Articles
The 3/4-Power Law Is Not
Universal: Evolution of
Isometric, Ontogenetic
Metabolic Scaling in Pelagic
Animals
DOUGLAS S. GLAZIER
It is commonly assumed that metabolic rate scales with body mass to the 3/4 power. However, during ontogeny, the metabolic rate of pelagic (openwater) animals often scales isometrically (in a 1:1 proportion) with body mass. This is a robust pattern, occurring in five different phyla. It can also
be seen by comparing pelagic and benthic (bottom-dwelling) species within phyla, as well as pelagic larvae and benthic adults within species. High
energy costs of continual swimming to stay afloat or of rapid rates of growth and reproduction in response to high levels of mortality (predation) in
open water, or both, may contribute to the isometric or nearly isometric metabolic scaling of pelagic animals. The observation of isometric scaling and
other kinds of metabolic scaling both within and among species suggests that metabolic scaling is not simply the result of physical constraints, but is
an evolutionarily malleable trait that responds to ecological circumstances.
Keywords: allometric scaling, evolution, metabolic rate, ontogeny, pelagic animals
G
iven our mortality, it is not surprising that the pace
of life is a fascinating subject to scientists and laypeople
alike. For centuries it has been known that larger organisms
(e.g., elephants) generally live longer, slower-paced lives than
smaller organisms (e.g., mice). However, it was not until
Lavoisier and Laplace (1783) first measured the rate of respiration and heat production in an organism (a guinea pig)
that a rigorous quantitative analysis of this body-size pattern
could be attempted.
By the 1930s, it was apparent that the respiration (metabolic) rate (R) of a mammal is closely related to its body
mass (M) and that this relationship could be expressed as a
power function, R = aMb (Brody and Proctor 1932, Kleiber
1932, Benedict 1938). Earlier work by Rubner (1883) suggested
that the scaling exponent b should be 2/3 in endothermic
(warm-blooded) birds and mammals because heat loss is
proportional to body surface area, which generally scales as
M2/3. To maintain a constant body temperature, metabolic heat
production would also have to scale as M2/3. However, this explanation is obviously not applicable to ectothermic (coldblooded) organisms whose metabolic scaling is also negatively
allometric with body mass (i.e., b < 1). Furthermore, Kleiber
(1932) and Brody and Proctor (1932) showed that b was
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closer to 3/4 than to 2/3 in mammals. Since that time, it has
been commonly assumed that b is typically 3/4, a generalization known as “Kleiber’s law” or “the 3/4-power law”
(Brody 1945, Hemmingsen 1960, Kleiber 1961, Peters 1983,
Calder 1984, Schmidt-Nielsen 1984, Brown and West 2000,
Savage et al. 2004, West and Brown 2005). Many theoretical
studies in physiology and ecology have been based on the
assumption that metabolic rate scales with body mass to the
3/4 power. Many comparative studies also have adjusted
metabolic rate to body size by using this relationship. Smil
(2000) even announced in a millennium essay in the journal
Nature that “every living thing obeys the rules of scaling
discovered by Max Kleiber.”
What the 3/4-power relationship means is that as log body
mass increases fourfold, log metabolic rate increases only
threefold. In other words, small animals have a higher metabolic rate per gram than large animals. Many unsuccessful
Douglas S. Glazier (e-mail: [email protected]) is a professor in the
Department of Biology, Juniata College, Huntingdon, PA 16652. His research
interests include physiological ecology, evolutionary ecology, and biogeography,
with particular emphasis on energetic approaches and life history patterns.
© 2006 American Institute of Biological Sciences.
April 2006 / Vol. 56 No. 4 • BioScience 325
Articles
attempts have been made to explain the 3/4-power law (see
reviews in Peters 1983, Schmidt-Nielsen 1984, Agutter and
Wheatley 2004), but recently several models have been proposed that appear to provide a strong theoretical basis for the
law, thus further reifying it (West et al. 1997, 1999, Banavar
et al. 1999).
