GROWTH AND YIELD MODELS IN SPAIN: HISTORICAL OVERVIEW, CONTEMPORARY EXAMPLES AND PERSPECTIVES
Coordinated by: FELIPE BRAVO • JUAN GABRIEL ÁLVAREZ • MIREN DEL RÍO
2012 73 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 1
Growth and yield models in spain: historical overview, contemporary examples and perspectives
Felipe Bravo 1,2 , Juan Gabriel Álvarez-González 3, miren del río 1,4 , marcos Barrio- anta 5, José antonio Bonet 6,11 , andrés Bravo-oviedo 1,4 , rafael calama 1,4 , Fernando castedo-dorado 7, Felipe crecente-campo 3, sonia condés 8, Ulises diéguez- aranda 3, santiago césar González-martínez 1,9 , iñigo lizarralde 10 , nikos nanos 8, alberto madrigal 8, Francisco Javier martínez-millán 8, Gregorio montero 1,4 , cristóbal ordóñez 1,2 , marc palahí 11 , miriam piqué 12 , Francisco rodríguez 10 , roque rodríguez-soalleiro 13 , alberto rojo 3, ricardo ruiz-peinado 1,4 , maria de la o sánchez-González 1,4 , antoni trasobares 14 , Javier vázquez-piqué 15
1 Sustainable Forest Management Research Institute University of Valladolid-INIA Spain. 2 Dpto. Producción Vegetal y Recursos Forestales, Universidad de Valladolid, Spain. 3 Unidad de Gestión Forestal Sostenible. Departamento de Ingeniería Agroforestal. Universidad de Santiago de Compostela, Escuela Politécnica Superior. Campus Universitario s/n. 27002 Lugo, Spain. 4 Dpto. Selvicultura y Gestión de Sistemas Forestales, CIFOR-INIA, Ctra. La Coruña, Km. 7.5, E-28040 Madrid, Spain. 5 Departamento de Biología de Organismos y Sistemas, Escuela Politécnica de Mieres. Universidad de Oviedo, Mieres, Spain. 6 Dept. Producción Vegetal y Ciencia Forestal, Universitat de Lleida, Spain. 7 Departamento de Ingeniería y Ciencias Agrarias, Universidad de León. Escuela Superior y Técnica de Ingeniería Agraria, Ponferrada, Spain. 8 Escuela Técnica Superior de Ingenieros de Montes, Universidad Politécnica de Madrid, Madrid, Spain. 9 Dpto. Ecología y Genética Forestal, CIFOR-INIA, Ctra. La Coruña, Km. 7.5, E-28040 Madrid, Spain. 10 Cesefor Foundation. Soria, Spain. 11 European Forest Institute, Mediterranean Regional Office, Barcelona, Spain 12 Centre Tecnològic Forestal de Catalunya , Ctra. Sant LLorenç de Morunys Km. 2. Solsona. Spain. 13 Unidad de Gestión Forestal Sostenible. Departamento de Producción Vegetal. Universidad de Santiago de Compostela, Spain. 14 Forest Ecology, Institute of Terrestrial Ecosystems. Department of Environmental Sciences. ETH Zurich. CH-8092 Zurich. Switzerland. 15 Departamento de Ciencias Agroforestales. Escuela Politécnica Superior. Universidad de Huelva, Palos de la Frontera, Spain.
2012 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 2
Authors : Felipe Bravo, Juan Gabriel Álvarez-González, miren del río, marcos Barrio- anta, José antonio Bonet, andrés Bravo-oviedo, rafael calama, Fernando castedo- dorado, Felipe crecente-campo, sonia condés, Ulises diéguez-aranda, santiago césar González-martínez, iñigo lizarralde, nikos nanos, alberto madrigal, Francisco Javier martínez-millán, Gregorio montero, cristóbal ordóñez, marc palahí, miriam piqué, Francisco rodríguez, roque rodríguez-soalleiro, alberto rojo, ricardo ruiz-peinado, maría de la o sánchez-González, antoni trasobares, Javier vázquez-piqué.
Cover desing : Felipe Bravo Cover pictures and graphs : Felipe Bravo, irene ruano, iñigo lizarralde and antonio muñoz
Edition : insituto Universitario de investigación en Gestión Forestal sostenible (Universidad de valladolid-inia) and Unidad de Gestión Forestal sostenible (Universidad de santiago de compostela)
Electronic versión available at: http://sostenible.palencia.uva.es/document/gfs/publicaciones/libros/2011_Growthyield_spain.pdf http://www.usc.es/uxfs/Books
ISBN : 978-84-615-7145-1 Depósito legal : p-35-2012
Maquetación y Producción : antonio cristo, s.l. ([email protected])
Imprime : Grafistaff, s.l. ([email protected])
2 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 3
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
• Índice
Foreword ...... 4 Abstract ...... 5 1. Introduction ...... 6 2. Driving processes ...... 7 a. Productivity ...... 7 b. Density and competition ...... 8 3. Data and model requirements ...... 9 a. Data ...... 9 b. Auxiliary functions for estimating missing variables ...... 10 4. Modeling approaches ...... 13 a. Empirical, Process and Hybrids ...... 13 b. Whole-stand models, size class models and individual-tree models ...... 14 5. Model modules ...... 21 a. Increment, growth and yield ...... 21 b. Silviculture response functions ...... 25 c. Demography ...... 27 d. Output functions ...... 30 6. Validation and calibration models ...... 39 7. Interfaces ...... 41 a. Yield tables ...... 41 b. Stand density management diagrams ...... 44 c. Simulators and decision support systems ...... 44 8. Perspectives ...... 48 Acknowledgments ...... 49 References ...... 50
3 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 4
• Foreword
This contribution summarized the development in forest modeling in Spain during the last fif - teen years. By including information on the different modeling approaches conducted in Spain and the databased used, authors wish to show the diversity and the wide scope of the forest models. Edition has been funded by Sustainable Forest Management Research Institute (University of Valladolid-INIA), Sustainable Forest Management Unit (University of Santiago de Compostela) and the SELVIRED network (Spanish Ministry of Science and Innovation). We hope that this book will be found useful both for researches and managers and serve as inspiration to develop new ideas and approaches.
4 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 5
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
• Abstract
This book presents a review of forest models developed in Spain in recent years for both, tim - ber and non timber production and forest dynamics (regeneration, mortality,...). It reviews the key factors that regulate growth and demographic processes included in the described models with spe - cial emphasis on productivity, density and competition. The models developed to date are based on data from permanent plots, silvicultural trials and the National Forest Inventory. The book describes the main data network available in Spain and the auxiliary functions adjusted to estimate missing variables in the databases. After discussing, the different approaches (empiri - cal, based on process or hybrid) used to date, the scales (whole stand models, class size and indi - vidual tree) commonly used in forest modeling are described. By describing the different sub- models included in the models developed so far are presented indicating both, the species and the geographic area where it can be used. Validation and calibration of models is treated briefly while the ways of presenting the models (yield tables, charts or computer programs) are described in detail. The book ends with a set of perspectives from which emphasizes the need for integration of different methodologies and scales and underlines than an effort must be done to improve the evaluation and calibratio n of the models. Finally it highlights the need to facilitate the use of models by foresters by including visualization tools, integrating geographic information systems and facilitating the use different data formats and generate silvicultural scenarios. Keywords : timber production, non-wood forest products, recruitment, modelling, forest
• Resumen
Este libro presenta una revisión sobre los modelos forestales desarrollados en España durante los últimos años, tanto para predecir la producción maderable y no maderable, como para simular la dinámica de los bosques (regeneración, mortalidad,..). Se repasan los factores fundamentales que regulan los procesos de crecimiento y demográficos incluidos en los modelos expuestos, con espe - cial énfasis en la productividad, la densidad y la competencia. Los modelos desarrollados hasta la fecha se han elaborado a partir de datos procedentes de parcelas permanentes, ensayos selvícolas y el Inventario Forestal Nacional. En el libro se describen las principales redes de datos disponibles en España y las funciones auxiliares ajustadas para estimar las variables ausentes en las bases de datos. Tras exponer las diferentes aproximaciones (empírica, de procesos o híbridas) utilizadas hasta la fecha se describen las escalas (modelos de rodal completo, de clases de tamaño y de árbol individual) habitualmente utilizadas en modelización forestal. Mediante la descripción de los diferentes submodelos que los componen, se presentan los mode - los indicando tanto la especie como el área geográfica donde se pueden utilizar. La validación y calibración de modelos se trata de forma sucinta, mientras que las formas de presentar los mode - los (tablas de producción, diagramas o programas de ordenador) son descritas en detalle. El libro termina con un conjunto de perspectivas, derivadas de la reflexión sobre los requerimientos aún no cubiertos, entre las que resalta la necesidad de integración de diferentes metodologías y escalas, así como el esfuerzo que se debe hacer para mejorar la evaluación y calibración de los modelos. Finalmente se incide en la necesidad de facilitar el uso de los modelos por parte de los gestores forestales mediante la inclusión de herramientas de visualización, la integración con sistemas de información geográfica y la flexibilidad para poder usar diferentes formatos de datos y generar escenarios selvícolas. Palabras claves: producción maderable, productos forestales no maderables, regeneración, modelización, forestal
5 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 6
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
• 1. Introduction
According to official statistics, forest lands cover 54.4% of the Spanish national territory. However, only 18.4 million ha (36% of the country) are true forests or plan - tations. Approximately 39.2% of Spanish forest lands are under different types of pro - tection, such as national and regional parks or Natura 2000 areas. Three main forest ecoregions can be distinguished in Spain: Mediterranean, Atlantic and Subtropical (Macaronesic). Forestry in Spain has diverse objectives and the ecoregions present different forest management attributes corresponding to the importance of biodiver - sity conservation (higher in the Macaronesic area and lower in the Atlantic), timber production (higher in the Atlantic) or multifunctionality and non-timber products (higher in the Mediterranean ). The harvest rate in Spain, expressed as the ratio between harvest volume and wood increment each year, reaches 64% in Galicia (NW Spain) and 30.2% for the country as a whole. The average harvest ratio in Europe (excluding of the Russian Federation) is 55%. Growth and yield studies began in Spain in the early 20th century when different per - manent plots were established in Pinus sylvestris and Pinus pinaster stands in central Spain. The first forest growth models in Spain were yield s developed in the 1940s for Pinus radiata and Pinus pinaster plantations in the Atlantic area (Echeverría, 1942 and Echeverría and Pedro, 1948, respectively). In the second half of the 20 th century there were new efforts at establishing permanent plots, which made it possible to construct new yield tables. However, in the last 15 years a new generation of forest researchers have combined previous data collection efforts with computer and statistics capabilities to revolutionize forest modeling in Spain. Advanced statistical approaches have been applied to develop models for different species, management purposes and regions (with the exception of the Macaronesic area) and at different scales (from whole stand to individual-tree models) . Modelers have also developed a wide variety of models and tools based on forest diversity and end-user aims. Internationalization has been an impor - tant feature of Spanish forest modeling during the last 15 years. Great efforts have been made to integrate research from other countries into Spanish forest dynamics modeling and to participate in forest dynamics modeling overseas. The aim of this work is to describe the current situation of forest growth and yield models in Spain and to give an overview of improvements made during the last centu - ry, from normal yield tables to the latest software. This will be followed by a reflection on future challenges, including suggestions for new lines of research and the need to include climate change and end-user needs in forest modeling.
6 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 7
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
• 2. Driving processes a. Productivity Forestry has been focused on timber productivity since it became a scientific disci - pline in the 17 th century. The advent of empirical analysis along with a rationale-based interpretation of nature and the driving processes of forest productivity brought about a shift from tradition-based methods to sustained wood yield science-based methods (Gamborg and Larsen, 2003). Forest productivity can be placed within the broader field of Production Ecology. Although both disciplines have their own particular and aims (Pretzsch, 2009) the former can be viewed as the harvestable standing biomass of the latter, which is demanded by society. Forest scientists and managers deal with forest productivity in terms of growth or increment in volume of the stand and its integration in yield. Growth and yield are determined by four factors (Clutter et al. , 1983): the age or age distribution of the stand, the timber production capacity of the site, stand density or site occupancy, and silvicul - tural treatments. The productive capacity of a site is often referred to as site quality and its estimation is a basic element of forest ecology and ecosystem management (Barnes et al. , 1997). Consequently, the concept of site quality should not be relegated only to timber pro - duction as it involves multifunctionality. Alternative to traditional biomass allocation in the stem, cork production (Montero, 1987) or annual cone production (Mutke et al. , 2005) could be alternative site productivity proxies for traditional biomass allocation in the stem. However, wood volume is still one of the most valuable products in forest ecosystems and is highly correlated to forest productivity, so most growth and yield models are dedicated to it. Site quality can be evaluated directly using the mean annual volume increment from historical records of managed stands. However, data of this type is scarce and forest managers must find indirect methods. The most popular indirect method is the stand dominant height at a reference age or site index. This value is usually extracted from a set of growth curves and is an indicator of the site potential for growing wood biomass. The main characteristics of these curves are inflection point, asymptote, polymorphism and base age invariance (Goelz and Burk, 1992). Forest managers need to know the age and height of dominant trees in order to obtain the site index. However, these data are not always available, for example in young stands where crown differentiation is not apparent. In such situations, site index is usually
7 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 8
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
related to climate or soil variables in a linear fashion (Sánchez-Rodriguez et al. , 2002, Romanyà and Vallejo, 2004, Afif-Khouri et al. , 2010, Álvarez-Álvarez et al. 2011) or by discriminant rules (Bravo and Montero, 2001, Bravo-Oviedo and Montero, 2005). Some site-related variables commonly included in the models to reflect site quality are elevation (Trasobares and Pukkla, 2004b; Condés and Sterba, 2004, 2008), soil types and attributes (Bravo and Montero, 2001, Condés and Sterba, 2004 and 2008) or lati - tude (Trasobares and Pukkala, 2004b). One successful way of incorporating site quality into diameter growth models has been to include the past growth index (GI). This was proposed by Trasobares and Pukkala (2004b) and used by Trasobares et al. (2004 b). Other authors have incorpo - rated different bioclimatic indexes for assessing the potential productivity of a par - ticular area. For example, the bioclimatic index (IBL) proposed by Montero de Burgos and González Rebollar (1974) measures the capacity of trees to produce biomass after their cells have recovered from summer stress. It was used by Condés and Sterba (2008) to develop an individual-tree growth model for Pinus halepensis . In another case, the potential climatic productivity (MAI) index of Sánchez-Palomares and Sánchez-Serrano (2000) was included as an independent variable in an individual-tree growth model for Pinus sylvestris (Condés and Sterba, 2004). Adame et al. (2008a) utilised the biogeoclimatic strata of Elena-Roselló (1997). Calama et al. (2008b) used a land classification based on soil, physiografic and climatic attributes to model indi - vidual cone production. b. Density and competition
Site productivity, density and competition are among the most important factors influencing forest growth. Growth modeling requires a good understanding of densi - ty/competition-growth relationships organized into indices that allow us to include them in growth functions. The effect of competition on the growth of forest species has long been studied in order to increase the accuracy and precision of individual-tree models. A tree’s competi - tive status is incorporated into the models using distance-dependent or distance-inde - pendent competition indices (Munro, 1974). In Spain, distance-independent competition expressions have been widely used to assess stand-level tree competition in individual- tree models. Number of trees per ha and basal area are the most commonly used distance- independent indices, but the crown competition factor or the basal area of larger trees have also been incorporated into different models (see Section 5.a.ii). In Mediterranean low-density forests, the number of trees per ha is a commonly used index (Calama and Montero, 2005; Sánchez-González et al. , 2006; Gea-Izquierdo and Cañellas, 2009) that reflects symmetric competition for water resources. Distance-dependent indices are not often used in Spain, mainly because the invento - ry data does not include tree coordinates. When they were calculated, they were not found to be better than distance-independent indices (Álvarez Taboada et al. , 2003; Crecente-Campo, 2008; Gea-Izquierdo and Cañellas, 2009). This could be due to the small plot size used in forest modeling. Vázquez-Piqué et al. (2008) selected a one-
8 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 9
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
sided version (dominant trees are not affected by competition from dominated trees) of a distance-dependent index for a cork oak growth model. It indicated high asymmetry in the competition process, but no comparison was made using distance-independent indices. Stand density reflects the average tree growing spaces available or average competi - tion among trees. At stand level, density-growth relationship for even-aged pure stands is described by the Wiedemann’s hypothesis (Assmann, 1970) or Langsaeter’s curve (Daniel et al. , 1979). These authors stated that stand volume increment does not vary across a wide range of densities. For Spanish forests, this curve has been analysed for Pinus sylvestris L. (Montero et al. , 2001a; Río et al. , 2008), P. pinaster Ait. (Montero et al. , 1999), Q. pyrenaica Willd. (Cañellas et al. , 2004) and for mixed stands of P. sylvestris and Q. pyrenaica (Río and Sterba, 2009). Density-induced mortality or self-thinning is another forest dynamic closely related to density and competition. Self-thinning based on Reineke s expression was modeled for Scots pine stands in central (Río et al. , 2001) and north-east Spain (Palahí et al. , 2003). Reineke’s maximum density line concept was also applied in developing the stand density management diagrams for some Spanish forests, and Reineke’s stand den - sity index was used in the yield model of Bravo and Montero (2003). Other density management diagrams rely on the Hart-Becking index, which was traditionally used in most Spanish yield tables to determine different thinning alternatives (Madrigal et al. , 1999). However, most of the Spanish dynamic whole-stand models are based on the state-space approach and use basal area and the number of trees per hectare (N) as state variables, so they do not include other stand density indices.
• 3. Data and model requirements
a. Data
All the models developed in Spain for practical uses are parametric models and their parameters must be estimated from observations. Since estimate accuracy and a model’s usefulness depend on the quality of data, the first step in growth model construction is to ensure that the available data is suitable for the model. When it is inadequate, a data collection process must also be designed (Rennolls, 1997). In recent decades, the automatic capture of forest state variables by various remote sensing techniques has substantially increased the amount of data available on stand dynamics. Even so, sample plots and stem analysis of felled sample trees continue to be
9 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 10
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
the two basic data sources for developing growth models. Felled-tree sampling provides information similar to that obtained when re-measuring permanent sample plots. However, it is economically expensive and the development of some variables cannot be reconstructed by this method. Thus, the majority of the data used for growth modeling is obtained from sample plots. Examples of different networks of sample plots could be created for growth analysis and designed according to resource management needs are: • Sample plots for resource inventory: The design is based on temporal plots, where the number of sample plots is calculated to achieve the desired precision for the analysed resource. The spatial distribution of the sample grid is usually oriented across environmental or physical gradients to maximize within-plot variation and thus reduce between-plot variance. • Continuous Forest Inventory: The main objective is to assess and monitor the extent, state and sustainable development of forests at the national or regional level in a timely and accurate manner (e.g. Spanish National Forest Inventory). The design is based on permanent plots in different types of forest and stand conditions in proportion to area. Sampling is done by passive monitoring. As with resource inventory, precision is gained by reducing between-plot variance. • Sample plots from field experiments: Growth data can be obtained from different field trials (spacing, thinning and pruning trials, fertilizer trials, growth trials, etc.). In Spain, these trials are established and maintained almost exclusively by govern - ment research organizations (Montero et al. , 2004a) or university research groups (Bravo et al. , 2004; Torres-Álvarez et al. , 2004; Diéguez-Aranda et al. , 2009). The design is based on permanent sample plots and the size, shape, number and distri - bution of sample plots depends on the objectives of the field experi ment. • Permanent plot networks (PPN): First attempts to establish a permanent plot net - work in Spain were made in 1915 when researchers from the former ‘ Instituto Central de Experiencias Técnico-Forestales ’ established a set of plots to study tim - ber production in Scots pine stands in the Central Range and to study resin yield in Pinus pinaster stands in the Northern Plateau. A second big effort to generate a PPN was made in the 1940s and another in the 1960s. Currently, different plot net - works belonging to universities and regional research centers are maintained across the country.
Two aspects of PPNs are relevant for the future: i) a critical analysis of the utility of the permanent sample plot networks in light of the specific requirements for the next generation of growth models, and ii ) development of open access historical data archives from different institutions for more extensive model development and validation.
b. Auxiliary functions for estimating missing variables
Several auxiliary functions are usually necessary for the application of growth and yield models. This is mainly due to the scarcity of input data or because some variables (i.e., height) are only measured in a sample of the trees, or because some input variables can not be directly measured. The most important functions include:
10 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 11
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
Bark thickness or bark percentage Bark thickness ( bw ) or bark percentage ( b%) equations usually act as auxiliary func - tions for growth models, which eliminates the need to calculate over-bark and under- bark volumes and facilitates correct estimates of diameter growth. Several bark models have been developed for Spain (Table 1).
Diameter-stump diameter and volume-stump diameter relationships When a tree has been cut and only the stump remains as an indicator of its size, it sometimes becomes necessary to use the stump diameter ( dst ) to estimate the tree diam - eter ( d) or even the tree volume ( v). Simple linear models are usually adequate for pre - dicting d from dst , whereas alometric or parabolic models are necessary for predicting v from dst . In Spain, equations of this kind have been developed for Betula alba , Eucalyptus globulus , Pinus pinaster , P. radiata , P. sylvestris and Quercus robur in the region of Galicia (Diéguez-Aranda et al. , 2003; Diéguez-Aranda et al. , 2009).
Height-diameter relationships The height of the trees in a stand is an important variable in forest management. It can be used to i) accurately predict total and commercial volume (together with d) using a volume equation, a tree taper equation, or a volume ratio equation, ii) estimate site quality in even-aged stands, and iii) characterize of the vertical structure of a stand (Gadow et al. , 2001). Local and generalized height-diameter ( h-d) models are com - monly used. Local h-d models are valid for a specific forest or stand, while generalized h-d models (local models that include stand variables in the formulation) are valid for a particular species in a particular region or regions (Table 2). Some generalized height- diameter models use a mixed-model approach that allows for model calibration when sample trees are available (Table 2).
Crown equations Crown attributes are key components of growth and yield models (Soares and Tomé, 2001) but are also important for assessing wood quality (Kershaw et al. , 1990), com - petitive level (Mitchell, 1975), tree vigour (Hasenauer and Monserud, 1996), fire sus - ceptibility (Keyes and O’Hara, 2002), mechanical stability (Wilson and Oliver, 2000), and microclimate (Grace et al. , 1987). The most typically measured tree attributes are i) height to the crown base ( hcb ), which, measured together with total height, makes it possible to estimate crown length ( cl ) and crown ratio ( cr ) or height to the base of the live foliage ( hblf ); ii) crown width, assessed as maximum potential width ( mcw ) or largest crown width ( lcw ), iii) height to the largest crown width ( hlcw ), in order to ascertain the competitive level of the lower part of the crown, and iv) crown radius which is used to develop the crown taper equations that are essential for estimating crown volume and cross-sectional areas (Table 1).
11 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 12
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
Table 1. Crown and bark functions developed in Spain by species and area
Variable and Species Area Independent Goodness References Variables of fit (R 2) Bark percentage several species Whole country d, h, bw martínez millán et al. (1993) Bark thickness Pinus sylvestris Castilla y León d, dib 0.961 lizarralde (2008) Pinus pinaster Castilla y León d, dib 0.884 lizarralde (2008) maximum crown width several species Whole country d martínez millán et al. (1993) condés and sterba (2005) largest crown width Pinus radiata Galicia d, h, mcw 0.730 crecente-campo et al. (2009a) Pinus sylvestris Castilla y León d, h, cr, cl 0.700 lizarralde (2008) Pinus pinaster Castilla y León d, h, cr, cl 0.752 lizarralde (2008) Quercus suber Whole country du, dg 0.894 sánchez-González et al. (2007c) several species Whole country d, h condés and sterba (2005) height to largest crown width Pinus radiata Galicia h, hblf 0.866 crecente-campo et al. (2009a) Pinus sylvestris Castilla y León h, BAL, G 0.898 lizarralde (2008) Pinus pinaster Castilla y León h, BAL, G 0.852 lizarralde (2008) height to crown base Pinus radiata Galicia d, h, t, H 0 0.640 crecente-campo et al. (2009a) Pinus sylvestris Castilla y León hlcw, h, BAL,G, 0.963 lizarralde (2008) Pinus pinaster Castilla y León hlcw, h, BAL,G, 0.921 lizarralde (2008) Upper crown radius (crown radius above largest crown width) Pinus radiata Galicia lcw, h, hblf, 0.901 crecente-campo et al. (2009a) hlcw lower crown radius (crown radius below largest crown width) Pinus radiata Galicia lcw, h, hblf, 0.859 crecente-campo et al. (2009a) hlcw where: d is diameter at breast height, h is total height, bw is bark thickness, dib is diameter inside bark, mcw is maximum crown width, cr is crown ratio, cl is crown length, du is diameter under cork, dg is quadratic mean diameter, hblf is height to the first living branch, BAL is the sum of basal areas of larger trees, G is basal area, t is age, H0 is dominant height, hlcw is height at the largest crown width and lcw is largest crown width.
12 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 13
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
Table 2. Height-diameter functions developed in Spain by species and area
Species Area Independent Goodness References Variables of fit (R 2)
Eucalyptus globulus Galicia d, d0, H0 0.835 diéguez-aranda et al. (2009) d, d0, H0 0.890 crecente-campo et al. (2010a)- m.m Populus sp . (clone i-214, North-east Spain d, d0, H0 0.97-0.99 rodríguez (2005) mc, luisa avanzo) Quercus pyrenaica Castilla y León d, H0, dg 0.756 adame et al. (2005) d, H0, G 0.823 adame et al. (2008b)- m.m. Quercus robur Galicia d, dg, Hm 0.778 Barrio-anta et al. (2004) d, d0, H0 0.753 diéguez-aranda et al. (2009) Quercus suber Whole country du, d0, H0 0.810 sánchez-González et al. (2007c) Pinus pinaster Southern Iberian d, dg, H0 0.866 lizarralde (2008) Range
Galicia d, dg, H0, G 0.919 schröder and Álvarez González (2001) d, d0, H0 0.938 castedo-dorado et al. (2005) Pinus pinea Central Range d, d0, H0 - cañadas et al. (1999) Valladolid d, H0 0.936 García Güemes et al. (2001) Whole country d, H0, P9010 0.953 calama and montero (2004)- m.m. and by regions Pinus radiata Galicia d, d0, H0, t, N 0.918 lópez-sánchez et al. (2003) d, d0, H0 0.933 castedo-dorado et al. (2006)- m.m. Asturias d, d0, H0, N 0.900 canga et al. (2007) Pinus sylvestris Castilla y León d, dg, H0 0.872 lizarralde (2008) Galicia d, d0, H0 0.938 diéguez-aranda et al. (2005b) Catalonia d, d0, H0, t 0.890 palahí et al. (2003) Pinus halepensis Middel Ebro Valley d, dg, Hm 0.821 cabanillas (2010) Pseudotsuga menziesii Northern Spain d, d0, H0 0.873 lópez-sánchez (2009)
where: d is diameter at breast height, do is dominant diameter, Ho is dominant height, dg is quadratic mean diameter, G is basal area, du is diameter under cork, P9010 is the difference between the percentiles 90 and 10 of the diameter distribution, t is age, N is number of trees, and Hm is mean height. m.m. is mixed model.
