J. Northeast For. Univ. Vol. 5, No. 3, Sep. 1994
THEORY AND APPLICATION OF CUTTAGE SEEDLING AND AFFORESTATION ON POPLAR Bao Q i n g ( ~
7)
Fu Zhixue ( ~ )
Heilongjiang Forest Management Institute
ABSTRACT Fii'st, a theoretical model of density of cuttage seedlings on poplar was evaluated by using mathematical tools based on anatomy and morphology of photosynthesis organ, then, according to this, an afforestation density of the trees was put forward, finally, the importance, scope and method of the theoretic application were described through a concrete calculation. The result showed that these density models had not only rigorous theory base, including biology and mathematics, but also wide applying prospect. And at the same time, the model parameters could be gotten easily in forestry practice. Key words: Poplar, Cuttage, A fforestation, Density
It is one of problems that woods
density of cuttage seedlings is unclosed ac-
quality and quantity per area are raised
cording to the characters of seedling and its
through studying stand density. According
colony. And then, an afforestation density
to principle of forming a rational stand
can be gotten through a kind of trans-
structure, we try to achieve a theoretical
porting method.
model of one tree photosynthesis nutrition area (PNA) or T P N A
connected with
GENERAL S I T U A T I O N
populus photosynthesis organ form (POF or PPOF) and to get rational management
The
plots
are
arranged
in
four
density using mathematical ways. As sci-
nurseries located at Huhehot, Yijingholo
ence and technique develop on, there are
Forest Farm, Xinjie Control Sand Station
many examples and methods to study af-
and
forestation by mathematical tools. But so
Mongolia. The soil is w i n d - s a n d - g r o u p
far, many shortages that the field work is
except Huhehot in which soil is chestnut.
great and the cost is high and data process
The annual precipitation is about 200mm
is over elaborate (for instance, Density
except Huhehot in which precipitation is
Control Table and Density Control Figure)
about 400mm.
Hongqi
Work
Area
in
are difficult to be resolved. This research takes its eye on the nursery stage. First, the --31
Inner
crown is as original point 0 so that an M A T E R I A L S AND M E T H O D S
abscissa Kxcan be drawn (See Fig. 1), when x values are given (1,2,... n), the relevant
Species
are
Populus
nigra
var.
y values can be measured (See Tab.l).
thevestina, P. canadensis, P. simonii, P.
Y
+
beijingenisis, P. alba var. pyramidalis, P. coorperata, P. stalinsis and P. canadensis x P. cathayana. All seedlings (1-2 age and 3-5 age) on diagonal line of seedbed are measured with height, base diameter, breast high diameter (bhd), branch angle (up, middle and low
x,
part on tree crown), crown width and branch form growth curve (BFGC). The curve is that the seedling major stem is as
Fig.!
BFGC measuring
the ordinate y, the base part of the tree B F G C of P.alba var. pyramidalis
Table I curve
I straight part (cm)
curvilinear part (cm)
Xt
1
2
3
4
5
6
7
8
9
I0
Yl
0.3
1.0
1.6
2.4
3.3
4.4
5.4
6.5
8.1
10.0 12.4 16.7
According to the Tab.l, we can draw Fig.2 which is called as BFGC.
11
12
13
14
15
16
18
17
populus has its PNA which determines its colony density. RESEARCH CONTENTS BFGC
'~
/
=L
Model
We
believe
that
B F G C Model should be imitated by power
"#/
function like: b y = ax Where,
(b >>-1) a and
b are
(1) branch
form
parameter (BFP). Especially when b = 1, the branch form is a straight one which P.canadensis belongs to 0
5
10
15
x
Fig.2 Poplar BFGC
among
the
8
populus species (see Fig.3). The situation 0 < b < 1 can be seen on-
The B F G C is very different with different
ly when colony density is so great that
populus species. That means that a certain
crowns squeeze and press together and the
--32 --
branch growth is winding down. The situa-
Table 2 Theoretical and real values of TPD
tion b > 1 is the most general one. Another character
of
BFGC
is
straight
y = kx+b'after power function, where, k is
slope and b is its cut distance on abscissa x. We call the joint between the two curves as turn point and its abscissa distance as turn point distance (TPD) X. Y
b>l
TPD / cm
part
b=l
relative error % samples
populus
Theore- Real tical
P.nigra
15.2
16.1
20
0.05
P.canadensis
22.4
24.1
20
0.07
P.coorperata
22.2
24.6
20
0.09
P.stalinsis
9.7
10.2
20
0.05
P.simonii
13.6
14.5
20
0.06
KP.alba
12.6
13.4
20
0.06
P.canadensis x P. cathayna
12.5
12.8
20
0.02
P.beifingenisis
i 8.9
19.2
20
0.02
~a
o
x
Cuttage Fig. 3 Branch Power Function
(CSNR)
Seedling
Nutrition
Radius
BFGC and BNR are the base
of the CSNR or R'. We imagine that a Branch Nutrition Radius (BNR)
cuttage seedling is inserted vertically in a
We can find the solution of the equa-
seedbed (see Fig.4).