However, empirical work reviewed in Riisgård (1998),
Dodds and colleagues (2001), Bokma (2004), and Glazier
(2005) suggests that the 3/4-power law is not universal, and
should at most be regarded as a statistical rule or trend, rather
than as an inviolable law. Significant variation in the metabolic scaling exponent has been observed both within and
among species. For example, my own work on the water flea
Daphnia magna first convinced me that metabolic scaling need
not follow the 3/4-power law (Glazier 1991). After removing
the effect of the low metabolic rate of the eggs or embryos
carried by adult females, I showed that metabolic rate is isometric or nearly isometric with body mass (b = 0.92–1.00) in
two clones of D. magna raised at two different ration levels
(figure 1; Glazier 1991, Glazier and Calow 1992). That is, as
body mass increases during ontogeny, mass-specific metabolic
rate remains constant or nearly constant. In addition, I have
shown that about 50% of the 642 intraspecific metabolic
scaling exponents that I compiled for 218 species of animals
are significantly different from 3/4, and that this percentage
increases to more than 70% for the data sets with sample sizes
of at least 50 and body-mass ranges of at least two orders
of magnitude (see Glazier 2005, especially table 5 of the
appendix online at http://faculty.juniata.edu/glazier/#publications).
This means that in the intraspecific studies with the most
Figure 1. The ontogenetic scaling of log10 respiration
(metabolic) rate with log10 body mass in a clone of Daphnia magna. The scaling exponent (slope) for the linear regression (solid line) is compared with that predicted from
the 3/4-power law (dashed line). Adapted from Glazier
1991. Abbreviations: h, hour; µg, microgram; µL, microliter; O2, oxygen.
326 BioScience • April 2006 / Vol. 56 No. 4
statistical power, the 3/4-power law is about 2.5 times more
likely to be rejected than provisionally accepted. Several interspecific studies of various animal taxa have also reported
metabolic scaling exponents significantly different from 3/4
(e.g., Ivleva 1980, Dodds et al. 2001, Kozlowski et al. 2003,
White and Seymour 2003, Glazier 2005, White et al. 2006).
Ontogenetic metabolic scaling in pelagic animals
In this article I describe and attempt to explain the remarkable and largely underappreciated differences in metabolic scaling exhibited during ontogeny by pelagic versus nonpelagic
animals. Pelagic animals live in open water, whereas nonpelagic
animals live on, in, or near substrates either underwater or on
land. In a survey of 413 invertebrate species, I have shown that
during ontogeny the mean scaling exponent for resting or routine metabolic rate (± 95% confidence limits [CL]) is nearly
1.0 (b = 0.947 ± 0.046, N = 58) for pelagic species, and is highly
significantly different (t = 8.686, P < 0.0000000001) from that
shown for nonpelagic species (b = 0.744 ± 0.018, N = 355;
Glazier 2005).
I have chosen to focus on this comparison for three major
reasons. First, it clearly demonstrates that the 3/4-power law
is not universal. Many pelagic animals show little or no decrease in mass-specific metabolic rate as they grow in body
mass, contrary to conventional belief. Therefore, pelagic animals not only represent a clear exception to the 3/4-power
law but also, in many cases, have metabolic rates that scale proportionately (isometrically) rather than disproportionately (allometrically) to body mass, a highly unexpected finding.
Second, this isometric or nearly isometric metabolic scaling is not a trivial or easily ignored exception to the 3/4power law, because it is shown by many different kinds of
pelagic animals, including some of the most abundant lifeforms on the planet, such as jellyfishes, comb jellies, sea
butterflies, squid, water fleas, krill, and salps. Furthermore, this
distinctive ontogenetic metabolic scaling can be seen at many
taxonomic levels, from species to phylum. As such, it is a
remarkable case of convergent evolution that demands our
attention.
Consider that pelagic species in five different phyla with very
different body designs show isometric or nearly isometric
metabolic scaling. The mean b values (± 95% CL) for pelagic
species in these phyla are as follows: Cnidaria, 0.950 ± 0.079;
Ctenophora, 0.935 ± 0.172; Mollusca, 0.922 ± 0.095; Arthropoda, 0.873 ± 0.038; and Chordata, 1.110 ± 0.233. Furthermore, significant differences in metabolic scaling between
pelagic and benthic (bottom-dwelling) animals can be observed within the four of these phyla for which sufficient
data are available (figures 2, 3, 4, 5). This distinction can be
seen within lower taxonomic groups as well. For example,
within the crustacean order Amphipoda, the mean metabolic scaling exponent of four pelagic species (0.900 ± 0.159;
data are from Yamada and Ikeda 2003) is significantly greater
(t = 2.134, P = 0.044) than that shown by 20 nonpelagic
species (b = 0.683 ± 0.092; data are from Glazier 2005).
