Reconstructing spatiotemporal dynamics of Central European natural beech forests: the rule-based forest model BEFORE

Forest Ecology and Management 194 (2004) 349–368

Reconstructing spatiotemporal dynamics of Central European natural beech forests: the rule-based forest model BEFORE Christine Rademachera, Christian Neuerta,1, Volker Grundmannb, Christian Wissela, Volker Grimma,* a

Department of Ecological Modelling, UFZ Centre for Environmental Research, Leipzig-Halle, P.O. Box 500 136, D-04301 Leipzig, Germany b Hessen-Forst FIV (Forsteinrichtung, Information, Versuchswesen), Gießen/Hannoversch Mu¨nden, Europastr. 10-12, D-35394 Gießen, Germany Received 14 March 2003; received in revised form 13 October 2003; accepted 27 February 2004

Abstract Without humans, large areas of central Europe would be covered by forests dominated by beech (Fagus silvatica). The spatiotemporal dynamics of natural beech forests are hence a subject of interest for both forest management and conservation. However, since in most regions there are no longer any natural beech forests, their structure and dynamics cannot routinely be analysed and compared to managed forests. The forest model BEech FOREst (BEFORE) is therefore, designed to reconstruct the spatiotemporal dynamics of natural beech forests. BEFORE is a grid-based and partly individual-based model which divides beeches into four different height classes. Changes to the forest structure due to growth, mortality and storm disturbances are entirely described by empirical ‘if-then’ rules. BEFORE is capable of reproducing two patterns which have been observed in remnants of natural beech forests: beech forests consist of a mosaic pattern of small areas (on average 0.3 ha) which are at different developmental stages; at the scale of these small areas, a cyclic succession of three developmental stages occurs, which are characterised by different vertical structures. One typical feature of natural beech forests is hence their very high structural diversity. Gaps in the canopy induce a local pulse of vitality and growth for younger beech trees. These pulses are spread into the vicinity by two mechanisms. Firstly, windfalls affect not only the site of the tree knocked over itself but also neighbouring sites due to the damage caused by the tree falling over. Moreover, since the light is diffuse and oblique, canopy gaps affect also vitality and growth in the neighbourhood of a gap. The results obtained with BEFORE show that natural beech forests achieve quasistationary dynamics, demonstrating considerable fluctuations in the forest structure. For example, the percentage of forest area at the optimal stage, which is characterised by a closed canopy and almost no understorey, varies between 10 and 40%, and after extreme storm events even between 0 and 60%. Beech forests with an inner area larger than 40 ha (corresponding to a total area of 70 ha) develop spatiotemporal dynamics which do not differ qualitatively or quantitatively from larger forests, but even very small natural beech forests would exhibit very high temporal and structural diversity. Thus, even small ‘islands’ of unmanaged stands within larger, managed forests would contribute significantly to providing structures typical of natural beech forests. # 2004 Elsevier B.V. All rights reserved. Keywords: Beech forest; Forest model; Spatial pattern; Disturbance; Synchronisation; Natural forest; Central Europe

*

Corresponding author. Tel.: þ49-341-235-2903; fax: þ49-341-235-3500. E-mail address: [email protected] (V. Grimm). 1 Present address: Deutsches Museum Verkehrszentrum, Museumsinsel 1, D-80538 Munich, Germany. 0378-1127/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.foreco.2004.02.022

