Ecology, 85(5), 2004, pp. 1203–1216
q 2004 by the Ecological Society of America
ORGANISMAL STOICHIOMETRY: QUANTIFYING NON-INDEPENDENCE
AMONG FOOD COMPONENTS
DAVID RAUBENHEIMER1,3
AND
STEPHEN J. SIMPSON1,2
1Department of Zoology, University of Oxford, South Parks Road, Oxford OX1 3PS, UK
University Museum of Natural History, University of Oxford, South Parks Road, Oxford OX1 3PS, UK
2
Abstract. Ecological stoichiometry represents an important innovation in ecological
modeling, both in its recognition of the causal role of species-specific regulatory physiology
in high-level ecological processes and in its adoption of multiple-substance models. In this
paper we provide an overview of a geometrical approach for studying the exchange of
nutrients between individual organisms and their environment that, although developed
independently, shares much in common with ecological stoichiometry and might, we believe,
contribute to its further development. In particular, the framework focuses on identifying
food components that interact in their effects on organismal nutrition, and quantifying the
consequences of these interactions for ingestive regulation, post-ingestive processing, and
animal performance. We illustrate our approach using data for terrestrial herbivores (insects)
and discuss the potential relevance of these data for models of ecological processes.
Key words: ecological stoichiometry; locust feeding; macronutrient excess; nutrient balance;
nutrient budgets.
INTRODUCTION
Manuscript received 26 April 2002; revised 4 June 2003; accepted 27 July 2003; final version received 27 August 2003. Corresponding Editor: R. M. Nisbet. For reprints of this Special Feature, see footnote 1, p. 1177.
3 Present address: School of Biological Sciences and Psychology Department, University of Auckland, Private Bag
92019, Auckland, New Zealand. E-mail: d.raubenheimer@
auckland.ac.nz
inance over the past several decades in terrestrial foraging theory of behavioral ecology and its emphasis
on normative models concerned with fitness outcomes
for individual organisms (Stephens and Krebs 1986),
in contrast with the more proximal, mass-balance considerations of energy and nutrient flow. Further, normative models of foraging have tended to assume as a
proxy for fitness the gains achieved by animals of a
single resource (usually energy or nitrogen), considering others only insofar as they impose constraints on
the levels of these gains. In this they have mirrored
conventional ecological models in their preoccupation
with energy flow (Reiners 1986), and provided little
incentive to measure nutritional processes in the broader context of multiple nutritional components.
Since Koehl’s (1989:49) exhortation that more studies are done of terrestrial organisms that deal with ‘‘detailed questions of nutrition . . . .. rather than simple
caloric intake,’’ several studies have demonstrated the
importance of the interactions among different nutrient
groups in influencing food selection and/or performance in terrestrial organisms (e.g., Waldbauer and
Friedman 1991, Ackroff 1992, Dearing and Schall
1992, Uetz et al. 1992, de Vries and Schippers 1994,
Joern and Behmer 1997, Eubanks and Denno 1999,
Evans et al. 1999, Cook et al. 2000). The phenomenological and mechanistic details of these interactions
have, by contrast, been systematically studied in very
few organisms.
In an attempt to better understand the interactive
effects of food components on animals, we have over
the past decade developed a geometrical framework
(henceforth ‘‘GF’’) for conceptualizing in more than
one dimension nutrient exchanges between organisms
and their environment (Raubenheimer and Simpson
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Special Feature
There is growing recognition that models of highlevel ecological processes, such as ecosystems, communities, and populations, may benefit from incorporating information about the behavior and physiology
of individual organisms (e.g., Roughgarden et al. 1989,
Hunter et al. 1992, Cappuccino and Price 1995, Jones
and Lawton 1995, Sutherland 1996). In this regard, an
important advance represented by ecological stoichiometry (henceforth ‘‘ES’’) is its overt recognition that
the basic causal unit in ecological processes is speciesspecific regulatory physiology, in contrast with the
coarser-grained trophic-level analyses. Added to this
emphasis on the mechanisms of ecological processes,
a second key innovation provided by ES is its replacement of the conventional univariate (mainly energy)
models of ecosystem exchanges with a multivariate approach that recognizes several nutrient dimensions as
well as energy (Reiners 1986, Sterner and Hessen
1994).
The mechanistic, multidimensional approach of ES
has been successfully applied to aquatic plankton communities (e.g., Sterner 1990, Makulla and Sommer
1993, Sterner and Hessen 1994, Hassett et al. 1997,
Elser et al. 1998, Anderson and Pond 2000), but has
received far less attention among terrestrial biologists
(Elser 2000). This is partly a consequence of the dom-
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DAVID RAUBENHEIMER AND STEPHEN J. SIMPSON
1993, 1994, 1997, 1998, 1999, Simpson and Raubenheimer 1993, 1995, 1996, 2000). Although independently derived, and developed primarily to explore
within an evolutionary context the relationships between individuals and their environment rather than the
high-level ecological consequences of this, GF has several key elements in common with ES. First, a keystone
concept is the nutrient budget (Raubenheimer and
Simpson 1994, 1995), which, like ES, applies the constraints of mass balance to understand the flow of matter and energy between organisms and their environment. Second, in common with ES our approach is
concerned both with individual food components and
the interactions that take place among these. Third, we
emphasize the importance of mechanism as well as
outcome (Simpson et al. 1995a, Simpson and Raubenheimer 2000), and in this find a close parallel with the
emphasis in ES on individual-level regulation of ecological processes. Our approach differs from ES, however, in placing greater emphasis on the absolute
amounts of nutrients consumed, retained, and excreted
by animals, as opposed to their proportional concentrations in foods (supply ratios) and consumers (demand ratios).