Pelagic versus benthic differences in metabolic scaling occur
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Figure 2. Frequency of pelagic and benthic cnidarian
species with various ontogenetic metabolic scaling exponents. Note the higher median and mean (± 95% confidence limits) values for pelagic hydrozoans and scyphozoans as compared with those for benthic anthozoans.
Data are from Glazier 2005.
even within species. For example, pelagic larvae of the common mussel Mytilus edulis show nearly isometric metabolic
scaling (b ≈ 0.9), whereas benthic adults show shallower
allometric scaling (b ≈ 0.7) (Riisgård 1998). Similar biphasic scaling is exhibited by many other aquatic fish and invertebrates with pelagic larvae (reviewed in Glazier 2005). These
large, repeated, ecologically related differences do not appear to be minor variations obscuring the major pattern of
3/4-power scaling; rather, they appear to represent major
deviations demanding new explanations.
Although isometric metabolic scaling appears to be common in pelagic animals, there may be some exceptions. For
example, limited data on appendicularians suggest that their
metabolic rate scales allometrically rather than isometrically
(Lombard et al. 2005). In addition, analyses that include the
very youngest stages of development may reveal shifts from
allometric to isometric scaling, as recently reported for the
jellyfish Aurelia aurita (Kinoshita et al. 1997) and the
ctenophore Beroe ovata (Svetlichny et al. 2004).
Third, pelagic animals clearly show that metabolic scaling
does not simply result from a single set of physical constraints, but can apparently evolve in response to ecological
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Figure 3. Frequency of pelagic and benthic mollusk
species with various ontogenetic metabolic scaling exponents. Note the higher median and mean (± 95% confidence limits) values for pelagic cephalopods and gastropods as compared with those for benthic bivalves and
gastropods. Data are from Glazier 2005.
circumstances. It is unlikely that structural constraints alone
can account for the similar metabolic scaling of pelagic animals that are so different in body design. The model of West
and colleagues (1997) explains the 3/4 metabolic scaling of animals as being the result of the fractal geometry of internal
transport networks, including the respiratory and circulatory
systems. Pelagic animals are especially troublesome for this
model, not only because they do not show 3/4-power scaling
but also because some of them (e.g., cnidarians and
ctenophores) do not even have the respiratory and circulatory
systems required by the model. Furthermore, the models of
West and colleagues (1997, 1999), Banavar and colleagues
(1999, 2002), and others that focus on internal transport
networks (regardless of whether or not they are fractal) cannot explain why pelagic versus benthic animals of similar body
design (with or without overt transport networks) exhibit such
strong differences in metabolic scaling (figures 2, 3, 4, 5). It
seems to be an inescapable conclusion that the open-water environment of pelagic animals is somehow favoring the evolution of isometric metabolic scaling (directly or indirectly),
regardless of body design.
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Figure 4. Frequency of pelagic and benthic arthropod
species with various ontogenetic metabolic scaling exponents. Note the higher median and mean (± 95% confidence limits) values for pelagic crustaceans as compared
with those for benthic crustaceans. Data are from Glazier
2005.
Figure 5. Frequency of pelagic and benthic chordate
species with various ontogenetic metabolic scaling exponents. Note the higher median and mean (± 95% confidence limits) values for pelagic salps as compared with
those for benthic ascidians. Data are from Glazier 2005.
Possible explanations of isometric metabolic
scaling in pelagic animals
continuously wiggle their whole bodies to move, whereas
older juveniles and adults use a more energy-efficient “beat
and glide” locomotion that involves bending movements of
the tail and tail fin. It may be no coincidence that this ontogenetic switch in swimming mode occurs at the same body
size at which a phase shift in metabolic scaling also occurs
(Wuenschel et al. 2000). The relatively large energy costs of
swimming may contribute to the isometric metabolic scaling
of many other pelagic animals (and larvae) as well.
