Pinogram : a pine growth area model

Ideas about forest and forestry in the Netherlands have changed in recent years, partly because nature and recreation are in greater demand, partly because of growing environmental problems (air pollution, global warming) and partly because of the decrease in forest area worldwide. This has led to a change in the government's forest policy (Anonymus 1985, 1986, 1990). Ile current aim is to achieve a more natural-looking forest (uneven aged, mixed, native species) and to have forest management linked to natural processes and which, while cheaper, has more benefits.

As a result of this shift in policy, forestry is expected to change significantly. In the first place, silvicultural practices in Dutch forests will be aimed at achieving a more continuous forest. Clear-cutting and large plantations will be replaced by silvicultural systems in which the cutting and regeneration processes are extended over several decades and in which mixing of species plays an important role. The management of such uneven-aged and mixed forests will have to be based much more on knowledge of the behaviour of the individual tree and its *interaction with the biotic and abiotic environment than is currently the case in even-aged and pure forests.

To be able to achieve the desired changes in composition, functions and management of the Dutch forests successfully, it will be necessary to make use of the natural dynamics and developmental processes of forests. However, our current knowledge of these is certainly not complete, or is not appropriate to the Dutch *situations or has not yet been translated in silvicultural strategy. There is a clear need to find out more about forest dynamics under specific Dutch circumstances.

Forest dynamics may be studied with the help of the *autoecology and *synecology of the different forest components. Because trees are the main components establishing forest architecture, it seems rational to start by investigating the autoecology and synecology of trees. The research presented here was directed at the Scots pine ( Pinus sylvestris L.), the most common tree species in the Netherlands. It aimed at developing silvicultural information diagrams for Scots pine for different sites, provenances and treatment (tree and stand history). Silvicultural information diagrams should give information on characteristics such as *tree architecture, crown form and -dimensions, stem form, stem diameter and stem volume, and the likelihood of flowering and fructification, disease and damage and their consequences.

In principle an infinite number of silvicultural information diagrams is possible; therefore, it is necessary to determine the influence of age, site, provenance and treatment on the *phenotype of a tree to fulfil the above aim. If these relations are known, the above aim can be achieved by developing an interactive model, in which the user can input age, site, provenance and treatment. Because the model should be dependent upon tree history and age, it was decided to develop a *growth model.

Growth models may be classified according to the hierarchical levels of their output; for instance the levels "organ", "organism", "*eco-unit" and silvatic-mosaic as defined by Oldeman (1990). Growth models rarely involve more than two levels. Growth may be understood as a process which is steered by growth factors inherent in a certain starting *situation and driving it towards a new situation over time. The starting situation may be understood as a *system of a certain hierarchical level, built up from subsystems of a lower hierarchical level. Growth models on a level between "organ" and "organism" have been developed by Aono and Kunii (1984), De Reffye et al. (1989) and others. Models such as those in the "JABOWA-family" (Botkin in West et al. 1981) mainly involve the levels "eco-unit" and "silvatic-mosaic". "Spatial models" (Hara 1988) are usually at the "organism" and "eco-unit" level.

As well as being classified according to the hierarchical levels mentioned, growth models may also be classified as physiological models, architectural models and mathematical models. This classification roughly indicates the method used to describe or declare the *situations or processes the model is dealing with. Physiological models are based on physiological processes; a process is described as the result of interacting underlying processes (see De Wit 1965, Borman and Likens 1979, Hari et al. 1985, Mohren 1987). Architectural models are based on the structural appearance of a *system, in which the appearance of a system (e.g. *silvatic-mosaic, *eco-unit, organism) is defined by the pattern and appearance of the subsystems (respectively eco-units, organisms, organs). Examples of these are the models developed by Aono and Kunii (1984), De Reffye et al. (1989), Koop (1989) and others. Mathematical growth models describe the changes in the appearance of a system over time and in relation to factors that probably influence these changes. Generally, correlations and not causal relations are used to find growth equations. The "spatial" and "nonspatial" models (see Hara 1988) can be classified as mathematical models.

Because a silvicultural information diagram should demonstrate the temporal changes of the *phenotype of a tree, the model should involve both the levels between "organism" and "eco-unit" The phenotype of a tree depends upon its "*normal growth" and also upon favourable and stress factors. "Normal growth" is defined by the genetic characteristics of a tree, by a more or less constant site quality and climate during its lifetime and by *competition for light, water and nutrients. Stress factors may be diseases and plagues, environmental pollution and damage by, for example, temporary climate extremes. Favourable factors may be fertilization, changing soil water supply, immigration of mycorrhiza, etc.

The model presented here has been restricted to "normal growth". Competition is understood as competition for qualified space and constraints are not defined (e.g. available light, water or nutrients). One of the most important ways of influencing tree growth is to provide more space by cutting neighbouring trees. The model does indeed show large similarities with "spatial" models.

The models present in the current literature are either related to another hierarchical level, or do not deal with crown growth or with the *growing space of individual trees and the architecture of the "*eco-unit" Therefore none of them are really appropriate for creating a silvicultural information diagram for the different circumstances required. This is why a new model is needed.