Here we present a selective review of GF. One aim
in doing so is to suggest a formal means for studying
the nutrient–organism interactions with which ES is
concerned, particularly as regards the overall theme of
this volume, the manner in which food components
impose constraints on the mass-balance dynamics of
other food components. We illustrate the approach using data on the relationships among intake, retention,
and recycling of carbon- and nitrogen-based nutrients
for two species of terrestrial herbivores, which we hope
will complement the studies of mass-balance analyses
of aquatic consumers presented elsewhere in this special feature (e.g., Anderson et al. 2004). Whereas ES
has to date been concerned mainly with elements and
micronutrients (Anderson and Pond 2000), our interest
in the evolution of behavioral and physiological regulatory phenomena has led us to think primarily in
terms of higher-level molecular complexes such as amino acids and carbohydrates, because it is most frequently to these that evolved regulatory mechanisms
have access. GF is, however, equally applicable to elemental analyses, but we have chosen in the present
paper to express our data in terms of macronutrients,
thereby (together with Anderson et al. 2004) introducing another level of organization towards Elser et al.’s
(2000) goal of a generalized ‘‘biological stoichiometry.’’
FROM NUTRIENT BUDGETS TO
GEOMETRICAL ANALYSIS
Quantitative investigations of the exchange of compounds between individual organisms and their environment involve, implicitly or explicitly, the derivation
of nutrient (and/or energy) budgets. The use of these
Ecology, Vol. 85, No. 5
is very widespread in the literature on the nutritional
ecology of terrestrial organisms. Our geometrical
framework (GF) is, at base, an elaboration of nutrient
budgets; here we reflect briefly on the relationships
between conventional nutrient budgets, GF, and ecological stoichiometry (ES).
At their simplest, nutrient/energy budgets comprise
an equation that relates intake to the post-ingestive fate
of the ingesta, the latter usually partitioned into two or
more compartments (Raubenheimer and Simpson
1995). The variables of interest in nutrient budgets
might be either food as a whole (‘‘unitary budgets’’)
or, more usefully, individual components of foods
(‘‘discriminatory budgets’’). In common with ES, GF
models unify unitary and discriminatory approaches,
through representing foods by their nutrient composition. Also in common with ES, GF does so with reference to two or more nutrients simultaneously. A useful device for tracking multiple food components in
this way is the ‘‘nutritional matrix,’’ in which relevant
nutrients appear as row headings and compartments as
column headings (Raubenheimer and Simpson 1995).
In contrast with constructing an independent nutrient
budget for each component, a nutritional matrix enables
the interactions among food components (e.g., interconversions among nutrient groups) to be quantified.
The quantitative study of nutrition is essentially concerned with the relationships among different compartments in nutrient budgets (for example, between
ingested nutrient and that allocated to growth, nutrient
absorbed vs. excreted, etc.). Most commonly, these are
expressed in the form of ratio indices where quantities
in one compartment (e.g., growth) are standardized for
those in another (e.g., consumption) (Waldbauer 1968).
A major problem with these indices is that they conceal
(or distort) many of the interesting biological details
that should be the goal of such studies (Raubenheimer
and Simpson 1992, Raubenheimer 1995). As an alternative, GF uses graphical analysis to quantify the relationships among (1) different food components and
(2) various budgetary compartments (intake, growth,
excretion, etc.) (Raubenheimer and Simpson 1994,
1995). While ES does not use ratios to express relationships among budgetary compartments, the elemental composition of foods and consumers are expressed
as proportions. This has some potential limitations, to
which we will return in the final section.
Nutrient budgets are most usually constructed as
simple mass-balance equations, where intake is partitioned into ‘‘retained’’ (as growth, storage etc.) and
‘‘dissociated’’ (respired, lost in the feces, etc.) components. This approach finds a very close parallel in
ES, which views the act of consumption as a ‘‘complex
chemical reaction involving reactants (resources) and
products (consumer biomass and wastes)’’ (Sterner
1995:241). GF, by contrast, emphasizes evolutionary
considerations, and so attempts to partition intake into
that which is ‘‘utilized’’ (for fitness gains) and that
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STOICHIOMETRIC ECOLOGY
BRIEF OVERVIEW OF THE GEOMETRICAL
FRAMEWORK
In our geometrical framework (GF) an organism’s
nutritional relations are modeled as an n-dimensional
nutrient space, where each dimension represents a nutrient. An animal’s current nutritional state with respect
to the ingestion of relevant nutrients can be described
as a point within the nutrient space, as can the state
that would maximize fitness (this ideal state being
termed the ‘‘intake target’’). Intake targets are not static
but move with, inter alia, levels of activity, growth,
and the reproductive status of an individual (Raubenheimer and Simpson 1997).
Foods are represented as linear trajectories that pass
from the origin through nutrient space at an angle determined by the balance of the nutrients they contain
(‘‘nutritional rails’’). By eating, the animal changes its
current nutritional state along a vector coincident with
the rail representing the chosen food. One behavioral
challenge for a consumer is to select a food whose rail
passes through the intake target (i.e., a nutritionally
balanced food), so enabling it to reduce to zero any
discrepancy between current state and optimal state. A
nutritionally imbalanced food, by contrast, does not
enable the animal to satisfy its optimal requirements
for all nutrients simultaneously, but forces it into a
compromise between over-ingesting some nutrients
and under-ingesting others. The animal can nonetheless
benefit from a nutritionally imbalanced food by mixing
its intake from this with a food containing a complementary imbalance of nutrients (i.e., one whose rail
falls on the opposite side in nutrient space of the intake
target). In this case, the excess nutrient ingested from
the one food can be used to redress the deficits incurred
on the other and vice versa.
When neither nutritionally balanced nor complementary foods are available the animal cannot balance
its nutrient intake, but can nonetheless utilize the imbalanced food by selectively excreting ingested excesses. However, if the degree of imbalance exceeds
the capacity of the animal to void the excesses, then it
is constrained to accept surpluses of some nutrients
and/or deficits of others. The challenge in this case is
to arrive at a balance between over- and under-ingestion
that minimizes the costs of this predicament. To the
extent that imbalanced foods are a feature of the nutritional environments of animals, it might be expected
that the balance of excesses and deficits aimed at is a
variable that is itself subject to natural selection and
therefore deserves attention in attempts to understand
the manner in which evolution shapes nutritional regulatory systems.