• 4. Modeling approaches
a. Empirical, Process and Hybrids
In Spain most modeling efforts have been aimed at developing empirical models as systems of interrelating equations that can use any desired combination of inputs to pre - dict future stand development. Based on Vanclay (1995), Gadow and Hui (1999) and Davis et al. (2001), empirical growth and yield models can be grouped into three types
13 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 14
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
of models that cover a wide spectrum: whole-stand models, size-class models and indi - vidual-tree models. The most appropriate model type varies according to intended use, stand characteristics, available resources and length of projection (Vanclay, 1994; Burkhart, 2003; García, 2003). These factors determine the data and precision required for the estimates. Most empirical models have a low model complexity, which makes them easier for managers and decision-makers to use in addressing forest management questions. In Spain, the regions of Galicia, Castille-and-León and Catalonia are already implementing some empirical models to develop forest management plans. However, with most empirical models there is an element of uncertainty due to the conditions for which the functions were calibrated, particularly when studying the impacts of environ - mental change on forest development. As an alternative to empirical models, process-based models can provide more robust model projections under changing environmental conditions, but require more parame - ters, substantial calibration data, and increased simulation time. Additionally, process- based models do not always provide interesting output that is easily applicable in forest management decision-making (see Landsberg et al. , 2003). The “GOTILWA+” process- based model (Keenan et al. , 2008, www.creaf.uab.es/gotilwa+/ ) was developed in Spain to simulate growth processes and explore how they are influenced by climate, tree stand structure, management alternatives, soil properties and climate change. It also simulates forest carbon and water fluxes for different environments and tree species under chang - ing environmental conditions. Choosing between process-based and empirical models involves trade-offs between model realism (simulating system behavior based on a qualitatively realistic model structure), model accuracy (simulating system behavior in a quantitatively accurate manner), and model generality (Odenbaugh, 2006). However, most groups in Spain are currently working towards hybrid modeling that uses different approaches. Some are exploring climate variables to explain growth or site in empirical models (Mutke et al. , 2005, Bogino and Bravo, 2008, Bravo-Oviedo et al. , 2008, Martín-Benito et al. , 2008a and 2010, Bogino et al. , 2009 and Gea-Izquierdo et al. , 2009) and others are using physiologically-based growth models with empirical functions. An example of this is the 3PG model (Landsberg and Waring , 1997), which has been parametrized for euca - lyptus (Rodríguez-Suárez et al. , 2010), Pinus pinaster and Pinus radiata plantations.
b. Whole-stand models, size class models and individual-tree models Individual-tree growth models provide the most detailed information (García, 1994 and 2003) and usually perform better than whole-stand models for short term projec - tions (Burkhart, 2003). Size class models offer a compromise between the other two approaches. Since aggregate outputs are usually required for forestry decision-making in Spain, individual-tree models can be overparamerized and too complicated for this purpose. Thus, whole -stand models continue to be an attractive alternative, at least for even-aged, single-species stands (including plantations). It is useful to distinguish between static and dynamic whole-stand models. Static models attempt to directly predict the course of the quantities of interest (volume, mean
14 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 15
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
diameter, etc) over time. Stand yield tables (SYT) and stand density management dia - grams (SDMD) are included in static whole-stand models, and they are the most advanced tools that can be developed when research plot measurements are only avail - able for one point in time. Dynamic models predict rates of change under different man - agement approaches and stand conditions. Data on experimental rates of change are necessary for model development and are obtained by measuring research plots on at least two occasions. Dynamic whole-stand models are more flexible and accurate than static models, and therefore are preferred when they are available. For more complex systems such as uneven-aged or mixed stands or for short-term projections, individual-tree models are sometimes preferred because they provide a more detailed description of stand structure and dynamics than whole-stand models. They can also be useful in assessing potential stand structures resulting from new silvi - cultural regimes (e.g., Condés and Sterba, 2008). Individual-tree growth models can be distance-dependent, if they include spatial competition indices in their formulation, or distance-independent if they do not. The first growth and yield models developed in Spain were static whole-stand mod - els (yield tables). Madrigal et al. (1999) elaborated a comprehensive compendium of the yield tables published in Spain since the end of the last century (see section 7.a). In recent years, SDMDs have been replacing yield tables because they facilitate quick and easy comparisons among different thinning schedules and they graphically illustrate the relationships among stand variables (See section 7.b.) Dynamic whole-stand models and distance-independent individual-tree models have been developed for Spain in the last decade (see Tables 3a to 3e). To date, only two size- class models have been developed in Spain (Sánchez Orois and Rodríguez Soalleiro, 2002 and Escalante et al. , 2011), both based on a transition matrix growth model. Also, some of the whole-stand models developed in Spain can be mathematically disaggre - gated using a diameter distribution function, which provides more detailed information about stand structure and volume (e.g., Río and Montero, 2001, Río et al. , 2005, Diéguez-Aranda et al. , 2006a; Castedo-Dorado et al. , 2007a, Cabanillas, 2010). Most of the models have been developed for pure, even-aged and predominantly coniferous stands. Two relevant exceptions are the works by Sánchez Orois and Rodríguez Soalleiro (2002) for mixed stands of P. pinaster and broadleaf species in the coastal region of Galicia, and the work of Trasobares et al. (2004a) for mixed, uneven- aged stands of P. sylvestris and P. nigra in Catalonia. Calama et al. (2008a) has also adapted an individual-tree model of even-aged Pinus pinea stands for use with uneven- aged stands.
15 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 16
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES , ) ) ) 9 b , 9 9 a , 0 9 ) 7 0 1 0 b ( 2 ) 0 6 ( . 8 l 2 0 . ( ) 0 l a 0
. . 2 0 a t l 2
5 0 2 e ( t a
( 9
0 e .
t z
l 9 2 e o e a (
a 1 l
p
d o . t á , l . n d e z m l a
s a a
n a a r a r e t
t o ) o c c e t a n
- e d G n - d r
e
- e e z a e t o z - o r e d r n d e o d e u r e e ö i f u e t r a c g r l t e r n s e e h v c i l r a a a c R n d Á c B s c c i
t n n o o o i n i t
t - a e a s e e e e e d r s d i n n n n n i l o a l o o o o o r
a a s v n V n n c n n m d a n r ) a r g
o ) a i i a r ) s t 2 e d s s t
8 8 9 9 9 6 2 9 2 1 9 6 e 9 o R t n 7 8 8 9 9 8 7 9 6 4 8 7 ( i c n 9 ......
n . ( ( d 0 t
0 0 0 0 0 0 0 0 0 0 0 e 0 i o 0 7 f
o 6 5 m . . f e 0 0 G o g , , ] ] ) ] ] ] a h a a m m t ] ] m ] ]
n h h c c , , , , a a c p / / a a [ [
R a ] ] ] ] [ s 2 ] , e , h h h h s s s s
S e 1 ] / / ] s / d / d 1 r r r r ]
m r e ) s s s
m n s 2 , [ C s r 3 l a a a a i
r ] a ) a e e
t e i ] r , e e e e s 9 [ 2 a e o m y e e h : : e m a o r i / [ e y y y y r r p t y r s s 1 t m : : : s G d e a t t
[ [ [ [ t i 2 [
d a y s s s : c d d [ [ : 2 [
N e y r s t [ ] e [
: o s 2 1 1 1 1
d d d [ n n : m t t s y c t t t t t 1 1 v 1 t G t d n d ( , n n n c
r [ a a i e
d 2 c n / ] , , , , , n m a t t t e , f , e
a t N n n a a a ) e ] ] ] ] ] f f e , , a ] 2 e s s a
c t t t f f l e 2 t t d r
] ] , , , , f e a a a a a d a h s s s e d
e s
] ] ] ] ] e / y p
a a f d d
,
h h h h h
h a m e ] s s s s s [ s s n g f o ] / / / / / / d d d e e d d h h g l
g ( r r r r r s e e / 2 2 2 2 2 / n 2 B e e e e e [ n 2 n n r n n a a a a a i n b
e 2 2 m i
t ( i m i i n p , n n n a r [ e e e e e
i n m m m m m a m a n w n ] t e , h h i r l [ [ [ [ [ e [ n n n m m h y y y y y t n [ t t n o n 2 2 t D i i i [ [ i r i d [ [ [ [ [ i r y s m 1 1 0 1 0 1 1 n n 1 a a n 2 S h h h [
h h h a n c c 1 2 2 2 2 G G T G t t G t t U T G t [ B h U t H G B T I v G G E ( U N T T T d n ] ] r r a ] ] ]
a a r r a t ] s ] e e a a h n ] a e / y y e e ] e a m / / l h s e y y / 2 2 c h · · d e l b m [ / 2 a a e b n c 2 m m a r [ h h n e m t a t c c
/ / i i
[ [ [ m [ p 2 2 3 [ r d m 2
e 2 9 l a G m m G G G N d p I G G [ [ D v I I I e i
y l l l l l ( l a a a a a
a s s s s s s s a a a a a
n a 2 r B B B B B o s B / / / / / o i l n
/
/ t e r r r r r r s m 3 e e e e e e a e d u t t t t t t l t 9 o e e e e e e u m p n i
/ m m m m d m m m a a a a a a a n l a a a a a a b o i e e e e e e i i i i i i p r r r r r r u
a a m d a a d d a a M s d d d e n
i d d r d e e p e n n n e e y
t
r r t t a a a b c e t t e t t t
d i n
n n s s s l l p g t n e e
r n ) o m a a i y
n e c c c e a o d d a n t i t i i i t t u u i i e e u
n n r t a u s e l d c d c d q
l e e e a m m m i
i b i e t n n c i a a a p p v m v h v n i r a a d m i t i e t e a n n n o t t t i A h i r o e
a d d t d s s d s c y y y c . t i i a i 3 s e n w n n n
e a i s r t d i i ( i e d d M p d d d e l 3 b
a t t e t l s s
a a e b e o o a s n c c
o T n .
d d o t : : d i i n n
t n n . a a p i i a
i
a a r y D r r
r c r p p o o t s a e i i s s e t t n r r
s d t t a e e u
a i t t s s a r e o l d n n e e n d c i i b i
a
e a w w r p e i a a a a - - v
r i i i i u s s e h h a c c c c a t t t q i i i i v u u r r
l l l l e s n r n n a o a o a a r a i i o o G n A p P G n G P B G F
16 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 17
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES ) ) a a , ) 0 6 ) ) 3 1 0 6 4 ) 0 0 0 0 0 1 0 2 2 0 ( ( 0 0 2
2 . ( .
2 0 ( l
l
(
, ) 2 .
a a o ) ) l (
2 r a t t 3 8 a ) e 0 b e
e o 0 t ) 0
t
r 8 r 0 0 a n ) e 5 0 e
p e 0 2
, t t d 2 o 0 2 ( d ) 0 o (
( m s n n 0
. e
2 9 d a . l s a . m o ( 2 l d l
r 9 e d
e a ( i c a
n a d 9 e c - u a
. m t
v a t l l
n - d t 1 e n e
l t ( e z
a e c o a d e s
,
a
- e n í í r é n t r n o o o o e u i r e h h a e d v
v
c v f v g a a a n t a a e l l a e a é o o z i r r r í í o r r i o a a R B B c r r p p c B l B d n
e n r n n o i o a o t i
i t a t s - r a a s e e e e e e e b d s d m i i n n n n n n n i l l o l a o o o o o o o r a a a r v c n n c V n n n n n g a ) / / s i 2 s 0 8 2 d 3 e 5 3 6
R . . . 9 t ( n .
0 0 0 d n t
/ / / 0 i o e 9 5 7 9 2 4 3 1 1 f
o 9 9 9 9 3 2 5 8 4 ...... f m 0 0 0 0 0 0 0 0 0 G o e , g ] ] a y m ] n
c ] m [ a
s n m ] ] m r i d m c a
, , a e , m S [ , m u ] ] r ] h ] e
, c
d / L d , s s a ] , y
[ A [
y ] r r s , , ] % S [ ]
,
h t [
a ] a a ] e , s
B 2 / m ] a
i , g g , ,
t ] r a [ e e a e h 2 i ] a ,
s ] ] h / v r 1 , a a r r h ] y y / h D h t a a ] 2 . / 0 /
n m [ [ e a 2 / h c [
s O 2 h h [ 2
/ ] 1 1 p 2 e e y r ,
/ / m t H t 1 2 , l N m [ o a
t [ 2 2 y
] d m m [ % , , , m r · w , e
[ G [ a 2 m n ] ] ] y [ [ i a
G L p m m t y [ e
e a a a ,
L d
[ [ [ [ B G h 1 , m ] , A
d V
h h h / 1 K 1 1 d ] A ] n , , a / / / s t G 3 ] ] s G B s
e ] ] s m n p C
s s s e a
G G
B , h s s l , r
, s s , , ,
u e r / ] t o e e e , r r m ] ] , , , r r ] ] ] a b r 3 ] [ d s e e e a p ] ] ] a a C a a e m [
a r r r p m h e e e m I [ m m i t t t e e m / [ m y R l m m m [ [ c [ d 2 [ [ [ [ y y 2 r i d [ y y [ [ c A [ [ 0 0 1 1 1 R [ [ E 1 [ [ I I [ I I I n o a n 1 2 2 m t S V S t N N N C P S d H d t H t t M S S S [ I v a
s ]
e s , , l r ] ]
, ] a , b s s ] r ) e r r , , , s ] ] ] , , , a t ,
a
] ] ] ] h a a r y ] ] ] t ) ) a a a t ] e n ] , a a a a e e a
a a a 0 e e h h h a ] e a y e h h h h y y / / / w h h h 1 / e d v v a / / / / h h / / / / d s s s l l y i i 5 5 2 / o 2 / 2 2 2 h 3 3 3 2 / / e e e r e b 5 v 2 v n / 2 r r r / i r r m 3 g e m m m m a t t t m m m m m m i m [ [ [ [ c u u [ [ [ m y [ [ [ n p c c c m [ [ [ r ( s i s m [ [ [ [ 2 2 2 2 e 2 2 2
( 2 2 2 ( ( [ a G g d d h g s N I P G V G N P N P V i V i i i G G D v V i G t s l l l e
a a a l l r y y s s s y t t a a o t a a a i i
s s i l l f r l
a a B B B a a s / / / a o t t e l /
/
a a
t B B r r e r r r r r
r y s e e n h o o / / / t e e e e e r r i t e d o i / t t t t t e e e l a a l t o p e e l e e
e m m w
a u h l l
m
m m m a t o / / / s m a a m m m m g d m r s u u u r a a a a a a t i s s l l l a a a a a a b o o g e e e e e e i i i i e i a a o o o o r r r r r r u n B c m a v a i a a a / d d d v d h B M s a v B d S .
d n n
a
e
d d d d e e e e e p e n n n n e e e e e n l v r r r r t t a a a a i t t t t e e t t t t d a t
n n s s s s l l l l d n p r a e e
i a a a a o y c
r c c c c d d i t i i i i u u u u e e e e e l
n n m l c c d d c d c d t
p e e m m m m i i i i i e i n n n n c a a a a p p t e v v v v i d a a a a d l i i i i t e e n n n n 3 t t t t
e o u a d d d d d s s d s s y y y y e t i i i i l n n n n n n i i i d s d d i i M d d m d i d d b M
a . t e
e b e g g e 3 n n
s
a ) a e n s l r r o .
n
i b t c c o l i p a i
n n i n i r i i t i r s r T e i s e a a a c t r a b s b p p t i n i e
s
s s B a d
e
d l d t t e o v n s s p n l r l ( a a a a b
y
b
a e e l l s i d d a a - -
e r a i i i i a
s r h r h r r a c c t a t t t h i i v u d d r r
l l e n n g r a a n a i o o a r e e i o G m n A m n c c h P F G
17 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 18
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES . ) . ) 8 . b 0 a ) l 4 0 3 a 0 2 0 k ( 0 0
k 2 a 2 ( u (
b
. p r . l
u e ) a d t a
b r n t s 4 s
a e G
e 0 d
s s ) c 0 n d e e n 2 d a n r r
e e , a a a s
r a b b í d é e 4 o o h f d u s s 0 a e l n l a a 0 c o r r a R 2 n p c ( t t i
t o n n o
e e i t e n n e e a r o o n n d a o o i n n
l s n n a V m
a
r
/ ) s g 9 4 2 s a 4 0 e . . i R ( n 0 0 d
4 / /
d t 1 6 8 5 t i - . o f 4 0 2 n
0 o . . . f e 0 0 0 o G m , e c
] g
, c
a
, t , ] , a a
] h 5 ] ]
p , / / a
+ a , ] y n ] 2
o ] 5
l m l h r
m a /
/ ] , m m c G m y , , m , p m 2 ]
[ a [ ] ] s [ c ] c
m ,
m m [ m p 0 a [ h d ( ] L c 0
m , /
m
m d u o a h m [ c / , ] A [ 0 2 H
y d / r
( k ) ] d , / a s h 0
t l / 2 1 B [ / [ ] p s r ] i
h m ) [ + y [ r 2 ,
m a H a [ a l s s , m ] g s , [ a i N h r e i h ] [ h ] O E a m n / L e t / p o a E a n y [ p h O 2 L ] L e 2 y [ e ] A S L / n h L L
t G L o
/ S 2 C E d e y
, r m
B m A A m 2 5 E
, ,
m , A
] [ [ 5 , / ,
[ d p ] ] [ m ] ] B B , /
] ] 0 d [ m B [
a a e ] n h m ) u , n
[ , m n s l
. i m , ] n e h h m s i H ] s , % h g e / / ]
b r a % ) b i h ] [ [ e m h a r p , 2 2 K [ t [ m s a t r a h ( n ] t e m / i ( r F 0 [ m e L E L L s L [ O O m [ m 2 r d L a
m c 0 y [ I I [ C L A A A A [ L [
L I e a n B 1 m d C h [ E S G d I v G I 5 S [ B S G G B B B y n
, a ] s
, , s r ] ] s r ] s a a r e a r e l t h , a ] e a / ) ) y r e n b
e y s e e a e ] y a 0 y 0 e / e v v e t d l e i i 1 5 1 2 m
y r / / / b n v v / c t d r r m [ [ e a m m m l i m c u u p c c c e N [ [ G r s s [ [ [ i I e ( ( a N h d g d d y D v i i i D I i i P P (
s
t l l l l s a a a a e y s s s s y t r t a a a a i
i l o r t l B B B B a f s / / / / a o t h l
t r h e r r r r g e r s t i o e e e e d e o n t t t t e l w i o e e e e m u o h m / p /
/ r m
m m d m m a a a a g a a a a b o o e e e e i i i i n r r r r u p i d s M d a a / d a d a p e . l
e e e e e p A
e e e e e r r r r t t t . d t t e t t d
n n n n l l l l p n n e e e r i a a a a y
a d d d t
a u u u u e e e e
n n n
l d c d c c d d c k e e e a i i i i e n n n n c r p p p v v v v a a a a d i i i i e e e a g e t t t t i l o d d d d 3 d d s s d s s
i i i i n n n n n n n n e B
i i M i i d d i d i i d l
s . b u a c n t a 3 i
. d e l P i e e l
r l s i
é & b n
l m o . a
i
: : t . l T s p
n n i i n i i s r s r i a a c r n s p p a t e e
a s
s s d p
a n e
t t t r e e v o s s s l l a a l g g i a a i a b i a y a a e e e n n
n s h i a r - - -
: r i o o r s s s h h h l l a n c a a t t t i v r u u u a a r r r
e t t a t r u n n n
o o o r a a i i i p o P n & A n P m P s c F n c
18 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 19
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
, ) ) ) 5 4 6 0 0 0 0 0 ) 0 2 2 9 ) ( 2 (
( 9 d , . o . l 9 ) r e l a 1 8 e ) a
d t (
t 0
8 t n ) u e s 0 e 0 l
o 0
e 2 0 c o ( o 0 s m 2 d m n d
0 . ( e i e e l
e d 2 i
c i ü a e ( t n v
v n d t a o s G e
l o e - o a r a
a - n - a r
d e o í o o r m f a e c v v v a a e r r ñ l a a a z a r a r r a i a R
B B G B l c c s t m n a e n r d o i g n t e a l e e e e a i p p n n n e d d e i o o o n
l m d o t a a n n n n n i s V n e 1 m ) s 5 e . 7 2 s 0 g 9 e / . R a 4 3 ( n 0
9 / 4 - - n d t . . i 5 a o 0 0 f / 9
o . 0 f m 0 4
G o . y 0 t i s ,
n ] , ] ] e p m d o m c
r [ [ p 0 d d [
, n ] H , ] R
]
a , p , s m C ] t ] ] r
o [ s , y r a p a
h
] ] ,
p h e o a a , m ] [ d / r ] y h h 2 a g [ p n / / m h F [ 1 2 m s D m / a u t / g c e
[ t 2 C d , m [ d e s [ n ] [ l
D r C d m , e / t e a
t L ] [ l , , [ a d h 1 a d a ] ]
A / b , ] N B c h a e n p s
G
] / B s l a , , ,
e h
o e s r t , , ] ] / ] b r
e m e p ] a ] 2 a r p e c e e m m m i d t [ r [ m m [ [ [ l [ m y t r d [ [ 0 0 g [ 1 R [ [ e I I I a n i 2 S t D N N C H S H G v I S y (
] , s s ]
, r t , s ] a s ) ] r
, s ] , t r , e
] e h a r ] ) a a t ] n a y r e a a e h
e a e e h y / o w h e v / 5 y h ] / d s l f i y 5 / / / o 2 3
/ e r b 2 v 5 n m r / e r m m g e s m a t m c m i m r [ c u [ [ n [ n p c m [ [ m r i i a s [ [ 2 g e 2 [ 2 ( ( e a p G r d d h
N P I y i i D G v P D V i i e n / o
t t l l h a S
a g s
l y i s t a
a e d a i s r l B s n
a B h / a o l / /
/
t a e r r r r B r s y
h / t e e e e t e d o e i t t t t e l l o e e e e w u a m m m t o / m i m m d m m r u r ) a a a t l a a a a b o o g i p e e e i i i i o r r r u n r u a d a d a M d i v s d m o a r g t t M
n n
n e e n a d d e a n n n e
e e e a d e e e n 3 p p r
n e e e r e e a e r r r t a l e t t t e t d d r t d
n b s i l l l n n p r a e
n i i d a a a y e
t c a d
t e i t t u u u e e e
n e i s l d d c c d c
e e m i i i m d e s n n n c ( a p
v v v i e
a a a d i i i n e t n . t t t o t o a d d d s s d s y i i t i i i M t n n n n
i d i d M i d i s d p a . i
r . d r c l e s 3
t e
s a d e
a e l d c e l i n n i b l i i r b l a o p p e a d i
a i e d b r T s s r r n n i a g t a a i i
u u d l v e n n a a l
d a n n r r a e a i i p p n o P m A P s r c s v a F
19 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 20
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES , , l - s s h ) i s
a t s e ) , i e s . . e e m m t 8 e l a r ) ) n w o r k t n
b 0 a
t
3 0
d ,
e w
f d
0 ) r e t 0 a 1 e o e s a e m e
2 t i e e 0 k 0 r
( e a s g a 8 s t 2
o r l r 2
e z . ( 0 l ( s r n a u u l e
H i l
a s a a c 0 l
.
a z l , a u e l l á
t i 2 n a e i t W d n a ( a n z u
i c
s
a e
e E . a m n t v r
a s
l r d i r e K e f a o
m b e r n d e
a
t S e o t l c
d a a
n
r z i G
n t
, a i l n n c t - ) d
t d e e a s a n n e e a
z h o o ) u i i s
t i t - e r
e e
r b a g t a m g o e e w í e h í
b m 7 i h i f r m
h
o p e c c e r g , t 0
r e a r d d r ) i
t r h n , e g t 0 c e n d a n a o
s
á R d h n a i h r 2 e t o i t
e
B a r ( G s e t
t s t n
l m e s
i f d t e a e s a t a h r i o c u
e t u n c r n l n n d L L e n e b a n c n n n n i
t A A d d
t o a a s o o
n i
a B i a B i i n
i t e 2
e n t t e , d
- l e
, r r r
a a a a x s t s s d e r p p a o e e e t e d e
s d d s f n a o e i l e n n i i e d e a e l m o m o l l a r
d
n o o n r r b t n m s a a a a i s
1 i
( n
a i a
l
f i v n v V c i n s c
e ( s h s b I o
d t
e r
e
y A i r d c e w t a r i e i n e
o l M o d b r ) a e r s
t
s a t t , n 9 2 d t
s r g n n i s m l
x 9 e n e e o
b o a u m a . e R i e f l v 9 4 u ( G n e u f n n d
0 a n
I
r i n c 9 4 / d s i n
o i d
t s 9 . . r i a
t , c
i i i
. 2
n o h v a s l 9 n 0 0 e ) g f i . 1 y e e a
c o o . N t p d r a s f 0 % v i
c a s i , a i 0 n
( a s G o
i t e
e e l
n d s B u g s h a
e e i c t a s s
t i
i e , r d a s d s
s n i I i o b i
t d n m
e , , ] t G s n r n o N u
]
i s , , e e t a c r t t
m
O n h v a , m e a t G o s e r o ] n
C
c i t e i ,
m w t s a w [ g
r ; s i t y a ) o u
e
n
h i a l 2 r t I / u b e c n t d e e i g i i s n
e d D r
t v , , n
e
t n m a i S ] ] , e w a s
a
d e l t a ] i s s
,
s i r e e e , r r i a y d m t m a r d ] t
b i a a
[
m e i h
u r l
l / s G e e n s s e y i m
c c s t a e a i t y y [ ] N n b e t o e e e i e e [ [ I
a v
a , r t o e 1 1 e s , m t r b m ] o m m t t r
g n
o
c
d a ] l o t n a H b i i , , s [ c r e a
o [ t a a a i e ] ] h , e i d
p t a u u / d
] h
a a e d r 2 a d q / 2
d e s r
N B m a e t r
n
i h h i t ,
s
l n h
/ / e s , , d e h ] , t m 0 r e d 2 2 / ] ]
b e h a P w 1 [ e p t f 0 r e
2 t
u m
a n ,
o r
g e o 1 m m m m i [ f r s q e , t r
L ( i a [ [ [ [
m c r
d [ o 1 a 3
t s o 1 1 [
l A m g n I I i a c s r
n 9 s i u
f o
H N G G c G I v S S B o l D i g e t o
t l o , R
d d c i a r v a t a , C e
v n t f e
] t n ,
d e r r n e a e l n n a n ,
e a c t e
] ] a o o m r
l s e
t i i n m a a a e e a t t s e i ] y 0 i e s e
p h u h h l t / d r e t
s a / / 1
b e
d l i m c / e b 2 2 i s B m p n r b n h i m ]
t a i t V t c m m
e e
s m m u a
s m t [ [ t d
i i r [ [ E c s
h , / o p i h t [ m r d a L 2 x c
i u
2 2 e d g
G e s 3 r a e c i n l E d d i i n
9 e d e d G v D G i i c y , e t s n h i P w m d e i
e
l , o o y r s i r m s e a i k ( r t L t a r s
i c i e n o
A o s e s i t d p
e
c t
B
l l l l n s m
f e h r l i s r , a a a a t d k e o a
a s
e I e s s s s
r c , i e s s t r d i S n a a a a i r s
y
a e l n , o h - n r t o s i B B B B a t u e s e 0 e t B f / / / / e
o
l u e
/
r
p a 1 r r k i m
e r r r r r d e s s e t F t r i r l a
t e e e e e d e ) i e a r x v t t t t t c e a o l i d e e o v o e e e e e v h
c d u m
c g n t z f
.
