Agriculture Reference
In-Depth Information
(Kikuzawa 1991, 1995a,b, 1996) has offered predictions about the factors determining
foliar habit. The analysis by Kikuzawa (1991) recognizes the existence of sus-
tained periods in the annual cycle that can be unfavorable for photosynthetic activ-
ity, and that hence would appear to compromise the raison d'etre for maintaining
leaves in these unfavorable seasons. These unfavorable periods may be set, for
example, by extreme cold, as in the winter of the temperate zone, or by droughts,
as in the aseasonal tropics. To address the existence of the deciduous versus ever-
green habits, Kikuzawa (1991, 1995a, 1996) adapted the basic theory shown by
(4.3) and Fig. 4.2 to seasonal environments. Photosynthesis during the favorable
period simply follows (4.3). If plants retain leaves during an unfavorable period, the
leaves do not yield photosynthetic gains and in fact incur maintenance costs (respi-
ration) during this period. Hence, (4.3) can be recast in the form:
f
1
+
f
t
∫
∫
∫
G pt t
= +
()d
pt t
()d
++ −
pt t
()d
0
1
[]
t
1
2
t
∫
∫
∫
(9.1)
mt t mt t
()d
+
()d
++
mt t c
()d
−
f
1
+
f
[]
t
+
f
where
f
is the fractional length of the favorable period within a year and
t
is the
Gaussian notation. This equation gives photosynthetic gain by subtracting mainte-
nance costs of leaves during the unfavorable periods from photosynthetic gains
during the favorable period. Note that the maintenance costs during favorable
periods are already subtracted from gross photosynthetic gain; thus,
p
(
t
) is net
gain, the outcome of this subtraction.
What then is the optimal replacement timing of leaves for individual plants in a
seasonal environment with a period unfavorable for photosynthetic production?
Much as in the aseasonal situation, the solution is obtained by finding
t
that
maximizes
g
=
G
/
t
, but now
G
is expressed by (9.1) and follows a zigzag curve
through time, increasing during summer and decreasing during winter (Fig.
9.3
).
The optimal timing again obtains at the point when the line from the origin touches
the zigzag curve. An analytical solution is not readily available, but numerical
solutions can be found through appropriate simulations. If the optimal leaf longevity
under certain conditions exceeds the length of the favorable period, then the plant
is predicted to be evergreen. If the solution is for leaf longevity shorter than or equal
to the length of the favorable period, then the plant should be deciduous.
Simulations carried out for regions differing in length of favorable period yield pre-
dictions for patterns of occurrence in evergreen and deciduous plant species (Kikuzawa
1991, 1995a, 1996). Where favorable period length (
f
) is equal to 1 year, all plants are
expected to be evergreen, because plants can carry out photosynthesis throughout a year
(Fig.
9.4
). Even in such locations, however, there can be species whose leaf longevity
is shorter than 1 year. The evergreen habit combined with leaf longevity less than the
full favorable period suggests that a tree retains leaves throughout a year but with a high,
asynchronous turnover in individual leaves. When the favorable period length becomes