GF thus provides a means of analyzing, and comparing among organisms, multi-factor metrics of nutrient requirements, of the relative values of foods in
relation to these requirements, and of higher-order responses of animals when ecologically constrained from
feeding on nutritionally optimal foods. In the sections
that follow we present data illustrating the application
of this approach.
UNCONSTRAINED REGULATION:
THE I NTAKE
TARGET
In common with ecological stoichiometry (ES), the
geometrical framework (GF) places strong emphasis
on active (homeostatic) regulation. A starting point is
usually to establish in the relevant nutrient space the
equilibrium point towards which the unconstrained regulatory mechanisms will tend, this providing an estimate of the position of the intake target. One way of
identifying this point is to present to the animal two
complementary foods from which it can self-compose
the preferred diet. While suggestive, the outcome of
such an experiment does not necessarily represent homeostatic regulation. For example, in a protein–carbohydrate nutrient space, if an animal distributed its
feeding randomly between a food containing 14% protein 1 28% digestible carbohydrate (food 14:28) and
Special Feature
which is ingested in excess of requirements, and so
‘‘wasted’’ (Raubenheimer and Simpson 1994, 1995).
This distinction between mass-balance and evolutionary categorizations in constructing nutrient budgets
is not merely semantic, but draws on fundamentally
different ways of viewing nutrition. Specifically, in
mass-balance budgets it is usually straightforward to
decide whether an ingested component belongs in the
‘‘retained’’ or the ‘‘dissociated’’ compartments. The
evolutionary approach introduces an additional reference point that is needed to determine whether a given
quantum of ingested nutrient is ‘‘utilized’’ (enhances
fitness) or is excessive and thus costly—this being a
measure of the animal’s optimal requirements for the
nutrient in question.
A central component of GF is thus the explicit consideration within a model of the nutritionally optimal
state an animal can achieve with respect to one or more
nutrients. In this, GF shares common ground with the
normative models of behavioral ecology. It differs,
however, in characterizing nutritional requirements as
an optimum, which is a more general case than the usual
practice in normative models where the ‘‘goal function’’ of animals is taken to be the maximization of
intake of one component or another (subject to stipulated constraints imposed by, inter-alia, other food
components) (Stephens and Krebs 1986). While maximization might well in some circumstances correspond
with optimization, there are no a priori grounds for
assuming that this should always (or even mostly) be
the case. Indeed, there is strong evidence that within
ecologically relevant ranges vertebrates and invertebrates alike regulate intake so as to avoid deficits and
excesses of macronutrients (Raubenheimer and Simpson 1997), and that animals forced to do otherwise
incur performance costs (S. J. Simpson, R. M. Sibly,
K.-P. Lee, and D. Raubenheimer, unpublished manuscript; see also Fig. 2).
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DAVID RAUBENHEIMER AND STEPHEN J. SIMPSON
Ecology, Vol. 85, No. 5
FIG. 1. Two experiments demonstrating defense by Locusta migratoria of a point of food intake in a protein–carbohydrate
nutrient space. In each case the open squares indicate the expected outcome if there were no homeostatic regulation. Error bars
represent 6 1 SE around bivariate means. (a) Locusts given one of four food combinations (%protein : %carbohydrate 5 14:28
or 7:14 and 28:14 or 14:7) reached the same point in nutrient space by altering the relative amounts eaten of the two foods
(data from Chambers et al. [1995]). (b) Locusts were provided with a single food containing a 1:1 mix of protein : carbohydrate,
but diluted over a fivefold range using cellulose (foods were 7:7, 14:14, 21:21, 28:28, or 35:35 [%protein : %carbohydrate]).
They adjusted the amounts of food eaten in order to achieve the same point of nutrient intake. (Data are from Raubenheimer
and Simpson [1993].)
a second food 28:14, it would on average end up midway between the rails representing the two foods, giving the false impression that it had regulated homeostatically. To definitively identify active regulation, animals are therefore challenged to ‘‘defend’’ the selected
point (Simpson and Raubenheimer 1995). This is
achieved by comparing the outcomes for two or more
experimental groups of animals given different food
treatments, so that failure to regulate would result in
a different average intake point for each group. If, despite the different food treatments, all groups converge
on a single point in nutrient space, this suggests that
the animals altered their feeding behavior in order to
defend a nutritional outcome—i.e., that active regulation occurred.
Results of such an experiment are presented in Fig. 1a.
Here four groups of 10 African migratory locusts (Locusta
migratoria) were each given a pair of protein : carbohydrate complementary foods over the first five days of
the fifth larval stadium. One, the other, both, or neither
of the foods in each pairing was diluted by 50% using
indigestible cellulose. The squares represent the outcome for each group if there was no homeostatic regulation. That all groups ended up at statistically the
same point indicates that this point is the target of the
regulatory mechanisms, providing strong evidence that
the selected ratio represents a balanced diet with respect to these nutrients (see also discussion of performance consequences, below). Fig. 1b demonstrates another context in which locusts defend a point in pro-
tein–carbohydrate nutrient space. Each group of insects
was given a single food containing a near-balanced
proportion of protein and carbohydrate, but diluted
over a fivefold range. That all groups reached statistically the same point in the nutrient space again demonstrates defense of that point. In this case, the strength
of homeostatic regulation is vividly illustrated by the
fact that in order to converge in this way, animals given
food 7:7 ingested five times as much food as those
given food 35:35. Other illustrations of target defense
include regulation in the face of different frequencies
(Behmer et al. 2001) or spacing (Behmer et al. 2003)
of complementary foods in the environment, as well
as compensation for a prior period of nutritional imbalance (D. Raubenheimer and S. A. Jones, unpublished manuscript).
