Agriculture Reference
In-Depth Information
This optimal timing is the point that a line originating from the origin touches the
cumulative gain curve. To obtain this optimal timing,
t
opt
, we differentiate
g
with
time
t
, and obtain the time
t
when the differential becomes 0. If at this point, the second
differential is negative, then this point is the maximum. The solution is given by
0.5
t
=
(2·
bC a
·
/
)
(4.5)
opt
This result suggests that optimum leaf longevity (
t
opt
) is determined by three para-
meters: (1) the daily photosynthetic rate of a young but fully mature leaf (
a
), (2) the age
of the leaf when the daily photosynthetic capacity becomes 0 (
b
), and (3) the unit cost
to produce the leaf (
C
). This solution, which is consistent with the conceptual model
proposed by Chabot and Hicks (1982), provides a comprehensive framework for the
analysis of leaf longevity; this framework also subsumes terms such as
C
/
a
that
Williams et al. (1989) had earlier related to longevity through their empirical studies.
Givnish (2002) criticized the focus on carbon in Kikuzawa's (1991) model for
leaf longevity, arguing that the only real constraint on leaf retention is the need to
retranslocate nutrients for use in new leaves, either immediately or for storage
through an unfavorable period in the annual cycle. He argued that even if leaves
have only very limited potential to secure further carbon gains, it is nonetheless
useful to take those gains so long as invested nutrients need not be recycled. He
points out that carbon, the main element of photosynthetic gain, is mainly used to
strengthen leaves through investments of cellulose, hemicellulose, and lignin in
cell walls and fiber - large polymers not easily broken down and reused. Givnish
(2002) would prefer a model for leaf longevity at the whole-plant level that con-
sidered jointly the economies of carbon and critical nutrients limiting leaf function
(e.g.,
N
,
P
), but is this really necessary to gain a fundamental understanding of
variation in foliar design? At least two lines of evidence suggest otherwise: (1)
foliar
N
and
P
concentrations are well correlated to photosynthetic function
(Wright et al. 2004) and to one another (Han et al. 2005; Reich et al. 2009), indi-
cating a close linkage in resource allocation and function at the leaf level, and (2)
species on average recover only about half their foliar
N
before leaf abscission
(Eckstein et al. 1999; Hemminga et al. 1999; Kobe et al. 2005; Yuan and Chen
2009). The important point that determines leaf replacement is not that the nutri-
ents concerned are or are not retranslocated, but that there is some limitation to
carbon gain in retaining leaves. It is simplest to assume that allocations of
N
and
P
follow rather than determine investments of carbon and the potential for carbon
gain. On the other hand, Oikawa et al. (2009) show that leaves can be shed before
they have recouped their full cost of construction if recovering foliar nitrogen and
investing it in new leaves confers an advantage at the whole-plant level when
nitrogen is limiting in the environment. If there are limitations set by either
endogenous or exogenous factors on the number of leaves a plant retains at a time,
it is better for a plant to replace leaves; if there are no limitations, plants should
retain leaves until their photosynthetic rate declines to zero. The fundamental
questions about leaf longevity then have more to do with the nature of factors
limiting or impairing leaf function as carbon-gaining organs at the leaf and whole-
plant levels than with ancillary concerns about retranslocation of mineral
nutrients.
