Agriculture Reference
In-Depth Information
Modeling Self-Shading Effects on Leaf Longevity
Self-shading in the course of canopy growth is one example of a factor at the
whole-plant level that can influence leaf longevity. In the Kikuzawa (1991) model,
photosynthetic rate is assumed to decline with leaf age, although not for any specific
reason. If there were no photosynthetic decline with leaf age, parameter
b
in (4.2)
and (4.5), and hence leaf longevity, would go to infinity. There is no need to replace
leaves for a plant if the photosynthetic rate of leaves does not decrease with time
for some reason. It may be, however, that the cause of declining photosynthetic
capacity is not aging per se, but rather the progression of self-shading and a con-
comitant decrease of nitrogen contents in leaves caused by retranslocation to more
well-lit leaves in the developing canopy (Ackerly and Bazzaz 1995; Ackerly 1999).
If we assume that the number of leaves on a growing shoot is maintained constant,
then leaf longevity will be given from (3.4) by
L Nr
=
/
(4.6)
where
L
is leaf longevity (days),
N
is leaf number per shoot, and
r
is leaf production rate
per shoot per day. Now let the photosynthetic production rate per shoot per day be
D
g
:
D N
=
·
(4.7)
g
where
a
is the mean daily photosynthetic rate averaged across all leaves on the
shoot. Photosynthetic carbon gain by the shoot then can be partitioned to new leaf
production (
D
c
) and to translocation at the whole-plant level (
D
s
), which will be
used for branch, stem, and root production and reproduction. Let the allocation
ratio to foliar production be
F
; then
D FNa
=
··
(4.8)
c
If the cost to produce one leaf is
C
, then leaf production rate per day (
r
) is given
by
r
=
D
c
/
C
where
D
c
is given by
D NC L
=
·/
(4.9)
c
As translocation is given by
D
g
−
D
c
, then the translocation
D
s
is given by
(4.10)
D NaCL
= −
·(
/
)
s
and by substitutions,
r
will be given by
r FNa C
=
··/
(4.11)
The preceding two equations are focal in maximizing translocation (4.10) and
shoot growth (4.11), but we have to know how mean daily photosynthetic gain
(
a
) changes. If the instantaneous photosynthetic rate declines with time, as shown
in (4.2), mean daily photosynthetic rate will be given by
A a aL b
=−
0
· /2
(4.12)
0
where
a
0
is the photosynthetic rate at time 0 and
b
is a constant. This equation is
the integration of (4.2) from time 0 to time
L
divided by
L
.
