Blakely's Red Gum

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2.2 In terms of leaf growth, does the canopy structure effect leaf shape?

Within the canopy of a tree, both competition and cooperation occur. To obtain as much sunshine as possible, leaves maximize exposure to sunshine, meanwhile minimizing their own shadows for the sake of the plant as a whole. That links a single leaf to the collection of leaves in the canopy. Some trees are extended and some are compact, on the other hand, some leaves are ovoid and some are pinnacle. If the connection between them can be verified, the question above is easy to answer.

- In terms of the plant overall, what’s the relation between the leaf shape and the tree?

This question focuses on an entire tree, and parameters related with the tree as a whole are needed.

- How to estimate the leaf mass of a tree?

According to the previous analysis of problems, this question is supposed to be solved by connecting leaf mass with parameters that relates to the overall appearance.

3. Variables and Assumptions

3.1 Variables

L

The length of leaves

W

the width of the leaves;

LWR

length-width ratio;

G

growing rate of tree’s height;

H

the height of the tree;

Y

the total leaves area of a tree;

d

the canopy diameter;

h

the height of canopy;

P

the possibility of variation;

3.2 Assumptions

- For the single tree investigated, it is isolated, still and in good conditions

It is assumed that the single tree to be investigated is set in an isolated area where appropriate nature conditions are provided. Sunshine or wind has no effect on the conclusion.

It is assumed that the tree investigated stops its growth of any of its organs.

It is assumed that the tree is healthy. The amount of leaves on a tree is moderate and the leaves are distributed evenly in all directions where they should.

- All leaves upon a tree are idetical.

Knowledge on the plant growth and canopy structure tell us that leaves grow differently resulting from the growth phase and position within the canopy. To simplify the problem, we neglect the difference among leaves on a tree. All the leaves are totally the same with an ideal geometrical appearance.

- This paper concentrates on the deciduous broad-leaf trees, exclusive bushes and evergreen broad-leaf trees.

4. The answers to the questions

Why do leaves have different shapes?

The diversity of tree leaves is the result of evolution over time, restrictive factors of ecological system may influence the shape of leaves.To the leaves, they must get enough sunshine to carry on the photosynthesis and through this process, they absorb heat.Leaves absorb carbon dioxide through the stomata .When stomata open, the internal water in the leaves will lost in the atmosphere .So’ balanced factors’make a great influence on the leaves: leaves get sunshine and carbon dioxide for photosynthesis, meanwhile the loss of water must be limited. That is to say that ’balanced factors’ are environment factors. The structure of the leaves veins also influences the shapes of the leaves. The veins support the leaves just like bones and transports water and nutrients justlike human blood vessels. It is inescapable that gene differences also cause various shapes of the leaves.

2 Each leaf grows larger as far as possible,to get more sunlight. Because the growth of the leaves space is limited, the leaves contest with each other.(mainly covered by the others). If too much competition occurs,the growth of plants will be adverse. So each leaf cannot be too big incase shade others.

Apparently, the leaves must be on the branches, so the distribution of the branches decides the distribution of the leaves in a certain extent. If branches are too close to each other and the areathe a single leaf is too large, leaves will shade each other and their growth can be affected. So we see that when the branches of the tree are in the close distribution, the single area of the leaf is not very big. If the branches arrangement is loose,larger leaves will have enough space to get the sunlight and avoid shade each other. In this situation (not covering each other), the bigger the tree of photosynthetic area, the better the tree grow.

If the tree branches extend to the air , large leaves can get enough room for receiving sunlight and do not cast shade on the others, under this condition ,the larger the leaves are, the more sunlight the tree can receive.

When we observe a leaf , we can find that there is an angle between leaf venations, this angle varies from species ,but to a certain kind of a tree, it remain the same. We think of fractal ,though fractal we can simulate the growth of leaves. Through observing the angle between trunks and branches , we find that the angle is nearly the same as the angle between venations , the angle between trucks and branches can also influence the shape if the tree. There are some relationships between the two angles , we think they are equal , cause venations are the extension of branches i.e. venations are the fractal of branches . In this way, we can explain the regular pattern of trees in the environment: trees with wide leaves extend to the air , looking huge and bloat ; trees with narrow leaves tight up , looking tall and straight.

5. Mathematical Models

- The model of neural network --to describe and classify leaves

- The basic principle of neural network

The