Using information from the literature and data from an old provenance trial in Kootwijk (Province of Gelderland, the Netherlands), the influence of genetic traits, site, growing space, age and phenotype on the growth of trees was studied. It was found that the height growth of trees is mainly defined by *genotype, site characteristics and climate and that *radial growth is mainly defined by height growth and growing space. It still seems impossible to precisely predict the height growth of an individual tree during its life time. But it is probably possible to forecast the mean height growth and standard deviation for a tree of a certain provenance and on certain site.

In order to calculate the influence of the *growing space on the radial growth of trees a field study was done, in which diameter, crown length, crown width, tree height, volume, age and *normal growth area of 158 trees divided over 13 stands were measured once. The normal growth area is defined as the area in which a tree has more competitive power than its neighbours. It is calculated with the help of the distances from the *sample tree to its neighbouring trees, the distances between the consecutive neighbours and the heights of all these trees. Non-linear regression was used to correlate crown length, mean crown width and stem diameter with tree height, age and mean *growth area vector. The resulting correlations were sufficiently good to enable growth equations to be derived.

A good non-linear correlation, based on 38 felled trees, was also found between form factor on the one side and tree length, crown length and diameter on the other side. In the resulting regression equation the crown length defines the form factor better than tree length does. A reasonably good non-linear correlation was also found between mean branch diameter in the lower part of the crown and tree length, crown length and mean crown width.

The derived growth equations were used to develop a growth simulation program, called "PINOGRAM". This program, written in "Microsoft C, visualizes the growth of individual trees in relation to the *competition they experience.

In the PINOGRAM program growth is simulated in a *transect of 50 * 20 metres. The user first enters the planting distance within a row and between rows. He must also enter a minimum and maximum *S value. These values are defined as respectively the minimum and maximum heights that a tree of a certain provenance on a certain site can reach at infinite age. In *homogeneous stands the minimum and maximum S value do not differ greatly, in contrast with *heterogeneous stands. The program then assigns to each tree an S value S _tree according to a normal distribution and a confidence interval of 95% between minimum and maximum S values. Finally, the user must enter the age at which he wants to see the transect.

The program calculates the height of each tree (called: sample tree) at the given age according to the Chapman-Richards function. Using the heights of a sample tree and its neighbours and the distances between these trees, the *normal growth area vectors between the sample tree and its neighbours are calculated first. Next the extent to which the trees can use these normal growth area vectors is calculated. This depends upon the possible crown length increment in the direction of the neighbour within the given time interval and without *competition (= *potential growth area vector). The normal growth area vectors and the potential growth area vectors of the sample tree and its neighbours are used to calculate the *maximum growth area that the sample tree can occupy (= maximum growth area vector). The perpendiculars of the maximum growth area vectors include the maximum growth area. Within this maximum growth area, new *maximum growth area vectors are calculated in sixteen compass points (N, NNE, NE, ENE, E, etc.). In order to find the growth area actually occupied (= * actual growth area), the potential growth area vectors in these sixteen directions are also calculated. The *actual growth area vectors are derived from the minimum of the maximum growth area vectors and the potential growth area vectors.

The actual growth area vectors are used to calculate the diameter, the crown length and crown width in sixteen directions. Next, form factor, volume and mean branch diameter (in the lower part of the crown) can be computed per tree and finally also the yield data per ha and the *canopy closure are computed. Now all the necessary data for drawing a crown map, a profile diagram or a threedimensional picture of the transect are available.

After one *situation has been computed and the crown map has been drawn, a new age can be entered and the user can request some trees to be felled. He can choose between *manual thinning (the user points out which trees have to be removed) and *automatic thinning (the user indicates whether a low thinning or a *high thinning has to be carried out and how many m ³have to be removed. At high thinning the user can indicate the critical h/cl ratio, at which a neighbouring tree should be removed). Natural mortality of a tree occurs when the tree height divided by the mean crown width of a tree exceeds six (= mortality factor M). The trees selected to be thinned are removed and now the heights and *growth areas of the remaining trees are calculated at the new age, from which the new tree dimensions are then derived.

The program displays information about stem number per ha, stem distribution, crown length and crown width, crown asymmetry, canopy closure and tree height by means of a crown map, profile diagrams and three-dimensional drawings. Underneath it displays a table showing data on the tree height, stem diameter, form factor, mean branch diameter in the lower part of the crown for individual trees, plus data on stem number per ha, basal area per ha and volume per ha of the remaining stand and of thinnings. Note that growth performance according to the equations as used in the model results in a mean expected growth for an individual tree at a given thinning regime.

This growth simulating program enables the growth of individual trees within a stand to be depicted graphically. Different silvicultural systems can be applied, to study their effects on stand growth. The graphical design makes this insight very communicable and useful (for instance, for teaching). And the results can be used in further modelling (for example, in a model of stand structure and light, or of cost and benefit, or of silvicultural system and timber quality).

The growth equations used in the model cannot be used directly on real trees. The *normal growth area of a tree, as measured in the field, often differs from the *actual growth area the tree is using at that moment. The actual growth area can be calculated using the crown widths measured in sixteen directions, but generally the matching crown lengths and diameters calculated differ from the measured ones, because these tree dimensions are not 100% correlated with age, height and actual growth area.

The model has only been tested for Scots pine on the Veluwe. It does not yet give information about *tree architecture, stem form, flowering and consequences of damage, diseases, climatic changes and environmental pollution. In its present form it also cannot yet be applied to mixed and uneven-aged stands. There is scope for improvement; fruitful avenues of future research are suggested in section 5.3.