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1. Introduction Both forest management and conservation biology are trying increasingly to gear their objectives and strategies to the structure and dynamics of natural forests. Conservation biology mainly focuses on natural structures. Coarse woody debris for example provides habitat for numerous species-rich communities and is assumed to improve environmental conditions at both local and regional scale (Reif, 1999/ 2000). Forest management strives to utilise natural processes within forests to maximise economic benefit (e.g. improved wood quality by self-selection within stands; reducing costs by natural regeneration), to minimise the impact of disturbances (e.g. pests and storms), and to optimise the environmental services of forests (e.g. the protection of forests in mountains). Therefore, natural forests are key study objects of forestry, ecology and biological conservation. In central Europe, natural forests would mainly be beech forests. Central Europe was comprised of woodlands in ca. 8000 BC. Beech (Fagus silvatica) began to expand at the end of the Neolithic and especially in the Bronze Age (ca. 5500–2500 BC); as of ca. 2000–500 BC, it became the dominating tree species (Lang, 1994). Beech tolerates a wide range of edaphic and climatic conditions. Casting heavy shade, it is also shade-tolerant, enabling it to outcompete other, less shade-tolerant species (Bohn, 1992; Pott, 1993; Peterken, 1996). However, due to intensive land use and management over the past 2000 years there are no natural beech forests left in central Europe except for few small areas such as in Bohemia and the Balkans. This means that managed beech forests cannot be easily and routinely compared to natural beech forests, making it difficult to assess the naturalness of managed forests. The exploration of the existing forest reserves containing beech forests in central Europe cannot fully supplant the analysis of larger, natural beech forests. Forest reserves are usually rather small and even the older reserves, which have been unmanaged for more than 100 years, still contain numerous traces of their management history. The existing natural beech forests in Eastern Europe, especially those in Bohemia (Korpel, 1995), have also been intensively studied. Important patterns have been identified and led to conceptual, verbal models of these forests’

dynamics (Leibundgut, 1993; Korpel, 1995; Peterken, 1996). Yet even these long-term studies encompass ‘only’ two or three decades, which is not much on the timescale of forest dynamics. Moreover, verbal models are difficult to test for completeness and consistency. For example, the verbal models are not sufficient to assess the temporal variability of spatial patterns identified as characteristic of natural beech forests. For all these reasons, the model BEech FOREst (BEFORE) was developed to integrate the existing knowledge of beech forests and to reconstruct the spatiotemporal dynamics of natural beech forests in central Europe (Neuert, 1999; Neuert et al., 2001; Rademacher et al., 2001; Rademacher and Grimm, 2002). The terms ‘virgin forest’ or ‘Urwald’ both refer to forests which have never been affected directly by humans. But since even the early beech forests in central Europe are very likely to have been influenced by humans (Lang, 1994), we prefer to use the term ‘natural’ (Peterken, 1996). The proximate objective of BEFORE is to identify those processes and structures in natural beech forests that determine their spatiotemporal dynamics and are thus responsible for the characteristic patterns observed in real forests. The ultimate objective is to answer the following questions: How large should forest reserves be to allow natural spatiotemporal dynamics to emerge? And how variable are the spatial and temporal patterns in natural beech forests? This paper presents the model BEFORE paying particular attention to these questions. In addition, it also addresses methodological issues of forest modelling. When developing BEFORE, the basic design decision was whether one of the numerous existing forest models should be used and tailored to beech forests. The problem is that many of the existing models focus on rather short time horizons and small plots and do not include natural regeneration (e.g. SILVA; Pretzsch, 2001; Pretzsch et al., 2002). And although other model types, for example gap models, have already been used successfully for modelling the long-term dynamics of large forests, they usually focus on species composition in mixed forests (e.g. Bugmann, 1994; Lischke et al., 2002) and not on spatial structures in monospecific forests. Therefore we decided to build a model from scratch which is able to cover large areas and time horizons, and which

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allows the user to focus on spatial structures and their dynamics. Our objective was to design BEFORE as a model of an idealised beech forest revealing typical general processes and structures. Therefore we did not include detailed data about the growth, demography or physiology of individual beech trees or specific forest stands. Instead, we based the model on empirical knowledge about the general behaviour of beech trees taken from the literature or based on our own empirical findings. BEFORE is entirely rule-based: every change in the forest’s structure is described by probabilistic ‘if-then’ rules which relate certain conditions (‘if’) to certain consequences (‘then’). The methodological issues addressed in this paper are thus: Is it at all possible to construct a realistic forest model which is entirely based on rules? How do we find the optimal degree of model resolution and complexity which is neither too coarse nor too detailed? The modelling strategy used to tackle the second issue was the approach of ‘pattern-oriented modelling’ (Grimm, 1994; Grimm et al., 1996; Grimm and Berger, 2003; Wiegand et al., 2003).

