Environmental Engineering Reference
In-Depth Information
maximum rates of both terrestrial and marine primary
productivity are subject to very similar body mass-related
energetic limits. Allometric regularities were also found
in the partitioning of phytomass in seed plants and the
density of autotrophs. Standing leaf mass (M
L
) scales as
the 3
=
4 power of stem mass (M
S
) and root mass (M
R
),
whereas M
S
and M
R
scale isometrically with respect to
each other (Enquist and Niklas 2002). This means that
the above-ground phytomass (M
A
¼
M
L
þ
M
S
) will scale
nearly isometrically with respect to roots and that the ra-
tio of M
A
=
M
R
(often called the shoot/rot ratio) declines
rapidly for small plants and becomes nearly asymptotic
for plants with M
>
10 kg. This size-specific prediction
makes it easier to estimate the below-ground phytomass
from more common assessments of above-ground phyto-
mass (Zens and Webb 2002).
At the same time, I must note that a high degree of
conformity across many orders of magnitude hides sub-
stantial differences at many levels. For example, for a
given M
S
, there is a 2 OM difference in M
L
among differ-
ent species. And while the scaling exponent is the same
for angiosperms and gymnosperms, their allometric con-
stants (intercepts on the y axis) are quite different (re-
spectively, 0.12 and 0.24) because conifers average 2.6
times more foliage (needles) than leafy trees of the same
stem size. But these realities do not fundamentally chal-
lenge the remarkable invariance of scaling exponents
across such autotrophic diversity and in such a range of
habitats. A fundamental challenge of the universal valid-
ity of 3
=
4 allometric scaling in plants came only with
direct measurements of plant respiration (Reich et al.
2006).
Some 500 observations of 43 perennial species—both
field- and laboratory-grown, ranging in age from 1
month to 25 years, and spanning 5 of the roughly 12
OM of size in vascular plants—lent no support to 3
=
4
power scaling of plant night-time respiration (and
hence its overall metabolism) and instead supported very
strongly isometric scaling (exponent@1). Moreover, the
study found no single universal relation between R
A
and
M but uncovered such a link between R
A
and total plant
nitrogen content (reflecting the fundamental role of the
nutrient in plant biochemistry), again with a scaling ex-
ponent of @1 (fig. 3.11). This demonstration of near-
isometric scaling of plant respiration eliminates the need
for complex fractal explanations of 3
=
4 power scaling
and makes it unlikely that there is a single size-dependent
law of metabolism for plants and animals.
The last remarkable mass-dependent regularity that
should not be omitted in this brief review of autotrophic
scaling is the self-thinning rule, which describes plant
mortality owing to competition in crowded even-aged
stands of terrestrial plants. Total phytomass of a stand
(M
tot
) can be increasing independently of the stem den-
sity (r, numbers/m
2
) until an intensive competition sets
in, lowers the density, and limits the average mass per
plant, in g) in a highly predictable way. Studies found
that in the allometric relation
M
¼
k
r
a
the exponent lies between
1.3 and
1.8 and has an
ideal value of
1.5, and k varies between 3.5 and 5.0 (J.
White 1985). Since M
¼
M
tot
=
r, an alternative formula
proposed by Westoby (1984) is M
tot
¼
k
r
0
:
5
(fig.
3.12). The
1.5 rule has three fascinating features: time
can be ignored because mortality depends only on phyto-
mass accumulation; this makes the thinning rate slower
