Original article
Comparing volume growth in pure and mixed stands of Pinus sylvestris and Quercus pyrenaica
Comparaison de la croissance en volume dans des peuplements purs et des peuplements mixtes de Pinus sylvestris et de Quercus pyrenaica
Miren del Río^{1}^{,2}^{*} and Hubert Sterba^{3}
^{1} Joint Research Unit INIAUVa on Sustainable Forest Management
^{2} Dep. Sistemas y Recursos Forestales CIFORINIA, Ctra. A Coruña, km 7.5,
28040 Madrid, Spain
^{3} Dept. of Forest and Soil Sciences, BOKU University of Natural Resources and Applied Life Sciences,
Peter Jordanstrasse 82, Vienna, Austria
^{*} Corresponding author: delrio@inia.es
Received: 22 September 2008
Accepted: 7 January 2009
• In Mediterranean forestry, it is important to improve knowledge about mixed stands dynamics, including their productivity. Previous studies have focused on the interactions between different species (competition, reduction of competition and facilitation) depending on site, species composition and structure.
• At the centre of this research are the possible differences between pure and mixed stands of Pinus sylvestris and Quercus pyrenaica in terms of densitygrowth relationships and volume growth per species.
• Using data from the second and third Spanish National Forest Inventory (606 plots), volume increment models for these species were fitted. Both species displayed a similar densitygrowth pattern for pure and mixed stands, with a maximum volume growth at maximum density. Volume increment per occupied area was also found to be greater in mixed stands as opposed to pure stands, suggesting a species interaction with reduced levels of competition in the former. However, the total volume growth was generally lower in mixed stands since the growth rate of oak is much lower.
• The results highlight the expedience of favouring P. sylvestrisQ. pyrenaica mixed stands with higher proportions of pine trees in order to gain the benefits of a more complex forest whilst retaining an acceptable level of wood production.
Résumé
• Dans la foresterie méditerranéenne, il est important d’améliorer les connaissances sur la dynamique des peuplements mixtes, y compris sur leur productivité. Des études antérieures ont mis l’accent sur les interactions entre espèces différentes (concurrence, réduction de la concurrence et facilitation), selon la station, la composition des essences et la structure.
• Cette recherche porte sur les différences possibles entre les peuplements purs et les peuplements mixtes de Pinus sylvestris et Quercus pyrenaica en termes de relation densitécroissance et croissance en volume par espèce.
• À partir des données du deuxième et du troisième Inventaire Forestier National Espagnol (606 placettes), des modèles d’accroissement en volume pour ces espèces ont été ajustés. Les deux espèces ont affiché un modèle densitécroissance similaire pour les peuplements purs et les peuplements mixtes, avec un volume maximum de croissance à une densité maximale. L’accroissement de volume par zone occupée a également été trouvé plus important dans les peuplements mixtes plutôt que dans les peuplements purs, ce qui suggère une interaction entre espèces avec réduction des niveaux de concurrence dans celuilà. Toutefois, la croissance totale en volume a été généralement plus faible dans les peuplements mixtes puisque le taux de croissance du chêne est beaucoup plus faible.
• Les résultats soulignent l’opportunité de favoriser les peuplements mixtes P. sylvestrisQ. pyrenaica avec une proportion plus élevée de pins afin d’obtenir les avantages d’une forêt plus complexe, tout en conservant un niveau acceptable de production de bois.
Key words: mixed forest / volume increment / densitygrowth relationship / Pinus sylvestris / Quercus pyrenaica
Mots clés : forêt mixte / accroissement en volume / relation densitécroissance / Pinus sylvestris / Quercus pyrenaica
© INRA, EDP Sciences, 2009
1. INTRODUCTION
In forestry, the importance of mixed stands has increased in recent decades due to the potential benefits which can be gained, such as increased production, greater diversity, improved nutrient cycling or reduced risk of biotic and abiotic damage (Cannell et al., 1992; Man and Lieffers, 1999). The question of potential productivity in mixed as opposed to pure stands has long been an area of interest in forest research (Assmann, 1970; Kelty, 1992) although there is a lack of general approaches for studying this topic.