/ a r , n a m n m m d m m m o P i n i e a a a a a a
x e
a l a a a a a t b o a d f h l e s
e e e e e i i i i i n
t i n i r r r r r o v u
d n s d
e i i a a a M d d s d d d a a g n i
h a m a i a i
c n a
e
u o i i t t , r e o a c f r d t d r i a n n
f
s r t u h
, a i s e e e l t
a i d g l u a o B
i n d d a
s m o c e e d . i l
n n s a d l e h
e a
e e e
m , b c , n l
e e h b t e p p 3 o t
n a r c d e e
i h i
t e e d c r r s n g b h o i e t e t d d n i
n t t a
m
l i
t s a e l
l l p n n
i t
V s , l e d i i l h b
a a s y i
) c c c e a 4 n
C t e t L i i i r d a i u u
e e f b a 4
s t , l 1 h
B d
l o d c d c a l t a T 1 n l I
m m m 2
e i i i a e e
n n a o r - s l n 2 e , a a a r d d d v v i i
i r a a d u - i i t o h b n n n t w
t t e n n n s i i t
d
o
u h t d d s
t s s i h t y y y a a a u i i t b a w a a t t t P e e c n n l v
i
c i . o s s s M d d i d i d d c e r s r n n i u G j r t i i d f e
l s o o b i b g , t n a
i r l l
n i e e d u i o r
n d e c c
l s ó
d o s , r e ( (
m e r i t u g e
o e r a b e t m
. . n f i t i
h h y l s e u t e t p p
t d s e
,
i p s a u s s s b t l m
s y
t n d m
a i h
e s s s i s s a a D p e r r e g a a r i y u u d a h i u u h l l - y n c e e r
t O i d l l d t t l l l e c c
l t
n
h e ó n i i c e r r a r i i h u u a t a e r i t t M i o n
e e e e r e t l e h c p p s s a m a L h u T t g m l h n u a u o r
a a a e u o o r p
A o A i f a r a y E s P G A P n Q Q w c c c y d L a l B w n o
20 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 21
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
• 5. Model modules
a. Increment, growth and yield
i. Site index equations Site index curves are the most commonly used technique for evaluating site produc - tivity on single -species, even -aged stands. A set of site index curves is a family of height (generally dominant height) development patterns with quantitative reference symbols or numbers associated with the curves. The most frequent referencing method uses the term site index , which is defined as the stand dominant height achieved at a specified index age or base age . Nearly all sets of site index curves published in recent decades were elaborated using statistical curve-fitting procedures; most of them can be viewed as special cases of three general equation-development methods (Clutter et al. , 1983): the guide curve method, the parameter prediction method, and the difference equation method. Most studies related to site index equations have used either the function proposed by von Bertalanffy (1949 and 1957) and studied by Richards (1959), or special log -logis - tic models, also known as the Hossfeld models (Cieszewski, 2000). The latter have a long history of describing a wide variety of population dynamics. The climate-based model developed by Bravo-Oviedo et al. (2008) is based on the GADA approach and includes climate attributes and parental material specific for each site. Bengoa (1999) and Bravo et al. (1996) used basal area-age functions as site productivity predictors in non-thinned stands. Most of the site index research is focused on pine species (Tables 4a and 4b) but a few other species have also been studied.
ii. Diameter and basal area growth functions
Individual growth models predict basal area or diameter increment based on growth as a function of site quality, competition and density variables, tree size and even vigor variables in some models. These growth models commonly use a site index to charac - terize the quality of the site (e.g., Palahí et al. , 2003; Sánchez-González et al. , 2006; Adame et al. , 2008a) . However, when the stand age is unknown, the site index cannot be calculated and site-related variables must be used instead (see Section 2a). Most of the individual growth models developed in Spain include the basal area of large trees, BAL (Wykoff, 1990), as a competition variable. This variable can be com - puted for all trees (Palahí et al. 2003; Palahí and Grau, 2003; Trasobares et al. , 2004b, Adame et al. , 2008a, Lizarralde, 2008), for thinned trees during the period between
21 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 22
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
Table 4.a. Site index equations for pine species in Spain
Species and area Methodology 1 Fitting procedure 2 References Pinus halepensis whole country Gcm onls erviti (1991), montero et al . (2001b) ada dvm ruiz-peinado et al . (2010) middle ebro valley Gada dvm cabanillas (2010) Pinus nigra catalonia ada onls palahí and Grau (2003) rest of the country Gada dvm martín-Benito et al . (2008b) castilla y león (afforestations) ada onls río et al . (2006) Pinus pinaster Galicia Gcm ols Bará and toval (1983) Gcm ols rodríguez-soalleiro (1995) ada onls Álvarez González et al . (2005) Gada dvm diéguez-aranda et al . (2009) mediterranean area Gcm ols pita (1967a) ada onls Bravo-oviedo et al . (2004) Gada dvm Bravo-oviedo et al . (2007) climate-based Gada dvm Bravo-oviedo et al . (2008) castilla y león (afforestations) ada onls río et al . (2006) Pinus pinea northern plateau Gcm onls García Güemes (1999) central range ada onls cañadas (2000) catalonia ada onls piqué (2003) whole country ada onls calama et al. (2003) whole country (afforestations ) Gada dvm madrigal et al. (2007) Pinus radiata Basque country Gcm onls madrigal and toval (1975) Galicia ppm onls sánchez-rodríguez et al. (2003) Gada dvm diéguez-aranda et al. (2005c) Pinus sylvestris whole country Gcm ols pita (1964) iberian mountain Gcm ols García abejón (1981) central mountain Gcm ols García abejón and Gómez loranca (1984) pyrenees Gcm ols García abejón and tella (1986) pyrenees, and central and ada ml ortega (1989) iberian mountain ranges central mountain Gcm onls rojo and montero (1996) high ebro Basin ppm onls Bravo and montero (2001) navarra Gcm ols puertas (2003) catalonia ada onls palahí et al. (2004b) Galicia ada onls diéguez-aranda et al. (2005a) castilla y león (afforestations) ada onls río et al. (2006) Pinus uncinata pyrenees Gcm ols pita (1967a) ada onls calama et al. (2004) 1Gcm: Guide curve method (includes also some variants and previous methods); ppm: parameter prediction method; ada: algebraic difference approach; Gada: Generalized algebraic difference approach. 2dvm: dummy variables method (cieszewski et al. , 2000); ml: maximum likelihood (García, 1983); ols: ordinary least squares; onls: ordinary nonlinear least squares.
22 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 23
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
Table 4.b. Site index equations for non pine species in Spain
Species and area Methodology 1 Fitting procedure 2 References Betula alba Galicia Gada dvm dieguez-aranda et al . (2006c) Eucalyptus globulus Galicia ada ols Fernández lópez (1982) Gcm ols Fernández lópez (1985) ada ml García and ruiz (2003) Juniperus thurifera castilla y león Gada dvm alonso and madrigal (2007) Populus x euramericana palencia and león Gcm onls González-antoñanzas (1986) duero basin Gcm ols Bravo et al . (1996) Populus tremula palencia and león Gcm onls Bravo et al . (2002) Pseudotsuga menziesii whole country Gada dvm lópez-sánchez (2009) Quecus faginea whole country Gada onls lópez-senespleda and sánchez- palomares (2007) Quecus ilex whole country (only dehesas) Gada dvm Gea-izquierdo et al . (2008) Quercus pyrenaica león torre (1994) la rioja Bengoa (1999) castilla y león Gada onls adame et al . (2006) Galicia Gada onls diaz-maroto et al . (2010) Quercus robur Galicia ada onls Barrio-anta and diéguez-aranda (2005) Quercus suber whole country ada onls sánchez-González et al . (2005) Fagus sylvatica navarra Gcm ols madrigal et al . (1992)
1Gcm: Guide curve method (includes also some variants and previous methods); ppm: parameter prediction method; ada: algebraic difference approach; Gada: Generalized algebraic difference approach. 2dvm: dummy variables method (cieszewski et al ., 2000); ml: maximum likelihood (García, 1983); ols: ordinary least squares; onls: ordinary nonlinear least squares.
inventories, BALthin (Trasobares et al. , 2004b), for residual trees after thinning, BALres (Condés and Sterba, 2008) or for each species in uneven-aged mixed stands (Trasobares and Pukkala, 2004b). Transformations of this index are sometimes used as the ratio between BAL and total basal area (Condés and Sterba, 2004) or the BALMOD proposed by Schröder and Gadow (1999) (see also Schröder et al. , 2002; Crecente-Campo, 2008). Other competition variables include the crown competition factor developed by
23 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 24
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
Krajicek et al. (1961), which is calculated for residual trees after thinning and mortali - ty by using open-grown equations (Condés and Sterba, 2005) fitted to the main Spanish forest species (Condés and Sterba, 2008). Competition has also been evaluated as the ratio between a tree and stand size indicators. Examples of this are the ratio between diameter at breast height and quadratic mean diameter (Calama and Montero, 2005), the ratio between total height and dominant height (Condés and Sterba, 2008), or the ratio between a section at breast height and stand basal area (Crecente-Campo, 2008). Independent variables in models can also include stand density or size characteris - tics. Stand density is usually included as the number of trees per hectare or basal area (see Section 2.b). Dominant height (Calama and Montero, 2005; Adame et al. , 2008a; Condés and Sterba, 2008) and stand age (Palahí and Grau, 2003; Palahí et al. , 2003; Crecente-Campo, 2008) are the variables most frequently used to describe stand size. Variables such as the diameter distribution skewness and coefficient of variation (Condés and Sterba, 2004) are rarely included. Size is expressed as either untrans - formed or transformed (squared or logarithm) diameter, to ensure that basal area or diameter will not increase indefinitely. The under-bark diameter at breast height is used (Sánchez-González, 2006) for Quercus suber models. Vigor is usually assessed by crown characteristics. Schröder et al. (2002) used the crown spread ratio CSR, calculated as crown width divided by total tree height, while Lizarralde (2008) used crown ratio (crown length divided by total height) as a proxy for tree vigor. Stand growth models estimate or predict basal area growth rates (e.g. Álvarez González et al. , 1999; García and Ruiz, 2003) or more frequently the basal area at a spe - cific age when basal area at any other age is known. Dynamic models derived from the ADA or GADA approaches have been used to project basal area over time (e.g. Río, 1999; Rodríguez et al. , 2010). The initial condition values to be introduced into the dynamic equations are usually obtained from a common forest inventory. However, this is not always available, so some models include a basal area prediction equation func - tion (e.g., Palahí et al. , 2002; Diéguez-Aranda et al. , 2005d and 2006a; Barrio-Anta et al. , 2006b; Castedo-Dorado et al. , 2007b). For Mediterranean maritime pine, Bravo- Oviedo et al. (2004) proposed a logarithmic function that projects basal area growth over a five-year period as a function of the initial basal area, initial age and site index. In some models, the expected variability in basal area growth has been analyzed by including regional and/or thinning effects as categorical dummy variables (e.g. Barrio- Anta et al. , 2006b; Castedo-Dorado et al. , 2007b; see also Section 5.b).
iii. Height growth functions Two different approaches can be used to estimate height growth once the height of all the trees or the diameter class has been determined, either by measurement of all the trees or estimation using a local or generalized height-diameter equation. The first approach is static and uses a height-diameter function (see Section 3.b) to estimate future tree height. The estimated heights at two different moments are then subtracted to obtain height growth. The second approach requires the use of true height growth
24 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 25
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
equations. The two main model development strategies generally used for this (Huang and Titus, 1999) are: (i) equations that directly estimate height growth as a function of tree and stand attributes and other variables such as competition indexes, and (ii) “potential x modifier” equations; in which a simple equation serves as the estimator for the maximum potential value of height growth and is then modified by different vari - ables. Growth models developed in Spain generally do not contain height growth functions. The rare exceptions to this are the equations developed for radiata pine (Crecente- Campo, 2008) and Scots pine (Crecente-Campo et al. , 2010a) in Galicia and those developed by Lizarralde (2008), which estimate height growth from tree and stand vari - ables for Scots pine and Mediterranean maritime pine in Central Spain.
iv. Volume growth functions Volume is impossible to measure directly in trees or stands and is therefore an esti - mated variable. Both current and increment tree or stand volumes must be estimated from tree or stand variables. Most whole-stand growth models developed to date in Spain do not incorporate volume growth functions explicitly. A combination of three state variables (i.e. num - ber of trees per hectare, stand basal area and dominant height) is usually found to be sufficient for obtaining an adequate stand state description (García, 2003), especially for pure and even-aged stands, which makes the use of stand volume unnecessary. The parsimony principle strengthens the argument for avoiding volume growth functions. Total (or merchantable) tree or stand volume is usually considered as an output variable. It is estimated by prediction functions that use the current or projected values of the state variables with the strongest correlation to tree or stand volume (see Barrio-Anta et al. , 2008; Crecente-Campo, 2008). However, some whole-stand growth models developed in Spain have included volume projection functions (Río et al. , 2001 and 2005; Palahí et al. , 2002, Bravo-Oviedo et al. , 2004) in a system with at least two pro - jection functions (for stand basal area and stand volume) that are fitted simultaneously to minimize the global sum of square error. Volume increment functions not included in individual-tree or whole-stand models have also been used in successive Spanish National Forest Inventories for the major Spanish timber species (Martínez-Millan et al. , 1993). These functions predict the mean annual volume increment as a function of diameter at breast height, total height and mean annual diameter increment.
b. Silviculture response functions Silviculture response functions are used to determine the effects of silvicultural prac - tices, such as initial spacing, pruning, thinning and fertilization, on tree growth and stand development (Westfall et al. , 2004). Two main approaches are used in developing such models. The first is to fit regression equations separately to data derived from a particular silvicultural regime. Examples of this approach include yield tables and spe -
25 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 26
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
cific models developed to represent a particular silvicultural regime, such as high- graded Scots pine stands (Bravo and Montero, 2003) and mixed pine-oak management (Sánchez Orois and Rodríguez Soalleiro, 2002). The second approach is to develop models that can be applied to a set of silvicultural regimes. The first attempt at this in Spanish forestry was the development of variable-density yield tables (Section 7.a.). More recent growth models include thinning and fertilization functions to simulate different silvicultural regimes. Thinning functions should be recognized as either thinning control functions or thin - ning response functions. The former evaluate immediate changes in forest conditions due to thinning, and the second consider the effects of thinning on growth, since stand growth characteristics and dynamics change after thinning. Several thinning control functions have been fitted for different species in Spain, usually by predicting the qua - dratic mean diameter after thinning from the same variable before thinning, along with the thinning weight (Río and Montero, 2001; Bravo-Oviedo et al. , 2004; Río et al. , 2005). In other cases the control function is determined by estimating the parameters of the diameter distribution after thinning (Espinel et al. , 1997; Álvárez González et al. , 2002). Álvarez González (1997) compared several methods for estimating the diameter distribution after thinning, and found the most accurate to be the prediction based on the Weibull parameters, which include parameters from before thinning as well as the per - centage of trees and basal area removed. Two approaches have commonly been used to estimate the thinning response effect: the development of different basal area growth functions for different types of stands (unthinned and thinned) or the inclusion of a thinning response function that expresses the basal area growth of a thinned stand as a product of a reference growth value and the thinning response function. The first approach was applied in Spain by employing categorical dummy variables for detecting simultaneous homogeneity among parame - ters. The results showed that the same functions could be applied to maritime and radi - ata pines (Barrio Anta et al. , 2006b; Castedo Dorado et al. , 2007b). Castedo-Dorado et al. (2004) developed a thinning response function that serves as a reference for evaluating the effects of fertilization treatments after thinning. This has made it possible to analyze the separate effects of thinning and fertilization on basal area growth (Santalla, 2010). Models describing the response to pruning scarcely appear in the Spanish literature. Rodríguez (2005) compared several pruning methods for three different poplar clones, a study that may serve as a reference for evaluating the effects of pruning treatments on height, basal area and volume growth. Along with several natural (and somewhat unknown) factors, pruning response is also affected by the pruning height. Snowdon (2002) identified two basic long-term responses of plantations to fertiliza - tion and other silvicultural treatments. Type 1 responses show an initial increase in growth that is not sustained long-term, while Type 2 responses are sustained long-term and can be regarded as to the result of a change in site quality. The lack of long-term data and the need to avoid overestimation of silvicultural effects has led to the use of the first approach most of the time in Spain. Parallel growth trends between treated and non-treated stands for a given age show the treated stands to be at a more advanced stage
26 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 27
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
of development. A growth multiplier coefficient can be calculated from an existing model, as was suggested by Carson et al. (1999):
(1)
-1 where: t2 and t1 are the final and initial ages at which the observations were made, F (C2) --1 is the age corresponding to a particular value of C2, according to the model, F (C1) is the age corresponding to a particular value of C1, and m is the growth multiplier. This method has been used to evaluate the basal area or dominant height growth effect of ash fertilization for Douglas fir (Solla et al. , 2006), radiata pine and chestnut (Solla, 2004). Other effects, such as the response to phosphorous fertilizer, are likely to be Type 2 responses, but long-term analyses of growth effects are needed to confirm this (Santalla, 2010).
c. Demography
i. Seed dispersal models Seed dispersal patterns determine the potential area of plant recruitment. For most forest trees, seed density decreases as the distance to the seed source increases, follow - ing leptokurtic curves with extended tails of long-distance dispersal. Dispersal kernels, i.e. the probability function of seed density decrease with greater distance, are normal - ly fitted using either inverse modeling or genetic markers. These require the establish - ment of seed traps (to estimate seed shadows) along with the spatial coordinates of the seed traps and seed sources. Inverse modeling relies on numerically intensive calcula - tions of the likelihood of obtaining the observed seed shadow using a particular disper - sal model. Popular models for kernel fitting are lognormal, 2Dt and two-parameter Weibull dispersal functions (see Greene et al. , 2004 for a comparison of these models). Tree fecundity can be estimated by the model itself, but is more frequently included in the model as a function of tree size (diameter) or direct seed counts. Alternatively, genetic markers, such as microsatellites, can be used to establish seed or seedling sources. In this case, two-parameter dispersal kernels from the exponential-power fam - ily are commonly used. This curve family is able to accommodate a wide range of func - tions (Gaussian, exponential) and also allows for fat-tailed long-distance dispersal. In Spain, there are different ongoing studies to determine seed dispersal kernel fit - tings for various forest trees and shrubs, such as English yew, Prunus mahaleb , oak, beech and pine. In Prunus mahaleb , the best-fitting dispersal kernels are very lep - tokurtic, resulting in large average seed dispersal distances of more than 100 m (Robledo-Arnuncio and García, 2007). Unpublished results using both inverse model - ing and genetic markers for Pinus pinaster on the Castilian Plateau showed much short - er (about half) mean seed wind-dispersal distances. Models that best fitted the observed data were log-normal and fitted better in a sampling design consisting of many small
27 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 28
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
seed traps rather than fewer but larger traps. Interestingly, five-fold variation in disper - sal distances was found for different dates in the same dispersal season, probably due to local climate factors such as storms. In addition, dispersal kernels based on established regeneration in Pinus pinaster had larger average dispersal distances than those based on seed shadows, indicating Janzen-Connell effects (González-Martínez et al. , 2006). Such effects highlight the importance of post-dispersal mortality in tree population structure and dynamics. There is a need to go beyond simple exponential curves and develop more explicit representation of dispersal kernels in growth and yield models. Along these lines, the integration of a recruitment behavior that includes dispersal functions into popular growth models such as SORTIE is promising. However, parametrization of the disper - sal model for different forest trees would necessarily involve specific studies for select - ed model species, based on their reproductive system and life-history traits. It could be difficult to fit the distribution tails (i.e. long-distance dispersal) due to scarce and unre - liable data.
ii. Regeneration models Models for natural regeneration under different silvicultural methods are not well developed in Spain, mainly due the scarcity of long-term data. Only four main experi - mental sites have been established during the last decade, in Valsaín, Segovia ( P. sylvestris ), Cuéllar, Segovia and Navas del Marqués, Ávila (both P. pinaster ) and Viana de Cega, Valladolid ( P. pinea ). Experimental data regarding seed production, dispersion, predation, germination and establishment have been recorded for these sites. Post-fire recruitment has been also studied, mainly for pine species in the Meditarrenean area. Results are available for Pinus nigra (Ordóñez et al., 2004, Ordóñez and Retana, 2004), Pinus halepensis (de las Heras et al. , 2002, Pausas et al. , 2004, Broncano et al. , 2008), Pinus sylvestris (Nuñez et al. , 2003) and Pinus pinaster (Calvo et al. , 2008, Vega et al. , 2010). Data from these experiments and other monitoring studies will be used to devel - op multiplicative type models for predicting the number of seedlings established, by incorporating different independent variables such as seed production, primary and sec - ondary dispersion, germination rate as a function of environmental conditions and establishment success as a funcition of environmental conditions and interaction with other species.
iii. Mortality models Tree mortality plays a huge part in forest dynamics, as it reduces competition and leads to self-thinning. There are three types of stress factors that cause tree vigour to decline and affect tree survival (Manion, 1981 in Pedersen, 1998): predisposing factors, inciting factors, and contributing factors. Mortality has been divided in two categories: regular, non-catastrophic or competition-induced mortality and irregular or catastrophic mortality. The first category has been studied at both the stand and tree level. Stand reg - ular mortality has generally been modeled in Spain using functions that describe the
28 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 29
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
number of trees at projection age as an algebraic difference equation of previous sur - viving trees and age at the beginning of the projection interval. Espinel et al. (1997) modeled mortality for two thinning treatments using a linear regression for Pinus radia - ta in the Basque Country. Río and Montero (2001) adapted the model proposed by Clutter and Jones (1980) to estimate mortality in unthinned stands, and Bravo-Oviedo et al. (2004) fitted an exponential function for Mediterranean Pinus pinaster . Using data from plots where natural mortality had occurred, Álvarez-González et al. (2004) and Diéguez-Aranda et al. (2005e) derived mortality functions from differential equations in Galicia for even-aged Pinus radiata and Pinus sylvestris plantations, respectively. There are two possible status values for an individual tree at a certain point in time: the tree is either alive or dead, so the response is typically binary. This also happens at stand level and is demonstrated by the fact that a relatively high number of perma - nent sample plots have no occurrences of mortality, even over periods of several years (Monserud and Sterba, 1999; Eid and Tuhus, 2001). Woollons (1998) suggested a two-step modeling strategy to account for the binomial nature of mortality: a logistic function predicting the probability of survival using all sample plots and an equation to determine tree density reduction, fitted only with the sample plots where mortali - ty occurs. The estimates derived from the tree-number reduction equation are modi - fied using deterministic or stochastic approaches (Monserud and Sterba, 1999). Álvarez González et al. (2004) compared three of these approaches, while Diéguez- Aranda et al. (2005e) made an alternative comparison that estimates tree number reduction without considering the probability of survival (i.e., a function for predict - ing the reduction in tree number that was fitted to include all plots –with and without occurrence of mortality). Both of them found that the three methods of the two-step modeling strategy provided satisfactory predictions. Diéguez-Aranda et al. (2005e) suggest that the second approach may be a good alternative when natural mortality is very frequent. At the individual tree level, the binomial nature of mortality makes Gaussian models inappropriate for expressing the probability of a tree dying or surviving. In Spain, logis - tic regression has been used to model individual-tree mortality for mixed-species, uneven-aged stands of Pinus sylvestris and Pinus nigra (Trasobares et al. , 2004a) and for single-species, uneven-aged stands of Pinus halepensis (Trasobares et al. , 2004b) in Catalonia; for separate single-species, even-aged stands of Pinus pinaster and Pinus sylvestris in continental and Mediterranean regions (Bravo -Oviedo et al. , 2006) and for Pinus radiata plantations in Galicia (Crecente-Campo et al. , 2009b). Adame et al. (2010b) used a multilevel logistic approach for predicting individual-tree mortality for Quercus pyrenaica from National Forest Inventory data. The application of these models requires the selection of a cut-off or threshold to determine if the tree is dead or alive. This threshold can be deterministic (survival rate or the point where sensitivity and specificity curves cross) or a random deviate. The logistic model can be used to classi - fy trees according to their status (alive or dead) or to make predictions of survival rates. However, prediction and classification do not follow the same pattern (Bravo-Oviedo et al. , 2006) and model users should select the best option according to management objectives.