2. The model BEFORE 2.1. Patterns in natural beech forests The natural forests in the western Carpathian Mountains were studied extensively for example by Leibundgut (1993) and Korpel (1995). These forests are almost completely dominated by beeches. Old stands are mostly uniform in aspect with a closed canopy and almost no understorey. This structure, also typical of managed stands ca. 120 years old, is reminiscent of the interior of cathedrals or halls and is therefore referred to in German as ‘Hallenwald’. Despite its apparent uniformity, the ‘Hallenwald’ is highly structured. Trees of equal height and similar aspect often are of different age and die at different times. Therefore the ‘Hallenwald’ collapses asynchronously, leading to a small-scale texture, or mosaic, of patches which are at different stages of local development. These developmental stages have been described by various authors (see overview in Peterken, 1996, p. 172). Leibundgut (1993), for example, distinguishes between five different stages. In the following we

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refer to the three stages described by Korpel (1995): (1) growing-up stage, which is characterised by many juveniles undergoing rather slow growth and only a few older trees. When the canopy gaps are closed by the older trees or by juveniles growing into the canopy, the (2) optimal stage is reached, which has a closed canopy and no understorey (i.e. which constitutes the ‘Hallenwald’). Upon the collapse of canopy trees, the (3) decaying stage starts, in which the number and size of gaps increases and regeneration starts again. Finally, the decaying stage develops into the growing stage again. One entire cycle takes about 260 years. One decisive feature of the developmental cycle is that the vertical structure of local stands changes routinely between one-layered (optimal stage) and multi-layered. There are thus two patterns which seem to characterise natural beech forests: a mosaic pattern of small patches at different developmental stages, and a temporal pattern in the vertical structure. However, the developmental cycle is a highly simplified view of the forest dynamics. Stand development is disrupted by disturbances, mainly by storms. These disturbances damage the forest with different strengths at different times and different locations. Wind data from central Germany (Frankfurt/Main airport) indicate that nearly 90% of the storm events are not very strong and cause therefore only local damages of the size of one or two beech trees preventing any sort of large-scale synchronisation in the forest. Consequently, we have an ever changing pattern of small patches of different developmental stages. Only the rare (1%) very heavy storm events cause severe damage of nearly the whole forest area and therefore a temporary large-scale synchronisation of forest development. Other characteristics of natural beech forest (albeit ones which are discussed much less frequently than the mosaic pattern and the developmental cycle) are the heterogeneous age structure of the canopy, the distribution and abundance of very old or large trees, and of coarse woody debris (Peterken, 1996). None of these detailed elements of the structural diversity of natural beech forests, which are ignored in the aggregating concept of the developmental cycles, were used to develop and calibrate BEFORE. Instead, we focused solely on the two patterns emphasised in the literature about natural beech forests: the mosaic and the developmental cycle.

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2.2. Model structure To reconstruct the mosaic pattern, the model has to be spatially explicit and the spatial units of the model have to be considerably smaller than the typical size of mosaic patches (0.1–2 ha). Therefore, BEFORE is a grid-based model: space is divided into quadratic grid cells measuring about 14  14 m2 (7  7 grid cells correspond to 1 ha; thus, the area of a cell corresponds to the canopy size of one very large beech). According to the typical assumption of grid-based, gap or cellular automaton models, the position of trees is not considered explicitly within the cells. In order to capture how the vertical structure changes during the developmental cycle, four height classes are distinguished within a grid-cell. All the trees which fall within one height class are grouped together and are not distinguished any farther with regard to their height. Due to the potentially high number of individuals in the two lower height classes, only percentage cover is considered. In the upper two height classes, individual trees are distinguished. BEFORE is thus a grid-based and partly individualbased forest model. Because it is based exclusively on empirical rules, BEFORE is also a rule-based model.

Furthermore, it should be noted that BEFORE is a three-dimensional grid-based or cellular automaton model, whereas most grid-based models in ecology are two-dimensional. 2.3. State variables The four height classes within a grid cell are (Fig. 1A):  upper canopy: 30–40 m (maximum height of a beech tree).  lower canopy: 20–30 m  juveniles: 0.3–20 m  seedlings: up to 0.3 m In the upper and lower canopy, we model the growth of beech individuals, whereas in the two lower layers we only deal with percentages of cover due to the high number of individuals which may occur. The state of each cell is described by the following variables (Fig. 1A): 2.3.1. Upper canopy (height class 4) These are the canopy trees which have immediate and vertically unrestricted access to light. Up to eight

Fig. 1. (A) Visualisation of the four height classes distinguished in BEFORE. Note that in the two lower height classes no individuals are distinguished, and in the two upper height classes individuals are only characterised by the cover, or crown projection area, respectively. (B) Neighbouring cells of a focal cell (bold boundaries) which are relevant for calculating the light factor LF within the focal cell (see text, Section 3.5).