According to ecological theory, there are three possible species interactions which take place in mixed stands, namely: competition, reduced competition and facilitation. The latter two result in greater productivity of mixtures (Kelty, 1992; Vandermeer 1989). In general, competition arises where the different species occupy the same niche. This frequently occurs when the species grow in the same canopy stratum and light is the most limiting resource (Assmann, 1970; Kelty, 1989; Linden and Agestam, 2003). A reduction in competition occurs when the different species use the above and belowground resources in a different way because of differences in shade tolerance, phenology, leaf canopy or root system, or due to mycorrhizal linkages (Kelty, 1992; Man and Lieffers, 1999). Facilitation is generally associated with the increase in available nitrogen resulting from increased litter decomposition rates or due to the presence of nitrogenfixing species (Kelty, 1992). Other possible forms of facilitation are the sheltering of one species by the other and the reduction of biotic and abiotic damage (Man and Lieffers, 1999).
To compare production levels between mixed stands and monospecific stands, one possibility is to relate the growth of the species in mixed stands to the area occupied by the respective species (Kennel, 1965). This approach has been used in studies at individual tree level to analyse the growing space efficiency or tree volume growth per unit of area, frequently through the crown projection area (Webster and Lorimer, 2003). Since the crowns may overlap or leave gaps in the canopy, the area available for each tree was defined by Kennel (1965) as the crown projection area, plus part of the adjacent gaps in the canopy, minus the overlaps with other crowns. When spatial information at tree level is not available, the species proportion by area (Prodan, 1959) can be used to assess the area occupied by each species at stand level, as it is frequently used in order to apply yield tables of pure stands to mixed species stands (Marschall, 1992; Speidel, 1972).
One aspect of mixed forest research that is largely neglected due to the lack of appropriate data is the densitygrowth relationship (Pretzsch, 2003). Wiedemann’s hypothesis (Assmann, 1970, p. 231) or Langsaeter’s plateau (Langsaeter, 1941) state that the volume increment does not vary over a wide range of densities. Results for different species growing in pure stands indicate that the density range, as well as the density at which volume increment is at a maximum, depend on species and site qualities (e.g. Assmann, 1970; Pretzsch, 2005). In the case of mixed stands, Pretzsch (2003) refers to the different growthdensity patterns observed for mixed stands of Norway spruce and common beech in relation to pure stands. The former display greater elasticity of growth against a reduction in stand density.
Scots pine (Pinus sylvestris L.) and Pyrenean oak (Quercus pyrenaica Willd.) are two of the most important forest species in Spain not only for their widespread distribution (approximately 1000000 and 700000 ha pure stands respectively) but also because of their ecological and socioeconomic value. The two species form mixed stands where their natural ecological distributions overlap (colder and higher areas of oak distribution) and where Scots pine has been introduced into the natural distribution areas of the oak. In spite of the higher economic value of Scots pine wood, the advantages associated with the complexity and diversity of mixed stands mean that the latter are currently attracting greater levels of interest (Spanish Forest Plan, MMA, 2002). The ability of mixed stands to regenerate after a forest fire through both seed dispersal and resprouting is of particular interest. It is therefore important to improve our knowledge with regard to the dynamics of these stands, including the effect of composition on stand productivity.
A number of studies concerning production in mixed stands of Scots pine in Northern and Central Europe have been conducted, the majority of which have centred on mixtures with Norway spruce, beech and birch (Assmann, 1970; Brown, 1992; Frivold and Frank, 2002; Linden and Agestam, 2003). However, none of the research carried out to date has focused on mixed stands of Scots pine and Mediterranean oak, such as Quercus pyrenaica . The objectives of this paper are to analyse the densitygrowth relationships in pure and mixed stands of P. sylvestris and Q. pyrenaica and to compare the growth of the species in pure and mixed stands with different compositions and stocking densities. This study used the species proportion by area (von Laer (cit. Prodan, 1959); Sterba, 1998) to define the composition of the mixture and to study the effect of composition on volume growth at stand level. In order to calculate the species proportion by area as well as the stocking degree, the maximum basal area according to Sterba (1987) was estimated for both species.
2. MATERIAL AND METHODS
2.1. Data
The study area covers the two main mountain areas in which mixed stands of P. sylvestris and Q. pyrenaica are present; the Central mountain range (Region 1) and the NorthIberic mountain range (Region 2) (Fig. 1). These areas represent two of the most important natural distribution areas of Scots pine in Spain, where it is also the main commercial species.