29 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 30
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
iv. Ingrowth models Ingrowth, like other stochastic events, is a key component in long-term forest pro - jection systems. However, most standard forest models do not include an explicit ingrowth submodel and assume that ingrowth is negligible or has no influence in any long-term silvicultural estimates. This assumption may be incorrect, at least for uneven- aged and highly structured stands (Vanclay, 1994) and low density forests. In Spain there are just a few exceptions that include an ingrowth submodel in growth and yield models. Two-step ingrowth models for maritime pine (Sánchez-Orois and Rodríguez- Soallerio, 2002), Scots pine and Mediterranean maritime pine in Central Spain (Bravo et al. , 2008) and Quercus pyrenaica (Adame et al. , 2010a) have been developed. They include a logistic model to predict the probability of ingrowth occurrence in a specific stand and a linear model for quantifying ingrowth in terms of basal area (m 2/ha) or num - ber of stems per ha. Sánchez-Orois and Rodríguez-Soallerio (2002) included basal area and number of stems per hectare as predictors for 10 year ingrowth projections for Maritime pine and accompanying broadleaf species. Bravo et al. (2008) used stand-level variables (basal area and quadratic mean diameter) as predictor variables, which together resulted in a model, that predicted 5 year basal area ingrowth equal to 63.5% for Scots pine and to 70.0% for Maritime pine. Finnally, Adame et al. (2010a) used quadratic mean diameter, average height, number of trees per hectare and average diameter as predictor variables. They obtained a 71.7% correct classification of ingrowth events but only a 0.358 coeffi - cient of determination in the 10 year linear model for the amount of ingrowth.
d. Output functions
i. Volume and biomass equations Volume equations are a fundamental part of individual-tree and whole-stand growth models, as they provide one of the key output variables for management plans. U ntil 1967, most of the published individual-tree volume equations with two variables were compiled by Pita (1967b). The Spanish National Forest Inventory (SNFI) has published provincial, regional and national individual-tree volume equations for the most represen - tative forest species. Martínez Millán et al. (1993) have also developed tree equations for the most important forest species in Spain. Other works exist for Pinus pinaster (Bravo- Oviedo et al. , 2004), P. sylvestris (Bravo and Montero, 2003; Diéguez-Aranda et al. , 2006b; Crecente-Campo et al. , 2009c), P. radiata (Castedo-Dorado and Álvarez González, 2007c), Populus x euramericana (Barrio Anta et al. , 2007b) or Quercus robur (Barrio Anta et al. , 2007a). Biomass equations are generally fitted in allometric form and have been developed for the different tree sections (stem, bark, branches of diverse sizes, crown, foliage, etc.) according to their importance in the nutrient cycle or for their use as bioenergy. In Spain, the species most studied are those with the highest economic value (wood or fire -
30 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 31
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
wood) or with the greatest distribution area, as Quercus ilex (Ferres et al. , 1980; Canadell et al. , 1988; Canadell and Roda, 1991), Q. pyrenaica (González Doncel, 1989; Allué and San Miguel, 1991; San Miguel et al. , 1992; Gallego et al. , 1993), Castanea sativa (Leonardi et al. , 1996; Santa Regina, 2000), Fagus sylvatica (Santa Regina et al. , 1997), Pinus radiata (Merino et al. , 2003) or P. sylvestris (Santa Regina et al. , 1997; Montero et al. , 2004b). In addition to these studies, Montero et al. (2005) fitted biomass models for 32 forest species in order to estimate the amount of carbon fixed by Spanish forests. Later, using SUR (Seemingly Unrelated Regressions) methodology with the additivity property guaranteed and the efficiency increased (Parresol, 1999), individual- tree models were fitted for Pinus pinaster and P. radiata (Balboa-Murias et al. , 2006a), Quercus robur (Balboa-Murias et al. , 2006b) as well as Betula alba , Eucalyptus globu - lus and E. nitens (reported in Diéguez-Aranda et al. , 2009). Stand biomass models were developed for Pinus pinaster (Barrio-Anta et al. 2006a) and P. radiata (Castedo-Dorado et al. , 2009b) with this methodology, using stand variables as predictors. The biomass models proposed by Montero et al. (2005) are currently being revised to include the additivity property and incorporate tree diameter and height as independent variables (Ruiz-Peinado et al. , 2011).
ii. Taper equations Accurate predictions involving wood products classified by merchantable sizes are a matter of interest for forest managers in Spain and many parts of the world. Volume prediction to any merchantable limit can be achieved by several methods, two of which are commonly applied. The first is to develop volume-ratio equations and the second involves elaborating an equation to describe the stem taper. Integration of the taper equation from the ground to any height provides an estimate of the merchantable volume to that height. Taper functions provide forest managers with estimates of (i) diameter at any point along the stem, (ii) total stem volume, (iii) merchantable volume and merchantable height to any top diameter and from any stump height, and (iv) individual volumes for logs of any length at any height from the ground. Data pairs of diameter and height along the stem are required for developing a taper function. This data was typically collected in Spain through destructive stem analysis, but now digital dendrometers are used (Rodríguez et al. , 2009). Most taper functions that have been developed in Spain can classified as single taper models, segmented taper models, and variable-form taper models. Ideally, a taper equation should also be compatible ; in other words the volume computed by a taper equation from the ground to the top of the tree should be equal to that calculated by a total volume equation (Demaerschalk, 1972; Clutter, 1980). The existing research indicates that segmented models appear to be more accurate than the others for creating compatible systems (e.g., Jiang et al. , 2005). Cervera (1973) made the first attempt at developing taper equations for major forest species in Spain. Since that time, many taper equations have been developed for particu - lar regions and species, mainly for softwoods but also for some hardwoods (Table 5). Due
31 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 32
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES ) n ) ) r a ) ) ) 9 ) e 9 7 6 6 7 h 0 6 0 y 0 0 0 t 0 t 0 0 0 0 u 0 0 i 0 2 0 l o 2 2 2 2 ( 2 i ( ( 2 ( ( s (
. ( . . . b , l
z l l z l i s a o t n a a n a n
r
i t a a a ) t t t ) e a r r e t e e t b e ) ) ) ) ) ) ) r r p 1
)
n n 5 0 e e 0 0 0 0 0 0 0 o 8 a a o u o 0 1 m c 1 1 1 1 1 1 0 0 d d h h d o r ) 0
0
0 0 0 0 0 0 o 2 0 n n
a m a ( 2 m d 2 d r c 2 2 2 2
2 2 a a 2 7
( (
( ( ( ( ( ( r r ( . n n o d s
0 n m
l . e a a s e - n a z z z z z z l a a e 0
a d i a h c - -
a e e e o e e e - a z z d 2 c l
t t
z z l i l ( n u u u n u u u e o e
t l a e
i e e a , e a
g g g g g g a n d n e a r l n í í í í í í
í u u í r a m d l e r r r r r r t r t í g a G i t e o g g a
r a r e d d d j d d d f , d n l s b v é e a z a s e i i e s a o a a o a o o o o a o i e g u s B r m c c l r d c r r R d r r m c r
n m s a a e r r
e e l l g r a p r t o t
r m f n n n n n n n n n e n a p o o o o o o o o o
i i i i i i i i o s c t t t t t t t t i
c e , e t t i a a a a a a a a l l e f a n d d d d d d d d p p i g i i i i i i i i e d l l l l l l l l n c i d m a a a a a a a a a l m e a n v v v v v v v v a r a p ------e
s v s s
s s s s s s s s
n p e e e e e e e e
t
s s s s s s s s a i e n e n n n n n n n n i r l o o o o o o o o i r d o o o o o o o o r r r r r r r r h o p o e n
t b n s n c n n c c n n c c J n c c i n c
s i
g r n o n r n i t e a o h r a d i t r l t r u a a u o l R t v c n a O n m ( n
i e F i n a r r r r r r r r r n s
i
, N m o c p a o o o o o o o o o a i e h n p p p A l F F F F F F F F F c i t e m i i i i i i i i i s B c c p n s
a b b b b b b b b b i n M w e n U c c i I p i u u u u u u u u u m o
- c c c - p S c c t G t I c w c c c c S s r
. e g e g
n g e i n y n
t n a i i s r a m
l
r i e n
u n n i l i h b o c i o a i o s s s s s s c t i t t e o o o o o o o o o o o o a v e e e e e e t n c
a e p
u n n n n n n n n n n n n a a n p y y y y y y r s
o t
o u h f m n f m r
t
o e i o d 6 j
e C w m n n a i i e a a ) l s t m
s m
² b p
e o e 9 4 5 3 9 4 7 1 7 5 9 9 3 5 6 8 3 e R
6 n m ( s h h 8 9 9 8 8 5 7 7 7 8 8 8 8 7 0 5 9 i i t
9 t d
9 8 9 9 9 9 9 9 9 9 9 9 9 9 . 9 9 9 t
...... s i n o e 0 r e f 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o o
r i h o f t a t f G a
o p
u
e , d m q ) t e o e n 9 g
a c a 0
n n
d 0 k a a
y
r 2 n e ( e d o r
o l
n .
) h l i w l
n a
t t y n a
a
s a r n n n n n
s s ) c ó i i t t v s o ó ó ó ó ó d
d r e h e n n e t t
e e e e e e n o n
e l u a t u r b a a l l l l ( l
n f d d o l l u i
, b e
) s s n b e a y y y y o y r c
e i i e i n 0 a
s
1 1 1
z y p r a r n 1 a a a a n a r e a i e a a r a y y p l l l l l e o i m 0 l i i i
a o r e a l l l l r l r u l , r - l i h n i i i i i 2 c c c d a p a a u a s t q i t t t t t z ( i i i e u a l
l d l v l B s e n t t n s s s s s n s a e u
i i v z a s a a r a o a a a a a a a a a l u p o e a e e l t g v G c e c B a s s c c c A G n c c m c G u
o n d é g i
h u a í s
r o d s w
i d
n h s n m o e t i
o n
i h i s r t e d
t
a o w e r e n c g a t i i o r
g a t f u u d
o d n e s d q p B t a i
e l l e u a t
d
a d m a n n r v p
e a . . e
u e d
p p a s e p b i n s s
r r a u a e e e l b b r o s e v d T i u u u e s s i b
a f
s i s s
b s . , i a h s s n n e
r o r r a c a l n e s . i o g a e e u l i h t e t t t g c n
5 e h r
l s a s a p
a a a t d s n a e
i v e a e r a e r o e l s u l d n l d
n n g n t e y o u i i a i i a n a m b b p s s
r r p p a c h n p
m y i e a
e
e s
s l r i s s s s s s s s s a p T e u c a e i i u u u u u u u h b e g c
h h n n n n n n n n i t i i i a u i i i i t t i p u 1 2 3 P P P F S E J P P P P
32 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 33
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES ) ) n c ) ) ) b r 9 3 3 3 e 6 0 0 0 0 h y 0 t ) ) 0 t 0 0 0 0 u i a b 2 2 2 2 l o 2 ( ( ( ( i 7 7 (
s .
) 0 0 . b a a a , l l i 9 0 0 s n n n a ) t a i i i
0 n 2 2
l l l i t 4 ( ( a t 0 a e o o o 0 e . . t
p ) ) ) ) ) 2 )
l l 0 ( n o 0 0 5 5 5 8 a
m m m a a u 2
m
p 1 1 0 0 0 z 0 d ( t t o d d d o e 0 0 0 0 0 0 n e e . m n n n m
l c h 2 2 2 2 2 a 2
a
( a ( ( ( a ( a a a r ( c a s
n t t
e c n e t a z z z z z z z z a e n n - i a h c - e e e e e e e e e d c e
t a z a l i t s n u u u u u u u u
l a - - - e a , e n g g g g g g g g a r o z o í í í í í í í í u r e m d i r i r r r r r r r r e G e g c r r a
a e d d d d d d d d f , p r l r é e z s e i e s r a a o o o o o o a o o i ó g u l d c l B c r R r r r r r B r r
n m s a a e r r
e l g r a t r o t
r f n n n n n n n e n p o o o o o o o
i i i i i i o c t t t t t t i
c e , t a a a a a a i l e f a d d d d d d p i g i i i i i i d l l l l l l n c i a a a a a a a l m e v v v v v v a a r p ------
v s s s s s s s s
n
e e e e e e e e e
s s s s s s a n e n n n n n n n n n i r o o o o o o i r o o o o o o o o o r r r r r r h o o e t
b c n n n n n c J n c c c n n c n
s i
g r n n o r n i t e o h d a i t l t r u d a l u o r n t c n a o n m (
n
i e F i r r r r r r n s
i
, n m o a o o o o o o e h n p p a l F F F F F F i t m i i i i i i s c p s
a b b b b b b m w e n c i p i u u u u u u m o
G - - c s - t c I - c - c - c c - S s r
. e g e g n
g e i n y
n t n a i i s r a m
l
r e i n
u n i n l i h b o c i a o i o s s s s s c t i t t e o o o o o o o o o o a v e e e e e t n c
a e p
u n n n n n n n n n n a a n p y y y y y r s
o t
o u h f m n f r m
t
o e i o d 6 j
e C w m n n a i i e a a ) l s t m
s m ² b p
e e o 2 7 2 0 8 8 5 2 5 9 2 4 1 5 3 e R
n m ( s h h 8 8 8 7 8 7 8 8 9 8 9 9 9 9 8 i i t
t d
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 t
...... s i n o e r e f 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o o
r i h o f t a t f G a
o p
u
e , d m q ) t o e n 9
a c 0 a
n d
0 k a
r 2 n e ( d o
o n . h i w l 1 a t
t
a
s n n n
u ) c i t s o a ó ó ó h e n t e t
e e e e
e t a t u l l l
n a d f d u
, l e
) n e b y y y r p
e 0 a
2 y p r a a a n l 1 a a a n n n i a a r r r p l l l 3 2 1 o a m 0 i i
a r r r a l l l ó ó ó l , r - i n i n i n 2 c c a a a p t a u s t i t i t i g g g e z ( i i l
l l v v v s e n s s s n a a a a a a e v
i z a a a r a r r r a o a a a e u p p p e a e e l t g v G s G c A s c n n c a c a a n s u
o n d é g i
h u a í s
r o d w
d
n h n 4 m o e t i o
c
i 1 h i s r t d
t 2
o w e r i m n a g t
i o r . . . .
a f u u v v v v d
d e c c c c d q p B t i
l e u a a a a a
d
a d n n n n n n r i v p
i e a a a a a e
u s e d
c c c c a p e e b i i i i i n i
r r r r r r a e z e e o e e e e a e v d n T s i c b
a
e m m m m
i s . , s o h s i a a a a a n a e
r c m b a t o r r r r r s
o . g n u t n l h z a u u u u c n
a e s 5 e a b
l n n e e e e a
r l g e d n i
o e a y e v r r o e u c x x x x B d l
l v
p
e s o n
s n t y m s s s s á b b s a
s a u s
u o m u u u u d i e
e a s
l l l l u a c r i s d s s a s a c r s e u u u u T c i e u u u n i h e e b e p p p p h h e a n n u i t u u i o i o o o s t t i p c l 1 2 3 P Q Q P S P P P P P
33 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 34
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
to their complicated formulations, most taper functions are implemented into specific programs for estimating total and merchantable volume from inventory data, such as cubiFor (Rodríguez et al. , 2008) or WinCP Navarra (Diéguez-Aranda et al. , 2007). They can also be submodels within complete growth and yield models for implementation in growth simulators such as GesMO (González-González et al. , 2009 available in Diéguez-Aranda et al. , 2009 and in www.usc.es/uxfs) or Simanfor (Bravo et al. , 2010 available at www.simanfor.es ).
iii. Non-timber product functions Mediterranean forests are characterized by their multifunctionality and the diversity of both wood products and non-wood forest products (NWFP) they provide. Pine nuts, cork, edible fungi and resins are probably the most valuable non-wood products; in fact their profitability sometimes exceeds that of timber products (Palahí et al. , 2009). Other indirect functions such as recreation can be included in forest production. Given their importance, information that aids prediction and clarifies requirements for optimal NWFP productivity should be integrated into forest management decisions and silvi - cultural practices. Several NWFP models have been developed in Spain in recent years (Table 6) for most non-timber production species (for example, Pinus pinea , Quercus suber , Pinus pinaster and Pinus spp. , for mushroom producing areas). Most of the approaches to modeling stone pine cone production have evaluated the inclusion of different tree or forest stand parameters such as: - tree size (Cañadas, 2000; Piqué, 2003; Calama and Montero, 2007), large trees are associated with greater production; - tree level competition (Calama et al. , 2008b); - stand density (GarcíaGüemes, 1999; Cañadas, 2000; Piqué, 2003; Calama et al. , 2008b), low density forest stands are recommended for fruit production; - stand maturity (García Güemes, 1999); - site index (Cañadas, 2000; Calama et al. , 2008b).
Site characteristics and soil attributes (Calama et al. , 2008b) are significant factors in predicting the cone yield for a given period. However, the effect of climate or other ecological factors on the variability of cone production is very important. Climatic factors such as rainfall and temperature before flowering explain much of the yearly variation in yield (Mutke et al. , 2005, Calama et al. , 2011). Quercus suber is the most economically important NWFP species, and a few models have been elaborated for it (Table 6). In the model developed by Montero (1987), the independent variables selected were a compromise between simplicity of measurement and approximation to the real stripped surface. Three models have been developed using three different methodologies for estimating total cork thickness at the time of debark - ing: linear regression (González-Adrados et al. , 2000), ordinary kriging (Montes et al. , 2005) and mixed models (Sánchez-González et al. , 2007a). For cork thickness estima - tion by complete years, Sánchez-González et al. (2008) used the GADA formulation derived by Krumland and Eng (2005) from the Richards model, which has a reliability
34 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 35
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
that ranges from almost 80% starting in the fourth year of cork rotation to nearly 90% from the eighth year onwards. All the models described above deal with mature cork; the only model for virgin cork (the cork obtained from the first debarking) predicts vir - gin cork thickness at different heights (Sánchez-González et al. , 2007d) using a taper equation. Models have recently been developed (Bonet et al. , 2008; Bonet et al. , 2010) that attempt to estimate wild mushroom production in pine forests of the Central Pyrenees. Based on their own mushroom inventory (Bonet et al., 2004) collected in 24 Scots pine plots over a three year period, Bonet et al. (2008) developed an empirical mixed model that established the relationship between species richness, the production of total, edible and marketable mushrooms, and stand and site factors. The results showed that produc - tion was greatest when stand basal area was approximately 20 m 2/ha, and species diver - sity (measured as number of species, Shannon index and Simpson index) was greatest when stand basal area varied between 15 and 25 m 2/ha. Using the same approach with new yearly mushroom inventories and a second set of 21 plots in P. sylvestris , P. nigra and P. halepensis forests (Martínez de Aragón et al. , 2007) in the county of Solsonès (Spain), Bonet et al. (2010) were able to establish new empirical models for pine forests. The results were similar to the previous studies, showing maximum mushroom produc - tivity with 15-20 m 2/ha of stand basal area. Aspect, slope and elevation were also pre - dictors of mushroom productivity. Resin yield is affected by several natural (and partially unknown) factors, but also by the tapping method and height of the tapping-face above the ground. Resin yield models are scarce in the literature due to difficulties in finding reliable models for resin production and the reduced industrial demand for national resin products. However, Nanos et al. (2000) developed a model for stands of Spanish maritime pine based on probability distributions, using maximum likelihood to estimate resin-yield distribution parameters. However, they had no prediction method for the parameters of their model, since stand-level predictor variables (such as stem density or stand basal area) showed no significant correlation with resin yield (and, by extension, with the probability distribution parameters). Regression models predicting the average stand production for resin have never been reported, suggesting that the mean stand produc - tion capacity for this NWFP is not related to (and can not be predicted by) either cli - matic variables or classical independent variables such as site-index and stand basal area (Valero Moreno, 1998). Nanos et al. (2001) proposed the use of geostatistics to estimate the average resin yield of some stands in central Spain. The need to use inde - pendent variables would be eliminated by employing spatial autocorrelation in con - junction with classical variogram analyses and a subsequent kriging interpolation. This geostatistical model can be used to identify stands with higher resin production capacity but it can not be extended to non-sampled stands.
35 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 36
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES ) ) e : ) l k t ) a d t r b 0 o o 8 7 7 a k o 0 o c i r 0 0 0 c r r 0
l o 0 0 0 a :
d 2 c ; 2 2 2 v
( e e )
( ( (
t e . s y a . . . h l % l l l l t (
m a m
u ) a a a f
r
t 2 r m t t t o m o )
e t 0 u e ; e e u r
5
c d u c 0 a s
z a z z 0 a c e : 2 f o e . e e 0 e
a ( y l l l t
d )
0 n 2 : á á á a a e é 2 ( 7 l o 2 t t z z z r i - u
8 . p e t , n n n d
l l i c q ) 9 t c o o o n i p a s s
e a 1 r
r ; e - p ( t p e G m G G ) a
c z - - - e h o e z
m t o e m z z z n c y r r s e l
o e e e ( e o m
e e á c u y r h h h
( t t e z n
q n e c c c n n n e
a n g z f r
n n n o o n t w : n á o e
á á á i i o o f t
r k
s R m v G s m s o ; r n c
)
a o e : i b t m g F e a a )
m c d c c :
( c i t
u c f
e
i o
i r ; c t ; t c )
w ) o l a t
f g e r e a o l g t e m s
n n v s g
c e s b n n r i
n
w e
( i s l n y d s t l
a r o o i i s
l e
U i i e s a o u o e s t t g n u a
e n e s s i
n e a a r u
k e
e m y o r r t s : r o
c c
d
o g n e i i k i f a e e e o U e n
t l n o
h l h l o n i v t ( t
a n o y
a h n
b
s o i r o r
a o
v v t c k s a ; e t e u w b a - s r l t r r n l a l
a n a e s s n o e e e a
b e u d p d o i e s
n c
i i s i d e
l t m n r l d m o d t m m r b o n ( r a d a r a k a t i o
i i n r a i o e c t n d i O v c s a m s f F o c f u a
t a o h l l i a t p a t
u a m k S m
r 9 9 m v
r e 8 o e u 9 9 s o l n . . - n c c 8 s 0 9 2 i
n e o 0 0 4 c
1
e 9 t d 9 7 : - - : c . a . . . i =
e n e d P 6 2 0 : t f l 3 e
0 0 i e
; d r a 8 9 t = F e f ) = l . . = = s o
o c 2 2 u ; o f 0 0 e v c m o ) e
( m = = r r ; m W s
c b ) t 2 2 G %
u r ( s h c N
m r r r
g c e a i a m r p e e
( : o
o y h l
1 g f s t e - e
t n n c s : e i
s i r a c o
l e k
l S l h r n ; e t i ) s b a
b d ;
a m m ) s m
i e ( o o
d
r o n d t d r
a a e f h r e : m v ( r g
0
D g i o t t g n f e h c i
n e h e r ; n e r b ) p i
g
d u e s t s m n i c a r s
n g i t c
c a i : (
e p
A o e p p x
p r y i s s e
e e r t t t
e d a n e
s e ;
h h e n n r : ) i m 1 2 3 s s
i e
I v t h a · · - - - h
z a t e c i s a h c c
i c c c
y
/ c s d ; e c c c c u S o
2 s ) r a c c M n e u c
m m t a i n . ( ( a f e
k
f r a a
c k e e e m ) i e r
e s s s t
6 l p r l e t h s s s o
c e k i t a e i e ) ) b l h c r e e e
)
m t e
r b d l a p k l g f o f f n e n n a r t i m m a o i o t r / r m ) e c o o o
k k k s b r e
m o
d
d ) v m d c c c m m a
m c m a m a
e d e e o a i i i e ( ( o
n w b : ( k
u v e c
e h h h a d m r
T m F t
e m m m t t t
q r g g s d e k ( t i ( i i l
t c o a n t e
s
r t l : t t n n n / l i
n k n k k
c
a i i s a , e a g
g o l
g r r r u e t e f e r e e k k s x d n n c r u s n o o o n
a r r
h i s h h e d
K i e i ; m k t : t t c c c e a a ( f e m ) d h k
a
n
g c u t r t t r a l l l s y b b u n i G r n e
m c i
i a a a a c h a a a e e e t
h ; k / u c p t t t r i t c b n e d d v c s c e t o a o o h i e F e r a i e
r i : t t s t t h e d D e
c t r 3 h :
f t - : i f g ( i c i
c s c e d
y o
l
; t t h ; c : r i
e
)
p s t 3 ; o l l l l d - ) r a e n m a e e e e
r o t e c
m c e k d d d r p m , d i
( r (
m
t e l o o o 3 y e
:
o a t - s r k t e r g c i
r n m m a p n m
t l d a d n
i
o u p i ; n
a e r r e o
c i d t t q a k ; 0
a a n d g e r ) s s r u 2 i m r
e e a
G o e l x i o o n r m n i n - b d v e ( i i a e h
e n n M t r e d l i m l n d G u o e
n
m v e w w
e u n r :
o o c
s o r e n i r f c
e e
s e e t r e b e g e
e m f
a s r
; m t r k k k k
r m a d a f a a a a i o
u e n o r d o o o o c r d
a y r
r t
: e e e e i i s k k k k
o d
c b d r r r r b e
f i u : u w i r o o o o o ) t
t v c s i a
s c d c c c i
g
u
s g u a s ; d n s c a n q h h h e i
( n u e t s s
c s s s s s r o e
o c l i i i t i t t t a n r a i n n
r r n s s s s a c t
l k i n i n n e t i a e a e e e e e a c a a a a a 6 h s t e t d i r r r r
u r p e p p p p o o n h o o o o n m t i r t w s Q A f s s s i f s f f s
36 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 37
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES e : l k t t r b o o a k o o c i r c r r
l o a :
d c ; v
e e )
t e s y a h % l t (
m m
u f r r m o m o ) )
)
) ) t u ; u r 0 0 c 9 d 8 8 u c a
a 0 0 a 0 c e : 0 0 f . e
a 0 0 y 0 t
0 0
0 n : 2 2 a 2 e 2 2 2 l o 2 ( ( t ( t ( ( i -
p e t , . . .
l i c . . ) l l l t l l c n p s s e
a a r a r a a ; e
p e m
) a t t t c t t h o e e e m t e m e e n c y
r
o
( e í s s t t o m
c y r
( h e e o e o n
n e n e a
a n n n n g f r l
n t w : a a n e o o
a i i o o f t
r k
B p n n B R o ; r n c
)
a .
o e : i r l
b s h t m g F t e a a e a h a i i l
t m c d e c : t
i ( i b t
y c w r f e
n i
d i
a r ; t w ; a t , e i )
) o d n l t a t e s , r f r l l g a e a n g o a t e m )
y e e v a n s l c s b n ( p v
d i e l
( s d
i
d
l l t t
r i a n
e s e e o g o e s a a o s f l o e t a i n l e l e v i s e t n e e r r n k i
m m e l y p s t s i s : t o
c
d k r
i i l l b
a f c r e e U o t g d g r i h a a a o n y v o t
i
a n n n
c c r n d o r o r m c
i n i i i
v a k ; a
e e b r r a s
r t d r r r d r n i i a n s m o e v e
d u i o o o u p e
p p c l i s
u t t l n
d t m n m e t c c c c n b o r ( t a a d a m m k i
u i i t r a a n e n c t n d i s f f a e s i n o e i O u a
t a o h l l i a t p a t
u a s m k S m
l r m d d
v
r e e o e u e e s o l n n t t c c d s i
n e s r r o c
d l e o t d : : c a o o i e
e
e n e d P : t f p p l m e
x d i
;
d r a t i e e F e f ) l o o
o d c r r u ; o f
c e m o ) m t t e
m ( W ; m x
b o o ) i t G %
u ( s h N c
m n n r
g c m e a i a r m p e e
( : o
o y h l
1 f g s t - e p p e
e
o o t n n c l : s s l s l e i s i r a c o l e k
e s s S l
l a a h r n ; e t i ) s b a
d b ;
a m m ) s m
i e ( o o
d
r o n d t d r
a a e G G f h r e : m v ( r
g 0
D g i o t t g n f e h c i
n e h e r ; n e r b ) i p
g
d u s
t e s m n c a r s
n g i c
c i a : (
e p
A o e p x p
p r y i s s e
e e r t t t
e d a n e
s e ;
e n n r : ) m i e
I v h a h
z a t e a i s h
i
y
/ s d ; e S c
2 s ) r a M n e u c
m m t a i n . ( ( a f e
k f r b a y c k ) ) e e m ) ) i e t r e
a 6 a l i p r l 2 2 h o c
t s a e h h i ) b c
)
m t / / e r
d m m
l e a k l e e a r
e g g i s a o t r r e e e
s 0 0 ) r b r v o d r v m K K d a t i y s m c t a 0 0 a
a / t ( ( o i
n / b : d
o
i u v
1 1 s a d
g
T F e g / / s s s
q o d e s t n l
c r s s t r e l : n K
K e n n m m e a e e ( a , a g h m ( l i i e t
e f p o o v x s d r u s o n c c i n
n e e d
e o o i i ; u i : l e o e f d m ) d r r s a n s r a r a p p u n G h h e e
m m i e
h s s c h t h
; s s / u
p s
i c r n e r s . c u u e t a h u e r i e
n n
P r i : t s e ( (
D e
c m m , r 3 h m :
f t - : i f g a ( i l c i
c r s l c ) e d e
y o
; g t r e h ; c : d r i i
) a d s t 3 l l ; o o n
- ) e r a n -
e o e m e
r . t y e n m n
m d d e t k p i m ,
P d
( m i r l o l (
) o o
l 3 y e
: , o - r i - a r k t n n g c s
r / n a m m a p n c
b i l n
o
r i o u p e o i ; n r a i t e
c a i d d t t q k ; 0 n
s n b d g e r ) s s e e i i r / 2 u r
t l o a
r o e e i n x x b n r m r a i b i i d a v v i ( t a e l
e l p n r e M ( s r e d t n d y u m m e n
n o
s s m i v e w i
e
u e l r :
. o o c ( d
s o r P e G n i r f c
( e e
s e
e t r e b s e a a g e
e m t f
a s r s s n n s
; m t r
r e e m a a a d e a f l l i o e e u r e n l l o r d c r
a n n o y r
e e r t
: e e t t e i e e i s F t
o d
r s r s c s b e
f . u a a : y y w i r o t a
t p c i a
d p p c c n g
u s g u
p
i ; n l l s c s n q i a a
p n
e t s a a t t
o e
o l r s r a n s r e e i
t t n a c t l k u e s s u i a n n a e a c h e e n t n e t d i r e e i i o o n h m t i r t w c m m P c P A
37 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 38
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES e : l k t t r b o o ) a k o o c i r c 7 r r
l o a 0 :
d c ; v
0 e e )
t e ) 2 s y a h ( % l 9 t
(
m m
u 9 f o r r 9 r b m o m ) ) o
t e u 1 ; 8 1 u r 1 5 t c ( d u c a 1 0
0 0
a n a c e : s f 0 0 0 0 . ) o e
a y e t
2 2
0 2 2 0 n : a ( ( e 2 . . m l o 0 2 m t ) t l l
i - . .
p e t 0 e , 3 l l a a
l i c d s )
t 2 ü 0 a a c n p e t n t s ( e
r r ;
0 c t t e a e G p e m ) a
s
e e 2 n h o e -
a a a a ( m t m e c
y a e e r
o d í r ( é m m m o m
k k c y a c e
( t t a a a u e n
r f l l l ñ n n e u u
q a g a e a a a a r i
n t w : n
i i G m c R m c p c c o o f t
r k
o ; r n
c
t )
a o
e e : e i
e b c t m g s F e e
n e a a n
m c d
n c r n o u : e
( i r ( ) t l
o
e c s o s f e
i
o i e l e i s s a r ; t h t ; s t b l t l l f ) )
t e e l ) o v
s l a t a a e e r f b
l F e o r d o e -
a t u t e m a d d d e e
e
j d n
v o e i i s d c c s b
w
a n o o g g
d l a e r
( o c . s
l n l
g r a a t m a o c i a o
e s n e a
e
e i m m r r a d n ) m o s e v .
v
l
t n a e c s i e
e e e
g s
m
n e e e r e s a e c k n t
s t
n e l u y t l n v v s n a : d c
e c e
v v o
e n a i u
n v b i o a a a l f r i i e t i s
e i U
s e g a e v t d t g h e
c t t e o n p r r e o i v i t l e
u d s n
d p n p s n n
n t p r a l o
a a c r o
i n : a
i i i i
n k a l n r u a ; p a v e e e r r s b s s r c o s r t n l t i e a e l e n r i
b c v a
l c c s c y y u u r o e
o t
e
p
s o
e u p h s a s e s h g l u i c c i
e
t e e s e e
d e e e t m n y e n c e m s n g e l n d o n ( i a d a v m v d n k o b d a d d d n e v e
e i i r i i i e
s n e n n c e n o n r e t n d i u F 4 ( i g m i O s r a 2 2 u o a t l F a ( d a
t a o h l l i a t p a t
u a m k S m
r m 2 v
3 r e
o e u r 4 0 r o 4
l n n s c c . a 8 3 a 0
n e i
s 9 o 3 3 4 0 c . .
e 0
e % % % % 0 d : : c e a 3 = t - 5 6 9 8 3 4
y
e . y e 3 1 6 d 9 . . . . 7 i
P : t
n l e 8
. 1 e f i 0 4 5 3 ; 3 0 0 0 0 r a - = t
x d 3 x 0 e ) F l s
o f .