Experiments such as these provide a quantitative description of regulatory targets in animal nutrition. From
an evolutionary viewpoint, these descriptions give rise
to interesting questions about the functional significance of the selected point: Why should locusts work
so hard (e.g., increase fivefold the volume of food processed) to defend a particular point in nutrient space,
rather than some other point to which they also had
access? Such questions can be addressed by comparing
the performance of animals allowed to reach the preferred point with those given foods or food combinations that confine them to other areas in the nutrient
space. Fig. 2, for example, compares survival, development rate, and resistance to starvation of locusts al-
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STOICHIOMETRIC ECOLOGY
1207
CONSTRAINED REGULATION: BALANCING
NUTRITIONAL EXCESSES AND DEFICITS
FIG. 2. Relationship between performance and the protein : carbohydrate ratio of synthetic foods (food rail) fed to
Locusta migratoria throughout the fifth larval stadium. The
solid vertical line represents the self-selected diet, and the
dashed horizontal line the value for performance measures
achieved by animals on that diet. (a) The proportion of locusts
surviving through the stadium. (b) The rate of development
from the beginning of the fifth stadium to the subsequent molt
(i.e., into adults). (c) The time to death by starvation for adults
that had been raised on one of the experimental foods and
then deprived of food from the molt into adulthood. (Modified
from Raubenheimer and Simpson [1997].)
lowed to select an intake point with those confined to
nutritionally imbalanced foods. Survival was low on
excess-protein foods, peaked at the target food, then
decreased as carbohydrates became excessive. Interestingly, development rate was highest on excess-protein foods, and decreased with increasing carbohydrate,
suggesting that the self-selecting animals could have
achieved more rapid development had they composed
a diet richer in protein. A probable reason that they did
not is that faster development would come at the cost
of increased mortality (Fig. 2a) and decreased resistance to starvation (Fig. 2c).
FIG. 3. Intake arrays for the first three days of the fifth
larval stadium of Locusta migratoria and Schistocerca gregaria. Dashed lines radiating from the origin are food rails,
depicting the protein : carbohydrate ratio of the foods. Data
are means 6 1 SE. The two points with bi-directional error bars
represent the self-selected intake point of animals given complementary foods of 7:35 and 35:7 (%protein : %carbohydrate).
Error bars for animals given a single food type are not bidirectional, as these were constrained to vary along the food
rails. (Modified from Raubenheimer and Simpson [2003].)
Special Feature
As illustrated above, locusts show an impressive capacity to regulate intake so as to achieve an adaptive
nutritional outcome when feeding on nutritionally balanced (Fig. 1b) or complementary (Fig. 1a) foods.
Knowing the position of this target point provides a
basis for making predictions about consumption in ecological circumstances where balanced and/or complementary foods are available, but suggests little about
how a consumer will behave where there is a mismatch
between the composition of available foods and intake
requirements. The intake target is not accessible to an
animal in this predicament, and its regulatory challenge
is to achieve a balance of nutritional excesses and deficits that maximizes the fitness gains from available
foods. In this and the following section we illustrate
how the geometrical framework (GF) explores this aspect of homeostatic regulation, a subject that has hitherto received very little empirical or theoretical attention.
Fig. 3 shows the outcome of an experiment in which
two species of locusts were provided over the first three
days of the fifth larval stadium either with complementary foods (and so able to compose a balanced diet)
or one of a range of foods imbalanced with respect to
protein and carbohydrate (Raubenheimer and Simpson
Special Feature
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DAVID RAUBENHEIMER AND STEPHEN J. SIMPSON
2003). The one species (Locusta migratoria) is a grassfeeding specialist, and the other (Schistocerca gregaria) a generalist that feeds on both grasses and forbs.
The position of the intake targets for the two species
was statistically indistinguishable, but the shapes of the
intake arrays on imbalanced foods differed, with that
for the grass specialist being more arc shaped and the
generalist more linear.
These data show that although the two species of
locusts have similar intake requirements over the measurement period, they responded differently to the excesses and deficits of nutrients (i.e., nutritional ‘‘errors’’) incurred when confined to imbalanced foods.
Specifically, on the excess-protein foods the generalist
ingested a greater surplus of protein (relative to the
intake target) compared with the grass-feeding species.
An interesting possibility is that the tendency of generalist feeders to ingest greater excesses of surplus nutrient compared with specialists is more widespread.
One reason for expecting so is that their broader host
range compared with specialists means that there is a
relatively higher probability that a generalist who has
ingested an excess of a nutrient will subsequently encounter a complementary food, so enabling it to redress
the imbalance (Raubenheimer and Simpson 1999,
2003, Simpson et al. 2002). This would render useable
the initial excess, and also supplement the deficient
nutrient in the second food. Ideally, this hypothesis
would be tested in a formal comparative analysis (Harvey and Pagel 1991), seeking statistical association between generalist vs. specialist feeding and linear vs.
arc-shaped intake arrays. Unfortunately relevant data
have not been collected for nearly enough species to
perform such an analysis.
Nonetheless, a recent comparison of a generalist- and
a specialist-feeding species of caterpillar yielded the
same outcome as observed in the two species of locusts
(Lee et al. 2002, 2003). We have also tested this in
another context, by capitalizing on an interesting peculiarity of locust biology. If S. gregaria is reared at
high population densities they develop into form gregaria, which are generalist feeders (and from which
the data in Fig. 3 were collected). By contrast, those
reared at low population densities have a very different
developmental trajectory, producing locusts that are
less mobile and so likely in the field to encounter a
narrower range of host plants (Simpson et al. 1999).
This provides a comparison of two groups that are genetically the same, but differ in the likelihood of encountering a broad range of plants upon which to feed.
As predicted, the specialist-feeding solitarious form
produced an arc-shaped intake array, compared with
the more-linear array of the generalist morph (Simpson
et al. 2002).
