➢
A mature plant in the process of growth retains geometric similarity. This
means that this mature plant does not change the ratio of geometric dimensions with
growth, for example, the ratio of height to diameter;
➢
the plant receives free energy (or active substance) only by means of
photosynthesis;
➢
free energy is spent on photosynthesis, on constructing living tissue and on
uptaking the nutrient solution from the soil;
➢
on average, during large periods of time, the plant receives a constant amount
of light per unit surface and can absorb the necessary substances from an unlimited
supply.
In these works, the equation of tree growth is presented in the form of the law of
energy conservation:
0
)
(
2
2
2
2
=
−
−
−
x
dt
d
x
x
x
ax
(10)
where х is the linear size of a tree; α, β, γ, δ, are some constants; ρ is plant density.
The crown surface of the tree is considered to be proportional to x
2
, the volume of
the tree is proportional to x
3
. The first term in the equation is equal to the energy
obtained as a result of photosynthesis, the second – the energy consumption for the
needs of photosynthesis, the third – the energy consumption for transporting the
nutrient solution in all parts of the plant which is proportional to the product of the
volume of the tree and height, since they are associated with overcoming gravity, the
fourth – the consumption for increasing the mass of the plant. In the works [23, 24], it
was noted that in case of limitation of light resources, the tree redistributes its growth
in favour of height increment. Therefore, it is believed that the tree that grows under
competition for light does not retain the geometric similarity between the increment of
volume and height. Kolobov proposed to express the height of a tree (H) as an
independent variable, and designate x
2
as volume (V), thus, taking into account the
changes in the geometric proportions of the tree during its growth, the equation (10) is
modified and looks as follows:
,
0
)
(
=
−
−
−
V
dt
d
VH
S
aS
(11)
where V is stem volume, Н is height, S is the area of the leaf surface of the tree.
Then
,
cVH
EbS
dT
dV
−
=
(12)
where
−
=
b
and
=
c
are constants, E is the rate of photosynthesis per
unit leaf surface.
- 1771 -