=
c ======4 o e u ; f t = e c 2 2 2 2 m o 0 ) F 7 F F F F e
2 o m ( s o e . ; m W
= l b r r r r r e ) e e e e t % 2
u r t G ( F p m s h c N
1 m r
g c e e r a i a m r p e e
( : o
o y h l
1 g t f 3 3 s t -
e 3 3 e
i _ _ o o n
t o U U n c : s _ _ e i
i l s p p r a c s e o k l H H
t t n n l
l S p h r n p p ; e t i ) s b a
b ; d
a m m ) s m
i e ( o F o
d
r o n d N t d r
a /
a C N N N N N
e G f h r e :
m
v 1 ( r g 0
C
D g i o t t n f e g h c i
n e h e r ; n e r b ) p i
g
d u e s t s 0 m n c a r t
n g i s 2 c
c a i t : (
e p
A o e p p
x p r y i s s e
e r e t t t e
d a e n e
t s
e ;
e g
n n r t h : ) e m g e g i v
I a h a h o g a g g z n r t d d e i i s d g d d d a h
i c
/ / y
d d e o / e s d ; e S c d L d
c 2 v s ) r a w n M e u c a m
m t a i n ( . ( a f e
k f r c a c k e e m i e r e
6 l p r l h
o c t a e i
b s s s c
e m t e
s d l e e e a l 1 ) k e a r t i n a o t r r r t n n n e +
u s b ) r o o a d
) ) h v o o o m ) d d a n e
c
) a c a e a
) l e e o
c c
c g e n b
: s s e
a u v
i f a e
y e e f a d e r T
F e . e i e f f f
q r h r e t d o h r e t o l
t / t c e / n t
n / t y o o e o l
: n / /
t
/
n n w t e a g g a o , o g a g t t t t l
g g r e t h e f g h t x k t d k r u h h h u s K c c n
/ g k ( e d (
g K K u e ( i ; i
g g g : ( i ( f ( g m ) d n i i i a n s e
e n r a u n G k e e e e
m i
n ( c h t
; l w / u p w i c n e w w w s c e t a h e r i e
r i : t s e D e
c r 3 h :
f t - : i f g ( i c i
c s ) c e d
y o
)
r
; t h ; c : r r i g
a
)
s t 3 ; a o
l l l l o e - ) l l l r a n - l - - e m e e e e e
r n t e e e - e n n n n i
m e k d d d d p m , i l d d d d d
( r l o o o (
l
- o o o o 3 y e e
: o o o o - a - r k t t n n n n g c
r n m m m m a p n
/ a / / l m m m o n
m l o r r r
u p o i ; n e r r r f
n c i d d r r r a a a q k ; 0
n
a a o d n g e e a a a r ) s / / r e e e 2 i r
e e
r n a
e e e o e x x i
n n n r n r m n i i n a i b i i d n n n v ( o i i a a e
i i i
e e r n M l l l r e l l l e d l l m m n d n e u e
n n i
m i l v e w Z
e u l r ( :
o o c (
s o r e n i r f c
e e
s e e t r e b e g e
e m f
a s r
; m t r
r u u u u u m a d a f i o a a a a a u e n o r d c e e e e e
a e y r
r t t t t t t
: e e e i g i s a a a a a
o d
c g l l l l l b n e
a f u : n w i r o a p p p p p t e
t c
i a a
d a n g r r
u s g u i n n n n n i ;
n s c r r r r r n q l l n i
p n e t s e e e e e
o a a e
o o l a n r s r r h h h h h l i
n t t a c t t t t t t l k e u a i a r r r r r a e a c n n t h t n e t d i o o o o r o e e a i o o n h m t i r w t n n A c P c c n n n
38 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 39
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
• 6. Validation and calibration models
Model evaluation is the process of qualitative and quantitative examination of the model to ensure that model predictions reflect the most likely real outcome (Soares and Tomé, 2007). According to Vanclay (1994), part of this process should be to expose any errors and deficiencies in the model by establishing: i) whether the equa - tions used adequately represent the processes involved; ii) if the equations have been combined correctly in the model; iii) whether the numerical coefficients obtained in fitting the model are the best estimates; iv) whether the model provides realistic pre - dictions throughout the likely range of application; v) if the model satisfies specified accuracy requirements; vi) how sensitive model predictions are to errors in estimated coefficients and input variables. Based on these six principles, a model evaluation should provide as much infor - mation as possible about the model’s behaviour and predictive ability. This allows the people affected by the decisions based on these models to decide whether or not the models represent the real world accurately enough for their intended uses. Soares et al. (1995) pointed out that “model evaluation should not be a mere afterthought to model construction, but should be considered at every stage of model design and construction, when component functions are formulated and fitted to data, and when these components are assembled to provide the completed model”. There is no universal approach to model evaluation, but it usually includes qualita - tive and quantitative aspects. Qualitative evaluation examines the structure and proper - ties of the model to verify that it is logically consistent and biologically realistic. Types of analyses can vary according to the modeling approach used, the purpose of the model, its complexity, and its generality. According to Oderwald and Hans (1993) a qualitative evaluation should at least confirm: i) the absence of contradictions within the complete model and among submodels; ii) that the variables included and omitted from the model meet expectations; iii) the signs and values of parameters; iv) that estimates out - side the range of the development data are reasonable and v) that limits and derivatives (maxima, minima, inflexion points) are in agreement with current forestry growth theo - ries. The first three features are included in most of the forest growth models developed in Spain, but the last two are not usually addressed. Quantitative evaluation is based on the comparison of model results with observa - tions. Graphical analysis and the use of statistical indices and tests are the usual meth - ods for comparison and should include an analysis of the model performance and robustness as well as a detailed characterization of errors (bias and precision of the
39 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 40
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
model and its components, distribution of residuals, dependencies of residuals on initial stand conditions and length of projection, correlations over time and between compo - nents, confidence intervals and critical errors, contributions by each model component to total error, etc.). The data used for quantitative evaluation should be independent from the observa - tions used to structure the model and estimate its parameters. Unfortunately, such observations are not usually available, and foresters generally use one of two alterna - tives: i) to randomly split the data set into model estimation and model testing subsets; ii) to use re-sampling techniques. However, some researchers have questioned whether these methods (especially the first one) actually provide relevant information for quan - titative model evaluation, when compared to error characterization from the entire data set (Kozak and Kozak, 2003). Both approaches have been widely used in Spain for modeling forest dynamics. The use of re-sampling techniques for double cross-valida - tion is currently the most commonly used criterion for model evaluation, until a new and independent data set for assessing the true quality of the predictions becomes available. Finally, Vanclay and Skovsgaard (1997) emphasized that the validity of con - clusions drawn from all these model evaluation procedures depends on the validity of the assumptions underlying both the model and the evaluation. Growth and yield model calibration to geographical areas or forestry practices different from those in which the original data were obtained is one of the most challenging situa - tions for end-users. In practice, calibration of a normal yield table prediction based on the ratio between actual basal area and basal area from the table is routinely done by assuming that the model is correct in shape but not in value, and then applying the necessary scalar modification. However, this method relies on the hypothesis that there are no differences between the silvicultural treatments applied in the stands used to elaborate the model and the stands where the model is going to be used. This leaves room for alternative calibration systems. Bravo and Montero (2003) proposed adding to their static volume model a simple linear component that included dominant height as an independent variable. The model efficiency increased from 0.4964 to 0.9856 with this approach.
40 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 41
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
• 7. Interfaces
a. Yield tables
Yield tables are numerical tables that show the evolution over time of the variables of a coetaneous or even-aged forest stand of a given species, within a given geographical area, for different site quality indices and for one or several silvicultural treatments (Madrigal, 1991). Yield tables can be classified as static models of growth and yield for even-aged forest stands. They have been, and still are, frequently used worldwide, although their use is declining as more reliable and flexible dynamic models for the same species and geographic areas become available. Yield tables are static models because they are elaborated from a single measure - ment. Occasionally they use data from plots inventoried more than once, but unlike dynamic models they disregard growth when applying methodologies for adjusting the equations used. Therefore, yield tables must be differentiated from numerical tables or charts generated from dynamic growth models (see Section 7.c). Dynamic growth models have a format similar to that of the yield tables but describe evolution using the age of the variables of an even-aged stand. To understand and apply yield tables correctly, it is essential to bear in mind that they are based on stands in which trees uniformly cover the entire surface, which is not always true. The yield and growth values of the tables must be adapted for each stand by using correction factors to account for their different characteristics (see Section 6). Vannière (1984) indicated that yield tables are “an idealized model, valid as an average for a given region and that must be used with caution. They are a certain number of reference points, of average values, but in no case lead to reliable and certain values.” This fact, however, does not diminish their usefulness as a management and planning tool, which is why it has enjoyed such a long tradition of use by so many European foresters (Madrigal, 1991). A set or family of yield tables is generally used for a species in a given geographi - cal area. The number of tables included in the set is determined by the number of site quality classes that are usually established for the study area (a table is constructed for each site index) and by the number of silvicultural regimes represented in the sample plots used (a table is constructed for each silvicultural treatment within each site quali - ty class). Thus, site index (see Section 5.a-i) is a fundamental variable that must be known in order to use growth and yield models. Rojo and Montero (1994) elaborated the first comprehensive review of yield tables
41 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 42
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
Table 7a Spanish yield tables 1. Broadleaves
Species and area Silviculture Observations References Others yield tables regimes Betula alba Galicia (nw spain) mts - diéguez et al . (2009) rojo et al . (2005a) Castanea sativa asturias (n spain) mos & tis coppice stands cabrera (1997) 2 cabrera and ochoa (1997) Eucalyptus globulus Galicia (nw spain) ntc different tables for first Fernández lópez and second rotation (1982) 2 - Galicia (nw spain) ntc different tables for initial spacing 2x2, Fernández lópez 2.5x2.5 and 3x3 m (1985) 2 - northern spain ntc different tables for initial spacing pita (1966) 1.80x1.80 and 2x2 m - sw spain ntc different tables for madrigal et al . echeverría (1952); sandy and slaty soils (1977) 2 pardo (1980) Fagus sylvatica navarra mos & tis - madrigal et al . (1992) - la rioja mos - ibáñez (1989) 3 - Populus x euramericana duero Basin ntc For 8x5 m initial Bravo et al . (1996) González antoñanzas spacing plantations (1986) Quercus pyrenaica león province ntc coppice stands torre (1994) 2 - Quercus robur Galicia (nw spain) mos different tables for two possible density diéguez et al . (2009) Barrio-anta (2003) evolutions Quercus suber spain (whole country) mos dehesas and open woodlands with basal montero et al . (1996) - area < 14 m 2/ha spain (whole country) mts even-aged and full montero stocked stands with 12 and cañellas (1999) - to 23 m 2/ha of basal area mos: mean observed silviculture, mts: mean theoretical silviculture (theoretic evolution of stems number), tis: theoretical intensive silviculture (theoretic evolution of stems number), ris: real intensive silviculture, ntc: no thinnings are considered, sd: silviculture in demand. 1 numerical tables or charts generated from dynamic growth models, which describe the evolution with age of the variables of an even-aged stand with a format similar to that of the yield tables (see section 7.c), are not included. 2 Unpublished. available in madrigal et al . (1999). 3 Unpublished.
42 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 43
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
Table 7b Spanish yield tables 1. Conifers
Species and area Silviculture Observations References Others yield tables regimes Pinus halepensis spain (whole country) mos& tis - montero et al . (2001b) montero et al . (2000) Pinus nigra iiberian mountain range mos & tis - Gómez loranca (1996) - navarra region mos & tis Pinus nigra ssp. eraso et al . (1996) 3 - austriaca pyrenees sd - González molina et al . (1999) - sierra de cazorla, segura mos & tis - Bautista et al . (2005) Bautista et al . (2001) y las villas (s spain) Pinus pinaster central mountain range mos & tis - García abejón and Gómez loranca (1989) - Galicia (nw spain) mos & tis - martínez millán and echeverría and de pedro (1948); madrigal (1992) 3 molina and ruiz (1976) different tables for león province mos three possible santamaría et al . (2009) - density evolutions Pinus pinea different tables for catalonia (ne spain) mos & tis two possible piqué (2003) - density evolutions Pinus radiata Basque country (n spain) mos - madrigal and toval (2009) - Basque country (n spain) mos & tis - muñoz (1985) - different tables for Galicia (nw spain) mos three possible sánchez rodríguez echeverría (1942); density evolutions et al . (2003) sánchez rodríguez (2001) asturias (n spain) mos different tables for three possible canga (2007) - density evolutions Pinus sylvestris different tables for sierra de Guadarrama mos & ris two possible density rojo and montero García abejón and Gómez (central mountain range) evolutions in the (1996) loranca (1984); picardo (1985); intensive silviculture rojo (1994) iberian mountain range mos & tis - García abejón (1981) - pyrenees mos - García abejón and tella Ferreiro (1986) - different tables for Galicia (nw spain) mos & tis two possible martínez chamorro - density evolutions (2004) different tables for navarra mos & tis two possible density puertas (2003) evolutions Pseudotsuga menziesii spain (whole country) mos - lópez-sánchez (2009) lópez-sánchez et al . (2009) For variable description and notes see table 7a
43 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 44
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
in Spain. Later, Madrigal et al. (1999) studied the definition, classification, struc - ture, construction and operational use of the yield tables. They included a compi - lation of all tables existing in Spain up to that time, as well as some foreign tables for species that yield tables had not yet been developed for with data collected in Spanish forests. Since then, numerous yield tables have been elaborated in Spain and are available for these species. The yield tables currently available in Spain are briefly described in Tables 7a and 7b, showing only the most recent tables when several works are available for the same species and regions.
b. Stand density management diagrams
Stand density management diagrams (SDMDs) are average and static stand- level models that graphically illustrate the relationship between yield and density- dependent mortality at all stages of stand development (Newton and Weetman, 1994). Two different types of SDMDs have been developed in Spain according to the density indices used for characterizing the growing stock level: i) SDMDs based on the relative spacing index (RS) (Hart, 1928, cited in Clutter et al. , 1983) and ii ) SDMDs based on the Reineke index (SD) (Reineke, 1933). SDMDs pro - vide information on the main relationship between average tree size, density or yield and a productivity indicator. All the variables included in those equations are graphically represented in a two-axis diagram from which density management outcomes can be evaluated by mean tree size and stand-level volumetric yields. If information about any other stand variable related to other aspects of resource management is available (e.g. non-timber resources, carbon pools, biot - ical and abiotical hazards, wild life management, etc), these variables can also be included in the diagram by fitting new equations and overlaying the information, which facilitates the decision-making process. In Spain, SDMDs have been devel - oped for pine and broadleaf species (Table 8) in Atlantic forests and a few Mediterranean forests.
c. Simulators and decision support systems
The first forest growth and yield model software developed in Spain was the PINASTER program (Rodríguez Soalleiro et al. , 1994), which included a dynam - ic stand growth model for even-aged Pinus pinaster stands in Galicia. PINASTER provides three “Pre-established silvicultural model” options for simulating stand growth and silvicultural treatments, according to site quality and product destina - tion. The program can run trial-and-error or target objective simulations of silvi - cultural treatments. Another forest growth and yield simulator was elaborated by Cantero et al. (1995) for Pinus radiata stands in the Basque Country. It projects stand develop - ment and describes the products that can be obtained with different thinning inten -
44 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 45
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES ) ) ) ) a b 4 9 9 9 ) ) ) 0 0 0 0 9 5 9 ) 0 0 - 0 0 0 0 a 0 2 z 2 2 2 0 0 ( 6 0 ( ( ) ( e
2 r 2 0 2 . ) 9 ) . . e ( ( ( l l l a ) 0
8 0 8
d .
a a a v 5 l 2 l o 0 0 0 o
l ( d t a 0 r t t a v 0 2 0 l i
. e n e e Á ( 0 a t 2 2
l
e
a ) r o ( ( 2 l . e a
a o o
d l l (
5
. . z B d d a d t d n l a l o
. 0 e
n l a a e a o n a a d t d 0
r r h a
a a s a e t n t a a r
2
c o o
- t t t z ( e a e s d n e
z
a e n n d d u r a á
c z - a e a a - - r l a a e a z o l s n n u n n o o l - i h - c - s e e e e e g d d - á c o n o z e í r u u u u e i e i z z r a u e t e t p r r g b b b e
n f a d r s b s r p l l l é r l e o i a a a h a a o a a a ó é e R d B c v v v c c c G B d r l p d d r r a a z z a a h h
e e n r r i i i f a f
p n n S w
w o d o r r e d r t c h c
a
s n i d z d e l a n n b a h m a
u s s p w w w
e o o o s s r r r s h h h m a t t t
a d d d k r n n n s i i i g o i o o o o o o o o o a i R n n w n n n n n w n n w n d
s t s n s n a o s e m a b m e r m t o
m n n a e i s s c
o o o b g s
i
d b b a a d b r r d n
n n a a e n a m
a u c c m u o l
n m i o e a o a d d t m r o u r t b e e e e e e e
i l s
n n g r g o t
l y m o t u u e a m m m m m m e t a d a
u v i t , o o v v l u u u u u u l
n s r r l l l l l l e l o o a m o o a t i g g o o o o o o n a s
b b
v t i l m e e , e a v v v v v v
a a s c
a l u
e v v b d l l l l l l t r e l l l
a
o o a a a a a a e l t o a a o m t t t t t t t t d t b b d a o
v u l t o o o o o o o m , o a a
n l t t
t e l o e t t t t t t
a
l l o i , m a t t a a i d v e m o Y t t
S c n l
u o o r m c l a - t t a e
.
t u o l s 8 d d o v m s
o
n n t a e l v a a l m
a l t m o b . a x o o t a c i e o t T d b t n i
y x t i e s d n e n i d
s s s s s s s s d d d d d y d t r r r r r r r r n s s s s s i a s t s n
: e d D s
, i
) i x n y s e n ó i e d e g l i a n l i a z a p
s a r e n s g n s i r y v e n
a
e r s i
e a t r t r n n c
m n i d g i i m
e a a w u n e d t t n n a n a p ) u a b u
s p a n i a n a a s p p s n g
o o i
( a e i d a b
r s s a e u l r c u d
l
n i
a e t
e v s i a s l s i a a t n s e n n p p a a a a a t
e p h r a m i r r i i i i u o a o y i n u
s r l a n l l c e e c c c c c
t d s s s c e l q i e i t t o i i i i r a a r l l l l l e n r s u t u u u a s e s u r e c t
a u a a a a e a e a a a b n n n p p : u n i i i e u s s S c G o e c e e ( B G G G s G P P P Q B P E r
45 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 46
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
sities based on diameter distributions (reviewed in Espinel et al. , 1997). The SILVES program (Río and Montero, 2001) is based on a stand growth model with diameter dis - tribution disaggregation. It was designed to model thinning in Pinus sylvestris L. even- aged stands, and thinning age, intensity and rotation can be selected for analysis. In the SILVES2 version, the model was adapted for P. sylvestris reforestation sites in Central Spain (Río et al. 2005). Bravo (2001) integrated a model developed for Scots pine in the High-Ebro basin into a Microsoft Excel spreadsheet from which static yield tables can be generated for the economic evaluation of silviculural paths. The GesMO © simulator was designed as a standard platform from which different stand growth models can be implemented. GesMo 1.0 (Castedo-Dorado, 2004; Diéguez-Aranda, 2004) and GesMO 2.0 (González González et al. , 2009 available in Diéguez-Aranda et al. , 2009 and http://www.usc.es/uxfs /) simulate diferent forest stand types and include dynamic stand growth models developed for even-aged stands of coastal and inland Pinus pinaster as well as Pinus radiata and Pinus sylvestris in Galicia. Models for other species such as for Betula alba and Quercus robur are being developed and will be added in the future. GesMO © makes it possible to simulate and evaluate different user-generated silvicultural alternatives according to the type, inten - sity and age of thinning and the rotation age. Tables, graphs and reports can be created to show the evolution of the main stand variables for each alternative analyzed. There is also the possibility of creating and applying “pre-defined silvicultural schemes”. A disaggregation module distributes the stand yield, biomass (total and partial) and fixed CO 2 by diameter class for each stand stage. There is a classification module for wood products obtained and an economic evaluation module for the simulated silvicultural alternatives. One software package available at the individual tree level is the integrated PINEA2 model, developed for the multifunctional management of even-aged Stone pine ( Pinus pinea L) stands (Calama et al. , 2007a and 2007b). Growth and yield (wood products, wood quality, cone production, biomass fractions and fixed CO 2) can be predicted in five-year increments and under different management scenarios. These are defined by thinning and rotation length and by simulating the evolution of each individual tree within the stand. PINEA2 is an inter-regional stochastic model that allows for the cali - bration of new locations. The PINEA2 (Madrigal et al. , 2009) software application only incorporates the model parameterized for the Northern Plateau and Central Range of Spain, but maintains its stochastic character by adding single-tree and stand-level ran - dom components into the diameter increment function. Future development of the soft - ware will include more regions (Andalucia and Catalonia), extensions of the growth model to uneven-aged stands and afforestations (Calama et al. , 2008a; 2009), simulta - neous prediction of different stands and simulation schedules and other complements such as annual cone production and pine nut production modules. Another software package available for individual trees is ALCORNOQUE 1.0 (Sánchez-González et al. , 2007b), an integrated growth and yield model for high-densi - ty cork oak forests (as opposed to lower-density woodlands). Its model interface is very similar to PINEA2, since it was programmed using the same environment. ALCORNOQUE 1.0 consists of a system of mathematical functions for simulating
46 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:52 Página 47
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
growth and yield (cork growth, cork thickness, cork weight) under different silvicultural regimes , thus providing important information for sustainable management of cork oak forests. It uses the parameterization for two of the most important cork-producing areas in Spain (the Natural Park of Los Alcornocales and Catalonia), and can be considered representative of Spanish cork oak forests. This version is also stochastic, so that a sin - gle tree random component can be added into the cork thickness function. Subsequent versions will include a module for low-density cork oak forests (dehesas) and a func - tion that defines site index based on ecological factors. Some growth models are integrated into more complex software with optimisation options, such as the MONTE and RODAL software designed for Catalonian forests. MONTE is an information system for forest-level planning (see www.forecotech.com ), designed to optimise forest resources and maximise forest owner benefit. MONTE is organized into various subsystems: 1) database management system; 2) simulation sys - tem, based on growth and yield models, fire risk models, etc. (Palahí et al. , 2003; Trasobares et al. , 2004a; 2004b; González et al. , 2006; 2007; Bonet et al. , 2008; Blasco et al. , 2009); 3) planning system that formulates and solves problems using an optimi - sation tool (mathematical programming or heuristics) (Pukkala, 2002); 4) sensitivity analysis system. RODAL is a similar information system that supports decision-making at the stand level. It can be applied to even-aged and uneven-aged management, as well as to pure and mixed stands. The optimisation algorithm automatically finds a manage - ment schedule for the stand that maximises the user-defined objective function. Multiple management objectives may be included in the planning model, such as land expectation value (Trasobares and Pukkala, 2004a), wood production, net income, bio - diversity (Palahí et al. , 2004a), mushroom production (Palahí et al. , 2009), or fire risk (González et al. , 2008). SIMANFOR (Bravo et al. , 2010) is a web-based platform that allows foresters to develop sustainable forest management alternatives. It integrates different modules for managing forest inventories, simulating and projecting stand conditions and maintaining systems security and integrity. SIMANFOR outputs are compatible with an Office envi - ronment (Microsoft or Open), allowing users to exchange data and files between SIMANFOR and their own software. It is freely available for use by the world-wide forestry community (foresters, scientists, students, etc.) through the www.simanfor.org web page and can be instrumental for research, teaching and developing new silvicul - tural scenarios. SIMANFOR is under permanent development and three new features will be included in the near future: ( i) new models, ( ii ) improvement of user-friendly interface and ( iii ) translation into other languages, starting with English and then Portuguese and French. Currently, SIMANFOR includes modules for simulating Scots pine and Mediterranean maritime pine stands in Central Spain, but it is open to incor - porating models from different ecosystems around the world and is supported by a server that can be scaled up to respond to future demands. In spite of the advances in forest growth simulators and decision support systems during the last decade, software development is still needed for many forest systems. This kind of software has become essential for forest managers and technicians in developing forest growth and yield models.