Figure 1 Plot locations in Spain. 
Data from the second and third Spanish National Forest Inventory (SNFI) were used for the purposes of the study. The SNFI is a systematic sample of permanent circular plots of variable radii distributed on a square grid of 1 km, with a measurement interval of 10 y (ICONA, 1990). The plots are composed of four subplots with radii of 5, 10, 15 and 25 meters, where trees with a diameter at breast height greater than 75, 125, 225 and 425 mm respectively, were measured. The data recorded for each sample tree are: azimuth, distance to the centre of the plot, species, diameter at breast height and total height. In this study, tree stem volume over bark was estimated from tree diameter and height through the volume equations proposed in the Second SNFI. Stand variables were estimated using factors to expand subplots to a hectare and volume increment per plot was calculated by subtracting the volume at the Second SNFI from the volume at the Third SNFI and then adding the volume removed (natural mortality and felling) between the two observations. Since the moment in time at which the trees were either felled or died is unknown, the volume of these trees was estimated using the dbh and height of the Second SNFI. In order to avoid large errors, plots from which more than 5% of the stand basal area had been removed were not considered in the study.
Plots were selected according to the species composition, including pure stands of both P. sylvestris and Q. pyrenaica as well as mixed stands in which both species were present. The criteria for selecting mixed plots were: presence of both species; the proportion of both species (number of trees per hectare) being higher than 10% (MAPA, 1970); and the proportion of other species being lower than 10%. In order to estimate stand variables, trees of other conifer species were considered as pines and trees of other broadleaved species as oaks.
In the case of pure stands, a total of 730 plots from the Second SNFI for Scots pine and 581 for oak were selected to study the maximum basal area, rejecting those plots where the density was very low (due to factors such as grazing, recent felling, rocky areas etc.). From these plots, only 310 plots for Scots pine and 215 for oak were used to analyse the volume increment (data from the Second and Third SNFI). The other plots were rejected either due to the removal of more than 5% of the basal area in the period between the two inventories, the lack of remeasurement data or, in some cases, due to growth anomalies. The final number of mixed plots included in the analysis was 81 (Tabs. I–III).
Main stand variables of plots used to fit the equation (9) (data from 2nd SNFI). N  Natural stands; P  Plantation stands.
Main stand variables of monospecies plots used to fit equation (13) (data from 2nd and 3rd SNFI). N  Natural stands; P  Plantation stands.
Main stand variables of mixed species plots by species and total, used to fit equation (13) (data from 2nd and 3rd SNFI). N  Natural stands; P  Plantation stands.
Plot age is not recorded in the SNFI, hence site index, which is a useful variable for studying the densitygrowth relationship, could not be estimated. Despite this shortcoming, the SNFI provides data from a large number of plots covering a wide geographical distribution.
2.2. Potentially available stand area for a speciesin mixed species stands
According to von Laer (cit. Prodan, 1959), the area available for a species in a mixed stand, in this study termed “species proportion by area”, can be calculated as
Calculation of the species proportion by area and volume increment of one species in mixed plots related to its occupied area.
In order to use this approach to calculate the area occupied by a given species, the potential, i.e. the maximum basal area per hectare had to be determined for the two species under investigation.
2.3. Maximum basal area in pure stands
Sterba (1987) developed a method to estimate the potential density based on the Competition Density Rule defined by Kira et al. (1959), the stand density index developed by Reineke (1933) and Assmann’s theory of maximum basal area (Assmann, 1970). The Competition Density Rule, modified by Goulding (1970), relates the quadratic mean diameter to stand density and stand height through the equation:
N_{Gmax} and Dg_{Gmax} are the stem number and the quadratic mean diameter at maximum basal area, and G_{max} is the maximum basal area. Relating these expressions to Reineke’s maximum stand density
The parameters b_{0} and a_{1} in equation (9) were estimated by non linear regression using the SAS “PROC NLIN” procedure (2004). In order to verify whether the maximum basal area differs between regions and stand origins, a comparison of models was made using the nonlinear residual sum of squares (Ratkowski, 1983). The full or complete model includes different parameters for each group, while the reduced model considers common parameters for all groups. The appropriate F statistic is
2.4. Densitygrowth relationships in pure and mixed stands
2.4.1. Volume increment
The volume increments per hectare and year in each plot were used in pure stands to study densitygrowth relationships. In order to compare the volume growth of the species in pure and in mixed stands, the volume increment of each species observed in each mixed plot was divided by the species proportion by area, thus achieving an increment per hectare of the respective species, which can be compared to the growth in the pure stand with the same stocking degree (I_{Vp} in Tab. IV).