FILTERING NUTRIENT GAINS: SELECTIVE RETENTION
OF INGESTA
The foregoing demonstrates that locusts are not passive recipients of nutrient supply ratios, but active par-
Ecology, Vol. 85, No. 5
ticipants in minimizing the discrepancy between the
composition of available foods in the environment and
preferred intake. Ingestive gains are, however, not an
end in their own right, but a means of satisfying the
tissue-level demands for growth, energy metabolism,
reproduction, etc. In the present context there are two
potentially important implications of this distinction
between ingestive requirements and tissue-level demand. First, limitations on the maximum efficiency of
nutrient processing might impose the requirement on
animals that they ingest more of a nutrient than is required by the tissues; ultimately, the ingested excess
will appear as recycled nutrient in the environment (see
also Anderson et al. 2004). Second, where the nutrient
content of available foods is not optimal, the physiological processes intervening between intake and allocation of nutrients to the tissues (digestion, absorption, excretion, etc.) provide a second node of control,
which supplements the role of ingestive regulation in
minimizing the discrepancy between nutrient supply
ratios and tissue-level demand. These variables, maximal processing efficiency and regulated processing efficiency, are both key individual-level parameters that
influence the quantitative dynamics of element flow
through ecosystems. In this section we present some
data illustrating how they have been investigated within
our system.
By representing together with intake in a single plot
the various post-ingestive compartments to which ingested nutrients are allocated, direct links can be made
between such interrelated components as optimal intake, realized intake, tissue-level demands, and nutrient
excretion. In Fig. 4, for example, growth derived from
protein and carbohydrate is plotted together with intake
across the fifth stadium for Locusta migratoria given
either complementary foods or 1 of 19 foods differing
in the protein : carbohydrate balance. The arc-shaped
array seen for this species over the first three days of
the fifth stadium (Fig. 3) is still visible for the more
central foods, but intake points on the more-extreme
foods have moved out of the arc as a consequence of
the animals on these foods having extended stadium
duration and so continuing to feed for several days
longer than those on more-balanced foods (Raubenheimer and Simpson 1993). The intake and growth
points achieved by locusts that were allowed to compose their own, balanced diet (represented in the figure
by squares with standard errors) provide estimates of
the targets for intake and growth, respectively.
A notable aspect of these data is the extent to which
growth points of animals fed imbalanced foods clustered tightly around the growth target (excepting the
extreme imbalanced foods, which are further discussed
below), despite the wide range of nutrient intakes. This
demonstrates that these animals have a well-developed
capacity to eliminate excess ingested nutrient. Gravimetric and physiological studies have established that
for proteins this is achieved by de-amination of amino
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acids and excretion in the feces of the nitrogen residues
(Zanotto et al. 1993), while excess carbohydrates are
metabolized and the carbon skeletons voided as carbon
dioxide in respiration (Zanotto et al. 1997).
The parameters of such post-ingestive regulation can
be investigated directly using bivariate plots relating
the intake of a nutrient to the quantity excreted (Raubenheimer and Simpson 1994). Fig. 5, for example,
shows this relationship for nitrogen in the experiment
with Locusta. Also represented is the N-coordinate of
the intake target (i.e., the amount ingested by animals
given free reign to compose a diet of their choice).
There are two clear phases in the relationship, with the
transition point coinciding with the target level of intake: at sub-target intakes the retention efficiency was
high, but incomplete (slope 5 0.46, 95% CI: 0.25–
0.69), while any excess ingested over and above the
target level was excreted with near 100% efficiency
(slope 5 0.92, 95% CI: 0.86–0.98). In Fig. 4, the effectiveness of this regulation can be seen in the extent
to which the growth points aligned on the x-axis.
By comparison with nitrogen, body composition was
more sensitive to excesses and deficits of carbohydrate
in the diet, as can be seen by the spread of growth
points along the y-axis of Fig. 4. Assuming that this
represents a limitation in the physiological regulatory
capability of the specialist-feeding L. migratoria, we
postulated that generalist feeders, which have an evolutionary history of dealing with heterogeneous foods,
might more effectively maintain body composition in
these circumstances. To test this we performed a separate experiment in which the body composition of L.
migratoria was compared with the generalist Schistocerca gregaria across a range of foods differing in
protein : carbohydrate balance (Raubenheimer and
Simpson 2003). Results were as predicted, with the
generalist maintaining body composition more effectively in the face of nutritional imbalance than the grass
specialist (Fig. 6). On excess-carbohydrate foods, both
species accumulated high levels of body lipids, but on
carbohydrate-deficient foods the generalist maintained
body composition much more effectively than did the
grass specialist. Data for the most extreme food (42:0)
suggest that this was achieved by extracting carbon
from excess ingested protein, since animals fed this
food had no dietary source of carbohydrate and only
trace levels of essential fatty acids, and yet maintained
body lipid content.
This comparison provides an interesting link with
the difference in the shapes of the intake arrays for the
two species (Fig. 3). Above we suggested an ecological
explanation for this difference: generalists are more
likely than specialists to encounter complementary
foods that redress any imbalance in current nutritional
state. The ability of the generalist S. gregaria to channel excess ingested amino acids into carbohydrate metabolism provides an additional, physiological, explanation. By de-aminating the excess of these molecules,
FIG. 5. Relationship between N ingested and N excreted
by locusts fed one of a range of foods differing in the ratio
by protein : digestible carbohydrate. Data for animals allowed
to self-select their diet are presented as an open square. Separate lines are fitted using least-squares regression separately
for intakes less than and greater than the self-selected value.
Special Feature
FIG. 4. Intake and growth points across the fifth stadium
of Locusta migratoria fed one of a range of foods differing
in the protein : digestible-carbohydrate ratio. Open squares
with bi-directional error bars represent intake and growth
(mean 6 1 SE) for locusts allowed to self-select a diet from
foods at 35:7 and 7:35 (%protein : %carbohydrate). Three
groups of animals that differed in their growth response (a
central cluster of points, and unusually high and unusually
low carbohydrate-derived growth) are matched to intake
points using solid ovals, open triangles, and open inverted
triangles, respectively. (Data are from Raubenheimer and
Simpson [1993].)
