Silvicultural alternatives to Spain’s Fagus sylvatica yield tables from another
European yield tables.
A. Sánchez de Medina1; E. Ayuga2; A. García3;M. A. Grande2; C González2.
1:
GARBEN Consultores (Madrid, ES). E-mail: alvarosmg@garben.com
: Economy and Forestry Management Department (ETSI Montes, Madrid, ES)
3
: Planning and Project Department (ETSI Montes, Madrid)
2
__________________________________________________________________________
Abstract
To use European yield tables as a selvicultural alternative to the Spanish yield tables was
tried to do. A statistical based-on model was proof to achieve similar tables that let to use
selvicultural models from different locations. Our hypothesis let to use yield tables from
different locations if these has the same site quality.
__________________________________________________________________________
Introduction
Just one Fagus sylvatica yield table exists for Spain, which was elaborated for the Navarra
region (MADRIGAL A.; PUERTAS F.; MARTÍNEZ MILLÁN J., 1992). These yield tables have
become a general reference for the different Fagus sylvatica forests of the country. They
show different variables in 10 years periods, spanning between 20 and 150 years and 5 site
quality levels.
A comparative study between Spanish, English (HAMILTON-CHRISTIE, 1971) and German
(SCHOBER, 1972) yield tables was performed.
Our hypothesis is that these three yield tables can be applied to any Fagus sylvatica forest
with equivalent site quality, in the sense that the different silvicultures in the yield tables
represent real and possible alternatives.
In order to prove this hypothesis, ANOVA analysis on the site quality indexes, showed that
Navarra first quality (NI), Hamilton-Christie third quality (HC6) and Schober third quality
(SCH5) were equivalent for the total production and height variables. Comparing mean
square error, founding the minimum distance between curves, completes proof. The same
method was applied to other quality index of Navarra yield tables.
The silviculture differences arise from the different values the Hart-Becking index presents in
the three yield tables. The mean diameter and the average tree current growth show lower
values in Spanish yield tables.
Two main objectives were aimed:
•
to obtain balanced beech trees in diameter and crown volume within a global aim to
get a sustainable forest. We look for a tree with a diameter bigger than 40 cm, at least
crown diameter 1/3 of total height and crown height 1/2 of the total height.
•
to get yield tables that let us to obtain the objective tree in a maximum of 150 years.
The Spanish tables are constructed for Navarra region. For these tables, five yield classes
are defined with the top height for 100 years. The thinning volume for each treatment is 9%
of the total volume and the spacing is almost constant in time (Hart-Becking index: 21-22%).
For the first yield class (NI) and when the age of the stand is 150 years, the mean diameter is
47,2 cm., the number of trees/ha is 199 and the top height is 33,3 m. This type of silviculture
does not produce the objective tree.
As Navarra yield tables do not let us to get the objective tree, we look for other European
yield tables. The yield tables selected are:
- United Kingdom yield tables (Hamilton-Christie, 1971)
- Germany yield tables (Schober, 1972)
Hamilton-Christie (1971)
Four yield classes are defined with the mean maximum growth. The thinning volume for each
treatment is 15,5% and the spacing is increasing in the time. For the third yield class (HC-6)
and when the age of the stand is 150 years the mean diameter is 60,7 cm., the number of
trees/ha is 122 and the top height is 26,5 m .
Schober (1972)
Four yield classes are defined with the mean growth (100 years). The thinning volume for
each treatment is 18,5% and the spacing is increasing in the time. For the third yield class
(SCH5) and when the age of the stand is 150 years the mean diameter is 45,9 cm, the
number of trees/ha is 149 and the top height is 30,3 m .
Comparison of dendrometrics data from yield tables with data from permanent plots in
French North and North West beech forests were made, taking data for:
- Top height growth
- Evolution of total yield volume (quality site)
Figure 1 : Growth in height (A) and volume (B) in the North-West of Bassin Parisien. Comparison with
Hamilton-Christie curves (yield classes 10 and 8) (TESSIER du CROSS, 1981; pp.: 329)
Figure 2 : Growth in height (A) and volume (B) in the North-East of France. Comparison with Shober
curves (yield classes 9 and 7) (TESSIER du CROSS, 1981; pp.: 330)
Method and results
The Objective of the method is to prove that the European yield tables can be applied to any
Fagus sylvatica forest with equivalent site quality. The different silvicultures in the yield tables
represent real and possible alternatives. The method has three steps:
- to recognize equivalent site quality index by means of comparison between yield tables.
