*Pinus sylvestris*L. stands in Central Spain

*Pinus sylvestris*
stands in relation to silvicultural treatment (light or heavy thinning) and site index.

Scots pine (
^{3}
of sawn timber (with a high proportion of good quality timber) which potentially could be cut annually and used to supply several sawmills, which are also an important source of employment in the area. However, the environmental, landscaping and social benefits of these forests, which are known to play an essential role in the biological balance and the social development of the area, are increasingly being recognised (

The silvicultural management of natural stands of

Defining the rotation age for a particular tree species in an area is very important and gives rise to great controversy both in forest research (forestry economics) and forest management. Numerous methods have been developed on the basis of mathematical, economic and financial criteria (

Few other studies have focused on determining the optimal rotation age of the species in the

It is universally known that as the age of a forest stand increases, the size of the trees and technological quality of the timber also increase, and the unit price thus increases simultaneously to the growth in volume, which is called "growth in quality" (

Growth and yield models (such as yield tables) or diameter distribution models were not used in the aforementioned study (

Yield tables were developed in a later study including light and heavy thinning regimes (corresponding to the treatments C and E defined by

Yield tables were previously constructed for Scots pine in the Central Range (

More recently,

Although the rotation age of

The objective of this study was to propose a new approach to defining rotation ages on the basis of productive and technological aspects and to present an example of application of the methodology to natural Scots pine stands in Central Spain in relation to silvicultural treatment (light or heavy thinning) and site index. For this purpose, we assumed that the price per m
^{3}
of logwood suitable for veneer is four times higher than logwood not apt for veneer. From this assumption, the changes in the average price index value and in the proportion of timber suitable for veneer were calculated for different age classes, site indexes and silvicultural treatments, considering the yield distribution for different technological and commercial classes used by

To apply the proposed methodology we used the same yield distribution for different technological and commercial classes and the information about prices determined by

We then assumed that a tree has timber suitable for veneer when a log of at least 2.5 m in length and 36-37 cm in diameter, with no bark at the mid-point and with no external knots, can be obtained. Consequently, we considered the same distribution of timber production in m
^{3}
over bark and the price index values for different diameter classes (

The proportion of trees from which at least one veneer log can be obtained begins to be important from d.b.h higher than 40 cm and increases thereafter (

We calculated the changes in an average price index for different age classes, site indexes and silvicultural treatments. This average price index is a measure of the value of yield that takes into account the volume and price of timber destined for veneer. This timber is of the highest technological quality and is therefore the most valuable type of wood obtained from Scots pine trees.

We used the yield tables developed for natural Scots pine stands in the

Alvarez-Taboada (2000) fitted the well-known biparametric form of the Weibull distribution function (

where:

The information provided by

The values of stems/ha used in

The diameter distributions generated with

_{1}
_{2}
_{3}
^{2}
[2]

where:
^{3}
);
_{1}
,
_{2}
and
_{3}
= fitted parameters for each site index, as shown in

We used the diameter distribution and volume to generate tables of the distribution of timber production similar to

A total of 110 tables including the distribution of timber production and price index values for different diameter classes and for all combinations of age class, site index and silvicultural treatment were generated. For example, the tables for trees aged 120 years, site index 23 and silvicultural treatments C and E are shown in

The variations in the average proportion of timber suitable for veneer and in the average price index for age class, site index and silvicultural treatments are shown in

As expected, the variations in the average proportion of timber suitable for veneer and in the average price index followed very similar patterns, as the second depends on the first. Both variables increase with the age of the stand and site index, as is logical. They also show an asymptotic trend, which is much less marked in the poorest sites, indicating that the average proportion of timber suitable for veneer (and thus the average price index) stabilizes much earlier in the best sites.

Moreover, treatment E (heavy thinning) always produces higher values of the average price index than treatment C (light thinning) for the same age and site index. This is because heavy thinning leads to wider spacing and thicker (more valuable) trees (

The average proportion of timber suitable for veneer only exceeds 25% in the two best sites for treatment E (about 95 and 125 years in site index 29 and 26 respectively), and in the best site (SI 29) close to 150 years for treatment C.

