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than expected from (4.15). Oikawa et al. (2009) reported that leaves were shed even
though their carbon gain was positive, which increased the efficiency of nitrogen
use in the whole plant. But when nitrogen was not limiting, leaves tended to be
retained until their carbon gain became zero. Reich et al. (2009) assessed whether
the daytime carbon balance at the average leaf longevity of ten Australian wood-
land species is positive, zero, or negative. Almost all leaves had a positive carbon
balance at the time of their fall. These per-leaf carbon surpluses were of similar
magnitude to the assumed whole-plant respiratory costs per leaf. Thus, the results
suggest that a whole-plant economic framework may be useful in assessing controls
on leaf longevity.
Time Value of a Leaf
Harper (1989) was perhaps the first to consider that the value of a leaf changes
with time. He recognized that the value of a leaf for a plant is not simply the
lifetime summation of its photosynthetic gains but also the gains accrued
through investment of organic matter translocated from the leaf. If organic
matter can be translocated and used for production of new leaves earlier, this is
advantageous for carbon gain at the whole-plant level compared to later translo-
cation for production of new leaves. The situation is analogous to the process of
population growth, in which individual organisms reproduce new individuals. If
a population is maintained at stable numbers, then population growth rate ( r ) is
given by
r e lx m x x
(4.18)
()· ()d 1
=
where l ( x ) is the survivorship by age x , and m ( x ) is the rate of production of new
individuals at age x per unit time d x . By analogy to age at first reproduction, young
leaves cannot contribute to translocation until they are expanded and fully func-
tional. Leaves that translocate photosynthates used for production of new leaves
several days earlier thus yield an advantage in carbon gains at the whole-plant level
(Harper 1989). If the photosynthate is stored for later leaf production, however,
then this potential advantage is diminished or lost entirely. For example, stored
photosynthates used for leaf production in the next year would confer no advantage
through earlier translocation because materials from new leaves and those from old
leaves do not differ in value. In trees, for example, earlier translocation is signifi-
cant in successive leafing species but not in species with a simultaneous leafing
habit. As a corollary, selection should favor hastened development in successive-
leafing species but not in simultaneous-leafing species; delayed greening thus can
be expected to occur in some simultaneous-leafing species but not in successive-
leafing species.
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