions in natural communities and improving our ability to quantify interaction strength, we extended the multi‐prey version of the Holling disk equation by including density‐dependent changes in predator foraging behavior. Our model, based on species traits and behavior, was inspired by the vertebrate community of the arctic tundra, where the main predator (the arctic fox) is an active forager feeding primarily on cyclic small rodent (lemming) and eggs of various tundra‐nesting bird species. Short‐term positive indirect effects of lemmings on birds have been documented over the circumpolar Arctic but the underlying mechanisms remain poorly understood. We used a unique data set, containing high‐frequency GPS tracking, accelerometer, behavioral, and experimental data to parameterize the multi‐prey model, and a 15‐year time series of prey densities and bird nesting success to evaluate interaction strength between species. We found that: (i) prey handling processes play a minor role in our system and (ii) changes in arctic fox daily activity budget and distance traveled can partly explain the predation release on birds observed during lemming peaks. These adjustments in predator foraging behavior with respect to the main prey density thus appear as the dominant mechanism leading to positive indirect effects commonly reported among arctic tundra prey. Density‐dependent changes in functional response components have been little studied in natural vertebrate communities and deserve more attention to improve our ability to quantify the strength of species interactions.
... Redefining our model to include a more accurate depiction of the capture rate (e.g. Dell et al., 2014;Pawar et al., 2012) may provide greater insight into the broader importance of thermal mismatch. ...
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Recent work has demonstrated that changes in resource availability can alter a consumer's thermal performance curve (TPC). When resources decline, the optimal temperature and breadth of thermal performance also decline, leading to a greater risk of warming than predicted by static TPCs. We investigate the effect of temperature on coupled consumer‐resource dynamics, focusing on the potential for changes in the consumer TPC to alter extinction risk. Coupling consumer and resource dynamics generally reduces the potential for resource decline to exacerbate the effects of warming via changes to the TPC due to a reduction in top‐down control when consumers near the limits of their thermal performance curve. However, if resources are more sensitive to warming, consumer TPCs can be reshaped by declining resources, leading to increased extinction risk. Our work elucidates the role of top‐down and bottom‐up regulation in determining the extent to which changes in resource density alter consumer TPCs. We investigate the relationship between resource density and temperature (warming) on the persistence of a consumer population. Our work elucidates the importance of jointly considering temperature and resource limitation when assessing the thermal performance of species. We demonstrate how knowledge of the thermal performance of a resource population can be used to generate realized consumer thermal performance curves.
... The combined analysis(6) of the zooplankton-algal community biomass growth gives a scaling exponent of ~ 0.71, agreeing with this analysis. Dimensionality has been recognized to play an important role in consumer search space in ecosystems (15,16). The current theory offers a first explanation for the wide range of scaling observations in biomass productions (6). ...
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Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is the 3/4- or and 2/3-power scaling law. It's observed in worldwide aquatic and land biomass productions, eukaryote growth, mammalian brain sizes, and city public facility distributions. Here, I show that these complex systems belong to a new universality class whose system dimensionality determines its growth scaling. The model uses producer-consumer dynamics to derive the n/(n+1) power scaling law for an n-dimensional system. Its predictions are validated with real-world two- and three-dimensional data. Dimensionality analysis thus provides a new paradigm for understanding growth and growth-related problems in a wide range of complex systems.
... 3b for marine invertebrates in Rall et al., 2012). Pawar et al. (2012) showed that scaling relationships for feeding rate tend to be steeper (~1) when resources are abundant, a common condition in laboratory experiments. Our large values of a might also have arisen from photographic methods in the feeding experiment; if feeding of smaller individuals was less likely to be detected in the photographs relative to that of larger individuals, we may have biased our estimation of a to larger values. ...
Physiological processes influence how individuals perform in various environmental contexts. The basis of such processes, metabolism, scales allometrically with body mass and nonlinearly with temperature, as described by a thermal performance curve. Past studies of thermal performance curves tend to focus on effects of temperature on a single body size or population, rather than variation in the thermal performance curve across sizes and populations. Here, we estimate intraspecific variation in parameters of the thermal performance curve in the salt marsh gastropod Littoraria irrorata. First, we quantify the thermal performance curve for respiration rate as a function of both temperature and body size in Littoraria and evaluate whether the thermal parameters and body size scaling are interdependent. Next, we quantify how parameters in the thermal performance curve for feeding rate vary between three Littoraria populations that occur along a latitudinal gradient. Our work suggests that the thermal traits describing Littoraria respiration are dependent on body mass and that both the thermal traits and the mass scaling of feeding vary across sites. We found limited evidence to suggest that mass scaling of Littoraria feeding or respiration rates depends on temperature. Variation in the thermal performance curves interacts with the size structure of the Littoraria population to generate divergent population-level responses to temperature. These results highlight the importance of considering variation in population size structure and physiological allometry when attempting to predict how temperature change will affect physiological responses and consumer-resource interactions.