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beech trees may be present, each characterised by its age A4 and crown projection area, or cover, Cro. The cover area is quantified in units of 1/8 cell area. Thus, a giant beech can have a cover of 8/8 (cf. definition of cell size), or, at the other extreme, eight trees each with a Cro of 1/8 may be present. The variable F4 represents the total cover of the upper canopy trees in a cell (ranging from 0 to 100%, in steps of 12.5%). 2.3.2. Lower canopy (height class 3) This is a class of trees characteristic of beech forests: rapidly growing juvenile trees can almost reach the upper canopy. But if the canopy above them is closed they no longer receive enough light to grow. However, since beech is shade-tolerant, these trees, which are tall but slim and have a rather small crown, can survive at this stage for about 90 years. In analogy to sapling banks, they play an important role in closing canopy gaps quickly. Up to eight such loitering trees may be present, each characterised by age A3 and ‘residence’ time D3 spent in layer 3. We assume that trees of this height class have a cover of 1/8 cell area. The variable F3 represents the total cover of the lower canopy trees in a cell (ranging from 0 to 100%, in steps of 12.5%). 2.3.3. Juveniles (height class 2) Characterised by the total cover F2 of all trees of this height class; F2 ranges from 0 to 100%. 2.3.4. Seedlings (height class 1) Characterised by the total cover F1 of all trees of this height class; F1 ranges from 0 to 100%. The state of the model forest is completely described by these state variables in all cells of the forest. This means in particular that BEFORE only considers beech and no other species. Soil and climatic conditions are assumed to be homogeneous in space, and a flat topography is supposed. 2.4. Time step The model proceeds in time steps of 15 years, meaning that the changes of the state variables which occur within 15 years are only summarised and updated in the model every 15 years. For example, storm events occurring within 15 years are aggregated into one virtual event.

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2.5. Local processes In the following, the model rules describing the different processes are numbered consecutively. All processes describe changes occurring within one time step: 2.5.1. R1: competition in the upper canopy In a cell with closed upper canopy, i.e. with total cover of 8/8 or 100%, competition occurs: larger trees grow at the cost of smaller ones. The largest (with respect to crown area) or, if all trees have the same size, the oldest beech enlarges its crown projection area at the expense of the smallest one by 1/8 of the cell area (i.e. the smallest one shrinks by 1/8, which includes the case that it may disappear completely) with a probability of 50%. This probability reflects individual variability in competition strength, which certainly exists but is not known precisely. 2.5.2. R2: closing of gaps in the upper canopy A gap in the upper canopy may have a size ranging from 1/8 to 8/8 cell area. It will be closed either by trees of the upper canopy in this cell enlarging their crown or by trees of the lower canopy growing into the upper canopy. First, in a random sequence all trees of the upper canopy are allowed to enlarge their canopy size, Cro, by 1/8. This is done until the gap is closed or all trees present have enlarged their size. Then, if the gap is still not closed, the trees in the lower canopy have a chance to grow into the upper canopy. Only trees which have stayed long enough in this lower canopy (D3  D3min ) are admitted; this assumption is based on the observation that the minimum age of trees in the upper canopy is 90 years and the minimum age in the lower canopy 60 years (Korpel, 1995). Hence there is an age difference D3min ¼ 30 years or two time steps, respectively. Now, ranked by the time they have spent in the lower canopy, the admitted trees grow one after the other into the upper canopy with a crown projection area Cro of 1/8. If the gap in the upper canopy is still not closed, the new recruits are enlarged one after the other, ranked by age, to a Cro of 2/8. This rule reflects the observation that large canopy gaps can create a real ‘burst’ of growth among the loitering trees of the lower canopy.