However, many pelagic animals are neutrally buoyant or
nearly so, thus presumably reducing locomotor costs required for maintaining position in the upper levels of open
water. Some water-filled, gelatinous forms, such as many
ctenophores and cnidarian medusae, are quite sluggish and
spend considerable periods of time drifting. Among pelagic
animals generally, there appears to be a negative association
between buoyancy and swimming activity (see Glazier 2005).
Therefore, swimming costs probably cannot account for all
cases of isometric scaling in pelagic animals. Nevertheless,
buoyancy maintenance itself entails other energy costs that
may contribute to isometric metabolic scaling in some pelagic
species (e.g., continual, active expulsion of heavy sulfate ions
from the body fluids; see Bidigare and Biggs 1980, Glazier
2005), a hypothesis that requires testing.
The isometric or nearly isometric metabolic scaling of pelagic
animals during ontogeny is a robust pattern crying out for explanation. Although several explanations are possible, two
seem to show the most promise (see also Glazier 2005). These
explanations are related to two fundamental problems facing
all pelagic animals: staying afloat and coping with high mortality (predation) in an exposed environment.
To stay afloat, many pelagic animals must continuously
swim, an energy-expensive activity. For example, the Antarctic krill Euphausia superba, which is nonbuoyant and thus constantly susceptible to sinking, uses a considerable proportion
of its metabolism to fuel its “hovering”activity, which increases
up to 60% as an individual grows and becomes even less
buoyant (Kils 1982). On the basis of energy-budget calculations, Kils (1982) argued that the ontogenetic increase in the
mass-specific energy costs of hovering may cause metabolic
scaling of krill to be isometric (b = 1) rather than negatively
allometric (b < 1), as is typical of benthic crustaceans. In addition, the energy costs of swimming have been implicated in
the switch from isometric to negatively allometric metabolic
scaling that occurs in some fish as they develop. For example,
in the spotted seatrout (Cynoscion nebulosus), pelagic larvae
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Since pelagic animals live in open water, they are continually exposed to predation, which has been partially offset in
many species by the evolution of transparency (Johnsen
2001). High mortality of both juveniles and adults may select
for rapid growth and maturation rates and large reproductive outputs. Since pelagic animals are generally short-lived,
they must rapidly expend energy to grow and reproduce before they die. High sustained production costs at all ages and
sizes may, in turn, result in a mass-specific metabolic rate that
does not decrease with increasing body mass (i.e., isometric
metabolic scaling). It is probably no coincidence that pelagic
salps, which have among the highest known growth rates in
animals, and which continue to grow rapidly throughout
their lifetime, have the highest metabolic scaling exponents
(up to 1.6) of the invertebrates that I have surveyed (Glazier
2005). Pelagic cnidarians, ctenophores, pteropods, squid,
cladocerans, and krill also typically have high rates of sustained
production during their relatively short lives, though we still
have much to learn about the life histories of many of these
animals (see Glazier 2005).
The second explanation may be more generally applicable
than the first, though these explanations are not mutually exclusive. For example, high production costs may require high
levels of feeding and associated locomotor activity, which
together may contribute to isometric metabolic scaling in
many pelagic animals. Future testing of these explanations
would benefit from the development of quantitative models.
A particularly promising approach would be to use optimization models relating body mass–dependent metabolic
rates to body mass–specific mortality and production rates,
as proposed by Kozlowski and Weiner (1997).
Other explanations of the isometric or nearly isometric
metabolic scaling of pelagic animals are possible and should
be explored, but most of these appear to be relatively taxon
specific or inadequate in other ways (see also Glazier 2005).
As one example, perhaps many benthic animals with shells
or exoskeletons exhibit allometric metabolic scaling because
the proportion of their body mass that is shell mass, and
thus metabolically inert, increases with age. In contrast, it may
be supposed that many pelagic animals without shells or
exoskeletons exhibit isometric metabolic scaling because they
do not show these changes in body composition. However,
this hypothesis is probably not generally applicable, because
both pelagic and benthic animals include species with and
without shells or exoskeletons. Furthermore, shell mass is isometric with total mass, or nearly so, both within and among
species of bivalves (Tokeshi et al. 2000, Vladimirova et al.