- ANOVA analysis to verify whether Hamilton-Christie and/or Schober curves are equivalent
to Navarra for the medium value of total production and height variables or not.
- evaluate proximity between curves through mean square error.
Comparison between yield tables
The comparison between yield tables show that Hamilton-Christie 6 (HC6) and Schober 5
(SCH5) curves are near of Navarra I (NI) quality.
Figure 3: Comparison between yield tables: Top height evolution (left) and Evolution of Total
Production (right)
SCHi: Schober (i quality)
HCi: Hamilton-Christie (i quality)
NI: Navarra I quality
Anova
Several ANOVA analysis are applied to similar yield curves of Navarra I: HC6, HC8, SCH7
and SCH5; the best result is produced for these curves: NI/HC6/SCH5
Table 1: Comparison between yield tables. ANOVA analysis: Top height Quality curves: Navarra I,
Hamilton-Christie 6 and Schober 5
Sum of
G1
Mean square
F-ratio
P-value
Source
squares
Between
43,0578
2
21,53
0,59
0,5585
groups
Intra groups
1235,04
34
36,32
Total (Corr.)
1278,1
36
P-value > 0,05: no statistically significant difference between top heights stratus
Table 2: Comparison between yield tables. ANOVA analysis: Total production Quality curves: Navarra
I, Hamilton-Christie 6 and Schober 5
Sum of
Source
G1
Mean square
F-ratio
P-value
squares
Between
47834,6
2
23917,3
0,59
0,4
groups
Intra groups
Total (Corr.)
2,02593E6
2,07377E6
34
36
59586,3
P-value > 0,05: no statistically significant difference between mean total productions.
Mean square error
This estimator is expressed as:
150
MSE =
∑ (X
i
− Yi )
2
20
n
with:
X i : variable value of X curve (i year).
Yi : variable value of Y curve (i year).
i : years periods, spanning between 20 and 150 years
n : total number of periods with values.
The nearest curves will be those with the minor mean square error. The results of
comparison between tables are:
Table 3: Mean Square Error: Comparison between different tables
NI_HC10
Ho (m)
Production (m3)
NI_HC8
NI_HC6
NI_HC4
29,83
4,92
11,50
62,37
NI_SCH9
NI_SCH7
NI_SCH5
NI_SCH3
66,59
NI_HC10
9,55
NI_HC8
16,58
NI_HC6
94,59
NI_HC4
117.107,52
29.533,71
595,17
36.461,23
NI_SCH9
NI_SCH7
NI_SCH5
NI_SCH3
116.410,09
31.579,30
15.584,73
80.111,30
Conclusions
1.- Hamilton-Christie 6 is the most similar table compared with Navarra I. Schober 5 is quite
similar but presents some more differences. Although the three curves are equivalent, a
silvicultural alternative to the Spanish is to reach values for stability and equilibrium indexes
closer to those in English tables (to use the same spacing).
2.- The spacing cannot be constant in the time (as it is in Navarra), it is better to use spacing
of HC6 as the management guideline. So it is obtained trees of a big diameter and high
crown volume.
3.- As an alternative to Spanish quality table I, we propose Hamilton-Christie quality table 6
since it gets more stable, mature and greater final size trees with similar quality parameters.
4.- A similar procedure has been followed to assign some silvicultural alternative from yield
tables to other qualities of Spanish yield tables.
Reference
Madrigal, A. et al. (1992). Tablas de Producción para Fagus sylvatica L., en Navarra.
Gobierno de Navarra. Pamplona.
Hamilton, G.J. and Christie, J.M. (1971). Forest management tables (metric). Forestry
Commission Booklet, 34, pp. 201.
Schober, R. (1972). Die Rotbuche 1971. Sauerländer’s Verlag. Frankfur.
Teissier du Cross, E., et al (eds) (1981). Le hêtre. INRA. París.