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DAVID RAUBENHEIMER AND STEPHEN J. SIMPSON
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Ecology, Vol. 85, No. 5
Special Feature
HIGHER-LEVEL TROPHIC INTERACTIONS
FIG. 6. Lipid content (means and 1 SE ) of the carcasses
of Locusta migratoria and Schistocerca gregaria fed one of
a range of foods differing in the ratio of protein : digestible
carbohydrate, or allowed to self-select a diet from foods 7:35
and 35:7 (Target). Data are from Raubenheimer and Simpson
(2003).
the animals reduce the surplus in the blood and at the
same time produce carbon residues that ameliorate the
deficit of carbohydrate incurred by feeding on imbalanced foods (Raubenheimer and Simpson 2003).
INTERACTIONS
WITH
NON-NUTRIENTS
The geometrical framework (GF) has been used not
only to study interactive effects of nutrients on animals,
but also other compounds that are known to exert a
strong influence on food ingestion and utilization, including plant-produced allelochemicals. These non-nutrient substances are relevant to an important distinction in trophic ecology—that between resource abundance and resource availability (Schultz 1992). The
failure to make this distinction between ‘‘apparent’’
and ‘‘available’’ resources has, according to Schultz
(1992:175), ‘‘handicapped the development of powerful generalizations in population biology and community ecology for a long time.’’ Effects of allelochemicals on resource availability may, however, be
complex. We have found, for example, that the levels
per se of allelochemicals in foods may have relatively
little bearing on the foods’ ‘‘availability’’ to locusts,
since the effects of allelochemicals on ingestion and
utilization can be strongly dependent on the balance of
macronutrients in the foods (Raubenheimer 1992,
Simpson and Raubenheimer 2001a, Behmer et al.
2002). Similarly, indigestible bulk in the foods of caterpillars has been found to exert complex effects on
nutrient utilization, by interfering with post-ingestive
processes (Lee et al. 2003).
The data we have presented here are for primary
consumers. Our geometrical framework (GF) can, however, equally be used to investigate nutritional interactions across higher trophic levels—in which case the
body composition of herbivores is expressed as food
rails, and carnivores are the focus of nutritional experiments. While relevant experiments on carnivores
are presently underway, existing data do allow us to
model the nutritional environment in which a carnivore
feeding exclusively on the locusts in our experiment
would exist.
Fig. 7 shows a range of nutritional rails representing
the composition of synthetic foods fed to Locusta migratoria and Schistocerca gregaria through the fifth larval stadium, and the carcass composition of animals
reared on these foods. This is a remarkably wide range
of body compositions, considering that it encompasses
only a single life stage in only two insect species. Furthermore, it probably underrepresents the range of carcass compositions that would be available to a predator,
because the y-axis of the second plot is expressed as
milligrams of lipid (which is both the main form of
energy storage by insects, and also the primary energy
nutrient of insect predators), and, per unit of mass lipids
are approximately twice as energy rich as carbohydrates. Expressing both locust foods and carcass compositions as a relationship between protein and the caloric content of carbohydrates and lipid would increase
the spread of the rails in the second plot relative to the
first. Although similar data for field-collected prey species are needed, these results suggest the possibility
that it is not only herbivores that face the problem of
obtaining a balanced intake of nutrients from chemically diverse foods (Chivers and Langer 1994), and
possibly explain reports of carnivores performing better on mixed diets (Krebs and Avery 1984, Uetz et al.
1992) and possessing the ability to select a nutritionally
balanced diet (Greenstone 1979).
Such data are potentially relevant to an interesting
anomaly in terrestrial ecological research. Experimentally altering the nutritional status of plants using, for
example, fertilizers often results in altered performance
of individual insect herbivores. Effects on herbivore
populations are, however, much more varied, and
sometimes even go in the opposite direction to what
would be expected given the individual-level effects
(Kytö et al. 1996). Our data suggest that in addition to
influencing herbivore performance (Fig. 2), altering the
composition of their foods can affect their body composition. If this in turn had an impact on the performance of their predators, then any bottom-up effect
due to altered herbivore nutrition could be counterbalanced, or even outweighed, by top-down effects resulting from altered carnivore nutrition. A decrease in
plant nitrogen, for example, might impair the performance of individual herbivores, but also reduce the
STOICHIOMETRIC ECOLOGY
May 2004
1211
nutritional quality of their carcasses for carnivores and
hence reduce predator populations.
AMOUNTS
AND
PROPORTIONS—COMPARISON
MODELS
OF
As discussed in the Introduction, ecological stoichiometry (ES) and the geometrical-framework (GF)
share much in common. They differ, however, in some
important respects. In ES, foods and consumers alike
are represented primarily by their proportional composition of two elements (the demand and supply ratios) and the discrepancy between these provides the
basis for identifying limiting elements and predicting
recycling rates. In GF, foods are also represented as
proportions (the slope of nutritional rails), and body
composition can be similarly represented (e.g., Fig. 7).
However, GF also explicitly includes representation of
the animal consuming a food (moving along a nutritional rail), and in so doing it shifts from a proportion
(food composition) to amounts of the various nutrients
consumed. In addition, the optimal requirement of the
animal (the intake target) is included as a moving point,
which is likewise a bivariate amount. The relationship
between ingested amounts and required amounts is the
key variable in GF, which provides a powerful predictive basis for the animal’s behavioral and physiological
responses.
In Fig. 8a, for example, a hypothetical situation is
modeled in which an animal has access to a nutrition-
ally balanced food, i.e., one whose rail passes through
its carbon–phosphorus (C and P, respectively) intake
target. We would predict that, all else being equal, the
animal would select the food and feed until it reached
the target (point T), hence incurring neither a deficit
nor a surplus of either element. However, if it was only
able to reach point A (e.g., if the food was in short
supply), then it would suffer a P deficit of A P2 and a
C deficit of AC2. In contrast, if it increased its consumption beyond the target level to point B, then it
would suffer a carbon excess of BC1 and simultaneously
a phosphorus surplus of BP1. We would predict higher
rates of P and C recycling at point B, compared with
points A and T.