tion group (2), withR = ~y = kx + bt y = ax
b
(2)
F o r instance, to P . b e i f i n g e n i s i s , we have y-= 0.8~la(r = 0 . 7 4 ) , f = 1 . 7 Z - 1.5(r =
0 . 7 9 ) ,
a n d
R
=
Surface of {
-R
~-
= 18.9cm; to P . a l b a var. p y r a m i d a l i s , i t is y = 0.5Zl'3(r = 0 . 8 1 ) , f = 1.4x--- 0.7(r =0.85) and R = X = 12.6(cm). The companion result of the theoretical T P D and its real values of the eight populus species is arranged in Tab.2. The table reflects first
that
when
populus
species
are
different, their BNRs are not the same as well; second, that the B N R can be determined by measuring in a concrete practice, and third, that real value is generally more than theoretical one.
Fig.4 Cuttage seedling in the seedbed
Its upper side of the cut is on top of the bed and the age of the cuttage seedling equals the one of the seedling which will be cultivated. If the length of the cuttage seedling is L, we will have
R' = (L / a)l/b
(3) m33 m
The equation shows that when the cultivat-
x 27cm separately. We can call the method
ed seedling age is certain, the R' is deter-
as branch way (BW).
mined by BFP and L. 2R x 2R is the spac-
Especially when b= 1, the branch will ex-
ing in the rows and ranks at a certain age.
pand under the branch angle ~. And now,
For instance, if we let the Lbe 20cm or
the relation between R'and Lis R " = Ltg~
15era to P. beijingenisis and P. alba and a
Among the equation, ~ is the angle of
b is known, we can get their R', then the row and rank spaces are 29 x 29cm and 27 Table3
(4)
branch layer (see Tab.3). If we
A n g l e o f seedling age
of poplar angle(degree)
populus
samples up
middle
down
P. canadensis • P. cathayna
46.3
53.8
60.9
22
P. beifingenisis
48.8
50.3
52.7
20
P. alba
56.7
61.7
65.6
20
P. simonii
35.6
42.0
48.1
22
P. stalinsis
44.1
46.9
52.0
36
P. nlgra
49.2
50.2
55.6
30
P. canadensis
49.0
52.3
58.1
30
P. coorperata
43.2
47.4
52.3
20
let L fix, R"will change with ct values. For
R~ d as nursery coefficient. Suppose the
example, using above value L and Tab. 3,
management
we can get value R"according to equation (4) so that spaces in the rows and ranks are
populus is D cm and the aim BNR is Lxcm, we call the rate Lx/ D as stand
52 x 52cm to P. beijingenisis and 66 x 66cm
coefficient. The proportion of breast diam-
to P. nigra. We can call this method as the
eter and its crown width is a fixed number
angle way. As you can see, the tree would
that cannot be affected by site condition,
have gotten unlimited nutrition space had
age, density and forth. According to this,
their branch expanded only under the
We can have R / d - Lx/ O
branch angle ~t. But controlled by density,
aim
diameter
of
the
(5)
the branch is limited by BFP at the same
The Tab.4 is an illustration of equa-
time so that the colony product and indi-
tion (5) too. This means that nursery
vidual evolution are in progress.
coefficient or stand coefficient has a rela-
Suppose the
tion only with species and has hardly rela-
base diameter (1 age) or breast high diame-
tion with other conditions. So based on (5),
ter (I> 2age) of nursery period of populus
there is
Afforestation density
is dcm and BNR is Rcm, we call the rate --
34
--
L =(R/d)D
[6)
Table 4
Species
comparison o f R ~ d with L x / D
P. beijingenisis
P. nigra
Xiao Huoluo Forest Sand Station Farm
Red Flag Work Area
soil
light texture sand
sand
age samples
2 20
8 30
R/d L/D
7.21
place
Xinjie control
P. canadensis
Xiao Huoluo Forest Farm
Da Huo Luo Forest Farm
Xiao Huoluo Forest Farm
silt after warping
sand
sand
sand
silt after warping
sand
3 20
8 25
2 20
12 24
3 20
15 36
Nursery
10.72
5.15
7.48
relative
P. simonii
9.12
10.93
0.03
Xiao Huoluo Forest Farm
Hong Qi Nursery
5.42
0.02
9.26
0.05
0.02
error
The significance of the equation (6) is that
Using the models imitated by several
can be determined by R~ d and
equations, we can calculate the space in the
Lx of D
rows and density of cuttage seedlings and
that space in the rows is 2L x x 2L~m.
