Agriculture Reference
In-Depth Information
Box 4.2
(continued)
where
N
0
and
N
x
are the number of individuals at times 0 and
x
, respectively,
and
r
is the
intrinsic rate of population growth
. Now let the number of indi-
viduals born 1 year ago be
n
1
; the number surviving from this cohort is then
n
1
l
1
, where
l
is survival rate. An individual bears
b
1
offspring; thus, in total the
cohort produces
n
1
l
1
b
1
offspring. Similarly, individuals born 2 years previ-
ously will produce
n
2
l
2
b
2
and so on. Thus, the total number of new individuals
born in a year is
∞
=
∑
n
nlb
(2)
0
ii i
0
where we consider that
b
0
= 0.
Now consider the relationship between the total number of offspring born
in this year (
n
0
) and those born last year (
n
1
). The growth must be exponential:
n
0
=
n
1
e
r
or
n
1
= e
−
r
n
0
.
Similarly,
−
ir
n
=
e
n
(3)
and substitution of (3) into
n
i
in (2) will give
0
∞
=
∑
e
ir
−
n
nlb
0
0
ii
0
Dividing both sides of the above equation by
n
0
will give the equation:
∞
=
∑
e
ri
ii
−
1
lb
i
=
0
Carbon Balance at the Time of Leaffall
Which of the leaf longevities given by (4.14) and (4.17), and which of the photo-
synthetic rates at the time of leaffall given by (4.15) or
a
* = 0, are nearer to the
truth? Kikuzawa (1991) held that if there were no constraints on the number of
leaves that could be retained by a single individual plant at a time, then leaves
should be retained for their full potential longevity and thus their photosynthetic
rate at the time of leaffall should be zero. But if there are some constraints to retain
a fixed number of leaves for a plant, then leaves should be shaded at the time of
t
opt
,
even while photosynthetic rate is positive. Ackerly (1999) tested the two alterna-
tives and suggested that leaf senescence is primarily a function of the position of
a leaf within a canopy rather than its chronological age. He also examined the
photosynthetic rates at leaf death, which were greater than zero but nearer to zero