... Thus, there is a minimum beyond which the handling time cannot be reduced, particularly when resource species exhibit defense mechanisms such as shells, spines, trichomes, and toxins, and the consumers themselves are limited by jaw size, gut capacity, ovipositor length and egg limitation (Saloniemi, 1993;Abrams and Matsuda, 1997;Sasaki and Godfray, 1999). Similarly, the attack rate, which involves searching and finding resources, depends on search velocity and detection distance (i.e., each individual has to search a space of some radius within which it can detect its prey), which themselves are subject to energetic and other constraints that set an upper limit on the attack rate (Pawar et al., 2013). One would therefore expect stabilizing selection to drive attack rates and handling times toward optima determined by energetic, physiological, and anatomical considerations. ...
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Intrinsically generated oscillations are a defining feature of consumer-resource interactions. They can have important consequences for the evolution of consumer functional responses. Functional response traits that maximize resource fitness (low attack rate and long handling time) and consumer fitness (high attack rate and short handling time) generate high-amplitude oscillations that can predispose species to extinction during periods of low abundances. This suggests that the ecological consequences of consumer-resource oscillations may impede evolutionary outcomes that maximize fitness. Data suggest this to be a strong possibility. Time series analyses reveal consumer-resource cycles to be infrequent in real communities, and functional response studies show a preponderance of low attack rates and/or short handling times that preclude oscillations but maximize neither species' fitness. Here I present a mathematical model to address this tension between ecological dynamics and the evolution of functional response traits. I show that the empirically observed attack rate-handling time distributions emerge naturally from the interplay between individual-level selection and the population-level constraint of oscillation-induced extinction. Extinction at low abundances curtails stabilizing selection toward trait values that maximize fitness but induce large-amplitude oscillations. As a result, persistent interactions are those in which the mean attack rate is low and/or the mean handling time is short. These findings emphasize the importance of incorporating oscillation-induced extinction into models that link food web topology to community persistence.
... This poses significant problems due to the finite ability of real-world agents to perceive and detect information from the environment in both space and time (Lima and Zollner 1996). An agent's information gathering and use abilities vary with its body size (Mech and Zollner 2002) and physiology (Abrahams 1989), its needs and goals (Powell and Mitchell 2012), the ecosystem's structure (Pawar et al. 2012) and the presence or absence of other agents (Nocera et al. 2009). In turn, these experiential differences in the way agents interact with information modify the way they move over and use resources across the landscape (Stephens and Krebs 1987, Guzman et al. 2019, Hein and Martin 2019. ...
Fluxes of matter, energy and information over space and time contribute to ecosystems' functioning and stability. The meta‐ecosystem framework addresses the dynamics of ecosystems linked by these fluxes but, to date, has focused solely on energy and matter. Here, we synthesize existing knowledge of information's effects on local and connected ecosystems and demonstrate how new hypotheses emerge from the integration of ecological information into meta‐ecosystem theory. We begin by defining information and reviewing how it flows among ecosystems to affect connectivity, local ecosystem function and meta‐ecosystem dynamics. We focus on the role of semiotic information: that which can reduce an individual's – or a group's – uncertainty about the state of the world. Semiotic information elicits behavioral, developmental and life history responses from organisms, potentially leading to fitness consequences. Organisms' responses to information can ripple through trophic interactions to influence ecosystem processes, their local and regional dynamics, and the spatiotemporal flows of energy and matter, therefore information should affect meta‐ecosystem dynamics such as stability and productivity. While specific subdisciplines of ecology currently consider different types of information (e.g. social and cultural information, natural and artificial light or sound, body condition, genotype and phenotype), many ecological models currently account for neither the spatio–temporal distribution of information nor its perception by organisms. We identify the empirical, theoretical and philosophical challenges in developing a robust information meta‐ecology and offer ways to overcome them. Finally, we present new hypotheses for how accounting for realistic information perception and responses by organisms could impact processes such as home range formation and spatial insurance, and thus our understanding of ecological dynamics across spatial and temporal scales. Accounting for information will be essential to understanding how dynamics such as fitness, organismal movement and trophic interactions influence meta‐ecosystem functioning, and predicting how ecosystem processes are affected by anthropogenic pressures.