47 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 48
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
• 8. Perspectives
Model development in Spain during the last decade has been dramatic. However, several challenges lie ahead. The gap between scientific evidence and practical rele - vance is increasing (Pretzsch, 2009) and models will have to fill this gap by providing accurate and useful information to stakeholders. Currently, this information is available in a disjointed manner, where not all the relevant factors are properly addressed by each model independently. Process models are far from operative, but hybrid models that incorporate tactical planning, climatic drivers and physiological responses could pro - vide more realistic long-term predictions. The development of dynamic site productivi - ty models based on environmental change is a key issue. In Spanish forestry, advances in the area of silvicultural response functions are limited. Models that include branch size, angle and distribution and other technological issues such as free knot bole size are lacking. There is a need for long-term trials that would provide information to adapt current models and, especially, for models that account for pre-crown closure growth changes derived from site preparation, herbaceous weed con - trol and fertilization at establishment. Integration is one of the main tasks for the future. Seed dispersal models and regen - eration models are not integrated with growth and yield models, for example. Vanclay (1994) recommends that information provided by models should be accurate, complete, concise, relevant, appropriate and timely. However, the long time required for developing models, the lack of adequate data sets or the chronic understaffing in univer - sities and research centers all add to the time it takes for forest models to reach a forester’s computer. Special care should be taken to ensure that models are flexible enough to meet manager and stakeholder demands while maintaining the desired generality (in terms of species, areas and management options), biological foundations, focus on available data and modularity for obtaining different outputs. Models must also be well documented and user-friendly. An effort at model evaluation and calibration must be made in the next few years. Integration of models to support decision-making and simulation tools at different scales will help to disseminate scientific output to the end-users. The use of tree- and stand-level variables based on standard forest inventory procedures as proxy variables for relevant services (carbon sequestration, recreation …) and non-timber products in currently available models could help to enhace the decision-making process. However, new models should be developed to address these specific needs. By improving deci - sion support systems to include visualization tools, geographical information systems output, more flexible data input and silvicultural scenarios, end-users will be more favourable to using models as they develop.
48 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 49
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
• Acknowledgments
The models described in this book were funded by different regional, national and European projects, and some of them were elaborated by the authors. This work was funded by the Spanish Government by the SELVIRED network (code AGL2008- 03740) and the strategic project ‘Restauración y Gestión Forestal’ (code PSE- 310000-2009-4).
49 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 50
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
• References
ADAME P., CAÑELLAS I., RÍO M., 2005. Modelo de la relación altura-diámetro para rebollares en Castilla y León. Actas del IV Congreso Forestal Español 4CFE05-365- T1, 320. [In Spanish]. ADAME P., CAÑELLAS I., RÍO M., 2008b. A mixed nonlinear height-diameter model for pyrenean oak ( Quercus pyrenaica Willd.). For Ecol Manage 256, 88-98. ADAME P., CAÑELLAS I., RÍO M., 2010a. Ingrowth model for pyrenean oak stands in north-western Spain using continuous forest inventory data. Eur J Forest Res 129(4), 669-678. ADAME P., CAÑELLAS I., RÍO M., 2010b. Modeling individual-tree mortality in Pyrinean oak ( Quercus pyrenaica Willd.) stands. Ann For Sci 67, 810 DOI: 10.1051/forest/2010046. ADAME P., CAÑELLAS I., RÍO M ., ROIG S., 2006. Modelling dominant height growth and site index curves for rebollo oak ( Quercus pyrenaica Willd.). Ann For Sci 63, 929-940. ADAME P., CAÑELLAS I., HYNYNEN J., RÍO M., 2008a. Individual-tree diameter growth model for rebollo oak ( Quercus pyrenaica Willd.) coppices. For Ecol Manage 255, 1011-1022. AFIF-KHOURI E., CÁMARA-OBREGÓN M.A., CANGA-LÍBANO E ., OLIVEIRA- PRENDES J.A., GORGOSO-VARELA J.J., 2010. Relationships among soil para - metrs, tree nutrition and site index of Pinus radiata D. Don in Asturias, NW Spain, Forest Systems 19, 77-88. ALLUÉ M., SAN MIGUEL A., 1991. Estructura, evolución y producción de tallares de Quercus pyrenaica Willd. en el centro de España. Invest Agrar: Sist Recur For 0, 35- 48. [In Spanish]. ALONSO R., MADRIGAL G., 2007. Modelo de crecimiento e índice de sitio para Juniperus thuriphera en España. Cuadernos SECF 23, 99-106. [In Spanish]. ÁLVAREZ-ÁLVAREZ P., AFIF-KHOURI E., CÁMARA-OBREGÓN A., CASTEDO- DORADO, F., BARRIO-ANTA, M., 2011. Effects of foliar nutrients and environ - mental factors on site productivity in Pinus pinaster Ait. stands in Asturias (NW Spain) Ann For Sci 68(3):497-509. ÁLVAREZ GONZÁLEZ J.G., 1997. Análisis y caracterización de las distribuciones dia - métricas de Pinus pinaster Ait en Galicia. Doctoral thesis. Universidad Politécnica de Madrid. [In Spanish]. ÁLVAREZ GONZÁLEZ J.G., RODRIGUEZ-SOALLEIRO R., VEGA G., 1999. Elaboración de un modelo de crecimiento dinámico para rodales regulares de Pinus
50 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 51
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
pinaster Ait en Galicia. Invest Agrar: Sist Recur For 8(2), 319-334. [In Spanish]. ÁLVAREZ GONZÁLEZ J.G., BARRIO ANTA M., RODRÍGUEZ SOALLEIRO R., RUÍZ GONZÁLEZ A.D., 2005. Ecoregional site index models for Pinus pinaster in Galicia (northwestern Spain). Ann For Sci 62, 115-127. ÁLVAREZ GONZÁLEZ J.G., RODRÍGUEZ SOALLEIRO R., RUÍZ GONZÁLEZ A.D., SCHRÖDER J., 2002. Modelling the effect of thinnings on the diameter distri - bution of even-aged Maritime pine stands. For Ecol Manage 165, 57-65. ÁLVAREZ GONZÁLEZ J.G., CASTEDO DORADO F., GADOW K.V., LÓPEZ SÁNCHEZ C.A., RUIZ GONZÁLEZ A.D., 2004. A two-step mortality model for even-aged stands of Pinus radiata D. Don in Galicia (northwestern Spain). Ann For Sci 61, 439-448. ÁLVAREZ TABOADA M.F., ÁLVAREZ GONZÁLEZ J.G., BARRIO ANTA M., GOR - GOSO VARELA J., 2003. Influencia de la competencia en el crecimiento en sección en Pinus radiata D. Don. Invest Agrar: Sist Recur For 12(2), 25-36. [In Spanish]. ASSMANN E., 1970. The principles of forest yield study. Pergamon Press, Oxford. BADÍA M., BROTO M., RODRÍGUEZ F., 2001. Modelos del perfil del árbol. Aplicación al pino radiata ( Pinus radiata D. Don). III Congreso Forestal Español. Granada, septiembre 2001. Mesa 5: 478-486. [In Spanish]. BALBOA-MURIAS M.A., ÁLVAREZ-GONZALEZ J.G., MERINO A., RODRIGUEZ- SOALLEIRO R., 2006a. Temporal variations and distribution of carbon stocks in aboveground biomass of radiata pine and maritime pine pure stands under different silvicultural alternatives. For Ecol Manage 237, 29-38. BALBOA-MURIAS M.A., ÁLVAREZ J.G., MERINO A., ROJO A., 2006b. Carbon and nutrient stocks in mature Quercus robur L. stands in NW Spain. Ann For Sci 63, 557- 565. BARÁ S., TOVAL G., 1983. Calidad de estación de Pinus pinaster Ait, en Galicia. Comunicaciones INIA, Serie Recursos Naturales nº 24. 166 p. Madrid. [In Spanish]. BARNES B.V., DENTON S.R., SPURR S.H ., ZAK D.R., 1997. Forest Ecology. John Wiley and Sons, New York. 774 pp. BARRIO-ANTA M., 2003. Crecimiento y producción de masas naturales de Quercus robur L. en Galicia. Doctoral thesis. University of Santiago de Compostela, Lugo. [In Spanish]. BARRIO-ANTA M., ÁLVAREZ-GONZÁLEZ J.G., 2005. Development of a stand den - sity management diagram for even-aged pedunculate oak stands and its use in designing thinning schedules. Forestry 78, 209-216. BARRIO-ANTA M., DIÉGUEZ-ARANDA U., 2005. Site quality of pedunculate oak (Quercus robur L.) stands in Galicia (northwest Spain). Eur J For Res 124, 19-28. BARRIO ANTA M., ÁLVAREZ GONZÁLEZ J.G., DÍAZ-MAROTO I.J., LOPEZ SÁNCHEZ C.A., 2004. Relación altura-diámetro generalizada para Quercus robur L. en Galicia. Cuadernos SECF 18, 141-146. [In Spanish]. BARRIO-ANTA M., CAÑELLAS I., CASTEDO-DORADO F., SIXTO-BLANCO H., 2008. Dynamic growth model for I-214 poplar plantations in the northern and cen -
51 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 52
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
tral plateaux in Spain. For Ecol Manage 255, 1167-1178. BARRIO-ANTA M., ÁLVAREZ-GONZÁLEZ J.G., BALBOA-MURIAS M., CASTE - DO-DORADO F., DIÉGUEZ-ARANDA U., 2006a. An ecoregional model for esti - mating volume, biomass and carbon in maritime pine stands in Galicia (northwestern Spain). For Ecol Manage 223, 24-34. BARRIO ANTA M., ÁLVAREZ GONZÁLEZ J.G., CASTEDO-DORADO F., DIÉGUEZ-ARANDA U., GADOW K.v., 2007a. Merchantable volume system for pedunculate oak in northwestern Spain. Ann For Sci 64, 511–520. BARRIO-ANTA M., ÁLVAREZ-GONZÁLEZ J.G., CASTEDO-DORADO F., DIÉGUEZ-ARANDA U., PARRESOL B., RODRÍGUEZ-SOALLEIRO R., 2006b. Development of a basal area growth system for maritime pine in northwestern Spain using the generalized algebraic difference approach. Can J For Res 36(6), 1461-1474. BARRIO-ANTA M., CAÑELLAS I., GONZÁLEZ-ANTOÑANZAS F., SIXTO-BLANCO H., 2007b. Sistema de cubicación con clasificación de productos para plantaciones de Populus x euramericana (Dode) Guinier cv. ‘I-214’ en la meseta norte y centro de España. Invest Agrar: Sist Recur For 16(1), 65-75. [In Spanish]. BAUTISTA R., ALONSO A., GÓMEZ LORANCA J.A., GRAU J.M., 2001. Tablas de producción de selvicultura media para las masas de Pinus nigra Arn. de la Sierra de Cazorla, Segura y Las Villas. III Congreso Forestal Nacional, Granada, Septiembre 2001. Mesa 5, 854-859. [In Spanish]. BAUTISTA R., MONTERO G., RÍO M., GRAU J.M., 2005. Tablas de producción de selvicultura varibale para las masas de Pinus nigra Arn. de la Sierra de Cazorla, Segura y Las Villas. In: Los pinares de Pinus nigra Arn. En España: Ecología, uso y gestión (Grande-Ortíz M.A., García-Abril A. eds.). Fundación Conde del Valle de Salazar, Madrid, pp. 559-584.[In Spanish]. BENGOA J.L., 1999. Análisis de un modelo de crecimiento en altura de masas foresta - les. Aplicación a las masas de Quercus pyrenaica de La Rioja. Doctoral thesis. Universidad Politécnica de Madrid. [In Spanish]. BERTALANFFY L.v., 1949. Problems of organic growth. Nature 163, 156-158. BERTALANFFY L.v., 1957. Quantitative laws in metabolism and growth. Quarterly Review of Biology 32, 217 -231. BLASCO E., GONZÁLEZ-OLABARRIA J.R., KOLEHMAINEN O., PALAHÍ M., PUKKALA T., RODRIGUÉZ-VEIGA P., 2009. Predicting scenic beauty of forest stands in Catalonia (North-east Spain). J For Res 20(1), 73−78. BOGINO S.M., BRAVO F., 2008. Growth response of Pinus pinaster Ait. to climatic variables in central Spanish forest. Ann For Sci 65, 506-518. BOGINO S.M., BRAVO F., FERNÁNDEZ NIETO M.J., 2009. Climate effect on radial growth of Pinus sylvestris at its southern and western distribution limits. Silva Fennica 43(4), 623-609. BONET J.A., COLINAS C., FISCHER C.R., 2004. The relationship between forest age and aspect on the production of sporocarps of ectomycorrhizal fungi in Pinus sylvestris forests of the central Pyrenees. For Ecol Manage 203, 157-175.
52 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 53
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
BONET J.A., COLINAS C., FISCHER C.R., MARTÍNEZ DE ARAGÓN J., PALAHÍ M., PUKKALA T., 2008. Empirical models for predicting the production of wild mushrooms in Scots pine forests in the Central Pyrenees. Ann For Sci 65(2), 206. DOI: 10.1051/forest: 2007089. BONET J.A., COLINAS C., FISCHER C.R., MARTÍNEZ DE ARAGÓN J., MIINA J., PALAHÍ M., PUKKALA T., 2010. Modelling the production and species richness of wild mushrooms in pine forests of Central Pyrenees in north-eastern Spain. Can J For Res 40, 347-356. BRAVO, F. 2001. Whole Stand Simulator “Alto Ebro” (freely available at http://sostenible.palencia.uva.es/gfs/rinv/List/Software+de+inter%C3%A9s/3/List.aspx ) BRAVO F., MONTERO G., 2001. Site index estimation in Scots pine ( Pinus sylvestris L.) stands in the High Ebro Basin (northern Spain) using soil attributes. Forestry 74, 395 -406. BRAVO F., MONTERO G., 2003. High-grading effects on Scots pine volume and basal area in pure stands in northern Spain. Ann For Sci 60, 11-18. BRAVO F., GONZÁLEZ ANTOÑANZAS F., GRAU J.M., 1996. Curvas de calidad y tablas de producción para Populus x euramericana en la cuenca del Duero. Montes 44, 43-46. [In Spanish]. BRAVO F., ORDOÑEZ A.C., RODRÍGUEZ F., 2010. SimanFor: Sistema de apoyo para la simulación de alternativas de manejo forestal sostenible. Available in www.siman - for.es (last access 15th april 2010). [In Spanish]. BRAVO F., LIZARRALDE, I., ORDOÑEZ, C., PANDO, V., 2008. Modelling ingrowth in mediterranean pine forests: A case study from scots pine ( Pinus sylvestris L.) and mediterranean maritime pine ( Pinus pinaster Ait.) stands in Spain. Invest Agrar: Sist Recur For 17(3), 250-260. BRAVO, F., FÉLIZ DE VARGAS, J.M., LUCAS, A.I., PESO, C. del, RÍO, M. del, 2002. Estructura de los rodales de Populus tremula en la vertiente meridional de la Cordillera Cantábrica Sierra, R. (Coordinator) El álamo temblón (Populus tremula L.) Bases para su cultivo, gestión y conservación, 135-150 Mundi-Prensa ISBN: 84- 8476-096-0. BRAVO F., BRAVO-OVIEDO A., DOMÍNGUEZ DOMÍNGUEZ M., GUERRA BUR - TON B., LIZARRALDE I., ORDÓÑEZ C., OSORIO VÉLEZ L.F., DEL PESO TARANCO C., 2004. Red de parcelas y experimentos del grupo de investigación sobre gestión forestal sostenible de la ETS de ingenierías agrarias de Palencia (Universidad de Valladolid). Cuadernos SECF 18, 237-242. [In Spanish]. BRAVO-OVIEDO A., MONTERO G., 2005. Site index in relation to edaphic variables in stone pine ( Pinus pinea L.) stands in south west Spain. Ann For Sci 62, 61-72. BRAVO-OVIEDO A, MONTERO G, RÍO M, 2004. Site index curves and growth model for Mediterranean maritime pine ( Pinus pinaster Ait.) in Spain. For Ecol Manage 201, 187-197. BRAVO-OVIEDO A., MONTERO G., RIO M., 2007. Geographic variation and para - meter assessment in generalized algebraic difference site index modeling. For Ecol Manage 247, 107-119.
53 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 54
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
BRAVO-OVIEDO A., BRAVO F., DEL RIO M., STERBA H., 2006. Competition- induced mortality for Mediterranean Pinus pinaster Ait. and P. sylvestris L. For Ecol Manage 222, 88-98. BRAVO-OVIEDO A., BRAVO F., MONTERO G., RÍO M., TOMÉ M., 2008. Dominant height growth equations including site attributes in the generalized algebraic difference approach. Can J For Res 38, 2348-2358. BRAVO-OVIEDO, A., BRAVO, F., MONTERO, G., RÍO, M ., ROIG. S., 2011. Environmental variability and its relationship to site index in Mediterrean Maritime pine. Forest Systems 20(1): 50-64. BRONCANO M.J., RETANA J., RODRIGO A., 2008. Post-dispersal seed pretaion in Pinus halepensis and consequences on seedling establishment after fire. Int J Wildland Fire 17(3), 407-414. BURKHART H.E., 2003. Suggestions for choosing an appropriate level for modelling forest stands, In: Modelling Forest Systems (Amaro A., Reed D., Soares P., eds.). CAB International, Wallingford, Oxfordshire, UK, pp. 3-10. CABANILLAS A., 2010. Bases para la gestión de masas naturales de Pinus halepensis Mill. en el Valle del Ebro. Doctoral thesis. Universidad Politécnica de Madrid. [In Spanish]. Available at http://oa.upm.es/4960/ CABANILLAS A., BARRIO-ANTA M., ROJO ALBORECA A., NOTIVOL PAÍNO E., 2009. Diagrama de manejo de la densidad para masas naturales de pino carrasco (Pinus halepensis Mill.) en la Depresión del Ebro. Actas del V Congreso Forestal Español. 21-25 de septiembre. Ávila. Ref: 5CFE01-213. [In Spanish]. CABRERA M., 1997. El monte bajo de castaño en Asturias: alternativas selvícolas. Doctoral thesis. Universidad Politécnica de Madrid. [In Spanish]. CABRERA M., OCHOA F., 1997. Tabla de producción de castaño ( Castanea sativa Mill.) tratado a monte bajo, en Asturias. Actas del II Congreso Forestal Español, Irati, septiembre 1997. Mesa 4, 131-136. [In Spanish]. CALAMA R., MONTERO G., 2004. Interregional nonlinear height-diameter model with random coefficients for stone pine in Spain. Can J For Res 34, 150-163. CALAMA R., MONTERO G., 2005. Multilevel Linear Mixed Model for tree diameter increment in Stone Pine ( Pinus pinea ): a calibrating approach. Silva Fenica 39(1), 37-54. CALAMA R., MONTERO G., 2006. Stand and tree level variability on stem form and tree volume in Pinus pinea L: a multilevel random components approach. Invest Agrar Sist Recur For 15(1), 24-41. [In Spanish]. CALAMA R., MONTERO G. 2007. Cone and seed production from stone pine ( Pinus pinea L.) stands in Central Range (Spain). Eur J Forest Res 126, 23-35. CALAMA R., CAÑADAS N., MONTERO G., 2003. Inter-regional variability in site index models for even-aged stands of stone pine ( Pinus pinea L.) in Spain, Ann For Sci 60, 259-269. CALAMA R., MONTERO G., SÁNCHEZ-GONZÁLEZ M., 2007b. Management ori - ented growth models for multifunctional Mediterranean Forests: the case of Stone Pine ( Pinus pinea L.). EFI Proceedings 56, 57-70.
54 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 55
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
CALAMA R., GORDO F.J., MONTERO G., MUTKE S., 2008b. An empirical ecologi - cal-type model for predicting stone pine ( Pinus pinea L.) cone production in the Northern Plateau (Spain). For Ecol Manage 255, 660-673. CALAMA R., BARBEITO I., MONTERO G., PARDOS M., RÍO M., 2008a. Adapting a model for even-aged Pinus pinea L. stands for complex multi-aged structures. For Ecol Manage 256, 1390-1399. CALAMA R., CAÑELLAS I., COQUILLAS V., MONTERO G., RÍO M., 2004. Modelos de calidad de estación y de perfil de fuste para masas de Pinus uncinata Ram. en el Pirineo español. Invest Agrar: Sist Recur For Fuera de serie, 176-190. [In Spanish]. CALAMA R., BACHILLER A., FINAT L., GARRIGA E., GORDO J., MONTERO G. 2007a. PINEA2: Un modelo integrado para la gestión de las masas regulares de Pinus pinea L. en la Meseta Norte. Cuadernos SECF 23, 147-152. [In Spanish]. CALAMA R., GORDO J., MONTERO G., MUTKE S., TOME J., TOME M., 2011. Modelling spatial and temporal variability in a zero-inflated variable: The case of stone pine ( Pinus pinea L.) cone production. Ecol Model 222(3):606-618 doi:10.1016/j.ecolmodel.2010.09.020. CALAMA R., GARRIGA E., MADRIGAL G., MONTERO G., MORO J., RÍO M., SÁNCHEZ-GONZÁLEZ M., 2009. Modelo para la gestión multifuncional de repo - blaciones de Pinus pinea L. en Sierra Morena y Meseta Sur. 5º Congreso Forestal Español. Ávila, septiembre 2009. [In Spanish]. CALVO L., SANTALLA S., VALBUENA L., MARCOS E., TARREGA R., LUIS- CALABUIG E. 2008. Post-fire natural regeneration of a Pinus pinaster forest in NW Spain. Plant Ecol 197(1), 81-90. CANADELL J., RODA F., 1991. Root biomass of Quercus ilex in a montane Mediterranean forest. Can J For Res 21, 1771-1778. CANADELL J., RIBA M., ANDRÉS P., 1988. Biomass equations for Quercus ilex L. in the Montseny Massif, northeastern Spain. Forestry 61, 137-147. CANGA E., 2007. Crecimiento y producción de pinares regulares de Pinus radiata D. Don en Asturias. Doctoral thesis. Universidad de Oviedo. [In Spanish]. CANGA E., AFIF KHOURI E., CÁMARA OBREGÓN A., GORGOSO VARELA J., 2007. Relación altura-diámetro generalizada para Pinus radiata D. Don en Asturias (Norte de España). II Reunión sobre aspectos prácticos de la Modelización Forestal. Cuadernos SECF 23, 153-158. [In Spanish]. CANTERO A., ESPINEL S., SÁENZ D., 1995. Un modelo de gestión para las masas de Pinus radiata en el País Vasco. Cuadernos SECF 1, 193-198. [In Spanish]. CAÑADAS M.N., 2000. Pinus pinea L. en el Sistema Central (Valles del Tiétar y del Alberche): Desarrollo de un modelo de crecimiento y producción de piña. Doctoral thesis. Universidad Politécnica de Madrid. [In Spanish]. CAÑADAS M.N., GARCÍA GÜEMES C., MONTERO G., 1999. Relación altura-diá - metro para Pinus pinea en el Sistema Central. Congreso de Ordenación y Gestión Sostenible de Montes Tomo I, 139-154. [In Spanish].
55 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 56
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
CAÑELLAS I., MONTERO G., RÍO M., ROIG S., 2004. Growth response to thinning in Quercus pyrenaica Willd. coppice stands in Spanish Central Mountain. Ann For Sci 61(3), 243-250. CARSON S.D., GARCIA O., HAYES J.D., 1999. Realized gain and prediction of yield with genetically improved Pinus radiata in New Zealand. For Sci 45, 186-200. CASTEDO-DORADO F., 2004. Modelo dinámico de crecimiento para las masas de Pinus radiata D. Don en Galicia. Simulación de alternativas selvícolas con inclusión del riesgo de incendio. Doctoral thesis. Universidad de Santiago de Compostela, Lugo. [In Spanish]. CASTEDO-DORADO F., ÁLVAREZ-GONZÁLEZ J.G., 2000. Construcción de una tarifa de cubicación con clasificación de productos para Pinus radiata D. Don en Galicia basada en una función del perfil del tronco. Invest Agrar: Sist Recur For 9(2), 253-268. [In Spanish]. CASTEDO-DORADO F., ÁLVAREZ-GONZALEZ J.G., DIÉGUEZ-ARANDA U., 2007a. A growth model for Pinus radiata D. Don stands in north-western Spain. Ann For Sci 64, 453-465. CASTEDO-DORADO F., ÁLVAREZ-ÁLVAREZ P., BARRIO-ANTA M., CRECENTE- CAMPO F., 2009b. Development a stand density management diagram for radiate pine stands including assessment of stand stability. Forestry 82, 1-16. CASTEDO DORADO F., ÁLVAREZ GONZÁLEZ J.G., BARRIO ANTA M., DIÉGUEZ-ARANDA U., 2007b. Modelling stand basal area growth for radiata pine plantations in Northwestern Spain using the GADA. Ann For Sci 64, 609–619. CASTEDO-DORADO F., ÁLVAREZ GONZÁLEZ J.G., BARRIO M., PARRESOL B.R., 2005. A stochastic height–diameter model for maritime pine ecoregions in Galicia (northwestern Spain). Ann For Sci 62, 455-465. CASTEDO-DORADO F., ÁLVAREZ-ÁLVAREZ P., BARRIO-ANTA M., QUINTAI - ROS R., 2009a. Inclusión de riesgos abióticos en diagramas de manejo de la densi - dad. Un caso de estudio en masas de Pinus pinaster Ait. 5º Congreso Forestal Español, Ávila, Septiembre 2009. Ref: 5CFE01-190. [In Spanish]. CASTEDO-DORADO F., BARRIO ANTA M., DIÉGUEZ-ARANDA U., GADOW K.v., SÁNCHEZ RODRÍGUEZ M., 2006. A generalized height–diameter model including random components for radiata pine plantations in northwestern Spain. For Ecol Manage 229, 202-213. CERVERA J.M., 1973. El área basimétrica reducida, el volumen reducido y el perfil. Montes: 415-418. [In Spanish]. CHAUCHARD L.M., OLALDE M., 2004. Diagrama de manejo de la densidad de masas de pino radiata en el País Vasco. Cuadernos SECF 18, 161-166. CIESZEWSKI C.J., 2000. Analytical solution to the generalized log-logistic equation. For Sci 46, 291-296. CIESZEWSKI C.J., HARRISON M., MARTIN S.W., 2000. Practical methods for esti - mating non-biased parameters in self-referencing growth and yield models. University of Georgia PMRC-TR 2000-7.