2.4.2. Stocking degree
The densitygrowth relationship was studied assuming that the maximum density for a given dominant height (H_{dom}) in a pure stand is represented by the estimated maximum basal area according to equation (5), where parameters a_{0} , a_{1} , b_{0} , b_{1} vary with the species, origin of stands, and region and are estimated with the help of equation (9). In pure stands this G_{max} represents the maximum density (S = 1) and the stocking degree of plots is expressed as the ratio between the plot basal area per hectare and this maximum (S = G / G_{max}) . In mixed stands the plot stocking degree is defined as the sum of the areas of fully stocked pure stands of both species together, A_{1} and A_{2} , exhibiting G_{1} and G_{2} , respectively (Tab. IV).
2.4.3. Dominant height as a surrogate of age and site
Volume growth for a given species and region depends on site quality and stand age as well as on stand density or stocking degree. When comparing volume growth in mixed and pure stands, it is important to consider these variables. As the SNFI offers neither age nor site index, the data sets cannot be split according to site quality and age, so a great variability in volume increments per stocking degree was found for each stand type.
Dominant height expresses a compound effect of site quality and age and is frequently used instead of age and site index to estimate stand yield and growth (e.g. Assmann (1970) when defining his general yield level, or Abetz (1975) in his thinning guidelines). In this study, dominant height has been included in growthdensity relationships to reduce the variability of data and to compare pure and mixed stands.
2.4.4. Models
The densitygrowth relationships were studied through a model in which volume increment of one species is the dependent variable and dominant height, stocking degree, and species proportion by area the independent variables.
This model was fitted to different data sets: natural and plantation Scots pine, region 1 and 2. In order to facilitate the comparison among data sets, the inclusion of dummy variables for each data set or the validity of a unique, reduced model was studied using the F test in the same way as in the fit of the competition density rule. All fits were made via linear regression using the SAS software and basic hypotheses of linear regression were checked. If residuals showed the presence of heteroscedasticity, the dependent variable was transformed to correct it. A significance level of p < 0.05was used throughout the study.
3. RESULTS
3.1. Maximum basal area in pure stands
The competition density rule depending on two parameters (Eq. (9)) was fitted to the Scots pine data, splitting the plots according to regions and origins. The comparisons between regions and origins indicated that different models were needed for natural and plantation stands, but that data from both regions could be combined in one model (Tab. V). In all the fits presented, the parameter estimates were statistically significant (Tab. VI).
Comparison of models for different data sets using the nonlinear sum of squares (F) for equation (9).
Fitstatistics and parameter estimates (standard errors in parenthesis) for equation (9). N is the number of plots, se the standard error of the estimate of the quadratic mean diameter, dg (cm).
Using the coefficients a_{1} and b_{0} found (Tab. VI), the equations for maximum basal area are
For Quercus pyrenaica the comparison between regions showed that different models are required for region 1 and 2 (Tab. V). The parameter estimates and model statistics for both regions are presented in Table VI. The maximum basal area expressions for both regions are
3.2. Densitygrowth relationships in pure and mixed stands for Pinus sylvestris
Scots pine presented higher volume increments in plantation stands than in natural ones in both pure and mixed stands (Tabs. II and III). Thus, the inclusion in equation (13) of a dummy variable representing the stand origin was investigated, as well as possible interactions with the other variables. The quadratic relationship on S did not prove statistically significant. The final model for pure Scots pine stands is
Fit statistics and parameter estimates (standard errors in parenthesis) of the equations (18), (19). N and se as in Table .
This model for Scots pine stands reveals a negative relationship between volume increment and dominant height, whereas the relationship between volume increment and stocking degree was found to be positive. In the latter case, the maximum volume increment is obtained for the maximum stocking degree (S = 1) (Fig. 2). The selected model does not include the interaction between stocking degree and species proportion by area, so the same relationships between volume growth and stocking degree can be assumed for both pure and mixed stands. However, the variability of data is very high (Tab. VII) and the number of plots with high densities (S > 0.8) is scarce, particularly in mixed stands, so this relationship is not well covered by high density plots. The ‘species proportion by area’ parameter (P) reveals a decrease in volume increment as the species proportion increases, indicating the lowest volume increment in pure stands (Fig. 2).