... Persistent scepticism about evolved prudence is not only evident from direct criticism (Matsuda, 2008) and recent proposals that attack rates follow from fundamental physical and physiological constraints (Hirt et al., 2020;Ho et al., 2019;Pawar et al., 2012;Portalier et al., 2019). It is also implied in assumptions of physiological trade-offs or pleiotropy in evolutionary models of consumer-resource interactions (Fleischer et al., 2018;Schreiber et al., 2018;van Velzen & Gaedke, 2017). ...
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Prudent predators catch sufficient prey to sustain their populations but not as much as to undermine their populations’ survival. The idea that predators evolve to be prudent has been dismissed in the 1970s, but the arguments invoked then are untenable in the light of modern evolution theory. The evolution of prudent predation has repeatedly been demonstrated in two‐species predator–prey metacommunity models. However, the vigorous population fluctuations that these models predict are not widely observed. Here we show that in complex model food webs prudent predation evolves as a result of consumer‐mediated (‘apparent’) competitive exclusion of resources, which disadvantages aggressive consumers and does not generate such fluctuations. We make testable predictions for empirical signatures of this mechanism and its outcomes. Then we discuss how these predictions are borne out across freshwater, marine and terrestrial ecosystems. Demonstrating explanatory power of evolved prudent predation well beyond the question of predator–prey coexistence, the predicted signatures explain unexpected declines of invasive alien species, the shape of stock–recruitment relations of fish, and the clearance rates of pelagic consumers across the latitudinal gradient and 15 orders of magnitude in body mass. Specific research to further test this theory is proposed. The authors propose a new theory explaining how predators can evolve to catch sufficient prey to sustain their populations but not as much as to undermine their populations’ survival. The key mechanism is consumer‐mediated ("apparent'") competitive exclusion of resources, which disadvantages aggressive predators in the metacommunity context by leaving them vulnerable to sudden extirpation in local communities. Testable empirical signatures of this mechanism and its outcomes include known but hitherto unexplained phenomena in fisheries science, invasion ecology, and the study of allometric scaling laws.
... We show that the average intraspecific whole-organism mass scaling exponent of metabolism is larger than that of maximum consumption, i.e., the inequality a < b holds at the intraspecific level. By contrast, Pawar et al. (2012) estimated larger mass exponents for consumption than the metabolic rate (0.84 and 1.04 in 2D and 3D foraging) from interspecific data, which reveals the importance of parameterizing processes occurring over ontogeny with intraspecific rather than interspecific data. When accounting for the smaller intraspecific mass exponent of consumption, and the unimodal thermal response of consumption, the thermal response of net energy gain is characterized by the optimum temperature being a function of body size (Morita et al., 2010). ...
Full-text available
According to the temperature-size rule, warming of aquatic ecosystems is generally predicted to increase individual growth rates but reduce asymptotic body sizes of ectotherms. However, we lack a comprehensive understanding of how growth and key processes affecting it, such as consumption and metabolism, depend on both temperature and body mass within species. This limits our ability to inform growth models, link experimental data to observed growth patterns, and advance mechanistic food web models. To examine the combined effects of body size and temperature on individual growth, as well as the link between maximum consumption, metabolism, and body growth, we conducted a systematic review and compiled experimental data on fishes from 52 studies that combined body mass and temperature treatments. By fitting hierarchical models accounting for variation between species, we estimated how maximum consumption and metabolic rate scale jointly with temperature and body mass within species. We found that whole-organism maximum consumption increases more slowly with body mass than metabolism, and is unimodal over the full temperature range, which leads to the prediction that optimum growth temperatures decline with body size. Using an independent dataset, we confirmed this negative relationship between optimum growth temperature and body size. Small individuals of a given population may, therefore, exhibit increased growth with initial warming, whereas larger conspecifics could be the first to experience negative impacts of warming on growth. These findings help advance mechanistic models of individual growth and food web dynamics and improve our understanding of how climate warming affects the growth and size structure of aquatic ectotherms.
... Further research is thus needed to determine the generality of the observed interactive effects of temperature and body size on functional response parameters and population stability. A growing number of studies also indicate that predator-prey interactions may exhibit different responses depending on the dimensionality of the interacting pair (Pawar et al., 2012;Uiterwaal and DeLong, 2020). Our study involved a sit-and-wait predator feeding on an active prey that can occupy three-dimensional space in the water column. ...
