To determine the parameters of photosynthesis, some preparatory transformations
must be made. Having performed elementary transformations from 7-10, we obtain the
equation for changing the diameter and height of the tree under competition for light
in the form:
,
2
1
1
1
2
2
2
2
+
+
−
−
=
D
H
H
P
D
H
D
c
dt
dH
H
D
dt
dD
(19)
We find the derivatives of D(t) and H(t) using the given (16), (17), and substitute
them in (18). We obtain a functional equation which depends on the required
parameters a, p,
max
P
, b, c, d, c
1
, c
2
, c
3
, d
1
, d
2
, d
3
,
0
t
, α, γ:
(
)
(
)
=
−
−
−
−
−
−
)
(
exp
))
(
(
exp
1
0
2
1
0
2
3
2
1
2
t
t
d
t
t
d
d
d
d
d
(
)
(
)
(
)
+
−
−
−
−
−
−
=
−
)
(
exp
)
(
exp
1
1
0
2
1
0
2
3
2
1
2
2
t
t
c
t
t
c
c
c
c
H
D
c
(
)
(
)
(
)
(
)
,
2
)
exp
ln
2
1
1
2
max
max
3
2
max
2
H
D
c
D
H
b
pV
aQ
P
aQ
P
p
V
P
D
d
−
−
+
+
+
+
(20)
For the site where a CPE is formed of a row of oak trees, this equation will be in
the form:
(
)
=
Q
p
P
d
c
b
a
t
G
,
max,
,
,
,
,
,
,
,
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
−
+
−
−
+
−
−
+
−
−
−
+
−
−
=
804
,
2
55
,
7
804
,
2
804
,
1
3
,
23
024
,
0
exp
1
5
,
26
6
,
17
029
,
0
exp
1
1
,
0
)
3
,
23
024
,
0
(
exp
1
8
,
1
)
3
,
23
024
,
0
(
exp
1
8
,
1
t
t
t
t
(
)
(
)
(
)
(
)
(
)
+
+
−
−
+
−
−
−
804
,
2
55
,
7
3
,
23
024
,
0
exp
1
5
,
26
)
6
,
17
029
,
0
exp
1
(
1
,
0
t
t
c
(
)
(
)
(
)
(
)
(
)
(
)
+
+
−
−
+
−
−
+
1
1
55
,
7
804
,
2
6
,
17
029
,
0
exp
1
1
,
0
4
3
,
23
024
,
0
exp
1
5
,
26
1
t
t
(
)
(
)
b
t
+
−
−
55
,
7
)
6
,
17
029
,
0
exp
1
(
1
,
0
- 1773 -