VANCLAY (1994) states that a model is an abstraction or a simplified representation of some
aspect of reality and classifies forest growth models as elements of one of three groups. Firstly, models for prediction (whole stand models, size class models and single tree models); secondly, models for understanding (eco-physiological process models and succession models) and thirdly hybrid models. For a detailed review of forest growth models see PORTE
&BARTELINK (2002).
Whole stand models. Whole stand models are used to predict yields in pure even-aged stands (BURKHART &TOME 2012). The development of whole stand models covered the period from
the end of the 18th century to the second half of the 20th century. The progress and evolution of whole stand models can be divided into four stages: (i) experience tables of the yield, (ii) standardized yield tables, (iii) computer supported yield table models and (iv) stand growth simulators (PRETZSCH 2009). First generation yield tables were developed mainly in the late
18th and the 19th centuries by PAULSEN (1795), HARTIG (1795), COTTA (1821), PRESSLER
(1865, 1870, 1877) and SMALIAN (1837) (all cited in PRETZSCH 2009). These yield tables
were characterised by unsatisfactory databases, regional limitations and limited compatibility due to the different methods used (PRETZSCH 2009).
In the end of the 19th century, the Association of German Research Stations decided on the
framework for the composition of yield tables and set a basic standard on which a new generation of standardized yield tables could emerge (PRETZSCH 2009), see for example the
forest yield tables presented by SCHIFFEL (1904), SCHWAPPACH (1908), MATULIONIS (1924)
and WIEDEMANN (1936/1942).
In the second half of the 20th century computer-supported yield table models emerged. These models had, as a core element, a biometric model in the form of a flexible system of mathematical equations, which could be parameterised using data from study sites (ASSMANN
CHAPTER 2: SCIENTIFIC BACKGROUND
13 (1968), REPŠYS et al. (1983) and KULIEŠIS (1993) all contributed significantly to thedevelopment of these type of yield tables and models.
The fourth generation stand growth simulators are shaped as computer programs that are capable of predicting stand development under a variety of site conditions for different initial stem numbers and management regimes (PRETZSCH 2009). In Lithuania, the yield model
developed by KULIEŠIS (1993) formed the basis of the stand growth simulator model
KUPOLIS, which is able to predict the dynamics of forests resources under different forest management, economic and environmental conditions (PETRAUSKAS &KULIEŠIS 2004).
PENG (2000) argues that whole stand models have some important shortcomings. Yield tables
do not provide any size-class information needed to evaluate various utilization options and cannot be used to analyse a wide range of stand silvicultural treatments.
Size class models. Size-class models for even-aged stands generate future diameter distributions (stand tables) according to an initial measured diameter distribution (BURKHART
& TOME 2012). Size class models represent a compromise between stand models and
individual tree models, since they expand the computational effort of stand models and reduce the level of detail required in a single tree model (GADOW &GANGYING 1999). When only
one class exists the method is a whole stand approach and then each tree is considered because the single class method is a single tree approach (VANCLAY 1994).
Size class models are divided into three groups: (i) advanced stand models based on a system of differential equations, (ii) transition matrices and (iii) models based on progressive distributions (VANCLAY 1994, PRETZSCH 2009).
Growth and yield in even-aged stands is simply a function of site quality, stand age and stand density. Stand density is a function of site quality, age and initial density. Indicators of site quality are a function of age (BURKHART & TOME 2012). These functions are some of the
elements that comprise the system of differential equations.
Matrix models consist of three parts: a matrix of forest areas that describe the state of the forest; a set of transition probabilities that under different treatments governs the transition of areas between the elements of the matrix, and lastly a set of activities (see SALLNÄS 1990).
Progressive distributions, as PRETZSCH (2009) explains describe a stand according its trees’
diameters and height distributions and models the stand’s development as a periodic progression of these frequency distributions. For typical examples of progressive distribution models see VANCLAY (1989), HAUHS et al. (1995), GADOW &GANGYING (1999),PENG et al.
CHAPTER 2: SCIENTIFIC BACKGROUND
14 By evaluating size class models, PENG (2000) states that these models require only overallstand values as input, provide detailed size-class information as output, but are insufficiently flexible to evaluate a broad range of stand silvicultural treatments.
Single tree level simulators (STLS) represent a stand as a mosaic of trees and simulate the growth of each single tree (MUNRO 1974). These models represent a much higher level of
resolution (NEWNHAM 1964, WYKOFF et al. 1982) that enables researchers to simulate mixed
or pure stands of different age and structures, thus providing more flexible possibilities for forest management (PRETZSCH et al. 2002). The STLS comprise two groups: distance
dependent, that use actual stem positions and distance independent that do not (MUNRO 1974).
Distance independent STLS use crown competitor factor (KRAJICEK et al. 1961) as a quotient
that reduces maximum possible diameter increment to certain conditions (ARNEY 1972) or
directly estimates competition effects to tree diameter increment. Examples of distance independent models are PROGNOSIS developed by STAGE (1973), STAND PROGNOSIS
MODEL developed by WYKOFF et al. (1982), and PROGNAUS developed by MONSERUD &
STERBA (1996), STERBA &MONSERUD (1997), and STERBA et al. (2002).