Figure 2 Volume increment of Scots pine (I_{V}) over stocking degree (S) according to equation (18): (a) varying species proportion by area (P) for a dominant height (H_{dom}) of 15 m; (b) varying origin (N natural; P plantation) and H_{dom} for P = 0.5; when P < 1, I_{V} is the volume increment of the species related to its occupied area, I_{Vp} in Table IV. 
3.3. Densitygrowth relationships in pure and mixed stands for Quercus pyrenaica
The model obtained for Q. pyrenaica also includes the logarithm of the dominant height and the logarithm of the stocking degree (Eq. (19)), although in this case the sign of the parameter for the dominant height is positive (Tab. VII), indicating a higher volume increment as dominant height increases (Fig. 3). The interaction between the species proportion by area (P) and the logarithm of dominant height was found to be significant, indicating lower volume increments as the species proportion by area increases, with a larger effect for higher dominant heights (Fig. 3). The maximum volume increment was also found at the maximum stocking degree (the inclusion of a quadratic term on S was not statistically significant). As in the model for Scots pine, the interaction between stocking degree and species proportion by area did not prove statistically significant. The final model is
Figure 3 Volume increment of Quercus pyrenaica according to equation (19): (a) varying the stocking degree (S) and dominant height (H_{dom}) for a species proportion by area (P) of 0.5; (b) varying P and H_{dom} for S = 0.5; when P < 1, I_{V} is the volume increment of the species related to its occupied area, I_{Vp} in Table IV. 
3.4. Growth comparisons in pure and mixed stands
Using the fitted models (Eq. (18) and (19)) to estimate the volume increments of both species growing in mixed stands, the effect of composition on total volume increment can be studied as in a replacement series (Kelty, 1992). Calculations were performed separately for both origins and with values near the observed means of the SNFI mixed stands in order to simulate conditions similar to those reflected in the real data.
For pine and oak with dominant heights of 13 m and 8 m, respectively, and a stocking degree of 0.5 (Fig. 4a), the maximum total increment was found for an oak proportion of 0.1, although this increment is only slightly higher (0.12 m^{3} ha^{−1} y^{−1}) than that of pure Scots pine stands. If similar dominant heights are introduced while increasing the stocking degree to 1 (Fig. 4b), the total growth is maximum for the pure stand. A similar pattern is found for mean conditions in mixed stands where Scots pine was planted (Fig. 4c).
Figure 4 Total and by species estimated volume increment in mixed stands over species composition (expressed as proportion by area of oak): (a) Scots pine is natural, the stocking degree (S) is 0.5 and the dominant heights (H_{dom}) of Scots pine and oak are 13 and 8 m respectively; (b) similar to (a) but with S = 1; and (c) Scots pine was planted, S = 0.5. and H_{dom} of Scots pine and oak are 7.5 and 7 m respectively. Dashed lines reflect the expected volume increment (total and by species) if there were not reduction of competition in mixed stands, that is the volume increment of each species is proportional to the species proportion by area. 
For each species as well as for the total stand, the estimated volume increments in the three examples were higher than those which would be expected if intra and interspecific interactions were equivalent (dashed lines in Fig. 4), indicating a reduction in competition in mixed stands.
The relative increments (RI) (Eq. (20)), defined as the ratio between volume increment in mixed stands and its corresponding volume increment in pure stands (similar to relative yield defined in Kelty (1982)), was calculated for different stocking degrees and for the mean dominant heights of natural and plantation mixed plots (Fig. 5).
Figure 5 Estimated relative increment (Eq. (20)) of Scots pine (RI pine) and oak (RI oak) in mixed stands with different species proportions by area (P) for different stocking degrees (S): (a) natural Scots pine with dominant height of 13 m; (b) Plantation Scots pine with dominant height of 7.5 m; and (c) oak with dominant height of 8.5 m. 