Full-text available
Environmental temperature and body size are two prominent drivers of predation. Despite the ample evidence of their independent effects, the combined impact of temperature and predator-prey body size ratio on the strength and stability of trophic interactions is not fully understood. We experimentally tested how water temperature alters the functional response and population stability of dragonfly nymphs ( Cordulegaster boltonii ) feeding on freshwater amphipods ( Gammarus pulex ) across a gradient of their body size ratios. Attack coefficients were highest for small predators feeding on small prey at low temperatures, but shifted toward the largest predators feeding on larger prey in warmer environments. Handling time appeared to decrease with increasing predator and prey body size in the cold environment, but increase at higher temperatures. These findings indicate interactive effects of temperature and body size on functional responses. There was also a negative effect of warming on the stability of predator and prey populations, but this was counteracted by a larger predator-prey body size ratio at higher temperatures. Here, a greater Hill exponent reduced feeding at low prey densities when predators were much larger than their prey, enhancing the persistence of both predator and prey populations in the warmer environment. These experimental findings provide new mechanistic insights into the destabilizing effect of warming on trophic interactions and the key role of predator-prey body size ratios in mitigating these effects.
Understanding and predicting species diversity in ecological communities is one of the great challenges in community ecology. Popular recent theory contends that the traits of species are "neutral" or unimportant to coexistence, yet abundant experimental evidence suggests that multiple species are able to coexist on the same limiting resource precisely because they differ in key traits, such as body size, diet, and resource demand. This book presents a new theory of coexistence that incorporates two important aspects of biodiversity in nature--scale and spatial variation in the supply of limiting resources.Introducing an innovative model that uses fractal geometry to describe the complex physical structure of nature, Mark Ritchie shows how species traits, particularly body size, lead to spatial patterns of resource use that allow species to coexist. He explains how this criterion for coexistence can be converted into a "rule" for how many species can be "packed" into an environment given the supply of resources and their spatial variability. He then demonstrates how this rule can be used to predict a range of patterns in ecological communities, such as body-size distributions, species-abundance distributions, and species-area relations. Ritchie illustrates how the predictions closely match data from many real communities, including those of mammalian herbivores, grasshoppers, dung beetles, and birds.This book offers a compelling alternative to "neutral" theory in community ecology, one that helps us better understand patterns of biodiversity across the Earth.
How can geckoes walk on the ceiling and basilisk lizards run over water? What are the aerodynamic effects that enable small insects to fly? What are the relative merits of squids' jet-propelled swimming and fishes' tail-powered swimming? Why do horses change gait as they increase speed? What determines our own vertical leap? Recent technical advances have greatly increased researchers' ability to answer these questions with certainty and in detail. This text provides an up-to-date overview of how animals run, walk, jump, crawl, swim, soar, hover, and fly. Excluding only the tiny creatures that use cilia, it covers all animals that power their movements with muscle--from roundworms to whales, clams to elephants, and gnats to albatrosses. The introduction sets out the general rules governing all modes of animal locomotion and considers the performance criteria--such as speed, endurance, and economy--that have shaped their selection. It introduces energetics and optimality as basic principles. The text then tackles each of the major modes by which animals move on land, in water, and through air. It explains the mechanisms involved and the physical and biological forces shaping those mechanisms, paying particular attention to energy costs. Focusing on general principles but extensively discussing a wide variety of individual cases, this is a superb synthesis of current knowledge about animal locomotion. It will be enormously useful to advanced undergraduates, graduate students, and a range of professional biologists, physicists, and engineers.
Question: Can we develop simple allometric relationships based on predator and prey body size to more easily parameterize optimal foraging models and thereby make them more useful to community ecologists interested in studying species interactions? Model: The rate at which a predator encounters its prey is often the most difficult parameter to estimate in any foraging model. We develop a simple geometric model to predict prey encounter rates as a function of predator mass, prey mass, and prey density using allometric relationships between predator search velocity and vision as a function of body size. Empirical test: We suggest that the model has both strategic and tactical uses. Tests geared towards both uses are performed and these tests validate the model within the limits of existing data. Conclusions: It appears possible to parameterize optimal foraging models through easily measured variables such as body size. This provides hope that Lotka-Voltera style community matrix models could be replaced with more mechanistic models based on optimal foraging that are easy to parameterize for an entire community. If so, this research agenda holds promise for developing the link between foraging models and species interactions that the original inventors of optimal foraging theory envisioned.
