Agriculture Reference
In-Depth Information
If we consider that photosynthetic rate of individual leaves is determined by the
position of each leaf on a shoot, then photosynthetic rate declines linearly with
position in a way analogous to decline with age in single leaves (4.2). Mean photo-
synthetic rate is described by the following equation:
aa aN p
=−
0
· /2
(4.13)
0
where
p
is a constant,
a
0
is the photosynthetic rate of a leaf at the top of the shoot,
and
N
is the number of leaves counted from the top of the shoot. Substitution of
either (4.12) or (4.13) into either (4.10) or (4.11) gives four equations. Ackerly
(1999) gave solutions for two of the four: (1) to maximize the translocation from
the shoot when photosynthetic rate declines with time and (2) to maximize leaf
production when photosynthetic rate declines with position. The other two cases
give solutions intermediate to these two extremes. The solution of the first model
maximizing translocation is
*
0.5
L bCa
=
(2 ·
·
/
)
(4.14)
0
where
L
* is the optimal leaf longevity to maximize the translocation from the shoot.
This solution is basically the same as (4.4) for a single leaf. The photosynthetic rate
at
L
* is given by
a a aCb
=−
(2 ·
/
)
0.5
(4.15)
*
0
0
where
a
* is the photosynthetic rate at the time of leaffall and usually takes a posi-
tive value. In contrast, in the second case, the number of leaves that maximizes the
leaf production per shoot is given by
*
N
=
(4.16)
and the corresponding leaf longevity is given by
L CaF
*
=
2· / ·
(4.17)
which is equivalent to the equation given by Williams et al. (1989). The photosynthetic
rate at the terminal leaf lifespan when shoot growth is maximized is then
a
* = 0.
Box 4.2
Population Growth Rates
Although leaves do not reproduce in the ways that individual plants and ani-
mals do, nonetheless the leaves in a plant canopy can be considered a popula-
tion subject to the equations governing population growth. In this case, the
following equation will hold:
∞
=
∑
e
ri
ii
−
1
lb
i
=
0
If a population increases without any constraints, it will grow exponentially:
0
e
rx
(1)
x
NN
=
(continued)
