Agriculture Reference
In-Depth Information
Estimating Leaf Longevity from Census of Leaf
Cohorts over Time
The primary alternative to following the emergence and fall of leaves on shoots is
to focus on the leaves themselves, following the fate of cohorts of leaves over time.
Whether estimates of leaf longevity are derived by shoot- or cohort-based methods,
the calculations depend fundamentally on records of the birth and death of leaves.
The cohort approach adapts methods of life table analysis well established in popu-
lation biology (Krebs 2008) that provide estimates not only of leaf longevity but
also age-dependent leaf mortality rates. The approach of Dungan et al. (2003) can
be used in shoot-based studies to derive age-dependent probabilities for leaf death
as well. The distinction between shoot-based and cohort-based approaches to esti-
mating leaf longevity has more to do with context and sampling design than with
any fundamental difference in the basis for estimation of leaf longevity. Both
dynamic and static sampling designs can be used in cohort-based estimates of leaf
longevity (Krebs 2008).
Estimates in dynamic analyses are derived by following single cohorts of leaves
from birth to death, which may impose a long and arduous sampling program. For
example, Xiao (2003) provides an example of a dynamic life table analysis based
on following a cohort of 1,000 leaves of
Pinus tabulaeformis
at annual intervals
over a 5-year period (Table
3.1
). The first column in the resulting life table records
leaf age in years, with age zero denoting the start of the census. The second column,
l
x
, is the number of the initial cohort surviving at age
x
. The third column,
d
x
, is the
mortality during age
x
, which is given by (
l
x
-
l
x
+1
).
L
x
, the average of
l
x
between two
needle ages, is given by (
l
x
+
l
x
+1
)/2, and defines the height of the histogram in
Fig.
3.5
.
T
x
is the summation of
L
x
from the older to younger age, which is equiva-
lent to the area of the histogram,
T
x
=
T
x
+1
+
L
x
.
T
x
divided by
l
x
represents the average
expected life at age
x
. The line in Fig.
3.5
is the
l
x
curve, which illustrates the sur-
vivorship of the 1,000 leaves over time. The average life expectancy at age zero is
the mean longevity of leaves. In the case of this pine species, the mean leaf longevity
Table 3.1
Dynamic life table for needles of
Pinus tabulaeformis
(after Xiao 2003)
Age (years)
l
x
d
x
L
x
T
x
e
x
0 1,000 240 880 2,000 2.00
1 760 282 619 1,120 1.47
2 478 246 355 501 1.05
3 232 205 130 146 0.63
4 27 24 15 16 0.59
5 3 3 1 1 0.33
l
x
, The number of the initial cohort surviving at age
x
;
d
x
, the mortal-
ity during age
x
;
L
x
, the average of
l
x
between two needle ages;
T
x
,
the summation of
L
x
from older to younger age;
e
x
, the average
expected life at age
x