4. DISCUSSION
A maximum basal area derived from the competition density rule was used in this study to estimate the stocking degree. The adjustment of this rule by fixing the two parameters related to the maximum density of Reineke seems to be a good method for estimating potential densities, since it gives the maximum density line previously fitted which is especially important when this line has been accurately fitted with nonthinned permanent plots, whilst also allowing the maximum basal area for each dominant height to be estimated (Sterba, 1987).
Differences in estimated maximum basal areas depending on Scots pine origins were larger for low dominant heights, probably due to the different dominant height growth patterns at young ages of natural and plantation stands, with higher increments in plantation forests (Río et al., 2006). The same dominant height indicates a different development stage for each origin, and consequently, different maximum basal areas. The differences found for oak growing in the two studied regions may be caused by the high variability found in stand typologies in Q. pyrenaica forests (Roig et al., 2007), ranging from open woodlands to very dense stands with stagnatingincrement.
Patterns found for densitygrowth relationships in Scots pine indicate a maximum volume growth for maximum density (Fig. 2), a similar pattern to that found for pure Scots pine stands in the same regions based on thinned permanent plots (Río et al., 2008), as well as for other areas in which Scots pine populations are found (Mäkinen and Isomäki, 2004). Regarding mixed stands, as the volume increment for both species growing in mixtures increases with the stocking degree, the sum follows the same pattern, although there are few plots at high densities. Pretzsch (2003) reported a saturation relationship between growth and density in mixed stands of Norway sprucebeech, with similar growth for medium and high densities and lower increment losses than in pure stands when density was reduced. The higher relative volume increments in mixed stands found in our study (Fig. 5), even where the stocking degree was lower, suggests a greater level of elasticity in mixed stands where the stocking degree is reduced.
The different behaviour of dominant height in densitygrowth models for both species can be explained by the compound effect expressed by dominant height. For Scots pine it seems to indicate the development stage (lower growth in more developed stands), while for oak it seems to indicate mainly site quality (positively related to volume increment). The effect of the species proportion by area in both models indicates better use of an occupied area whenever the competition comes from the other species, i.e. a reduction of competition in mixed stands. The higher volume increments in plantation stands may be due to the lack of older plantation forests since most of the reforestations were carried out during the second half of the 20 century (Gil and Prada, 1993).
The low variability explained by the growthdensity models may be due to the lack of age and site index information and to the characteristics of the SNFI data, in which measurement errors are frequent. The height measurements are usually even more inaccurate for broadleaved trees, explaining the poorer results for oak. Nevertheless, similar variabilities were obtained by Pretzsch (2005) in densitygrowth models developed for pure stands which included site index and diameter as covariates and which were based on longterm experimental plots.
Both studied species showed higher volume increments per hectare in mixed stands than in the respective monospecies stands. Similar results were found for mixtures of Scots pine with Norway spruce, alder and oak (Brown, 1992; Linden and Agestam, 2003). However, Frivold and Frank (2002) were not able to report a positive mixture effect where Scots pine grows alongside birch, probably because of the similar volume growth patterns of both species.
Despite the fact that the growth rate of each component species is higher in mixed than in pure stands, the total volume increment in mixed stands is generally lower than in pure Scots pine stands with a similar stocking degree. This fact is explained by the much higher productivity of one species in pure stands (Kelty, 1992). In the case of P. sylvestris and Q. pyrenaica , the differences in volume growth are very large; hence the reduction in area available to the Scots pine is not compensated by the increased growth of both species in mixed stands. Other studies concerned with mixed stands in which Scots pine are present reported a larger total production in comparison to pure stands for mixtures with Norway spruce and beech (Assmann, 1970; Brown, 1992; Linden and Agestam, 2003), although lower production was found where the mixture included oak and alder (Brown, 1992) because of the much smaller yield of these species.
Among the possible causes of a reduction in competition in mixed stands (Kelty, 1992; Man and Lieffers, 1999), the reduction in crown competition is probably one the main factors in stand compositions such as that considered in the present study. P. sylvestris and Q. pyrenaica present different shade tolerance and height growth patterns (Ruíz de la Torre, 1979), so mixed stands are frequently stratified with an overstory canopy of pine and an understory of oak (more shade tolerant and lower height growth). However, the influence of other factors should also be considered since the aforementioned stratification is not so patent for planted as opposed to natural stands of Scots pine (Tab. III).