Newnham (1964) developed the first distance dependent approach that used potential tree diameter growth and then reduced it to a particular status by applying competition index (CI). EK & DUDEK (1980) in a review of forest modelling state that up to 1980 the majority of
forest growth models were based on this approach, see for example HEGYI (1974) and
DANIELS et al. (1979). Various modellers have, since 1980, continued to use the distant
dependent approach, such as WENSEL et al. (1987), DANIELS & BURKHART (1988), and
specific models like PTAEDA2 (BURKHART et al. 1987), MOSES (HASENAUER 1994), and
SILVA, (PRETZSCH 1992, PRETZSCH 2002, PRETZSCH et al. 2002).
Parallel to approaches that predict potential tree growth according to modifiers, an approach has been developed that uses distance dependent competition indices (CIs) to estimate competition effects to tree diameter increment, STAND model, (PUKKALA 1987, PUKKALA et
al. 1994a, PUKKALA et al. 1994b, PUKKALA et al. 1998), and BWINPro model, (NAGEL 1999,
DÖBBELER et al. 2007).
Individual tree models provide maximum detail and flexibility for evaluating alternative utilization options and stand treatments; however, these models are more expensive to develop and require a more detailed database to implement (PENG 2000).
Eco-physiological process models. Process models are essential scientific tools, providing a framework that connects disparate pieces of information and knowledge (MÄKELÄ et al.
CHAPTER 2: SCIENTIFIC BACKGROUND
15 2000). They are based on basic physical, chemical, and eco-physiological relationships and provide information about carbon, nitrogen, and water cycles, supporting comprehensive understanding and management of ecosystems (PRETZSCH 2009).BARTELINK (2000) developed the process based model COMMIX on three major
assumptions: radiation is crucial in growth, the dry matter production of a tree is related to the radiation it absorbs and the partitioning of the dry matter growth over the biomass components is dependent both on tree state and on growing conditions. The same structural patterns are found in the process based model BALANCE, developed by GROTE &PRETZSCH
(2002). However, as PRETZSCH et al. (2008) contend, eco-physiological process models have
not reached their potential to predict future trends because as “Yet, actual forest yield predictions without guiding empirical functions are not yet very precise”.
Succession models (gap models). Gap models are, as PRETZSCH (2009) explains, used to
investigate competition and succession processes in near natural forest stands, to predict long- term succession patterns in unmanaged forest stands and to promote ecological understanding of biomass production during the succession. BUGMANN (2001) in an overview of gap models
underlines their four assumptions: (i) the forest stand is abstracted as a composite of many small patches of land with different ages or succession stages, (ii) patches are horizontally homogeneous, with no exact tree positions within the patch, (iii) the leaves of each tree are located in an indefinitely thin layer (disk) at the top of the stem, and (iv) successional processes in each patch are described independently, with no interactions. Typical examples of gap models are JABOWA (BOTKIN et al. 1972), FINNFOR (KELLOMÄKI et al. 1993,
KELLOMÄKI & VÄISÄNEN 1997), SORTIE (PACALA et al. 1993, PACALA et al. 1996), and
FORSKA-M (LINDNER et al. 1997, LANDSBERG &COOPS 1999).
Gap models also provide output data relevant to forest management like diameter, height and volume development of individual trees or stands, yet, input and output variables are less suited to forest management demands (PRETZSCH 2009).
Hybrid models. MÄKELÄ et al. (2000) states that hybrid models advantageously contain both
causal and empirical elements. Hybrid models have, as PRETZSCH (2009) explains, functions
that estimate the productivity of biomass and wood volume in relation to primary factors like precipitation, leaf nitrogen content, temperature, and radiation. PENG et al. (2002) argue that
while it is almost always possible to find an empirical model that fits better to certain data than process based models, empirical and process models can be joined into hybrid models to avoid to some extent the shortcomings of both approaches. BATTAGLIA &SANDS (1998) state
CHAPTER 2: SCIENTIFIC BACKGROUND
16 that the needs of potential users of forest models are so various that empirical models can hardly satisfy all of them. PENG (2000) argues that due to the challenges of forest research inthe future (predictions of growth and yield, of mixed species, forest responses to environmental changes) the hybrid approach may be useful. A representative hybrid model is TRIPLEX developed by PENG et al. (2002). Yet, hybrid models, as PRETZSCH et al. (2008:
1071) have little practical use, as “neither gap models nor hybrid models have been found reliable enough to reach any practical relevance as management tools”.
To conclude, whole stand models as well as size class models are appropriate to predict yields in pure even-aged stands. STLS are used to simulate the growth of mixed or pure stands of different age and structures. Eco-physiological process models support comprehensive understanding and management of ecosystems. Succession or gap models are used to investigate succession processes and to predict long-term succession patterns. Hybrid models are used for the prediction and understanding of stand development. Taking into account the present status of research in Lithuania, development of STLS is recommended.