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How an animal's mass affects its
physiology has intrigued scientists for over
a century. Animals range in size from tiny
shrews weighing in at a few grams up to
the truly colossal. Despite countless
attempts to define scaling laws that predict
how an animal's size affects many aspects
of its physiology, from locomotion to
lifespan, the debate is far from over. In
particular, two rival theories concerning the
relationship between metabolic rate and
body mass continue to stimulate lively
discussion. While some researchers argue
that basal metabolic rate scales with body
mass raised to the power of 2/3, others
staunchly defend a 3/4 scaling exponent.
But at present there is no compelling
evidence to suggest that either of these is
the `true' value; perhaps it lies somewhere
in between, or perhaps there simply isn't a
universal scaling law.
There have been many attempts to find a
universal law that predicts relationships
between an organism's size and
physiological functions. But as the theories
and data accumulate, it has become ever
more difficult to navigate through the
controversial field of allometric scaling. To
assess our current understanding of scaling
laws, Hans Hoppeler and Ewald Weibel
from the University of Bern gathered
together contributions from physicists,
engineers and biologists, discussing their
latest ideas and observations on allometric
scaling. `There is a lot of controversy in
this field,' Hoppeler says, `because we still
don't have a single scaling theory that
predicts everything you see in the data.'
Weibel adds, `the main incentive for this
collection was to encourage theoreticians
and empiricists to work together to
reconsider and possibly revise scaling
theories in light of the rapidly
accumulating data.'
BASAL METABOLIC RATE
AND CELLULAR
ENERGETICS
Launching the collection on a controversial
note, Geoffrey West and James Brown
make their case for a universal scaling law
that spans biological systems ranging in
size from molecular units of the cells'
metabolic machinery to trees and mammals
(p. 1575). They propose that the universal
fractal-like branching networks of fuel
delivery systems, such as animal blood
vessels and plant vascular systems, account
for the scaling of whole body metabolic
rate with body mass to the 3/4 power. They
conclude with a `bold but exciting vision'
for the future: `we see the prospects for the
emergence of a general theory of
metabolism that will play a role in biology
similar to the theory of genetics.'
Moving from the organismal to the cellular
level, Anthony Hulbert and Paul Else
suggest that the chemical composition of
cell membranes has a dramatic effect on a
creature's metabolic rate (p. 1593).
Knowing that cell membrane fatty acid
composition varies with changing body
mass in mammals and birds, Hulbert and
Else have developed the `membrane
pacemaker' theory of metabolism. They
present evidence that animals with higher
levels of poly-unsaturated fatty acids in
their cell membranes usually have higher
metabolic rates, leading to the suggestion
that cell membrane composition acts as a
pacemaker. Hulbert and Else speculate that,
besides regulating the pace of life,
differences in cell membrane composition
may even be related to lifespan in
different-sized animals.
Other metabolic factors that vary with body
size are the levels of metabolic enzyme
activities in muscle; larger animals have
lower mitochondrial enzyme activity and
higher glycolytic enzyme activity than
smaller animals. Christopher Moyes and
Christophe LeMoine survey genetic
explanations for this relationship between
bioenergetic enzymes and body mass
(p. 1601). They comprehensively review
the role of various transcriptional
regulators that control mitochondrial gene
expression in muscle cells. But their
attempt to uncover allometric patterns in
the enzymes that support metabolic rate
reveals that none of these regulators
provides a satisfactory explanation for the
observed differences between enzyme
activity in large and small animals.
Several contributions in this collection
argue for a universal scaling law. However,
Craig White and Roger Seymour sound a
note of caution (p. 1611). Many early
studies of the relationship between basal
metabolic rate and body mass were based
on data sets comprising animals ranging in
body mass by 18 orders of magnitude. But
White and Seymour suspect that large
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SIZE MATTERS
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Inside JEB
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systems would be better viewed as having
co-evolved, ensuring that fuel delivery and
consumption rates are matched to each
other at any activity level.
