Coefficients of the Richards-Chapman function
3
)))
(
exp
1
(
)
(
0
2
1
c
t
t
c
c
t
H
−
−
−
=
have
meaningful biological treatment:
1
c
– represents the maximum possible value of the
growth function (asymptote), that is, reflects the magnitude of the used potential and
the growth environment;
2
c – scales the time axis and characterizes the growth rate of
the forest stand, being proportional to the maximum of growth. The values
(
)
1
exp
1
1
3
3
2
1
−
−
c
c
c
c
give the maximum value of the current increment, and
()
2
3
ln
c
c
is
the bend point of the growth function. Modeling of numerous YTs in this work has
shown that the sets of coefficients
3
2
1
,
,
c
c
c
adequately describe the peculiarities of the
growth of different species for different growth conditions [16, p. 190].
On the basis of experimental information, by the least squares method, the authors
calculated parameters
0
3
2
1
3
2
1
,
,
,
,
,
,
t
d
d
d
c
c
c
.
3
)))
(
exp
1
(
)
(
0
2
1
c
t
t
c
c
t
H
−
−
−
=
,
(8)
where
.
3
,
23
;
804
,
2
;
024
,
0
;
5
,
26
0
3
2
1
−
=
=
=
=
t
c
c
c
2
)))
(
exp
1
(
)
(
0
2
1
d
t
t
d
d
t
D
−
−
−
=
,
(9)
where
6
,
17
;
772
,
3
;
029
,
0
;
31
,
0
0
3
2
1
−
=
=
=
=
t
d
d
d
Presentation of the main material. To take into account the effect of
photosynthesis on the growth of trees, it is necessary to proceed to mathematical
modeling of the growth of linear parameters by the differential equation, which is
obtained on the basis of transparent physical and biological principles.
Mathematical modeling of tree growth is a highly developed area of scientific
research. One of the merits of this area is a significant ordering of a large number of
empirical data on growth [17]. However, the generally accepted model (tree growth
function) has not yet been found, nor have been identified models for different tree
species, although it is believed that the basic phenomenology of the growth process is
well known. Therefore, different models are used for different tree species based on
the experience of processing experimental data on CPEs which can be used.
In yield table 1, there are are models in which the influence of forest stand age is
manifested only in the deterministic component with a certain degree of reliability and
validity. Regression (linear or curvelinear) can usually be used for analytical alignment
of experimental data, but it should be used very carefully for extrapolation or prediction
of stand growth. Finally, research, as a rule, is carried out under conditions of so-called
passive experiment, where the experiment is carried out by nature (the tree grows under
the influence of environmental factors), taking into account human economic activity.
This fact explains one of the reasons for the low suitability of regression models
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