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2.5.3. R3: growth within the lower canopy A beech which has just grown from height class 2 to class 3 is assigned an age A3 at random between 60 and 120 years and a residence time of D3 ¼ 0 years. Only trees which have stayed sufficiently long in height class 3 (D3  D3min ) can grow to the upper canopy. If the upper canopy is closed during the entire residence time D3 of a tree, then due to the unfavourable light conditions D3min is enlarged by one time step, i.e. 15 years. If a loitering tree stays in the lower canopy for more than 90 years (D3 > 90 years), it will die. 2.5.4. R4: growth from juveniles to lower canopy The transition of trees from the juveniles’ height class to the lower canopy depends on the light conditions. With F3 and F4 being the cover in the lower and the upper crown canopy, we can take M3; 4 ¼ ð1  F3Þð1  F4Þ as a measure of the area within the juveniles’ height class which is not covered by trees from the higher height classes. Now, for every free position or gap in the lower canopy, the probability W determines whether this position is filled by a tree emerging from the juveniles’ height class. This, however, can only happen if F2 (cover of seedlings) has been larger than zero for at least two time steps, because trees of course need a minimum amount of time to grow into the lower canopy with its minimum height of 20 m. The probability W is calculated according to the assumption that if the light conditions in the cell are favourable (M3; 4  0:5), W depends only on F2: W ¼ F2 Wmax . Otherwise, the amount of light relative to its maximum decreases the probability: W ¼ F2 Wmax LF=LFmax , where LF is ‘light factor’, which is a measure of the amount of light in the cell and LFmax the maximum value of LF (for calculation of LF see rule R8 below). 2.5.5. R5: growth of seedlings into juveniles Because of the shade tolerance of young beeches, the seedlings grow irrespective of the amount of light available. Thus, the proportion ð1  F2ÞF1 of F1 grows into the juveniles’ height class. The other seedlings die. 2.5.6. R6: regeneration Regeneration only occurs if trees in the upper or lower canopy height class exist somewhere in the forest, because the sapling bank cannot survive 15 years.

The maximum regeneration rate in a cell, Smax, is reduced stochastically by up to 20% to the new value Smax,red (due to, for example, browsing). In analogy to rule R4 we use M2; 3; 4 ¼ ð1  F2Þð1  F3Þð1  F4Þ as a measure of the area not covered by trees in higher height classes. Again we assume that with favourable light conditions (M2; 3; 4  0:5) the actual amount of established seedlings is maximum (F1 ¼ Smax;red ) or reduced due to the prevailing light conditions F1 ¼ Smax;red LF=LFmax . 2.5.7. R7: ageing and mortality All the trees in the upper canopy age by one time step or die owing to their individual mortality probability M4, which increases by 0.3 each time step for trees older than agemax. Therefore, there are no beeches older than agemax þ 60 years. All beeches in the lower canopy age by one time step or die owing to the mortality probability M3 (or because of R3). The cover of height classes 1 and 2 are at the beginning of each time step reduced by a random factor between 0 and 20%, which takes into account various environmental factors, for example browsing, and subsequently by the mortality rates M2 and M1. Note that in each cell, in each time step, the basic mortality rates M1, M2 and M3 are modified according to the prevailing light conditions (see following rule R8). 2.6. Neighbourhood interactions As the mosaic pattern in real beech forests consists of patches which are 10 to 100 times larger than a single grid cell, there have to be interactions between states and dynamics of neighbouring cells. BEFORE takes into account two types of neighbourhood interactions we assume to be the most important in beech forests: (1) Light coming in through canopy gaps benefits not only trees within the same cell, but to some degree also trees in neighbour cells. (2) Wind-thrown trees cause damage to neighbour cells; moreover, for the trees in a focal cell, gaps in the neighbourhood increase the susceptibility to windfall. 2.6.1. R8: neighbourhood interaction ‘light’ The growth and mortality of trees in the lower height classes depend on the amount of light available

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and are thus influenced by gaps in the higher height classes. Both the gaps in the cell itself and in its neighbour cells contribute to the light conditions for the lower canopy and the juveniles. Thus, the amount of available light can be computed from the cover F3 and F4 (cf. rule R4) of the relevant cells (Fig. 1B). Neighbour cells to the north-east or north-west do not contribute. To calculate the light factor LF which quantifies the amount of light available in the lower height classes, let a be the cell in focus and B the set of cells contributing to the light factor LF of a. Each gap in height class 3 or 4 adds to LF by the factors L3 or L4, describing the average input of light by a gap of size 1/8 cell size in height classes 3 and 4, respectively. Thus, LF can be calculated as: LF ¼ 4  8  ½ð1  F3a Þ  L3 þ ð1  F4a Þ X 8  ½ð1  F3b Þ  L4 þ b2B