CIRCULATION AND BODY
SIZE
herbivores were over-represented in these
studies, resulting in an inflated mass-
scaling exponent because the ruminants'
fermenting digestion process makes it
impossible to measure `true' basal
metabolic rate. Their re-analyses of these
previous data sets indicate that the value of
the exponent clearly depends on the
conditions under which data are selected,
and that truly basal mammalian
metabolism does not scale as body mass to
the 3/4 power. They recommend that, in
future, researchers should carefully
consider whether the metabolic rates that
they include in their analyses have really
been calculated under identical conditions.
ACTIVITY-INDUCED
VARIATION OF
METABOLISM
While much effort has been devoted to
deriving scaling laws for basal metabolic
rate, this may not be the best metabolic
measurement to focus on, since most
animals routinely function at much higher
metabolic rates during their daily chores.
Analysing 229 species of birds, mammals
and reptiles, Kenneth Nagy suggests that
an animal's field metabolic rate ­ the
metabolic rate while it's going about its
day-to-day business ­ may be a more
relevant measure of an animal's energy
demands (p. 1621). Ewald Weibel and
Hans Hoppeler in turn focus on maximal
sustained oxygen consumption rate ­ the
upper limit of an organism's aerobic
metabolism (p. 1635). Investigating 11
mammalian species, they find that variation
of maximal metabolic rate with body size
is closely linked to the volume of
mitochondria and capillaries in locomotor
muscle. They conclude that the scaling of
maximal metabolic rate is determined by
the energy needs of maximally working
muscle cells, and that scaling is determined
by variations of this demand with body
size.
But deciding which type of metabolic rate
has the greatest biological relevance is
overshadowed by another problem;
analyses of basal, field and maximal
metabolic rates all report different scaling
exponents. To explain this, Raul Suarez
and Charles Darveau argue that simple
models based on the assumption that
metabolic rates are supply-limited, such as
Geoffrey West's model, can only be part of
the story (p. 1627). `Metabolic scaling is
such a wonderful, many-splendoured thing
that models based on supply-limitation
alone fail to do it justice,' they say.
Reviewing the evidence from multiple-
cause models, Suarez and Darveau
conclude that energy supply and demand
LOCOMOTION AND
ENERGY DEMAND
Staying with the theme of energy supply
and demand, R. McNeill Alexander
discusses how muscle efficiency scales
with body mass across different modes of
locomotion (p. 1645). He highlights how
simple locomotion models ­ birds flying
like aircraft, insects hovering like
helicopters and fish swimming like
submarines ­ can offer valuable insights
into complex physiological and
biomechanical functions. He concludes that
larger animals, at least those that are
running or flying, have more efficient
muscles than smaller animals.
James Marden examines another scale
effect in locomotion; how net force
production relates to body mass (p. 1653).
He finds that size-assorted groups of
biological and man-made machines ­ from
muscle proteins through animals that are
flying, running and swimming, up to
piston engines and jets ­ have similar
performance characteristics because they
are constrained by fundamental physical
limits. This leads Marden to the startling
conclusion that a motor's force output is
always proportional to its mass raised to a
scaling exponent that ranges from 2/3 to 1,
depending on the motor's size, and that
this holds for both biological and man-
made motors.
But all these systems are subject to
damaging forces. How have organisms
adapted to withstand the ever-increasing
forces as they scale up ­ for example, as
animals mature? Andrew Biewener rounds
off this section with a review of skeletal
scaling in terrestrial animals; how limb
bones scale to tolerate the forces that they
have to endure during walking and running
(p. 1665). Perhaps surprisingly, bone and
muscle stresses don't simply increase with
body size. By changing their posture and
becoming more erect as they grow, animals
manage to keep bone and muscle stresses
fairly constant over a broad size range from
0.04 to 300 kg.
To meet the body's energetic demands, an
animal needs to have an efficient fuel
supply system, such as the branching
delivery network systems found in plants
and animals. Building on this concept,
Adrian Bejan has constructed a general
theory of optimal design for biological
systems based on the constructal law,
which states that a flow system's
architecture will evolve in such a way that
it provides easier access to its currents
(p. 1677). Applying this design law to
living systems, Bejan shows that the
constructal law accounts for a 3/4 mass
scaling exponent in an astounding variety
of situations, ranging from hair diameter in
fur to optimal organ sizes. He concludes
with the intriguing suggestion that `biology
and natural selection have just been made a
part of physics.'