The size structure of aquatic communities is generally measured using size spectra, an approach which is tedious or inapplicable in benthic and terrestrial communities. This has inhibited comparison of size structure of aquatic and terrestrial communities. This study uses an approach more common among terrestrial ecologists to develop a general density-body size relationship for lacustrine communities, based on mean annual population densities for dominant species of phytoplankton, zooplankton, zoobenthos and fish measured in 18 lakes worldwide. Overall, mean annual population density (D, individuals m-2) decreases log-linearly with increasing species body size (M, μg fresh mass) as D = 4 x 105 · M-0.89 (n = 280, r2 = 0.92), although the exponent appeared smaller (-0.55 ± 0.04) within broad taxonomic groups (algae, invertebrates). We found that density-body size relationships for dominant species are quantitatively similar to size spectra, a pattern which suggests that density-body size relationships may provide an interesting alternative to size spectra for the prediction of ecosystem processes. These relationships also suggest that aquatic species reach, on average, 6-60 times higher densities than terrestrial species, depending on their body size and on their thermoregulatory system (ectotherms vs endotherms). The implications of these differences in size structure for size-related patterns of energy use and other processes depend on which physiological groups (unicells, ectotherms, endotherms) are being compared.
SUMMARY Carbon stocks and flows give a picture of marine and continental biotas different from that based on food webs. Measured per unit of volun1e or per unit: of surface area, biomass is thousands to hundreds of thousands of times more dilute in the oceans than on the continents. The number of described species is lower for the oceans than for the continents. One might expect that each species of organism would therefore feed on or be consumed by fewer other species in the oceans than on the continents. Yet in reported food webs, the average oceanic species interacts trophically with more other species than the average terrestrial or aquatic species. Carbon turnover times imply that the mean adult body length of oceanic organisms is 240 to 730 times shorter than that of continental organisms. By contrast, in reported food webs, marine anirnal predators are larger than continental animal predators, and marine animal prey are larger than continental animal prey, by as much as one to two orders of magnitude. Estimates of net primary productivity (NPP) per unit of surface area or per unit of occupied volume indicate that the oceans are several to hundreds of times less productive than the continents, on average. If NPP limited mean chain length in food webs, oceanic food chains should be shorter than continental chains. Yet average chain lengths reported in published food webs are longer in oceans than on land or in fresh water. In reconciling these unexpected contrasts, the challenge is to determine which (if any) of the many plausible explanations is or are correct.
The Late Cretaceous Oldman Formation comprises sediments that were deposited along the margin of a great inland sea that covered much of the western interior of North America. The environment of deposition appears to have been tracts of fluvial marshes that separated "islands" of higher, drier ground. The climate was probably warm-temperate, and it is suggested that upland plant communities were parkland-like in aspect. The large dinosaurs of this community comprised animals that were between a hippopotamus and a large African elephant in adult weight. Some workers have suggested that dinosaurs had metabolic rates comparable to those of living birds or mammals. By extrapolating from the food consumption rates of these living endotherms it is possible to obtain crude estimates of the ingestion rates of endothermic dinosaurs. Similar extrapolations from the ingestion rates of living reptiles and amphibians provide estimates of the ingestion rates of ectothermic dinosaurs. By deriving an empirical equation relating the ratio of annual secondary productivity/average annual biomass to adult weight in living mammals, and employing estimates of adult weight and biomass for the herbivorous dinosaur populations, it is possible to estimate the annual secondary production of endothermic Oldman herbivorous dinosaurs. If the body weight vs. production/biomass relation derived for mammals can be applied to ectothermic tetrapods, it is possible to estimate annual secondary production of ectothermic dinosaur populations. These calculations suggest that the annual secondary production of endothermic herbivorous dinosaurs would have been insufficient to meet the food requirements of an endothermic carnivorous dinosaur population as large as is preserved in the Oldman Formation. However, ectothermic carnivorous dinosaurs would have been easily able to make energetic ends meet. Unfortunately, the situation is complicated by the possibility that carnivores are overrepresented in collection from the Oldman. Because of this, I cannot presently decide between ectothermy and endothermy in dinosaurs on the basis of methods presented in this paper. Alternative methods that may be more successful in this regard are discussed. It is hoped that as paleontologists collect fossils from an ecological point of view the methods presented in this paper can be employed to make realistic statements about the trophic dynamics of ancient vertebrate communities.