The maximum value of the average price index reached is 1.80 (logically for the best site and the heavy thinning treatment E), which indicates that the maximum improvement in the value of these stands that could be obtained by considering the higher price of timber destined for veneer is 80%, although only in exceptional cases.

The average values of the proportion of timber suitable for veneer and of the price index are expected to be somewhat higher than those reported here, as the trees used by

In order to assess the increases in the average values of the price index, we estimated the total change (for the age range of 80 to 180 years) for different site indexes and silvicultural treatments (

The range of improvement for the average price index varied and was larger for light thinning (C) in the age range studied, except for site index 17. However, higher values were given for heavy thinning (E) at a particular age, indicating that this treatment yields a price increase before treatment C.

Increases in the price index value were found to be less than 1% before 180 years for all site indexes and heavy thinning, and also for site indexes 26 and 29 and light thinning.

A mean increase of 3.02% in the average price index for a ten-year period within the age range studied (80-180 years), for all site indexes and both silvicultural treatments, was calculated from the data in

The data included in

Moreover, according to

The silviculture treatment proposed in the yield tables for these stands produces a high proportion of trees in the diameter classes higher than 40 cm in all cases (and therefore an improvement of the price of wood products), but especially for the highest site indexes and the heavy thinning regime (treatment E) (

In addition, as expected, the trend for the change in the proportion of trees with a d.b.h. higher than 40 cm (

As previously mentioned, the proportions of timber suitable for veneer may actually be higher, and the difference relative to the proportion of trees with a d.b.h. higher than 40 cm may be lower.

Considering all of the above, the following criteria could be established for defining the rotation age for Scots pine natural stands in the

1) Rotation age should not be higher or equal than 140 years in any case, to prevent fungal rot.

2) When possible, the rotation age should be less or equal than age at which the ten-year increase in the price index is less than 3%.

3) When possible, the price index should be higher or equal than 1.50 (at least a 50% improvement over the value of the stand without considering the price of veneer timber should be achieved).

Thus, technological, productive and limitations imposed by the criteria regarding sanitary risk were combined. As indicated by

We propose the rotation ages shown in

The rotation ages shown in

Otherwise, the proposed rotation ages (

The proposed rotation ages (

The proposed approach is based on technological and productive criteria, with the limitations imposed by sanitary risks. The methodology can be applied to generate rotation ages in relation to different site indexes and silvicultural treatments, provided that the timber market prices and the yield distribution for different technological and commercial classes are known, and that a model of diameter distributions and yield tables for the species in the studied area are available.

Applying the proposed methodology to the natural Scots pine stands in the Sistema Central we found that resulting rotation ages are all much longer than the maximum income rotation ages reported for the species in the study area, but are similar to the rotation ages considered in the usual silvicultural shelterwood schemes proposed, with rotations of 100 and 120 years for heavy and light thinning regimes respectively. As expected, heavy thinning produced a greater number of trees of larger diameter and better technological quality, and earlier than with light thinning.

Considering the resulting rotation ages of between 90-100 and 140 years, periods of regeneration would occur in a broader age range than when considering the criterion of maximum income or the traditional rotation age of 100-120 years for all the site indexes in these stands. Thus a higher diversity of the age classes would be achieved, and the presence of continuous cover would be enhanced.

In order to apply the rotation ages proposed in this work a more detailed study on the evolution of the timber market in the area in the last years should be made to ensure the assumption of the used ratio between the price of the logwood suitable for veneer and the rest of the timber, and it also must be assumed that the prices of different types of wood will be maintained in the same current proportions, although they may vary with demand.

The definition of rotation ages based on the methodology discussed in this work could be complemented by the application of decision-making tools, with which it would also be possible to consider criteria that are not easily quantifiable, such as environmental and social aspects, which would help justify the application of thinning regime and a rotation age in different scenarios and contexts.

Finally, the risk of fire or forest pests and other natural phenomena that may negatively affect the stands must also be taken into account, given the slow recovery inherent in forest systems. This factor becomes even more important when the stands must fulfil a wide variety of social and ecological functions in addition to the purely productive aims, as in the natural Scots pine stands in the