ABSTRACT. The choice between different forest management practices is a crucial step in short, medium, and long-term decision making in forestry and when setting up measures to support a regional or national forest policy. Some conditions such as biogeographically determined site factors, exposure to major disturbances, and societal demands are predetermined, whereas operational processes such as species selection, site preparation, planting, tending, or thinning can be altered by management. In principle, the concept of a forest management approach provides a framework for decision making, including a range of silvicultural operations that influence the development of a stand or group of trees over time. These operations vary among silvicultural systems and can be formulated as a set of basic principles. Consequently, forest management approaches are essentially defined by coherent sets of forest operation processes at a stand level.Five ideal forest management approaches (FMAs) representing a gradient of management intensity are described using specific sets of basic principles that enable comparison across European forests. Each approach is illustrated by a regional European case study. The observed regional variations resulting from changing species composition, stand density, age structure, stand edges, and site conditions can be interpreted using the FMA framework. Despite being arranged along an intensity gradient, the forest management approaches are not considered to be mutually exclusive, as the range of options allows for greater freedom in selecting potential silvicultural operations. As derived goods and services are clearly affected, the five forest management approaches have implications for sustainability. Thus, management objectives can influence the balance between the economic, ecological, and social dimensions of sustainability. The utility of this framework is further demonstrated through the different contributions to this special issue.

While sustainable forestry in Europe is characterized by the provision of a multitude of forest ecosystem services, there exists no comprehensive study that scrutinizes their sensitivity to forest management on a pan-European scale, so far. We compile scenario runs from regionally tailored forest growth models and Decision Support Systems (DSS) from 20 case studies throughout Europe and analyze whether the ecosystem service provision depends on management intensity and other co-variables, comprising regional affiliation, social environment, and tree species composition. The simulation runs provide information about the case-specifically most important ecosystem services in terms of appropriate indicators. We found a strong positive correlation between management intensity and wood production, but only weak correlation with protective and socioeconomic forest functions. Interestingly, depending on the forest region, we found that biodiversity can react in both ways, positively and negatively, to increased management intensity. Thus, it may be in tradeoff or in synergy with wood production and forest resource maintenance. The covariables species composition and social environment are of punctual interest only, while the affiliation to a certain region often makes an important difference in terms of an ecosystem service's treatment sensitivity.

Aim of study: We aim at (i) developing a reference definition of mixed forests in order to harmonize comparative research in mixed forests and (ii) review the research perspectives in mixed forests.Area of study: The definition is developed in Europe but can be tested worldwide.Material and Methods: Review of existent definitions of mixed forests based and literature review encompassing dynamics, management and economic valuation of mixed forests.Main results: A mixed forest is defined as a forest unit, excluding linear formations, where at least two tree species coexist at any developmental stage, sharing common resources (light, water, and/or soil nutrients). The presence of each of the component species is normally quantified as a proportion of the number of stems or of basal area, although volume, biomass or canopy cover as well as proportions by occupied stand area may be used for specific objectives. A variety of structures and patterns of mixtures can occur, and the interactions between the component species and their relative proportions may change over time.The research perspectives identified are (i) species interactions and responses to hazards, (ii) the concept of maximum density in mixed forests, (iii) conversion of monocultures to mixed-species forest and (iv) economic valuation of ecosystem services provided by mixed forests.Research highlights: The definition is considered a high-level one which encompasses previous attempts to define mixed forests. Current fields of research indicate that gradient studies, experimental design approaches, and model simulations are key topics providing new research opportunities.Keywords: COST Action; EuMIXFOR; mixed-species forests; admixtures of species.

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Modelling growth of trees or stands when age is not available is often necessary. This is the case in national forest inventories or when age is not a main determinant of growth (e.g., trees growing in uneven-aged stands). Even if age is not known, functions used to model growth should follow the required pattern, with a maximum and a slow decline after the maximum is attained. There are some empirical functions with these properties; however, direct modelling with difference equations derived from the so-called theoretical growth functions has not been used for this purpose, as they are age dependent. This paper presents a methodology to formulate growth functions as ageindependent difference equations. These can be used when age is not available or is not relevant. The proposed equations have the advantage of allowing the direct modelling of yield instead of growth. If the parameters are expressed as a function of site variables, the equations are invariant for projection length and therefore can be used when data is not equally spaced in time, as is the case of most data sets. The methodology is applied to the Lundqvist and Richards growth functions, the most commonly used in growth and yield modelling. The use of the age-independent growth functions is illustrated by using two case studies in Portugal: dominant height growth of eucalyptus (Eucalyptus globulus Labill.) plantations and individual tree growth in diameter at breast height in sparse cork oak (Quercus suber L.) stands.Résumé : La modélisation de la croissance des arbres ou des peuplements est souvent nécessaire alors que l'âge n'est pas disponible. C'est le cas pour les inventaires des forêts nationales ou lorsque l'âge n'est pas le déterminant principal de la croissance, par exemple, dans le cas des arbres croissant dans des peuplements inéquiennes. Même si l'âge n'est pas connu, les fonctions utilisées pour modéliser la croissance devraient obligatoirement suivrent un patron comportant un maximum suivi d'un lent déclin une fois le maximum atteint. Il existe quelques fonctions empiriques ayant ces propriétés. Pourtant, la modélisation directe à l'aide d'équations différentielles dérivées de fonctions de croissance dites théoriques n'a jamais été utilisée à cet effet, car elles sont toutes dépendantes de l'âge. Cet article présente une métho-dologie pour formuler des fonctions de croissance sous forme d'équations différentielles indépendantes de l'âge et utilisables lorsque l'âge n'est pas disponible ou n'est pas pertinent. Les équations proposées ont l'avantage de permettre une modélisation directe du rendement au lieu de la croissance. Si les paramètres sont exprimés en fonction de variables de site, les équations sont indépendantes de l'étendue de la projection et peuvent donc être utilisées lorsque les données ne sont pas espacées régulièrement dans le temps, comme c'est le cas de la plupart des jeux de données. La méthodologie est appliquée aux fonctions de croissance de Richards et de Lundqvist qui sont les plus souvent utilisées pour modélis...

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