56 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 57
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
CLUTTER J.L., 1980. Development of taper functions from variable top merchantable volume equations. For Sci 26: 117–120. CLUTTER J.L., JONES E.P., 1980. Prediction of growth after thinning in old-field slash pine plantations. USDA Forest Service, Res Pap SE-217, 19pp. CLUTTER J.L., BAILEY R.L., BRISTER G.H., FORTSON J.C., PIENAAR L.V., 1983. Timber management: a quantitative approach. Wiley, New York, Chichester, Brisbane, Toronto, Singapore. 333 pp. CONDÉS S., STERBA H., 2004. Modelo de crecimiento individual para Pinus sylves - tris , con datos de los inventarios forestales nacionales 2º y 3º, en la provincia de Madrid. Cuadernos SECF 18, 211-217. [In Spanish]. CONDÉS S., STERBA H., 2005. Derivation of compatible crown width equations for some important tree species of Spain. For Ecol Manage 217(2-3), 203-218. CONDÉS S., STERBA H., 2008. Comparing an individual tree growth model for Pinus halepensis Mill. in the Spanish region of Murcia with yield tables gained from the same area. Eur J Forest Res 127, 253-261. CRECENTE-CAMPO F., 2008. Individual-tree basal area and height growth models for Pinus radiata D. Don in Galicia. Modelo de crecimiento de árbol individual para Pinus radiata D. Don en Galicia. Doctoral thesis. Universidad de Santiago de Compostela, Lugo. [In Spanish and English]. CRECENTE-CAMPO F., DIÉGUEZ-ARANDA U., ROJO A., 2009c. A merchantable volume system for Pinus sylvestris L. in the major mountain ranges of Spain. Ann For Sci 66 (8) 808. DOI: 10.1051/forest/2009078. CRECENTE-CAMPO F., MARSHALL P., RODRIGUEZ-SOALLEIRO R., 2009b. Modeling non-catastrophic individual-tree mortality for Pinus radiata plantations in northwestern Spain. For Ecol Manage 257, 1542-1550. CRECENTE-CAMPO F., DIÉGUEZ-ARANDA U., MARSHALL P., LEMAY V., 2009a. A crown profile model for Pinus radiata D. Don in northwestern Spain. For Ecol Manage 257, 2370-2379. CRECENTE-CAMPO F., DIÉGUEZ-ARANDA U., SOARES P., TOMÉ, M., 2010a. Modelling anual individual-tree growth and mortality of Scots pine with data obtained at irregular measurement intervals and containing missing observations. For Ecol Manage 260, 1965-1974. CRECENTE-CAMPO F., DIÉGUEZ-ARANDA U., SOARES P., TOMÉ M., 2010b. A generalized nonlinear mixed-effects height-diameter model for Eucalyptus globulus L. in northwestern Spain. For Ecol Manage 259, 943-952. DANIEL T.W., BAKER F.S., HELMS J.A., 1979. Principles of silviculture, 2nd edition, McGraw-Hill Book Co., New York. DAVIS L.S., BETTINGER P.S., HOWARD T.E., JOHNSON K.N., 2001. Forest Management: To Sustain Ecological, Economic, and Social Values. McGraw-Hill, New York. DE LAS HERAS J., FERRANDIS P., GONZÁLEZ-OCHOA A.I., HERRANZ J.M., MARTÍNEZ-SÁNCHEZ J.J., 2002. Establishment of Pinus halepensis Mill. Saplings following fire: effects of competition with shrub species. Acta Oecol - Int J Ecol 23(2), 91-97.
57 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 58
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
DEL PESO C., BRAVO F., ORDOÑEZ C., VALBUENA P., 2005. Diagramas para el manejo de la densidad de rodales de pino negral ( Pinus pinaster Ait.) en el Sistema Central. Actas del IV Congreso Forestal Español. 26-30 de septiembre. Zaragoza. [In Spanish]. DEMAERSCHALK J., 1972. Converting volume equations to compatible taper equa - tions. For Sci 18, 241–245. DIAZ-MAROTO I.J., BARCALA-PÉREZ E., FERNANDEZ-PAJARES J., VILA- LAMEIRO P., 2010 Site index model for natural stands of Rebollo oak ( Quercus pyrenaica Willd.) in Galicia, NW Iberian Peninsula. Ciência Florestal, 20(1), 57-69. DIÉGUEZ-ARANDA U., 2004. Modelo dinámico de crecimiento para masas de Pinus sylvestris L. procedentes de plantación en Galicia. Doctoral thesis. Universidad de Santiago de Compostela. [In Spanish]. DIÉGUEZ-ARANDA U., ÁLVAREZ-GONZALEZ J.G., CASTEDO-DORADO F., 2005d. Funciones de crecimiento en área basimétrica para masas de Pinus sylvestris L. procedentes de repoblación en Galicia. Invest Agrar: Sist Rec For 14(2), 253-266. [In Spanish]. DIÉGUEZ-ARANDA U., BARRIO ANTA M., CASTEDO DORADO F., 2005b. Relación altura-diámetro generalizada para masas de Pinus sylvestris L. procedentes de repoblación en el noroeste de España. Invest Agrar: Sist Recur For 14, 229-241. [In Spanish]. DIÉGUEZ-ARANDA U., BURKHART H.E., RODRÍGUEZ-SOALLEIRO R., 2005c. Modeling dominant height growth of radiata pine ( Pinus radiata D. Don) plantations in north-western Spain. For Ecol Manage. 215, 271-284. DIÉGUEZ-ARANDA U., ÁLVAREZ-GONZÁLEZ J.G., BARRIO ANTA M., ROJO ALBORECA A., 2005a. Site quality equations for Pinus sylvestris L. plantations in Galicia (northwestern Spain). Ann For Sci 62, 142-152. DIÉGUEZ-ARANDA U., ÁLVAREZ-GONZÁLEZ J.G., CASTEDO-DORADO F., RODRÍGUEZ-SOALLEIRO R., 2005e. Modelling mortality of Scots pine ( Pinus sylvestris L.) plantations in the northwest of Spain. Eur J Forest Res 124, 143-153. DIÉGUEZ-ARANDA U., ÁLVAREZ-GONZÁLEZ J.G., CASTEDO-DORADO F., ROJO A., 2006a. Dynamic growth model for Scots pine ( Pinus sylvestris L.) planta - tions in Galicia (north-western) Spain. Ecol Model 191, 225-242. DIÉGUEZ-ARANDA U., ÁLVAREZ-GONZÁLEZ J.G., CASTEDO-DORADO F., ROJO A., 2006b. Compatible taper function for Scots pine plantations in north - western Spain. Can J For Res. 36, 1190-1205. DIÉGUEZ-ARANDA U., ÁLVAREZ-GONZÁLEZ J.G., GADOW K.v, GRANDAS- ARIAS J.A., 2006c. Site Quality Curves for Birch Stands in North-Western Spain. Silva Fennica 40(4), 631-644. DIÉGUEZ-ARANDA U., BALBOA-MURIAS M., BARRIO-ANTA M., CASTEDO- DORADO F., 2003. Estimación del diámetro normal y del volumen del tronco a par - tir de las dimensiones del tocón para seis especies forestales comerciales de Galicia. Invest Agrar: Sist Rec For 12(2), 131-139. [In Spanish].
58 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 59
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
DIÉGUEZ-ARANDA U., ÁLVAREZ-GONZÁLEZ J.G., CRECENTE-CAMPO F., GONZÁLEZ GONZÁLEZ J.M., ROJO ALBORECA A., 2007. Aplicación informá - tica para la cubicación con clasificación de productos de Fagus sylvatica L. en Navarra. Gobierno de Navarra. [In Spanish]. DIÉGUEZ-ARANDA U., ÁLVAREZ GONZÁLEZ J.G., BALBOA-MURIAS M.A., BARRIO-ANTA M., CASTEDO-DORADO F., CRECENTE-CAMPO F., GONZÁLEZ GONZÁLEZ J.M., GORGOSO VARELA J.J., LÓPEZ-SÁNCHEZ C.A., PÉREZ-CRUZADO C., RODRÍGUEZ SOALLEIRO R., ROJO ALBORECA A., SÁNCHEZ RODRÍGUEZ F., 2009. Herramientas selvícolas para la gestión forestal sostenible en Galicia. Consellería do Medio Rural, Xunta de Galicia. 268 pp. + CD-Rom. . [In Spanish]. ECHEVERRÍA I., 1942. Ensayo de tablas de producción del Pinus insignis en el norte de España. Boletines del I.F.I.E., nº 22, Madrid. 67 pp. [In Spanish]. ECHEVERRÍA I., 1952. Producción del Eucalyptus globulus . Estudio de las leyes de crecimiento en la zona forestal de Huelva del Patrimonio Forestal del Estado. Boletines del I.F.I.E., nº 62, Madrid. 39 pp. [In Spanish]. ECHEVERRÍA I., DE PEDRO S., 1948. El Pinus pinaster en Pontevedra. Su producti - vidad normal y aplicación a la celulosa industrial. Boletines del I.F.I.E., nº 38, Madrid. 147 pp. [In Spanish]. EID T., TUHUS E., 2001. Models for individual tree mortality in Norway. For Ecol Manage 154, 69-84. ELENA-ROSELLÓ R., 1997. Clasificación biogeoclimática de España Peninsular y Balear. MAPA. Madrid. [In Spanish]. ERASO E., OLABE F., PUERTAS F., 1996. Tablas de producción de selvicultura media y de referencia para masas artificiales de Pinus nigra ssp. austriaca en la Comunidad Foral de Navarra. [Unpublished]. [In Spanish]. ERVITI J.J., 1991. Desarrollo de Modelos de crecimiento y producción de las masas de Pinus halepensis Mill. en España. Doctoral thesis. Universidad Politécnica de Madrid. [In Spanish]. ESCALANTE E., BRAVO F., ORDÓÑEZ C., PANDO V., 2011. Multinomial logit esti - mation of a diameter growth matrix model of two Mediterranean pine species in Spain. Ann For Sci 68(4), 715-726. ESPINEL S., SÁENZ D., CANTERO A., 1997. Un modelo de simulación para rodales de Pinus radiata D. Don en el País Vasco. II Congreso Forestal Español- Irati 97, vol. IV, pp. 201–206. [In Spanish]. FERNÁNDEZ LÓPEZ A.B., 1982. Evaluación del crecimiento y productividad del monte bajo de Eucalyptus globulus en rotaciones sucesivas. Premio Excma. Diputación de Pontevedra. 70 pp. [Unpublished]. [In Spanish]. FERNÁNDEZ LÓPEZ A.B., 1985. Efecto del espaciamiento inicial en la producción de Eucalyptus globulus . Departamento Forestal de Lourizán. 45 pp. [Unpublished]. [In Spanish]. FERRES L., RODA F., TERRADAS J., VERDÚ A.M.C., 1980. Estructura y funciona -
59 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 60
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
lismo de un encinar montano en el Montseny. Mediterranea 4, 23-36. [In Spanish]. GADOW K.v., HUI G.Y., 1999. Modelling forest development. Kluwer Academic Publishers, Dordrecht. 213 pp. GADOW K.v., ÁLVAREZ-GONZÁLEZ J.G., REAL P., 2001. Modelización del creci - miento y la evolución de bosques. IUFRO World Series vol. 12, Vienna. [In Spanish]. GALLEGO H. A., RICO M., SANTA REGINA I., 1993. Biomass equations and nutrient distribution for Quercus pyrenaica forests. Mesogee 53, 75-82. GAMBORG G., LARSEN J.B. , 2003. “Back to nature” -a sustainable future for forestry?. For Ecol Manage 179, 559-571. GARCÍA ABEJÓN J.L., 1981. Tablas de producción de densidad variable para Pinus sylvestris L. en el Sistema Ibérico. Comunicaciones I.N.I.A. Serie: Recursos Naturales, 10. 47 pp. [In Spanish]. GARCÍA ABEJÓN J.L., GÓMEZ LORANCA J.A., 1984. Tablas de producción de den - sidad variable para Pinus sylvestris L. en el Sistema Central. Comunicaciones I.N.I.A. Serie: Recursos Naturales, 29. 36 pp. [In Spanish]. GARCÍA ABEJÓN J.L., GÓMEZ LORANCA J.A., 1989. Tablas de producción de den - sidad variable para Pinus pinaster Ait. en el Sistema Central. Comunicaciones I.N.I.A. Serie: Recursos Naturales, 47. 45 pp. [In Spanish]. GARCÍA ABEJÓN J.L., TELLA FERREIRO G., 1986. Tablas de producción de densi - dad variable para Pinus sylvestris L. en el Sistema Pirenaico. Comunicaciones I.N.I.A. Serie: Recursos Naturales, 43. 28 pp. [In Spanish]. GARCÍA GÜEMES C., 1999. Modelo de simulación selvícola para Pinus pinea L. en la provincia de Valladolid. Monografía INIA. Serie forestal: nº 6. [In Spanish]. GARCÍA GÜEMES C., CAÑADAS N., MONTERO G., 2001. Modelo de estimación de alturas en Pinus pinea L. para la provincia de Valladolid. III Congreso Forestal Español, Granada, Septiembre 2001. 3CFE03-121-T3, 794-799. [In Spanish]. GARCÍA O., 1983. A stochastic differential equation model for the height growth of forest stands. Biometrics 39, 1059-1072. GARCÍA O., 1994. The state-space approach in growth modelling. Can J For Res 24, 1894-1903. GARCÍA O., 2003. Dimensionality reduction in growth models: an example. FBMIS 1, 1-15. GARCÍA O., RUIZ F., 2003. A growth model for eucalypt in Galicia, Spain. For Ecol Manage 173, 49-62. GEA-IZQUIERDO G., CAÑELLAS I., 2009. Analysis of Holm Oak intraspecific com - petition using gamma regression. For Sci 55, 310-322. GEA-IZQUIERDO G., CAÑELLAS I., MONTERO G., 2008. Site index in agroforestry systems: age-dependent and age-independent dynamic diameter growth models for Quercus ilex L. in Iberian open oak woodlands. Can J For Res 38, 101-113. GEA-IZQUIERDO G., CAÑELLAS I., CHERUBINI P., MARTÍN-BENITO D., 2009. Climate-growth variability in Quercus ilex L. west Iberian open woodlands of different stand density. Ann For Sci 66, 802. DOI: 10.1051/forest/2009080.
60 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 61
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
GOELZ J.C.G., BURK T.E., 1992. Development of a well-behaved site index equation: jack pine in north central Ontario. Can J For Res 22, 776-784. GÓMEZ LORANCA J.A., 1996. Pinus nigra Arn. en el Sistema Ibérico: tablas de cre - cimiento y producción. Monografías I.N.I.A. 93. 106 pp. [In Spanish]. GONZALEZ F., 1986. Crecimiento y producción, en la meseta central, según cali - dades de estación, de plantaciones de Populus x euroamericana (Dode) Guinier “Campeador”. Comunicaciones INIA, Serie Recursos Naturales, nº 44. [In Spanish]. GONZÁLEZ ADRADOS J.R., CALVO HARO R., GONZÁLEZ HERNÁNDEZ R., 2000. La predicción del calibre de corcho al final del turno y su aplicación al mues - treo de la producción. Invest Agrar: Sist Recur For 9, 363-373. [In Spanish]. GONZÁLEZ ANTOÑANZAS F., 1986. Crecimiento y producción, en la Meseta Central, según calidades de estación, de plantaciones de Populus x euramericana (Dode) Guinier “Campeador”. Comunicaciones I.N.I.A. Serie: Recursos Naturales 44. 56 pp. [In Spanish]. GONZÁLEZ DONCEL I., 1989. Tablas ponderales para la estimación de la biomasa de rebollo ( Quercus pyrenaica Willd.) en la provincia de León. INIA-MAPA, Madrid, 56 pp. [In Spanish]. GONZÁLEZ GONZÁLEZ J.M., ÁLVAREZ GONZÁLEZ J.G., CASTEDO-DORADO F., DIÉGUEZ-ARANDA U., ROJO ALBORECA A., 2009. GesMO 2009. Simulador de crecimiento y producción de rodales forestales. Universidad de Santiago de Compostela. (available at www.usc.es/uxfs ). GONZÁLEZ J.R., PALAHÍ M., PUKKALA T., TRASOBARES A., 2006. A fire proba - bility model for forest stands in Catalonia. Ann For Sci 63, 169-176. GONZÁLEZ J.R., PALAHÍ M., PUKKALA T., TRASOBARES A., 2007. Predicting tree survival in burned forests in Catalonia (North-East Spain) for strategic forest planning. Ann For Sci 64, 733-742. GONZÁLEZ J.R., PALAHÍ M., PUKKALA T., TRASOBARES A., 2008. Optimising the management of Pinus nigra Arn. Stands under endogenous risk of fire in Catalonia. Invest Agrar: Sist Recur For 17(1), 10-17. GONZÁLEZ MOLINA J.M., ARRUFAT D., MEYA D., 1999. Primeras tablas de selvi - cultura a la carta para masas regulares de Pinus nigra Arn. del Prepirineo catalán. Invest Agrar: Sist Recur For 8(1), 49-61. [In Spanish]. GONZÁLEZ-MARTÍNEZ S.C., ALÍA R., BURCZYK J., GIL L., NANOS N., NATHAN R., 2006. Effective gene dispersal and female reproductive success in Mediterranean maritime pine ( Pinus pinaster Aiton). Mol Ecol 15, 4577-4588. GRACE J.C., JARVIS P.G., NORMAN J.M., 1987. Modelling the interception of solar radiant energy in intensively managed stands. New Zeal J For Sci 17, 193-209. GREENE D.F., CANHAM C.D., COATES K.D., LEPAGE P.T., 2004. An evaluation of alternative dispersal functions for trees. J Ecol 92, 758-766. HASENAUER H., MONSERUD R.A., 1996. A crown ratio model for Austrian forests. For Ecol Manage 84, 49-60.
61 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 62
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
HUANG S., TITUS S.J., 1999. Estimating a system of nonlinear simultaneous indi - vidual tree models for white spruce in boreal mixed-species stands. Can J For Res 29, 1805-1811. IBÁÑEZ J.I., 1989. El haya ( Fagus sylvatica L.) en la Rioja. Selvicultura y ordenación. Doctoral thesis. Universidad Politécnica de Madrid. [In Spanish]. JIANG L., BROOKS J.R., WANG J., 2005. Compatible taper and volume equations for yellow-poplar in West Virginia. For Ecol Manage 213, 399–409. KEENAN T., GRACIA C.A., SABATE S., 2008. Forest Ecophysiological Models and Carbon Sequestration. In: Managing forest ecosystems: The Challenge of Climate Change, (Bravo F., LeMay V., Jandl R., Gadow K.v., eds). Springer, Berlin, 83-102. KERSHAW J.A., HANN D.W., MAGUIRE D.A., 1990. Longevity and duration of radial growth in Douglas-fir branches. Can J For Res 20, 1690-1695. KEYES C.R., O’HARA K.L., 2002. Quantifying stand targets for silvicultural preven - tion of crown fires. West J Appl For 17, 101-109. KOZAK A., KOZAK R., 2003. Does cross validation provide additional information in the evaluation of regression models? Can J For Res 33, 976-987. KRAJICEK J.E., BRINKMAN K.A., GRINGRICH S.F., 1961. Crown competition: a measure of density. For Sci 7, 35-42. KRUMLAND B.E., ENG H., 2005. Site index systems for major young-growth forest and woodland species in northern California. Cal. Dept. Forestry and Fire Protection. Cal. For. Rep. No. 4. LANDSBERG J., LEMAY V.M., MARSHALL P.L., 2003. Modelling forest ecosys - tems: state of the art, challenges, and future directions. Can J For Res 33, 385-397. LANDSBERG, J.L., WARING, R.H. , 1997. A generalised model of forest productivity using simplified concepts of radiation-use efficiency, carbon balance and partitioning. For Ecol Manage 95, 209-228. LEONARDI S., GALLEGO H.A., RAPP M., RICO M., SANTA REGINA I., 1996. Biomass, litterfall and nutrient content in Castanea sativa coppice stands of southern Spain. Ann Sci For 53, 1071-1081. LIZARRALDE I., 2008. Dinámica de rodales y competencia en las masas de pino silves - tre ( Pinus sylvestris L.) y pino negral ( Pinus pinaster Ait.) de los Sistemas Central e Ibérico Meridional. Doctoral thesis. Universidad de Valladolid, Palencia. [In Spanish]. LÓPEZ-SÁNCHEZ C.A., 2009. Estado selvícola y modelos de crecimiento y gestión de plantaciones de Pseudotsuga menziesii (Mirb.) Franco en España. Doctoral thesis. Universidad de Santiago de Compostela, Lugo. [In Spanish]. LÓPEZ SÁNCHEZ C.A., ÁLVAREZ GONZÁLEZ J.G., CASTEDO DORADO F., DIÉGUEZ-ARANDA U., RIBOT DE PORTA E., RODRÍGUEZ SOALLEIRO R.J. 2009. Tablas de producción de plantaciones de abeto Douglas en España. 5º Congreso Forestal Español, Ávila, Septiembre 2009. [In Spanish]. LÓPEZ-SÁNCHEZ C., RODRÍGUEZ-SOALLEIRO R. 2009. A density management diagram including stand stability and crown fire risk for Pseudotsuga menziesii (Mirb.) Franco in Spain. Mt Res Dev 29(2),169-176.
62 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 63
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
LÓPEZ-SÁNCHEZ C.A., ÁLVAREZ GONZÁLEZ J.G., CASTEDO F., GORGOSO J.J., RODRÍGUEZ R., ROJO A., SÁNCHEZ F., 2003. A height-diameter model for Pinus radiata D. Don in Galicia (Northwest Spain). Ann For Sci 60, 237-245. LÓPEZ-SENESPLEDA E., SÁNCHEZ-PALOMARES O., 2007. Modelo de calidad de estación y altura dominante para Quercus faginea Lam. en España. Cuadernos SECF 23, 199-206. [In Spanish]. MADRIGAL A., 1991. Tablas de producción. Seminario sobre inventario y ordenación de montes, Valsaín, Segovia (Spain), Vol. II: 32-70. [In Spanish]. MADRIGAL A., TOVAL G., 1975. Tablas de producción, cubicación y tarifas de Pinus radiata D. Don. en las Provincias Vascongadas. Dirección General de la Producción Agraria. Mº de Agricultura. Madrid. 75 pp. [In Spanish]. MADRIGAL A., MARTÍNEZ MILLÁN F.J., PUERTAS F., 1992. Tablas de producción para Fagus sylvatica L. en Navarra. Serie Agraria, nº 3. Departamento de Agricultura, Ganadería y Montes. Gobierno de Navarra. Pamplona, 122 pp. [In Spanish]. MADRIGAL A., ÁLVAREZ-GONZÁLEZ J.G., RODRÍGUEZ-SOALLEIRO R., ROJO ALBORECA A. 1999. Tablas de producción para los montes españoles. Fundación Conde del Valle de Salazar. Escuela Técnica Superior de Ingenieros de Montes, Madrid. 253 pp. [In Spanish]. MADRIGAL G., CALAMA R., GORDO J., MONTERO G., 2009. PINEA2 v1.0: apli - cación informática para la gestión de las masas regulares de Pinus pinea L. en la Meseta Norte. 5º Congreso Forestal Español. Mesa 2. Ávila, septiembre 2009. [In Spanish]. MADRIGAL A., HERRANZ J., LÓPEZ M., MOSQUERA R., 1977. Tablas de produc - ción de Eucalyptus globulus Labill. en el Sudoeste de España. Dirección General de la Producción Agraria. Ministerio de Agricultura. Madrid, 109 pp. [Unpublished]. [In Spanish]. MADRIGAL G., ALONSO R., CALAMA R., MONTERO G., MORO J., 2007. Patrón de crecimiento en altura dominante en masas naturales y artificiales de Pinus pinea L.: comparación a través de modelos dinámicos. Cuadernos SECF 23, 207-214. [In Spanish]. MANION P.D., 1981. Tree disease concepts. Prentice-Hall, Englewood cliffs, New Jersey, USA. MARTÍN-BENITO D., CAÑELLAS I., RÍO M., 2010. Black pine ( Pinus nigra Arn.) growth divergence along a latitudinal gradient in Western Mediterranean mountains. Ann For Sci 401. MARTÍN-BENITO D., CAÑELLAS I., CHERUBINI P., RÍO M., 2008a. Growth response to climate and drought in Pinus nigra Arn. trees of different crown classes. Trees Struct Funct 22, 363-373. MARTIN-BENITO D., CAÑELLAS I., GEA-IZQUIERDO G., RÍO M., 2008b. Long- term trends in dominant-height growth of Black pine using dynamic models. For Ecol Manage 256, 1230-1238. MARTÍNEZ Y., HERRANZ O. 2006. Tarifas de cubicación y curvas de perfil de Pinus
63 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 64
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
canariensis y Pinus radiata en la isla de Tenerife. Cabildo de Tenerife. Área de Medio Ambiente y Paisaje. Servicio Técnico Forestal. 29 pp. [In Spanish]. MARTÍNEZ CHAMORRO E., 2004. Estudio del crecimiento, producción y gestión de las masas de Pinus sylvestris L. en Galicia. Doctoral thesis. Universidad de Santiago de Compostela, Lugo. [In Spanish]. MARTÍNEZ DE ARAGÓN J., BONET J.A., COLINAS C., FISCHER C.R., 2007. Productivity of ectomycorrhizal and selected edible saprotrophic fungi in pine forests of the pre-Pyrenees mountains, Spain: Predictive equations for forest management of mycological resources. For Ecol Manage 252, 239-256. MARTÍNEZ MILLÁN F.J., MADRIGAL A., 1992. Alternativas selvícolas y de pro - ducción del Pinus pinaster Ait. en Galicia. Premio E.N.C.E. 1992. 151 pp. [Unpublished]. [In Spanish]. MARTÍNEZ-MILLAN F.J., ARA LAZARO P., GONZÁLEZ DONCEL I., 1993. Ecuaciones alometricas de tres variables: estimación del volumen, crecimiento y por - centaje de corteza de las principales especies maderables españolas. Invest Agrar: Sist Recur For, 2, 211-228. [In Spanish]. MERINO A., BRAÑAS J., REY C., RODRIGUEZ-SOALLEIRO R., 2003. Biomasa arbórea y acumulación de nutrientes en plantaciones de Pinus radiata D. Don en Galicia. Invest Agrar: Sist Recur For 12, 85-98. [In Spanish]. MITCHELL K.J., 1975. Dynamics and simulated yield of Douglas-fir. For Sci Monogr. 17. 39 pp. MOLINA F., RUIZ P., 1976. Tablas de producción de Pinus pinaster Ait. en Galicia. I.N.I.A., CRIDA 01. Departamento Forestal de Lourizán. 93 pp. [Unpublished]. [In Spanish]. MONSERUD R.A., STERBA H., 1999. Modeling individual tree mortality for Austrian forest species. For Ecol Manage 113: 109-123. MONTERO DE BURGOS, J.L., GONZÁLEZ-REBOLLAR, J.L., 1974. Diagramas bioclimáticos. Instituto Nacional para la Conservación de la Naturaleza (ICONA). Madrid. 380 pp. [In Spanish]. MONTERO G., 1987. Modelos para cuantificar la producción de corcho en alcornoca - les ( Quercus suber L.) en función de la calidad de estación y los tratamientos selví - colas. Doctoral thesis. INIA Madrid. [In Spanish]. MONTERO G., CAÑELLAS I., 1999. Manual de reforestación, cultivo y aprovecha - miento del alcornoque. INIA, Ministerio de Agricultura, Pesca y Alimentación, Madrid. 103 pp. [In Spanish]. MONTERO G., CAÑELLAS I., RUIZ-PEINADO R., 2001b. Growth and yield models for Pinus halepensis Mill. Invest Agrar: Sist Recur For 10(1), 179-201. MONTERO G., MUÑOZ M., RUIZ-PEINADO R., 2005. Producción de biomasa y fijación de CO 2 por los bosques españoles. Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria, Ministerio de Educación y Ciencia, Madrid, 270 pp. [In Spanish]. MONTERO G., BACHILLER A., CAÑELLAS I., ORTEGA C., 1999. Productividad
64 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 65
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
aérea y dinámica de nutrientes en una repoblación de Pinus pinaster Ait. sometida a distintos regímenes de claras. Invest Agrar: Sist Recur For Fuera de Serie nº1, 175- 206. [In Spanish]. MONTERO G., BACHILLER A., MADRIGAL G., RUIZ-PEINADO R., 2004a. Red de parcelas experimentales permanentes del CIFOR-INIA. Cuadernos SECF 18, 229-236. [In Spanish]. MONTERO G., CAÑELLAS I., ORTEGA C., RÍO M., 2001a. Results from a thinning regime experiment in a Scots pine ( Pinus sylvestris L.) natural regeneration stand in the Sistema Ibérico mountain range (Spain). For Ecol Manage 145, 151-161. MONTERO G., CAÑELLAS I., ORTEGA C., TORRES E., 1996. Modelos para la esti - mación de corcho en alcornocales. Invest Agrar: Sist Recur For 5(1), 97-127. [In Spanish]. MONTERO G., MUÑOZ M., DONÉS J., ROJO A., 2004b. Fijación de CO 2 por Pinus sylvestris L. y Quercus pyrenaica Willd. en los montes “Pinar de Valsaín” y “Matas de Valsaín”. Invest Agrar: Sist Recur For 13, 399-415. [In Spanish]. MONTERO G., CAÑELLAS I., GRAU J. M., ORTEGA C., RUIZ-PEINADO R., 2000. Tablas de producción para Pinus halepensis Mill. Cuadernos SECF 10, 183-188. [In Spanish]. MONTES F., HERNÁNDEZ M.J., CAÑELLAS I., 2005. A geostatistical approach to cork production sampling estiamtion in Quercus suber forests. Can J For Res 35, 2787-2796. MUNRO D.D., 1974. Forest growth models - a prognosis. In: Growth models for tree and stand simulation. (Fries J., ed.). Royal Coll. For., Res. Notes 30, p. 7-21. MUÑOZ P., 1985. Alternativas selvícolas en la producción del Pinus radiata D. Don. Doctoral thesis. Universidad Politécnica de Madrid. [In Spanish]. MUTKE S., GIL L., GORDO J., 2001. Modelo individual de producción de piñón de Pinus pinea L. como criterio de selección fenotípica. 3er Congreso Forestal Español. Granada, Septiembre 2001 Volumen 3, 172-178. [In Spanish]. MUTKE S., GIL L., GORDO J., 2005. Variability of Mediterranean Stone pine cone production: Yield loss as response to climate change. Agr Forest Meteorol 132(3-4), 263-272. NANOS N., ALÍA R., GIL L., MONTERO G., TADESSE W., 2000. Modelling resin production distributions for Pinus pinaster Ait using two probability functions. Ann For Sci 57, 369-377. NANOS N., ALÍA R., GIL L., MONTERO G., TADESSE W., 2001. Spatial stochastic modeling of resin yield from pine stands. Can J For Res 31, 1140-1147. NEWTON P.F., WEETMAN G.F., 1994. Stand density management diagram for managed black spruce stands. For Chron 70, 65-74. NÚÑEZ M.R., BRAVO F., CALVO L., 2003. Predicting the probability of seed germi - nation Pinus sylvestris L. and four competitor shrub species after fire. Ann For Sci 60(1), 75-81. ODENBAUGH J., 2006. The strategy of model building in population biology. Biology and Philosophy 21, 607-621.