There is evidence of differences in phenology and in the physiological responses of both species, although few studies have been developed in mixed stands (Inclan et al., 2007; RodríguezCalcerrada et al., 2008). A reduction in root competition might also occur in this mixture because of differences in the secondary roots, which are large and oblique in pine whereas oak develops stolons and abundant horizontal roots (Ruíz de la Torre, 1979). It is also likely that the deciduous leaves of the oak have a positive effect on nutrient cycling (facilitation) (Kelty, 1992), although previous studies concerning nutritional interactions in mixed forests revealed differing responses depending on species and environmental factors (Rothe and Binkley, 2001). Therefore, further research into the ecology of mixed stands with this composition are required.
5. CONCLUSIONS
The results of this study help to further our knowledge with regard to mixed stands of P. sylvestris and Q. pyrenaica and thus contribute towards achieving the objective of sustainable forest management in such stands. Although mixed stands are less productive than stands of pure Scots pine, the reduction in pine volume increment in mixed stands is lower than the corresponding reduction in occupied area. Therefore, by retaining or including a proportion of oak at around 20–30% per area, certain benefits associated with more complex forests could be gained without bringing about a great loss in pine wood production.
Acknowledgments
This study was conducted during the stay of M. del Río at the Institute for Forest Growth Research, BOKU University of Natural Resources and Applied Life Sciences. Funding was provided by the Spanish Ministry of Science and Innovation under the program “José Castillejo” for researcher mobility. The authors want to thank A. BravoOviedo, S. Roig and D. Sánchez de Ron for their assistance in the cartography work and bibliography revision.
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All Tables
Main stand variables of plots used to fit the equation (9) (data from 2nd SNFI). N  Natural stands; P  Plantation stands.
Main stand variables of monospecies plots used to fit equation (13) (data from 2nd and 3rd SNFI). N  Natural stands; P  Plantation stands.
Main stand variables of mixed species plots by species and total, used to fit equation (13) (data from 2nd and 3rd SNFI). N  Natural stands; P  Plantation stands.
Calculation of the species proportion by area and volume increment of one species in mixed plots related to its occupied area.
Comparison of models for different data sets using the nonlinear sum of squares (F) for equation (9).
Fitstatistics and parameter estimates (standard errors in parenthesis) for equation (9). N is the number of plots, se the standard error of the estimate of the quadratic mean diameter, dg (cm).
Fit statistics and parameter estimates (standard errors in parenthesis) of the equations (18), (19). N and se as in Table .
All Figures
Figure 1 Plot locations in Spain. 

In the text 
Figure 2 Volume increment of Scots pine (I_{V}) over stocking degree (S) according to equation (18): (a) varying species proportion by area (P) for a dominant height (H_{dom}) of 15 m; (b) varying origin (N natural; P plantation) and H_{dom} for P = 0.5; when P < 1, I_{V} is the volume increment of the species related to its occupied area, I_{Vp} in Table IV. 

In the text 
Figure 3 Volume increment of Quercus pyrenaica according to equation (19): (a) varying the stocking degree (S) and dominant height (H_{dom}) for a species proportion by area (P) of 0.5; (b) varying P and H_{dom} for S = 0.5; when P < 1, I_{V} is the volume increment of the species related to its occupied area, I_{Vp} in Table IV. 

In the text 
Figure 4 Total and by species estimated volume increment in mixed stands over species composition (expressed as proportion by area of oak): (a) Scots pine is natural, the stocking degree (S) is 0.5 and the dominant heights (H_{dom}) of Scots pine and oak are 13 and 8 m respectively; (b) similar to (a) but with S = 1; and (c) Scots pine was planted, S = 0.5. and H_{dom} of Scots pine and oak are 7.5 and 7 m respectively. Dashed lines reflect the expected volume increment (total and by species) if there were not reduction of competition in mixed stands, that is the volume increment of each species is proportional to the species proportion by area. 

In the text 
Figure 5 Estimated relative increment (Eq. (20)) of Scots pine (RI pine) and oak (RI oak) in mixed stands with different species proportions by area (P) for different stocking degrees (S): (a) natural Scots pine with dominant height of 13 m; (b) Plantation Scots pine with dominant height of 7.5 m; and (c) oak with dominant height of 8.5 m. 

In the text 