Agriculture Reference
In-Depth Information
to fall, we can calculate leaf longevity based on observations over any reasonable
interval (Williams et al. 1989) by using this equation:
(
)
( )
( )
/
L NdN N bt t
= −−
/
−
(3.2)
2
2
1
2
1
where
N
1
is the standing number of leaves at the initial observation (
t
1
),
N
2
is the sum
of
N
1
and newly produced leaves during
t
2
−
t
1
,
d
is the rate of leaffall during the obser-
vation period
t
2
−
t
1
, and
b
is the rate of leaf production during this period. When
N
2
−
N
1
is equal to
b
, this can be reduced to the following equation (Fonseca 1994):
(
)
( )
( )
/
L Nbd t
=+ −−
1
t
(3.3)
1
2
1
These equations assume stable leaf numbers during the period of observation,
which allows leaf longevity to be estimated using either the leaf production rate or
the rate of leaffall. If
b
=
d
in either equation, then leaf longevity can be estimated
even more simply as follows (Southwood et al. 1986; Navas et al. 2003):
/
(3.4)
LNd
=
1
where
t
2
−
t
1
is 1 (year, month, day, etc.). In a situation in which the number of
leaves fluctuates somewhat around an essentially stable state within the period of
observation, King (1994) provides an alternative version of (3.4) utilizing the average
number of leaves (
N
av
) instead of the initial leaf number (
N
1
):
( )
/
(
)
( )
(3.5)
L t tN bd
=−
0.5
+
2
1
av
Finally, consider (3.2)-(3.5) in relationship to the graphical framework (see
Fig.
3.3
) introduced by Navas et al. (2003). Because
b
=
N
/
t
and
d
=
N
/
t
, the number
of leaves (
N
i
) at any time
t
i
is given by
(
{ }
(3.6)
N
=− −+
bt
d t
t
t
i
i
i
p
and leaf longevity by
( )
(3.7)
L Nd bd t t t
= = − ++
/
/ 1
i
p
If
b
=
d
, (3.7) reduces to
L
=
t
p
+
t
, which is the same as (3.1) from Navas et al.
(2003). These various calculations of leaf longevity are all variants on a theme that
arise in the juxtaposition of alternative sampling designs and interspecific contrasts
in leaf demography. All the calculations use data on the relative timing of leaf
emergence and leaffall in different demographic scenarios that can be visualized in
the graphical framework introduced by Navas et al. (2003).
In all the calculations of leaf longevity based on repeated census of leaf emer-
gence and leaffall, the precision of the leaf longevity estimate ultimately depends
on the census interval. The longer the interval between observations, the less
precise will be the estimate of leaf longevity. Leaves may emerge or fall at any
