Environmental Engineering Reference
In-Depth Information
the variable of size (most often M), and b is an exponent
(isometry is maintained when b
¼
1). Restated logarith-
mically,
log y
¼
log a
þ
b log x
;
the exponent determines the slope of the straight line on
a log-log graph; a is then the intercept of y (it represents
the value of y when x
¼
1).
Allometric scaling has been a common tool in investi-
gating functional (particularly metabolic) and structural
regularities in heterotrophs (see chapter 4), but a series
of scaling studies published since the late 1990s claimed
that autotrophs share the same basic scaling exponent
as far as the intensity of their metabolism (NPP) is con-
cerned. Enquist et al. (1999) examined life history varia-
tion of 45 species of tropical trees that attain similar
canopy sizes despite substantial differences in their rates
of growth and ages of maturity, and found that their
metabolism scales as M
3
=
4
, much like the metabolism of
many heterotrophs (see section 4.1). Niklas and Enquist
(2001) extended this study of interspecific phytomass
production rates and body size to photosynthesizers,
including unicellular and multicellular autotrophs repre-
senting three algal phyla, aquatic ferns, aquatic and ter-
restrial herbaceous plants, and trees (monocots, dicots,
and conifers). The examined set spanned over 20 OM of
body size and over 22 OM of body length (cell diameter
or plant height).
Annualized growth rates (in kg DM/plant) scaled as
M
3
=
4
, and plant body length scaled as M
1
=
4
(fig. 3.11).
Light-harvesting capacity (pigment content of an algal
cell or foliage phytomass of higher plants) also scaled as
M
3
=
4
, as did foliage photosynthesizing phytomass
(foliage) in relation to nonphotosynthesizing plant mass.
3.10 Carbon losses from land use changes, 1850-2000.
From Houghton and Hackler (2002).
3.5 Autotrophic Scaling
Changes in size have both structural and functional con-
sequences for otherwise very similar organisms. If there is
no change in similarity between the studied variables
across a wide range of values, then they scale isometri-
cally and the plot of this relationship will be a straight
line. If the similarity is not maintained, the scaling is allo-
metric and the plotted lines are curved. Both autotrophs
or heterotrophs rarely maintain geometric similarity rela-
tive to the mass of the whole body (M, the most com-
monly considered independent variable) or to the mass
or size of its parts. Their allometric scaling is expressed
by the general equation
y
¼
ax
b
;
where y is the variable of interest, a is a constant multi-
plier needed to express the result in particular units, x is
