Agriculture Reference
In-Depth Information
b
G
r
a
r
p
G
p
0
−
C
0
−
C
2t
opt
0
0
t
opt
t
e
t
opt
t
e
Time (t)
Fig. 4.2
Leaf longevity is set by the optimal timing for replacing a leaf to maximize its cumulative
photosynthetic gain at the whole-plant level. The potential photosynthetic gain by a single leaf over
its lifetime is illustrated in (
a
). If an individual plant could retain a single leaf, the optimal time for
replacing that leaf to maximize gain is
t
opt
, or the point at which the line from the origin touches the
curve.
C
is the construction cost of the leaf and t
e
is the timing when the instantaneous photosyn-
thetic rate of the leaf becomes zero. The graph in (
b
) suggests that replacing the leaf at
t
opt
will yield
a greater total gain than retaining the leaf for a second season.
G
r
and
G
p
represents the cumulative
gain by a leaf when replacing (
r
) and persisting (
p
) leaves at t
e
. (From Kikuzawa 1991)
The qualitative consequences of these relationships for leaf longevity can be illus-
trated graphically (Fig.
4.2
). At the moment the leaf matures (time 0), there has been
no photosynthetic gain but the cost of leaf construction has been incurred, so the
cumulative gain curve has value (0, -
C
). Cumulative gain increases monotonically
with time, paying back the invested cost and then achieving net carbon gains. Through
the combination of decreased function with leaf age specific to a species and the
annual progression of environmental conditions in a locality, we expect that generally
the rate of carbon gain will diminish with time, until at some leaf age or environmen-
tal condition photosynthetic function is lost and respiratory costs associated with
maintenance and defense actually lead to a net loss of carbon produced by the leaf.
Thus, the point when the gain curve is a horizontal line is the time of maximum
potential gain by the leaf. If we designate the time of maximum gain as
t
e
, it will be
clear from (4.2) that
t
e
=
b
, the potential leaf longevity. So long as there are no limita-
tions imposing a longer period of leaf retention, this is also the optimal timing for leaf
turnover at the whole-plant level if photosynthetic gains are to be maximized.
To better illustrate the basic logic of Kikuzawa's model, consider a situation in
which a plant can retain only one leaf at a time, and hence the optimal strategy at
the whole-plant level collapses to simply replacing this single leaf. Then the optimal
timing to maximize gain by the plant is not to maximize cumulative gain (
G
) but to
maximize marginal gain (
g
), or
gG
=
/
(4.4)