afforestation of different populus species (See Tab. 5 and 6). Lvalues of Tab. 5 come
APPLICATION CALCULATION
from real production. Calculation of cuttage space and density
Table 5
methods branch way a
b
P. nigra P. canadensis
0.40 0.49
1.25
P. slmonii 4 P. beUtngenisis P. coorperata
0.46 0.80 0.33
P. alba P. stallnsis P. canadensis • P. Cathayna
2R x 2R (cm)
11 15
28 x 28
8495
56
32 x 32
6504
44 x 44
3440
58
48 x 48
2891
28 x 28
8495
48
28 x 28
8495
22 x22
13760
53
40 x40
4163
44 x44
3440
52
48 x 48
2891
20 x 20
16650
66
45 x 45
3289
20 x20
16650
52
20 x20
16650
26 x 26
9852
61
26 • 26
9852
I.I0
13 15 19
1.28 1.20 1.31
0.50 0,40
1.32
10 8
0.28
1.27
7
1.30
Table 6
angle way
L cm
density number / mu
a ( ~)
2R x 2R (cm)
density number / mu
Calculation of afforestation space and density methods
P. nigra
d (cm) 1.63
R (cm) 14
P. canadensis P. simonii
1.86 0.70
22 1.4
branch way D 2L x x 2L x (cm) (cm) 20 3.4 x 3.4 20 20
4.7 x 4.7 8x8
density number / mu 58 30 10
R' (cm) 16 24 14
angle way 2L x x 2L x density (m) number / nu 3.9 x 3.9 44 5.2 • 5,2 8x8
25 10
P. beijingenisis
1.32
il
20
3.3 •
61
20
6.1 x6.1
18
P. coorperata P. alba
1.74
22
20
5.1 x5.1
26
24
5.5 x 5.5
22
2.03
10
20
2x2
167
23
4.5 x4.5
33
P. stalinsis P. canadensis x
1.05 1.55
10 13
20 20
3.8 x3.8 3.4 x3.4
46 58
10 13
3.8 x3.8 3.4•
46 58
P. cathayna
--35--
Dvalue of Tab. 6 can be supposed and oth-
determined using R' = ( L / b ) l / b and R ''=
er parameters may be really measured or
Ltg~t. The former is called as branch way
calculated. The calculation indicates that
and the latter as the angle way. When the
the different populus species needs differ-
age of the cultivated seedling is equal to the
ent the rows and density, that when BFGC
cutting, we have X = R' or X = R". Its for-
is power function, the equation (3) is suita-
estry means lie on the calculation of space
ble for space calculation, but when BFGC
in the rows 2R x 2Rcm and density.
is straight form, the equation (4) will be
When D value is given, the final fel-
suitable for it, that BFGC is very impor-
ling density of a populus stand can be de-
tant because when you select different
termined using L~= ( R /
methods of BNR calculation, the density
R ~ d is called as the nursery coefficient.
results ofcuttage and afforestation are very
Regulating 2L~ x 2L~,, we can get the first
different too, that the field planting density
planting density. The result shows that the
can be acquired through regulating 2Lx x
theoretical key of cuttage and plantation
2L~with crown overlapping coefficients,
density is the BFGC which can be gotten
finally that the process of the field work
easily in production.
d)D. The rate
and the data dealing with is easily and not tedious.
REFERENCES CONCLUSION
I. Gap Xinzeng, Botany (Morphology and Anatomy), Advanced Education Press,
Through the study of eight populus species, we think that the BFGC is com-
2. BeiJing Forestry University, Silviculture,
posed of y = aX~ and y = kx+b'. The joint
China Forestry Press, 1981, Page 166--
of the two curves is called as turn point and
168.
the turn point distance is the BNR o f a cer. tain age and density condition. The BNR of Cuttage seedlings can be
--36--
1985, Page 61--66.
3. Zejiang Forestry college, Forest Management Comprehensive Study (Inner Mate-
rials), 1991, Page 189--194.