2003), and thus age- and body size–related changes in shell
mass cannot explain the allometric scaling of metabolic rate
in these animals. In addition, although the proportion of
body mass that is relatively inert cuticle increases as cladocerans grow, it appears to have only a slight effect on their
metabolic scaling (Glazier 1991). The metabolic rate of the
amphipod Gammarus fossarum also scales similarly to body
mass with or without chitin mass included, though agerelated accumulation of other inert materials may help account
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for the negative allometry of metabolic rate in this species
(Simcic and Brancelj 2003). Obviously, more data are needed,
but in general the large differences between pelagic and benthic animals in ontogenetic metabolic scaling are probably not
simply a function of differences in how their body composition changes with age.
Major lessons to be learned from metabolic
scaling in pelagic animals
Three major lessons can be learned from examining the
metabolic scaling of pelagic animals. First, the 3/4-power
law is clearly not universal. Pelagic animals show that massspecific metabolic rate need not decrease with increasing
body size, contrary to common belief.
Second, the isometric scaling of pelagic animals represents just one example of the extensive variation in intraspecific metabolic scaling that exists. Ontogenetic metabolic
scaling not only may show a variety of slopes (b = 0.1–1.6)
but also may be nonlinear, exhibiting distinct phase transitions (reviewed in Glazier 2005). Studies are now needed to
uncover the proximate (functional) and ultimate (evolutionary) causes underlying this variation.
Third, the isometric scaling of pelagic animals shows that
metabolic scaling is not simply the result of physical or geometric constraints, but can be profoundly influenced by ecological circumstances. Physiological and structural constraints
may act as boundaries within which natural selection can adjust metabolic scaling to cope with specific environmental
challenges. These boundary constraints include surface-area
limits on the flux of resources or wastes (b is expected to be
approximately 2/3) and mass/volume limits on power production (b is expected to be approximately 1), thus causing
metabolism to scale to body mass with a power most often
between 2/3 and 1 (for further details on this approach, see
Kooijman 2000, Glazier 2005).
Is ontogenetic metabolic scaling relevant
to the 3/4-power law and theory?
One might argue that the variation in ontogenetic scaling patterns described here and elsewhere (Glazier 2005) is irrelevant
to the 3/4-power law, because intraspecific patterns of metabolic scaling are distinctly different from interspecific patterns,
as pointed out by Wieser (1984) and others. Intraspecific
metabolic scaling results from ontogenetic changes in body
mass, whereas interspecific metabolic scaling results from
evolutionary changes in body mass. In addition, since intraspecific analyses are usually based on narrower body-size
ranges than interspecific analyses, estimates of their scaling
exponents (slopes) are subject to more error, thus perhaps
accounting for much of the considerable variation in intraspecific metabolic scaling that has been observed. Also,
metabolism in growing animals includes the costs of nonmaintenance processes such as growth and development,
and thus is not strictly comparable to interspecific comparisons of adult metabolism. The 3/4-power law has been derived from interspecific, not intraspecific, comparisons.
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Furthermore, the theory proposed to explain the 3/4-power
law has been chiefly directed at interspecific scaling (West et
al. 1997, 1999, Banavar et al. 1999). Finally, as already mentioned, the routine metabolic rates of many pelagic animals
include antigravity swimming activity, and thus it could be
argued that their ontogenetic metabolic scaling is not relevant
to the 3/4-power law and associated theory, which is based on
basal, or resting, metabolic rates involving minimal activity.
There are six major reasons why the above arguments do
not protect the universality of the 3/4-power law and the
theory used to explain it. First, interspecific analyses reveal
considerable variation in the metabolic scaling exponent
(b = 0.5–1.1), as do intraspecific analyses (reviewed in
Withers 1992, Dodds et al. 2001, Glazier 2005; but see Savage
et al. 2004). For example, several studies have shown that
endothermic vertebrates tend to exhibit shallower metabolic
scaling exponents (b ≤ 3/4) than ectothermic vertebrates
(b ≥ 3/4) (Glazier 2005, White et al. 2006).