Although in most circumstances it seems unrealistic
to postulate that an animal would voluntarily exceed
its optimal intake of both nutrients (as at point B in
Fig. 8a), GF enables us to identify circumstances where
this might be expected. For example, if a third substance, say nitrogen (N), was present in the food at
suboptimal levels in relation to the other two, then
regulation for the limiting element might cause the animal to over-ingest the other two—in much the same
manner that locusts in our experiments over-ingested
carbohydrate in N-deficient foods (Fig. 3). This could
be shown schematically in a three-dimensional P–C–
N plot, or as a series of three two-dimensional plots
(P vs. C, P vs. N, N vs. C). Alternatively, where two
nutrients are present in a food in balanced proportions,
Special Feature
FIG. 7. Comparison of nutritional rails representing (a) the proportional composition of locust synthetic foods and (b)
the carcass composition of Locusta migratoria and Schistocerca gregaria locusts reared through the fifth larval stadium on
these foods. The y-axis variables differ for the two plots, because the primary dietary energy source for locusts is carbohydrates
(hence the y variables in panel a) while the energy storage product (and also the primary energy nutrient for many predators)
is lipid (b). In (a) the heavy solid line represents the composition of the self-selected diet for L. migratoria, while the dashed
line represents that for S. gregaria. In (b) the body compositions of L. migratoria and S. gregaria that self-selected their
diets are represented by the heavy solid and dashed lines, respectively. In (a) the thin solid lines represent the composition
of the nutritionally imbalanced food fed to both L. migratoria and S. gregaria, while in (b) the thin solid and dotted lines
represent the carcass compositions of L. migratoria and S. gregaria, respectively, fed these foods.
Special Feature
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DAVID RAUBENHEIMER AND STEPHEN J. SIMPSON
Ecology, Vol. 85, No. 5
FIG. 8. Hypothetical nutrient spaces including intake target (T), food rails, and realized ingestion (points A and B) of
nutrients by animals feeding on these foods. Nutrients (C, N, and P) are set as subscripts on points A and B, with ‘‘1’’
indicating excess consumption beyond the target level and ‘‘2’’ indicating a deficit. For further explanation see Amounts
and proportions—comparison of models.
they effectively constitute a single resource, since once
the animal has eaten enough of one so too has it eaten
enough of the other (Raubenheimer and Simpson
1999). In this case, the three-dimensional relationship
can be viewed in two dimensions, as a plot of P 1 C
vs. N (Fig. 8b). The figure shows that the food contains
excess P 1 C relative to N, and so its rail passes to
the left of the (P 1 C; N) intake target. If the animal
fed to point B, it would have a smaller N deficit (BN2)
relative to point A, but in so doing it would have ingested an excess of P 1 C (BPC1).
Note that the predictions derived from a simple comparison of demand and supply ratios need not necessarily accord with predictions based on analysis of
amounts ingested. In Fig. 8a, for example, points A
and B represent the same demand ratio–supply ratio
relationship, so a comparison on this basis would not
distinguish between them; by contrast, as stated above,
GF predicts different recycling rates at the two points.
Conversely, there are instances where a comparison of
demand and supply ratios might predict different degrees of recycling (different demand ratio–supply ratio
relationships), but GF would predict similar outcomes.
In Fig. 8c, for instance, point A is reached by feeding
on an optimal food where P/C supply ratio ø demand
ratio, and point B is reached by feeding on an imbalanced food where P/C supply ratio k demand ratio.
Here a comparison of demand and supply ratios would
predict greater recycling of P on the imbalanced food,
which contains a surplus of this element (although see
Boersma and Kreutzer [2002] for a discussion of the
complexities involved in this situation). However, this
is only a ‘‘surplus’’ in relation to the proportional balance of the optimal food, not in relation to the amounts
of the nutrients actually eaten. Consideration of
amounts eaten would lead to a different expectation:
there would be minimal recycling of both nutrients at
points A and B, because at neither point would the
animals have reached the required intake for the respective nutrients (AC2, AP2, BC2 and BP2 are all ,0).
DISCUSSION
Models of complex phenomena such as organisms
and ecosystems necessarily entail simplifications. A
common simplification in ecosystem analysis is to consider organisms to comprise a single substance such as
biomass or energy (Sterner 1995), and in behavioral
ecology the equivalent simplification is that patterns of
behavior and physiology can be understood primarily
with reference to a single resource. Although such single-substance simplifications are in some contexts useful, they are not warranted when the details of the composition of animals and their foods affect how they
locate, ingest, and process foods (Sterner 1995). In this
case models of multiple substances are preferable, such
as those developed in ES (ecological stoichiometry)
and GF.
One motivation in the development of GF has been
to determine the extent to which multiple resources
influence the nutritional biology and life histories of
consumers, and to explore the parameters of such effects. Data presented in this paper demonstrate that for
May 2004
STOICHIOMETRIC ECOLOGY
portant topic in their own right, and one of considerable
relevance to models of elemental flow through ecosystems.
In addition to differences in utilization efficiencies,
the two species of locusts differed in their ingestive
responses to nutritional imbalance, with the generalist
ingesting a larger surplus (relative to the intake target)
of protein than the specialist (Fig. 3). Other studies
indicate that this association between the levels of nutrient over-ingestion on imbalanced foods and breadth
of host range might be more general (Raubenheimer
and Simpson 2003), a prediction that accords with
Chapin’s (1980) hypothesis that plasticity in nutrient
use is itself a trait that is selected for or against in
different ecological circumstances. Whether or not this
particular instance stands up to further testing, it is
nonetheless relevant to ES that important parameters
of nutrient regulation might be predictable for groups
of species belonging to different ecological guilds, such
as generalists vs. specialists. It would add resolution
to existing generalizations, including the related observation that autotrophs tend to be more plastic in their
biochemical and elemental composition than are heterotrophs (Sterner and Hessen 1994).
One consequence of using as a starting point in our
models the optimal requirements for nutrients (the intake target) is that we can objectively distinguish the
regulatory responses of animals when ingesting excesses, optimal amounts, and deficits of the various
nutrients. Fig. 5, for example, clearly distinguished
three phases of nitrogen regulation by L. migratoria.
