Environmental Engineering Reference
In-Depth Information
solution to the issue of light capture that needed to be solved
as plants went from water to land.
When leaves are arranged in a spiral in order to not shade
adjacent leaves, the pattern follows a geometric series called
the Fibonacci series, or numbers, after Leonardo of Pisa, also
known as Leonardo Fibonacci (1175-?), a mathematician
from the thirteenth century. In 1202, Fibonacci was inter-
ested in the potential reproductive prowess of rabbits.
Rabbits can mate at the age of 1 month. If a male and female
rabbit are placed together, and the female gives birth to only
two babies, one male and one female, at the end of the first
month there will be one pair, the original rabbits. At the end
of the second month there will now be two pairs, the original
pair plus the new pair (the two offspring), and at the end of
the third month, there will be three pairs, and so on.
Although these reproductive assumptions are rarely met,
Fibonacci realized that this progression had an interesting
numerical order of 0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,
235, and so on, for each number is the sum of the two
proceeding numbers. Such sequences are seen across many
natural and physical sciences.
The manner in which some plants produce lateral shoots
from the main stem also can follow a Fibonacci series. For
instance, examination of the number of lateral branches from
the main stem of a tree above ground can follow the pattern
of one, and then another branch above this one, so that a
horizontal line drawn through this node will intersect it and
the previous branch, so now there are two, and then a line
drawn though this reveals three branches, and so on through
the next branch, five, and then the next, eight. This is in the
vertical plane, and there also is a sequence of growth that
follows the Fibonacci numbers for the lateral plane around
the main stem, expressed as the arrangement of branches, or
leaves for herbaceous plants around the main stem. To arrive
at this conclusion, the leaves are counted from the bottom,
and the number of leaves per complete 360
revolution
around the plant is counted. For example, if branches,
twigs, and leaves can be arranged at 180
, 120
, and 144
intervals, this also is ½ (1 revolution
Fig. 3.18
The repetition of a common departure angle (137.5
) that
most plants exhibit is in response to the most efficient exposure to
sunlight and, therefore, food and energy production.
exposure to the leaves as well as downward penetration of
light. If this angle is changed only slightly, the amount of
leaves that can be packed most efficiently into the smallest
area or space will be decreased. The arrangement of leaves
for maximum sunlight exposure is related to the transpira-
tion rate of plants and, therefore, water use. The plants that
have higher transpiration rates have more leaves, as would
be expected. Both poplar and willow trees are characterized
by high
ET
rates and often are selected for use in the
phytoremediation of contaminated groundwater. These
trees have 8 leaves per 3 revolutions, and some willows
have 13 leaves per 5 revolutions. Again, this arrangement
helps explain why the trees are found where the water table
is shallow or where water is not limiting; the leaf surface
area, therefore, does not become a factor in growth and
reproduction.
Leaves of plants differ in many respects, such as shape,
but the largest classification criterion is the timing of leaf
drop. Deciduous (from the Latin
decidu-
, for falling off)
trees make and drop their leaves in one growing season,
whereas evergreen trees hold onto their leaves for multiple
growing seasons. Contrary to popular belief, not all
evergreens are coniferous plants. Live oaks (
Quercus spp.
),
wax myrtle, ligustrum, and many hollies are not coniferous
but retain their leaves. Like the conifers, these plants tend to
be found in drier soils, so once leaves are produced,
dropping them and regrowing new ones each year would
be too costly. Also, conifers are dominant in colder areas and
maintain their leaves because they have a very small surface
area, are covered by a thick cuticle, and are insulated by
wax. The needles, or leaves, of spruce trees go so far as to
¼
2 leaves), 1/3 (one
revolution
¼
5 leaves), and so on. Therefore, these spirals all have a
uniform ratio regardless of the plant type. This is believed
to be a result of the natural selection of branch and leaf
arrangement to maximize the leaf exposure to sunlight.
The study of this relation is called phyllotaxis, and even
though most plant species grow in some manner following
these patterns, it is not a universal phenomenon and can
change for each plant with respect
¼
3
leaves),
and
2/5
(two
revolutions
to environmental
variables.
What do Fibonacci numbers have to do with the plants
selected for phytoremediation purposes? The most common
arrangement of branches or leaves from a stem is the angle
137.5
(Fig.
3.18
). This angle provides maximum sunlight
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