124 Egbert G. Leigh, Jr
How much photosynthesis does this leaf area
carry out? Let a leaf receiving IμEs−^1 of
photosynthetic photons m−^2 leaf surface photo-
synth esiz eat th erat eA(I), where
A(I)=mI/( 1 +mI/Amax)μmolCs−^1 m−^2 leaf
Herem = 0.05 andAmaxis th el eaf’s max-
imum rate of photosynthesis. In canopy leaves
of tropical forest, taking all species together,
Amaxusually averages 2 g C hour−^1 m−^2 leaf, or
12.5μmolCs−^1 m−^2 leaf (Kira 1978, p. 571,
Zotz and Winter 1993). If the leaf area index above
our leaf isL,setI=Qe−kL, whereQis th eabov e-
canopy light level andk=0.7, which ensures
thate−kL=Q/2 whenL=1.Lneed not be an
integer: if half the sky overhead is covered by non-
overlapping horizontal leaves, thenL= 1 /2 and
Qe−k/^2 =Q/
√
2.
To calculat eth etotal photosynth etic rat ePTof
a forest with total leaf area indexLAI, receiving
QμEs−^1 of light per square meter of ground,
following Leigh (1999), set
PT(Q)=
∫LAI
0mQe−kLdL
1 +mQe−kL/Amax=
Amax
kln[
1 +mQ/Amax
1 +mQe−kLAI/Amax]
To do the integral, setu= 1 +mQe−kL/Amax,
du=−kmQe−kL/Amax.IfmQe−kLAIAmax,
then we may approximatePT by (Amax/k)ln
(1+mQ/Amax).
To estimate this forest’s total daily photosynthe-
sisPdaily,letQ=0 from 6 p.m. to 6 a.m., rise
linearly to 4Q∗between 6 a.m. and noon, and
decline linearly back to zero at 6 p.m. Here,Q∗is
the long-term average light level above the canopy.
ThenPdailyis
∫6 p.m.6 a.m.PT[Q(t)]dt=0.0432A^2 max
4 kmQ∗×
[(
1 +
4 mQ∗
Amax)
ln(
1 +
4 mQ∗
Amax)
−
4 mQ∗
Amax]
If Q∗ = 390 μEs−^1 m−^2 leaf (close to the
pantropical forest average) and ifk=0.7,m=
0.05, andAmax =12.5μmolCs−^1 m−^2 leaf,
then Pyearly = 365 Pdaily = 4.4 kg C m−^2.
Th er eal valu eis about 3 kg m−^2 (Loescher
et al. 2003). This theory gives a “ball-park” esti-
mat eof gross production, but it contains too
many “givens.” It does not explain why each
layer of leaves should take up half the remain-
ing light, even though canopy leaves are more
steeply inclined than understory ones, or why
Amaxof canopy sun leaves should average about
12.5μmolCs−^1 m−^2 leaf.
If foliage is equally productive in different
forests, gross production should depend little on
soil quality unless the soil is extremely poor. Fer-
tilizing a HawaiianEucalyptusplantation in a
rainforest climate at 20◦N increased itsLAIfrom
4.7 to 6.5 and its gross production from 3 to
4 kgCm−^2 (Giardinaet al. 2003). On th eoth er
hand, annual gross production on poor soil in cen-
tral Amazonia and on much richer soil in Costa
Rica ar eboth n ear 3 kg C ha−^1 (Tabl e8.1), as if, in
the long term, gross production were independent
of soil quality.
Competition for light, in which trees grow tall
trunks to shade their neighbors, creates majestic
forests of great beauty.Yet the competition among
trees to shade each other is a “tragedy of the com-
mons” (Hardin 1968), which reduces the forest’s
productivity (Iwasaetal. 1984, King 1990, Falster
and Westoby 2003). If light were distributed more
evenly among a forest’s leaves, its productivity
would be much higher. Sea palms,Postelsiapalmae-
formis, annual intertidal kelps of the northeastern
Pacific, can maintain over 14 m^2 fronds m−^2 sub-
strate, and produce up to 7 kg dry matter m−^2
substrat ein 6 months (L eighetal. 1987, Holbrook
et al. 1991), far higher than a rainforest’s annual
dry matter production. This productivity is possi-
ble because these kelps are restricted to the most
wave-beaten shores (Paine 1979, 1988), where
the waves keep them short (Denny 1999), and
continually stir their narrow, light-weight fronds,
assuring them far more nearly equal access to
light than a forest’s leaves receive. Indeed, a for-
est’s productivity declines sharply when its canopy
closes and the access of different trees to light
becomes progressively less equal (Binkley 2004).