Second, the considerable variation observed in intraspecific
metabolic scaling is not simply the result of narrower bodysize ranges causing more error than that observed in interspecific analyses. For example, my study of D. magna, which
was based on a 70-fold body-size range, clearly revealed metabolic scaling exponents that, at 1 or nearly 1, were significantly
greater than 3/4 (figure 1; Glazier 1991, Glazier and Calow
1992). The 3/4-power law is also not shown in several other
studies of intraspecific metabolic scaling in animals with
broad body-mass ranges (two orders of magnitude or greater).
A striking example is the carp Cyprinus carpio, which can grow
more than 100,000 times in mass from larva to adult. The
metabolic scaling exponents (± 95% CL) of young larvae
and juveniles (0.949 ± 0.022) and of older juveniles and
adults (0.872 ± 0.034) are both significantly different from 3/4
(Post and Lee 1996, Glazier 2005). Furthermore, the highly
significant difference observed between the intraspecific
metabolic scaling exponents of pelagic versus nonpelagic
animals cannot be attributed simply to measurement error.
Third, although the costs of nonmaintenance processes are
obviously involved in intraspecific (ontogenetic) metabolic
scaling, this may be true for interspecific metabolic scaling as
well. For example, growth costs may be included in estimates
of the metabolic rate of adult animals with indeterminate
growth (i.e., growth after reproductive maturity; Parry 1983,
Peterson et al. 1999). Various levels and patterns of heat production over and above the costs of simple tissue maintenance
may also affect the scaling of metabolic rate in adult vertebrate
animals (see McNab 2002, Glazier 2005, White et al. 2006).
In any case, isometric metabolic scaling has been observed
in pelagic animals even when they have fasted to the point
where they are not gaining weight or are losing weight. The
metabolic rate of these animals is likely to be at or near maintenance levels (Jobling 1985, Wieser 1994). Nevertheless, isometric or nearly isometric metabolic scaling has still been
observed under these conditions in krill (Paranjape 1967), sea
butterflies (Conover and Lalli 1974), water fleas (Glazier
1991, Glazier and Calow 1992), and ctenophores (Anninsky
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et al. 2005). Ontogenetic patterns of metabolic scaling, such
as the isometric scaling of pelagic animals, do not appear to
be mere artifacts of methodology.
Fourth, although the routine metabolic rates of many
pelagic species analyzed here include antisinking swimming
activity and thus do not represent basal or resting rates, the
theory developed to explain the 3/4-power law should still
apply. Optimally designed supply networks, proposed by
West and colleagues (1997) and Banavar and colleagues
(1999), should be able to accommodate metabolic rates at various levels of activity. In any case, as already noted, isometric metabolic scaling occurs in buoyant pelagic animals that
are sluggish swimmers, and thus is not always a result of
swimming activity. As one example, in the ctenophore B.
ovata, anesthesia (and thus complete cessation of locomotion)
has little effect on the metabolic scaling exponent, which remains nearly isometric (0.9; Svetlichny et al. 2004).
Fifth, although it can be argued that intraspecific metabolic
scaling has no bearing on interspecific patterns and on the general models proposed to explain them, this distinction is not
always clearly maintained by researchers, including leaders in
the field. Even Kleiber (1961), one of the founders of the
3/4-power law, claimed that this law applied to both withinand among-species comparisons. In addition, the authors
of one of the most publicized models (West et al. 1997) have
recently assumed that the 3/4-power law applies universally
not only to interspecific comparisons but also to ontogenetic
changes in body mass (West et al. 2001). Banavar and colleagues (2002) have applied their general model to ontogenetic scaling, as well. Whatever the relationship between
intra- and interspecific metabolic scaling may be, Glazier
(2005) has argued that a truly general theory of metabolic scaling should be able to explain both kinds of allometric patterns.
After all, both involve changes in body mass that may exert
similar physical constraints on metabolic rate, as predicted by
theory (Bokma 2004). In addition, evolution may act to ensure that both intra- and interspecific metabolic scaling are
optimal responses within certain structural limits (cf.
Kozlowski and Weiner 1997, Kozlowski et al. 2003). Indeed,
in some animals the mean intraspecific metabolic scaling
exponent is not significantly different from the interspecific
scaling exponent (e.g., teleost fish; Clarke and Johnston 1999).
