Biology Reference
In-Depth Information
The relationship between metabolic rate and body weight is an example of a biological
pattern called allometry, which compares how the value of any biological trait, such as
metabolic rate or leg length, changes with the total size of a plant or animal. (15.7)
The so-called
quarter-power scaling laws
(Whitfield 2006, pp. 78-79) stating
that many biological traits scale as body mass raised to the power of one or more
quarters may be derived from the postulate that
the phenomenon of life is
The
allometry equation
has the following deceptively simple form:
a
x
b
y
¼
(15.8)
where y is biological trait, either processes or structures, x is the total size of a cell, a
plant or animal, and
a
is the
allometric coefficient
, and
b
is the
allometric exponent
which can be greater or less than 1. If
b
is greater than 1, for example, as in the case
of deer antlers, the trait gets proportionately larger, and, if
b
is less than 1 as is the
case with metabolic rate, it gets proportionately smaller so that, when the body size
doubles, the metabolic rate increases by less than twofold.
During the past one and a half century, it has been found that, over a very wide
range of body sizes of organisms (covering 27 orders of magnitude from unicellular
organisms to whales), the metabolic rate scales as (or is proportional to) the bodymass
raised to the power of approximately (White and Seymour 2005). In Fig.
15.13
,
the metabolic rates of organisms from single cells to the elephant are plotted against
their body masses on a log-log scale. The figure has three parallel lines, one each for
homeotherms, poikilotherms
(also called ectotherms), and
unicellular organisms
.
They all have the same slope, that is,
b
3/4 but intercept the
y
-axis at different
points, resulting in different values for
a
: The lower the intercept, the lower the
average
metabolic rate for each group. The allosteric exponent of shown in this figure
is not the only possibility. There are many cases where it differs from and hovers
around 2/3 (see Table 1 inWhite and Seymour 2005). It will be assumed here that the
power law reflects at least some of the principles underlying the scaling phenomena
in biology and that even the allometric exponent of 2/3 may be viewed as an example
of the quarter-power scaling since 2/3 is equal to 2.666/4. Thus, any viable theory of
allometric scaling should be able to provide a reasonable theoretical basis to account
for the numerical values of both
a
and
b
in Eq.
15.8
. It should be noted here that certain
traits such as life span, heart beats, blood circulation time, and unicellular genome
length scale as the body mass raised to the power of ¼, and the radii of aortas and tree
trunks scale as body mass raised to the power of 3/8 or 1.5/4 (West and Brown 2004).
These are examples of “quarter-power scaling,” and the key question that has been
challenging theoretical biologists for more than a century is why these exponents are
multiples of 1/4, not 1/3 as expected on the basis of the scaling in the Euclidean space.
One of the currently most widely discussed and intensely debated theories to
account for the 3/4 allometric exponent of the power law relating metabolic rate (y)
to body mass (x) is the one proposed by West and Brown (2004, Whitfield 2006).
Their theory accounts for the 3/4th scale exponent on the basis of the assumption that
natural selection evolved hierarchical fractal-like branching networks that distribute
energy, metabolites, and information from macroscopic reservoirs to microscopic sites.
(West and Brown 2004)
¼