65 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 66
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
ODERWALD R.G., HANS R. P., 1993. Corroborating models with model properties. For Ecol Manage 62, 271-283. ORDOÑEZ, J.L., RETANA, J., 2004. Early reduction of post-fire recruitment of Pinus nigra by post-dispersal seed predation in different time-since-fire habitats Ecography 27(4), 449-458. ORDOÑEZ J.L., FRANCO S., RETANA J., 2004. Limitation of the recruitment of Pinus nigra in a gradient of post-fire environmental conditiions Ecoscience 11(3), 296-304. ORTEGA A., 1989. Modelos de evolución de masas de Pinus sylvestris L. Doctoral the - sis. Universidad Politécnica de Madrid. [In Spanish]. PALAHI M., GRAU J.M., 2003. Preliminary site index model and individual tree and mortality models for black pine ( Pinus nigra Arn.) in Catalonia (Spain). Invest Agrar: Sist Recur For 12, 137-148. PALAHÍ M., MIINA, J., MONTERO, G., PUKKALA, T., 2003. Individual-tree growth and mortality models for Scots pine ( Pinus sylvestris L.) in north-east Spain. Ann For Sci 60, 1-10. PALAHI M., MIINA J., MONTERO G., TOMÉ M., 2002. Stand-level yield model for Scots pine ( Pinus sylvestris L.) in north-east Spain. Invest Agrar: Sist Recur For 11, 409-424. PALAHÍ M., MONTERO G., PUKKALA T., TRASOBARES A., 2004b. Site index models for Pinus sylvestris in NE Spain. For Ecol Manage 187, 35-47. PALAHÍ M., PASCUAL L., PUKKALA T., TRASOBARES A., 2004a. Examining alternative landscape metrics in ecological forest landscape planning: a case for capercaillie in Catalonia. Invest Agrar: Sist Recur For13 (3), 1-12. PALAHÍ M., BONET J.A., COLINAS C., FISCHER C.R., MARTÍNEZ DE ARAGÓN J., PUKKALA T., 2009. Effect of the inclusion of mushroom values on the optimal management of even-aged pine stands of Catalonia. For Sci 55(6), 503-511. PARDO M., 1980. Tablas de producción para Eucalyptus globulus en el sudoeste de España. ENCE. Departamento de Inventariación Forestal. [Unpublished]. [In Spanish]. PARRESOL B.R., 1999. Assessing tree and stand biomass: A review with examples and critical comparisons. For Sci 45, 573-593. PAUSAS J.G., RIBEIRO E., VALLEJO R., 2004. Post-fire regeneration variability of Pinus halepensis in the eastern Iberian Peninsula. For Ecol Manage 203(1-3), 251- 259. PEDERSEN B.S., 1998. Modeling tree mortality in response to short- and long-term environmental stresses. Ecol Model 105, 347-351. PÉREZ-CRUZADO C., FERNÁNDEZ-RIVAS E., MERINO A., RODRÍGUEZ- DACOSTA L.M., RODRÍGUEZ-SOALLEIRO R., 2009. Diagramas de manejo de la densidad para plantaciones de Eucalyptus nitens Maid. en el norte de España con evaluación del carbono fijado en biomasa arbórea. 5º Congreso Forestal Español. Ávila, Septiembre 2009. Ref: 5CFE01-132. [In Spanish]. PICARDO A., 1985. Tablas de gestión a la carta. Aplicación a montes de pino silvestre.
66 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 67
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
Doctoral thesis. Universidad Politécnica de Madrid. [In Spanish]. PIQUÉ M., 2003. Modelos de producción para las masas de Pinus pinea L. en Catalunya: orientaciones para la gestión y el aprovechamiento sostenible de madera y piña. Doctoral thesis. Universidad de Lleida. [In Spanish]. PITA P.A., 1964. La calidad de estación en las masas de Pinus sylvestris L. en la Península Ibérica. Anales IFIE 9, 5-28. [In Spanish]. PITA P.A., 1966. La producción de las masas de Eucalyptus globulus en el norte de España. Anales del Instituto Forestal de Investigaciones y Experiencias, Tomo I: 45- 60. [In Spanish]. PITA P.A., 1967a. Clasificación provisional de las calidades de la estación en las masas de “ P. pinaster ” Sol (continental) y “ P. uncinata ” Ram. de la península Ibérica. Anales del IFIE, 125-138. [In Spanish]. PITA P.A., 1967b. Tablas de cubicación por diámetros normales y alturas totales. Ministerio de Agricultura, Madrid. [In Spanish]. PRETZSCH H. , 2009. Forest Dynamics, Growth and Yield. Springer, Berlin. PUERTAS F., 2003. Scots pine in Navarre: Economic importance and production. In: Silviculture and sustainable management in mountain forests in the western Pyrenees, IUFRO Conference, Navarre, September 2003, 32 pp. PUKKALA T. (ed.), 2002. Multi-objective Forest Planning. Kluwer Academic Publishers. REINEKE L.H., 1933. Perfecting a stand density index for even-aged forests. J Agric Res 46, 627-6238. RENNOLLS K., 1997. Data requirements for forest modelling. In: Empirical and process-based models for forest tree and stand growth simulation. (Amaro A., Tomé M., eds). Edições Salamandra. Lisboa. pp 11-22. RICHARDS F.J., 1959. A flexible growth function for empirical use. Journal of Experimental Botany 10, 290 -300. RÍO M., 1999. Régimen de claras y modelo de producción para Pinus sylvestris L. en los Sistemas Central e Ibérico. Doctorales INIA. Serie: Forestal 2, 257 pp. [In Spanish]. RÍO M., MONTERO G., 2001. Modelo de simulación de claras en masas de Pinus syl - vestris L. Monografías INIA. Serie Forestal 3, 114 pp. [In Spanish]. RÍO M., STERBA H., 2009. Comparing volume growth in pure and mixed stands of Pinus sylvestris and Quercus pyrenaica . Ann For Sci 66, DOI: 10.1051/forest/2009035. RÍO M., BRAVO F., MONTERO G., 2001. Analysis of diameter-density relationships and self-thinning in non-thinning even-aged Scots pine stands. For Ecol Manage 142, 79-87. RÍO M., LÓPEZ-SENESPLEDA E., MONTERO G., 2006. Manual de gestión para masas procedentes de repoblación de Pinus pinaster Ait., Pinus sylvestris L. y Pinus nigra Arn. en Castilla y León. Serie Técnica. Consejería de Medio Ambiente. Junta de Castilla y León. 76 pp + anexos. [In Spanish]. RÍO M, CAÑELLAS I, MONTERO G., ROIG S, 2005. Programación de claras en repoblaciones de Pinus sylvestris L. Seguimiento de sitios de ensayo en la
67 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 68
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
Comunidad de Madrid. Monografías del INIA: Serie forestal 12, 46 pp. [In Spanish]. RÍO M., CALAMA R., CAÑELLAS I., MONTERO G., ROIG S., 2008. Thinning intensity and growth response in SW-European Scots pine stands. Ann For Sci 65, 308. ROBLEDO-ARNUNCIO J. J., GARCÍA C., 2007. Estimation of the seed dispersal ker - nel from exact identification of source plants. Mol Ecol 16, 5098-5109. RODRÍGUEZ F., 2005. Modelos de producción de las choperas del valle del Cinca. Doctoral thesis. Universidad de Lleida. [In Spanish]. RODRIGUEZ, F., 2010. Ecuaciones de volumen comercial para las principales especies maderables de Castilla y León. Disponible en www.cesefor.com/cubifor (último acceso el 15 de abril de 2010) RODRÍGUEZ F., MOLINA C., 2003. Modelos de perfil de fuste para tres clones de chopo ( Populus × euramerica ) en Navarra. Invest Agrar: Sist Recur For 12(3), 73-85. [In Spanish]. RODRÍGUEZ F., AUNÓS A., PEMAN J., 2010. A reduced growth model based on stand basal area. A case for hybrid poplar plantations in northeast Spain. For Ecol Manage 259, 2093-2102. RODRÍGUEZ F., BROTO M., LIZARRALDE I., 2008. CubiFOR: Herramienta para cubicar, clasificar productos y calcular biomasa y CO 2 en masas forestales de Castilla y León. Revista Montes 95:33-39 (available at www.cesefor.com/cubifor). RODRIGUEZ F., CONDÉS S., FERNANDEZ A., LIZARRALDE I., 2009. CriterionTM RD1000: Una oportunidad para calcular el volumen de árboles en pie. 5º Congreso Forestal Español, Ávila, septiembre 2009. Ref 5CFE01-175. [In Spanish]. RODRÍGUEZ-SOALLEIRO R., 1995. Crecimiento y Producción de masas forestales regulares de Pinus pinaster Ait. en Galicia. Alternativas selvícolas posibles. Doctoral thesis. Universidad Politécnica de Madrid [In Spanish]. RODRÍGUEZ SOALLEIRO R., ÁLVAREZ GONZÁLEZ J.G., VEGA G., 1994. Piñeiro do país: modelo dinámico de crecemento de masas regulares de Pinus pinaster Aiton en Galicia (Guía para o usuario do programa PINASTER). Capacitación e Extensión. Serie Manuais Prácticos 8. Consellería de Agricultura, Gandería e Montes, Xunta de Galicia. Santiago de Compostela. 40 pp. [In Spanish]. RODRIGUEZ-SUAREZ J.A., DIAZ-FIERROS F., IGLESIAS M.L., SOTO B., 2010. Application of the 3PG forest growth model to a Eucalyptus globulus plantation in Northwest Spain Eur J Forest Res DOI 10.1007/s10342-010-0355-6. ROJO A., 1994. Crecimiento y producción de Pinus sylvestris L. en la Sierra de Guadarrama. Doctoral thesis. Universidad Politécnica de Madrid. [In Spanish]. ROJO A., MONTERO G., 1994. Tablas de producción españolas. Montes 38, 35-42. [In Spanish]. ROJO A., MONTERO G., 1996. El pino silvestre en la Sierra de Guadarrama. Historia y sel - vicultura de los pinares de Cercedilla, Navacerrada y Valsaín. Ministerio de Agricultura, Pesca y Alimentación. Secretaría General Técnica. Madrid. 293 pp. [In Spanish].
68 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 69
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
ROJO A., ÁLVAREZ-GONZÁLEZ J.G., DIÉGUEZ-ARANDA U., GRANDAS J.A., 2005a. Tablas de producción de selvicultura media para el abedul ( Betula alba L.) en Galicia. 4º Congreso Forestal Español, Zaragoza, Septiembre 2005. [In Spanish]. ROJO A., ÁLVAREZ-GONZÁLEZ J. G., GADOW K.v, PERALES X., SÁNCHEZ- RODRÍGUEZ F., 2005b. Stem taper functions for maritime pine ( Pinus pinaster Ait.) in Galicia (Northwestern Spain). Eur J Forest Res 124, 177–186. ROMANYÀ J., VALLEJO V. R., 2004. Productivity of Pinus radiata plantations in Spain in response to climate and soil. For Ecol Manage 195, 177-189. RUIZ-PEINADO R., BRAVO-OVIEDO A., CAÑELLAS I., RÍO M., 2010. Modelling dominant height growth in Aleppo pine ( Pinus halepensis Mill.) forests. IUFRO meeting Global change and Mediterranean Pines: Alternatives for management. Abstract Book p. 78. RUIZ-PEINADO R., MONTERO G., RÍO M., 2011. New models for estimating the carbon sink capacity of Spanish softwood species. Forest Systems 20, 176-188. SAN MIGUEL A., FERNÁNDEZ CANCIO A., SAN MIGUEL J., 1992. Tablas de peso para pies individuales de rebollo ( Quercus pyrenaica Willd.) en montes bajos del Sistema Central español. Invest Agrar: Sist Recur For 1, 173-179. [In Spanish]. SÁNCHEZ GONZÁLEZ M., 2006. Modelo de crecimiento y producción para monte alcornocal. Doctoral thesis. Universidad Politécnica de Madrid. [In Spanish]. SÁNCHEZ-GONZÁLEZ M., CAÑELLAS I., MONTERO G., 2007c. Generalized height-diameter and crown diameter models for cork oak forests in Spain. Invest Agrar: Sist Recur For 16(1), 76-88. SÁNCHEZ-GONZÁLEZ M., CAÑELLAS I., MONTERO G., 2008. Base-age invariant cork growth model for Spanish cork oak ( Quercus suber L.) forests. Eur J Forest Res 127, 173-182. SÁNCHEZ-GONZÁLEZ M., CAÑELLAS I., SÁNCHEZ M.M., 2007d. Modelo de predicción del calibre de bornizo mediante funciones de perfil del tronco. Cuadernos SECF 23, 239-243. [In Spanish]. SÁNCHEZ-GONZÁLEZ M., MONTERO G., TOMÉ M., 2005. Modelling height and diameter growth of dominant cork oak trees in Spain. Ann For Sci 62, 633-643. SÁNCHEZ-GONZÁLEZ M., CALAMA R., CAÑELLAS I., MONTERO G., 2007a. Variables influencing cork thickness in Spanish cork oak forests: A Modelling Approach. Ann For Sci 64, 1-12. SÁNCHEZ-GONZÁLEZ M., CALAMA R., CAÑELLAS I., MONTERO G., 2007b. Management oriented growth models for multifunctional Mediterranean Forests: the case of Cork Oak ( Quercus suber L.). EFI Proceedings 56, 71-84. SÁNCHEZ-GONZÁLEZ M., CAÑELLAS I., MONTERO G., RÍO M., 2006. Distance independent tree diameter growth model for cork oak stands. For Ecol Manage 225, 262-270. SÁNCHEZ OROIS S., RODRÍGUEZ SOALLEIRO R., 2002. Modelling the growth and management of mixed uneven-aged maritime pine-broadleaves species forests in Galicia (Northwestern Spain). Scan J For Res 17 (6), 538-547.
69 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 70
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
SÁNCHEZ-PALOMARES O., SÁNCHEZ-SERRANO F., 2000. Mapa de la Productividad Potencial Forestal de España. Cartografía Digital. Ed. Ministerio de Medio Ambiente. Dirección General de Conservación de la Naturaleza. Madrid. [In Spanish]. SÁNCHEZ-RODRÍGUEZ F., 2001. Estudio de la calidad de estación, crecimiento, pro - ducción y selvicultura de Pinus radiata D. Don en Galicia. Doctoral thesis. Universidad de Santiago de Compostela, Lugo. [In Spanish]. SÁNCHEZ-RODRIGUEZ F., ESPAÑOL E., LÓPEZ C.A., MERINO A., RODRÍGUEZ-SOALLEIRO R., 2002. Influence of edaphic factors and tree nutritive status on the productivity of Pinus radiata D. Don plantations in northwestern Spain. For Ecol Manage 171, 181-189. SÁNCHEZ-RODRÍGUEZ F., ÁLVAREZ-GONZÁLEZ J. G., CASTEDO F., GOR - GOSO J., LÓPEZ-SÁNCHEZ C., RODRÍGUEZ-SOALLEIRO R., ROJO A., 2003. Crecimiento y tablas de producción de Pinus radiata D. Don en Galicia. Invest Agrar: Sist Recur For 12(2), 65-83. [In Spanish]. SANTA REGINA I., 2000. Organic matter distribution and nutrient fluxes within a sweet chestnut ( Castanea sativa Mill.) stand of the Sierra de Gata, Spain. Ann For Sci 57, 691-700. SANTA REGINA I., CALVO R., TARAZONA T., 1997. Aboveground biomass in a beech forest and a scots pine plantation in the Sierra de la Demanda area of northern Spain. Ann Sci For 54, 261-269. SANTALLA M., 2010. Empleo de cenizas de las industrias de tableros como restitu - yente de nutrientes en plantaciones aclaradas de Pinus radiata D. Don. Doctoral the - sis. Universidad de Santiago de Compostela, Lugo. [In Spanish]. SANTAMARÍA J.E., CASTEDO-DORADO, F., FERNÁNDEZ MANSO A., 2009. Tablas de producción de selvicultura media observada para el pino pinaster de la Sierra del Teleno (León). 5º Congreso Forestal Español, Ávila, Septiembre 2009. [In Spanish]. SCHRÖDER J., ÁLVAREZ GONZÁLEZ J.G., 2001. Comparing the performance of generalized diameter-height equations for maritime pine in Northwestern Spain. Forstw Cbl 120, 18-23. SCHRÖDER J., GADOW K. v., 1999. Testing a new competition index for maritime pine in northwestern Spain. Can J For Res 148, 7-17. SCHRÖDER J., RODRIGUEZ SOALLEIRO R., VEGA ALONSO G., 2002. An age- independent basal area increment model for maritime pine trees in northwestern Spain. For Ecol Manage 157 (1-3), 55-64. SEVILLANO-MARCO E., CASTEDO-DORADO F., FERNÁNDEZ-MANSO A., 2009. Development and applications of a growth model for Pinus radiata D. Don plantations in El Bierzo (Spain). Invest Agrar: Sist Recur For 18(1), 64-80. [In Spanish]. SNOWDON P., 2002. Modeling Type 1 and Type 2 growth responses in plantations after application of fertilizer or other silvicultural treatments. For Ecol Manage 163, 229–244.
70 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 13/03/12 18:53 Página 71
GROWTH AND YIELD MODELS IN SPAIN : H ISTORICAL OVERVIEW , C ONTEMPORARY EXAMPLES AND PERSPECTIVES
SOARES P., TOMÉ M., 2001. A tree crown ratio prediction equation for eucalypt plan - tations. Ann For Sci 58, 193-202. SOARES P., TOMÉ M., 2007. Model evaluation: from model components to sustainable forest management indicators. Cuadernos SECF 23, 27-34. SOARES P., SKOVSGAARD J.P., TOMÉ M., VANCLAY J.K., 1995. Evaluating a growth model for forest management using continuous forest inventory data. For Ecol Manage 71, 251-265. SOLLA F., 2004. Aplicación de cenizas de biomasa arbórea como fertilizante y enca - lante de plantaciones forestales en Galicia. Doctoral thesis. Universidad de Santiago de Compostela, Lugo. [In Spanish]. SOLLA F., MERINO A., RODRÍGUEZ SOALLEIRO R., SANTALLA M., 2006. Nutritional status and growth of a young Pseudotsuga menziesii plantation in a temperate region after application of wood-bark ash. For Ecol Manage 237, 312- 321. TORRE M., 1994. Degradación inducida por algunas prácticas agrarias tradicionales. El caso de los rebollares ( Quercus pyrenaica Willd.) de la provincia de León. Doctoral thesis. Universidad Politécnica de Madrid. [In Spanish]. TORRES ÁLVAREZ E., CALZADO CARRETERO J.A., SUÁREZ M.A., VÁZQUEZ PIQUÉ J., 2004. Dispositivo experimental para el estudio de la influencia de los fac - tores ambientales y silvícolas sobre el crecimiento de alcornoque. Cuadernos SECF 18, 261-268. [In Spanish]. TRASOBARES A., PUKKALA T., 2004a. Optimising the management of uneven-aged Pinus sylvestris L. and Pinus nigra Arn. mixed stands in Catalonia, north-east Spain. Ann For Sci 61 (8), 747-758. TRASOBARES A., PUKKALA T., 2004b. Using past growth to improve individual- tree diameter growth models for uneven-aged mixtures of Pinus sylvestris L. and Pinus nigra Arn. in Catalonia, north-east Spain. Ann For Sci 61, 409-417. TRASOBARES A., MIINA J., PUKKALA T., 2004a. Growth and yield model for uneven-aged mixtures of Pinus sylvestris L. and Pinus nigra Arn. in Catalonia, north-east Spain. Ann For Sci 61 (1), 9-24. TRASOBARES A., MIINA J., TOMÉ M., 2004b. Growth and yield model for Pinus halepensis Mill. in Catalonia, north-east Spain. For Ecol Manage 203 (1-3), 49-62. VALBUENA P., BRAVO F., 2005. Diagramas para el manejo de la densidad de rodales de pino carrasco ( Pinus halepensis Miller) en la zona catalana interior y aragonesa. IV Congreso Forestal Español. 26-30 de septiembre. Zaragoza. [In Spanish]. VALBUENA P., BRAVO F., DEL PESO C., 2008. Stand Density Management Diagrams for two Mediterranean pine species in Eastern Spain. Invest Agrar: Sist Recur For 17(2), 97-104. VALERO MORENO J., 1998. Experiencias de producción de resina mediante el méto - do de “pica de corteza descendente con estimulación continua con pasta zeta” en Cataluña. Proc. 1er Simposio de aprovechamiento de resinas naturales. Segovia, Spain, Feb. 5-7. [In Spanish].
71 GrowthYield Spain Corregido Tablas 3- 5º DEFINIT_GROWTH AND YIELD 04/04/12 19:42 Página 72
GROWTH AND YIELD MODELS IN SPAIN: HISTORICAL OVERVIEW, CONTEMPORARY EXAMPLES AND PERSPECTIVES
VANCLAY J.K., 1994. Modelling forest growth and yield. Applications to mixed tropi- cal forests. CAB International, Wallingford, 312 p. VANCLAY J.K., 1995. Growth models for tropical forests: a synthesis of models and methods. For Sci 41, 7-42. VANCLAY J.K., SKOVSGAARD J.P., 1997. Evaluating forest growth models. Ecol Model 98, 1-12. VANNIÈRE B., 1984. Tables de production pour les forêts françaises. E.N.G.R.E.F., I.N.R.A., O.N.F. 2ª Ed. Ecole Nationale du Génie Rural, des Eaux et des Forêts. Nancy. 158 pp. [In French]. VÁZQUEZ PIQUÉ J., 2002. Modelos predictivos de producción de corcho y detección precoz de la calidad. Doctoral thesis. Universidade Técnica de Lisboa. Lisboa. VÁZQUEZ-PIQUÉ J., SUAREZ M.A., TAPIAS R., TORRES E., 2008. Influence of sil- viculture and environment on cork+wood growth based on band dendrometer data. In: Suberwood. New challenges for the integration of cork oak forests and products. (Vázquez-Piqué J., Pereira H. González-Pérez A., eds). University of Huelva. pp. 183-194 VEGA J.A., FERNÁNDEZ C., FONTURBEL T., PÉREZ-GOROSTIAGA P., 2010. Response of maritime pine (Pinus pinaster Ait.) recruitment to fire severity and post- fire management in a coastal burned area in Galicia (NW Spain). Plant Ecol 206(2), 297-308. WESTFALL J.A., ALLEN H.L., BURKHART H.E., 2004. Young stand growth modelling of intensively-managed loblolly pine plantations in Southeastern US. For Sci 50(6), 823-835. WILSON J.S., OLIVER C.D., 2000. Stability and density management in Douglas-fir plantations. Can J For Res 30, 910–920. WOOLLONS R.C., 1998. Even-aged stand mortality estimation through a two-step regression process. For Ecol Manage 105,189-195. WYKOFF W.R., 1990. A basal area increment model for individual conifers in the Northern Rocky Mountains. For Sci 36(4), 1077-1104.
72 73 Edition funded by: Instituto Universitario de Investigación en GESTIÓN FORESTAL SOSTENIBLE Universidad de Valladolid-INIA
Instituto Nacional de Investigación Universidad de Valladolid y Tecnología Agraria y Alimentaria
www.research4forestry.eu
UNIDAD DE GESTIÓN FORESTAL SOSTENIBLE Universidad de Santiago de Compostela
www.usc.es/uxfs
Red temática sobre Selvicultura y Gestión Sostenible de los Sistemas Forestales (SELVIRED)
Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria www.inia.es/selvired