Moving from the large scale to the
microscopic, Thomas Dawson focuses on
the scaling of animal vascular systems to
body mass, and finds that the radius, length
and number of blood vessels in microscale
capillary networks follow essentially the
same pattern in all mammals (p. 1687).
Knowing that vascular networks function
as oxygen transfer systems, Dawson also
finds that oxygen transfer rates vary with
mammal body mass raised to the 3/4
power.
Scaling of vascular systems is just as
important for birds as it is for mammals;
Charles Bishop explains that flight
performance depends on well-oxygenated
flight muscle fibres. But since heart rate
drops with increasing body mass, this may
reduce blood flow rate to the flight muscles
of larger birds, compromising their
performance. Wondering if circulatory
THE JOURNAL OF EXPERIMENTAL BIOLOGY
Inside JEB
iii
constraints limit large birds, Bishop
modelled the maximum sustainable flight
performance of 15 migrating bird species
(p. 1695). These aerodynamic models led
Bishop to the conclusion that birds' flight
muscle efficiency scales with body mass,
and that circulatory constraints may indeed
ultimately limit flight performance.
Returning to the basic connection between
metabolic rate and body temperature, José
Chaui-Berlinck and colleagues note that
unusual body temperature patterns have
been reported for small mammals.
Wondering whether small warm-blooded
creatures might be a special case when it
comes to body temperature control, they
modelled changes in metabolic rate and
body temperature over time for a range of
mammalian body sizes (p. 1709). The
team's models suggest that the body
temperature control mechanism itself is
subject to size effects, a problem that
should not be overlooked in the future.
LIFE SPAN,
REPRODUCTION AND
ECOLOGY
Why do bigger animals live longer than
small ones? John Speakman revisits this
age-old observation in his investigation of
the scaling relationship between metabolic
rate and aging (p. 1717). It seems simple
enough: total energy expenditure over a
creature's lifetime is fixed, and since a
gram of elephant expends its energy more
slowly than a gram of shrew, elephants live
longer than shrews. `Live fast, die young'
encapsulates this `rate of living' theory. A
possible mechanism that links metabolism
to aging is provided by the `free radical
theory', which suggests that oxygen free
radicals, a by-product of metabolism,
damage cells and cause mortality. But the
data don't fit the expectations of these
models; clearly, the truth is more
complicated than either of these theories
suggests. Comparing birds and mammals to
test these theories may not be fair,
Speakman argues, since these groups will
differ in many other biological aspects
besides metabolic rate and lifespan. He
concludes that a potential avenue for future
research is to look at individual variation in
the relationship between metabolic rate and
lifespan within species rather than between
species.
Also with a view to improving future
allometric studies, Robert Martin and
colleagues highlight some of the potential
methodological problems with allometric
scaling analyses (p. 1731). An
understanding of these technical problems
and how to circumvent them is clearly
important for future work in this already
contentious field.
While Speakman and Martin consider
allometric relationships at the level of the
individual organism, Pablo Marquet and
colleagues point out that scaling
relationships are also found at the
ecosystem level (p. 1749). To show how
body size scaling relationships `provide a
fresh perspective to tackle ecological
complexity' they review the remarkable
diversity of these relationships from
invertebrates to mammals in marine,
freshwater and terrestrial ecosystems. They
identify encouraging recent theoretical
developments such as the metabolic theory
of ecology, which `attempts to explain
material and energetic fluxes, in ecological
systems, from first principles of
thermodynamics, chemical reaction
kinetics, and fractal-like biological
structures.' They conclude that `the way
ahead is certainly challenging.'
AT THE CROSSROADS OF
THEORY AND EXPERIMENT
So, where do we go from here? Hoppeler
and Weibel hope that the scientific
community will take up the challenge to
understand why experimental data don't
always fit the models. `To make headway
and adjust the models to accommodate new
data, modellers and experimentalists will
have to work together to solve these
controversial issues,' Weibel says. `A
universal scaling theory may never be
found,' Hoppeler admits. But they are
optimistic that this thought-provoking
collection of scaling papers will trigger
fruitful collaborations between empiricists
and theoreticians.
10.1242/jeb.01626
Yfke van Bergen and Kathryn Phillips
The Company of Biologists 2005
THE JOURNAL OF EXPERIMENTAL BIOLOGY