Where intake exceeded requirements, excretion of the
excess occurred with near-complete efficiency, with the
consequence that body N remained relatively constant
across a wide range of food compositions (Fig. 4).
While this accords with the general assumption in ES
that animals recycle ingested excesses into the environment, the same was not true for ingested excesses
of carbohydrate, which was stored in the body as fat
(Fig. 6). Interestingly, even at the target level of protein
ingestion the utilization efficiency of N was ,100%,
indicating that these animals ingest N at levels in excess
of their immediate requirements. At sub-target intakes,
although efficiency was generally higher than that beyond the target level, there was nonetheless a loss of
N in the feces, suggesting some constraint on the efficiency with which N can be retained. This has implications for structuring ES models, which generally
assume that limiting elemental nutrients can be used
with a maximum growth efficiency of 1.0 (Olsen et al.
1986, Anderson 1992, Anderson et al. 2004).
Unlike ES where elements are usually the focus,
throughout this paper we have expressed intake in
terms of the macronutrients protein and carbohydrates.
The emphasis on these molecular complexes makes
sense where the primary aim of a study is to investigate
the mechanistic and evolutionary basis of the association between foods and consumers, since it is to these
Special Feature
two species of locusts the macronutrients protein and
digestible carbohydrates exert a strong interactive influence on the ingestive behavior, nutrient processing,
body composition, and the demographic variables survival, development rate and starvation resistance—to
the extent that the observed effects could not be explained by the levels in the foods of one or other of
the macronutrients, but only by the levels of both.
There are comparable data for other organisms including insects (Simpson et al. 1995b, Jones and Raubenheimer 2001; D. Raubenheimer and S. A. Jones, unpublished manuscript), fish (Simpson and Raubenheimer 2001b), birds (Raubenheimer and Simpson 1997),
rats (Simpson and Raubenheimer 1997), and humans
(Simpson et al. 2003). Further, a large number of studies representing diverse taxa have demonstrated in other contexts that food selection and/or performance are
influenced by the interactions among different nutrient
groups (Greenstone 1979, Krebs and Avery 1984,
Bjorndal 1991, Waldbauer and Friedman 1991, Ackroff
1992, Dearing and Schall 1992, Gallego et al. 1993,
Uetz et al. 1992, de Vries and Schippers 1994, Bowen
et al. 1995, Eubanks and Denno 1999, Evans et al.
1999, Cook et al. 2000). Together these observations
suggest that such interactions are widespread, if not
ubiquitous, and must surely vindicate ecological models that consider multiple substances, and call into
question the generality of single-substance models.
The patterns of interrelationships we have observed
between proteins and carbohydrates have a bearing on
two phenomena central to ES: the regulation of rates
of elemental transfer within ecosystems, and the constraints on the composition of organisms (Sterner
1995). As a first example, the protein : carbohydrate
ratio of the foods of Locusta migratoria markedly influenced their development rate and mortality (Fig. 2),
both of which strongly influence population dynamics
(Stearns 1992) and hence the rates of flow of materials
through ecosystems (Schachak and Jones 1995). Second, the nutrient balance of their foods also influenced
the body composition both of L. migratoria and Schistocerca gregaria (Fig. 7), despite counterbalancing homeostatic responses in intake and utilization efficiencies. The data also demonstrate that the parameters of
the influence of foods on body composition might differ
even between species that are taxonomically closely
related, since the generalist feeding S. gregaria was
better able to maintain body composition in the face
of nutritional imbalance than the grass specialist L.
migratoria (Fig. 6).
Such variation in the carcass composition of primary
consumers suggests that predators, like herbivores,
might encounter appreciable variance in the composition of their foods (Fig. 7). The spread in herbivorecarcass compositions was nonetheless compressed relative to their foods, as a consequence of the homeostatic responses of the animals. The parameters of such
‘‘damping’’ across successive trophic levels are an im-
1213
Special Feature
1214
DAVID RAUBENHEIMER AND STEPHEN J. SIMPSON
or their immediate components (e.g., amino acids) that
the sensory systems of heterotrophs usually have access, rather than directly to carbon or nitrogen. This is
not always the case, however: some nutrients, notably
minerals, are tasted in elemental form (Schulkin 1991),
in which case we express the data accordingly (Trumper
and Simpson 1993). This general issue of the units and
scaling of axes in geometrical plots of nutrition is not
arbitrary, and can be decided using objective tests of
which molecular complexes are most directly of physiological relevance to animals (Simpson and Raubenheimer 1993, 1995). There is, similarly, flexibility in
the units in which post-ingestive processes are investigated. Locusts, for example, do not excrete protein
and excrete only very low levels of amino acids, their
major nitrogenous excretory product being uric acid
(Zanotto et al. 1993). For this reason the y-axis of Fig.
5 is expressed as units of nitrogen, and, to make the
measures readily comparable, intake is expressed in the
same units.
Similar considerations arise in ES. Here the emphasis
on elements is convenient because they provide a common currency for expressing the flow of matter across
organisms with diverse physiological and behavioral
characteristics. However, exceptions are to be found
where molecular complexes have proved more appropriate, as is the case when the limiting factor in the
flow of matter in ecosystems is fatty acids rather than
carbon (Anderson and Pond 2000, Muller-Nevara et al.
2000); further cases are given by Anderson et al.
(2004).
In conclusion, there are similarities and differences
in the aims and structure of GF and ES models. Both
stress the importance of interactions among multiple
substances, and also of accessing underlying mechanistic details in exploring higher-level phenomena.
They differ, however, in emphasizing different scales
and, consequently, different levels of biological resolution. ES is motivated primarily by considerations of
high-level ecosystem processes, for which the homeostatic responses of organisms provide the underlying
mechanisms. These homeostatic responses are the primary target of GF. It remains to be seen how much ES
can benefit from increasing the degree of biological
resolution incorporated into its models.
ACKNOWLEDGMENTS
We are grateful to Tom Anderson for helpful comments on
an earlier draft.
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