Sixth, analyses of intra- and interspecific metabolic scaling
may illuminate each other in many ways. Intraspecific responses of metabolic scaling to environmental stresses (e.g.,
high temperatures) may help reveal the mechanisms underlying metabolic scaling both within and among species. For
example, juvenile sowbugs (Porcellio scaber) show shallower
scaling of metabolic rate in relation to body mass at 30 degrees Celsius (ºC) (b = 0.687) than at 20ºC (b = 0.917), perhaps because high metabolic rates at high temperatures are
more limited by surface-dependent processes of nutrient
and waste exchange (Wieser and Oberhauser 1984). A similar effect of temperature has also been observed in interspecific comparisons of metabolic scaling in crustaceans (Ivleva
1980), though other effects (or noneffects) of temperature on
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the scaling exponent have been observed in some animals, as
well (see Glazier 2005).
Analyses of interspecific metabolic scaling may also provide insight into causes of intraspecific metabolic scaling. For
example, the relatively high interspecific scaling exponent
of maximal metabolic rate during locomotor activity (b ≈ 0.9
in birds and mammals; Bishop 1999, Weibel et al. 2004) may
help explain why the intraspecific scaling exponent of actively
swimming pelagic larvae is also relatively high, as already
discussed. Other examples are reviewed in Glazier (2005).
In any case, intraspecific metabolic scaling is worthy of study
in its own right and has been sadly neglected, despite various
attempts to draw attention to it (Zeuthen 1953, Bertalanffy
1957, Heusner 1982, Wieser 1984, Riisgård 1998, Bokma
2004). Intraspecific metabolic scaling is evolutionarily malleable, just like other morphological, physiological, behavioral,
and ecological traits. A whole new research program awaits
the comparative, experimental, and theoretical analysis of
variation in ontogenetic metabolic scaling. Comparisons of
pelagic and benthic animals within various taxonomic groups
may be especially helpful in this regard because they represent numerous replicated natural experiments. Pelagic forms
occur in 11 different phyla (May 1994, Johnsen 2001), though
metabolic scaling data are presently available for only 5.
Moreover, intraspecific analyses of metabolic scaling have
three advantages over interspecific analyses. First, intraspecific
analyses avoid the problems of phylogenetic effects that
plague interspecific analyses (Bokma 2004, Glazier 2005).
Second, intraspecific analyses are more amenable to repeated
experimental tests. Correlative and theoretical approaches
have dominated the study of metabolic scaling, but although
they are necessary and useful, they are poor at establishing
cause-and-effect relationships. Experimental analyses are
best for causal analyses. Third, environmental effects on
metabolic scaling are more likely to be detected in intraspecific rather than interspecific analyses. This is because environmental effects are more likely to be clearly seen when
comparing the metabolic scaling of individual species or
conspecific populations, each from a specific environment,
than when comparing collections of species derived from
numerous different environments. Furthermore, adaptive
evolution in response to ecological circumstances occurs
mainly (if not solely) within species (or populations), not
among species.
Conclusions
For more than 70 years, the 3/4-power law has had a dominant influence on the field of metabolic scaling. Some useful and insightful work has been produced within this
paradigm, but further progress requires that we look beyond
the 3/4-power law to consider the great diversity of metabolic
scaling relationships that exist in the living world. Both intraand interspecific scaling relationships require study, but
intraspecific analyses show the most promise for increasing
our understanding of the mechanistic and evolutionary
causes of metabolic scaling, because they are amenable to the
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experimental method, they provide more replicate systems for
study, and intraspecific scaling relationships are more diverse than interspecific relationships. As a result of such studies, we are likely to find that ontogenetic metabolic scaling
represents an adaptive strategy that has evolved in the context of multiple physical, chemical, and ecological constraints.
Acknowledgments
This paper has benefited from comments by David Atkinson,
Marcin Czarnoleski, Jan Kozlowski, Hans Riisgård, and three
anonymous reviewers. I also thank Peter Calow for the use of
his laboratory in the Department of Animal and Plant Sciences
at the University of Sheffield, where I discovered the isometric scaling of metabolic rate in Daphnia, a finding that first
made me realize that metabolic scaling may be evolutionarily
malleable.
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