 L3 þ ð1  F4b Þ  L4

The maximum light factor is LFmax ¼ 80ðL3 þ L4Þ. Note the special emphasis (factor 4) on the cell a in focus. The light factor LF is used to modify the mortality rates M1, M2 and M3: Mimodified ¼ Mi  maxð1  LF; 0:2Þ; 1 i 3 (for L3 and L4 values have to be chosen such that LF 1). This means favourable light conditions (LF close to 1) reduce mortality, but even with optimal light conditions the mortality rates are at least 20% of the maximum Mi, because there are always other sources of mortality besides unfavourable light conditions. 2.6.2. R9: neighbourhood interaction ‘wind’ First of all, at every time step we decide for the whole forest area by probability pwind whether any storm event occurs at all. This probability is set to 1 in this study, because in most parts of Central Europe storms occur virtually every year. Therefore, the probability that storm damages occur within a period of 15 years can safely be assumed to be 1. Then, the direction and the strength of the virtual storm event has to be calculated. The direction is randomly chosen from the wind rose registered at Frankfurt/Main airport (as an example of typical wind directions in Central Europe): SW (29%), W (26%), NW (11%), N (1%), NE (1%), E (26%), SE (3%) and S (3%). The strength

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of a storm event is quantified by the parameters pkipp1 < pkipp2 < pkipp3 describing the basic probability of an individual tree in the upper canopy being knocked down. It is assumed that 89% of storms are normal (pKipp1), 10% are strong (pKipp2) and 1% extremely strong (pKipp3); these proportions were implemented using evenly distributed random numbers. The neighbourhood effect regarding windfalls are as follows: in each cell, the probability Kipp of a tree being wind-thrown is increased by gaps in the upper canopy of adjacent cells. For a closed crown canopy in the upwind cell relative to the cell in focus, we have Kipp ¼ pkipp . Now, gaps in the crown canopy of the cell upwind (measured by (1  F4upwind )) enhance Kipp by pkipp  Epkipp  ð1  F4upwind Þ. If these gaps occur, gaps in the cell downwind (measured by (1  F4downwind )) also increase Kipp by pkipp  Epkipp  ð1  F4downwind Þ. Here, the parameter EpKipp describes the strength of the effect of gaps in the neighbouring cells. Thus, Kipp depends on the strength of the storm (parameter pkipp) and on gaps in the upper crown canopy of the two relevant neighbour cells. If a tree is wind-thrown, it will die and can damage the crowns in the next three cells downwind. If a cell is hit by a falling tree, its upper canopy trees are damaged with a probability of 0.5. The amount of damage (size of the smashed crown, measured in units of 1/8 cell area) is taken at random between 1/8 and the actual crown size (meaning the death of the tree). Trees of the lower canopy are damaged with a probability of 50%, too, although in this case damage means immediate death. All these neighbourhood interactions imply that damages by a storm in one cell enhance the probability of damages in the neighbouring cells. Thus, the neighbourhood interaction wind starting off as a local process finally ends up to synchronise aisles of cells, where the lengths of the aisles depend on the strength of the storm (Fig. 2A). Consequently, during extreme storm events large areas are damaged simultaneously, but still these areas are not clear-cut but heterogeneous in structure (Fig. 2B) so that they contain some ‘‘legacy’’ of the forest structure before the extreme storm event. Such legacies are common even after extreme disturbance events (Turner et al., 1998).

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Fig. 2. Damage caused by a (a) ‘‘normal’’ (pkipp1) and (b) ‘‘extreme’’ (pkipp3) storm event. The forest area here is a small part (15  15 cells or 4.7 ha) of a model forest of 54  54 cells (or 64 ha), which prior to the storm was in a typical mosaic stage as shown in Fig. 4. The damage ranges from a gap of 8/8 cell size (black) to no damage at all (white). The wind direction is from the west.

2.7. Boundaries We examine quadratic forest areas of different sizes with an open boundary, i.e. fields or meadows. Hence the exposure to the light at the boundary is maximum, and the trees are more resistant to wind damage than trees from the inner forest. Thus, the light factor LF of border cells is increased by the open canopies in the non-forest neighbourhood, but these ‘virtual’ gaps do not increase the probability Kipp of a tree being windthrown. 2.8. Assignment of developmental stages In order to compare model results with the description of real forests we have to assign some of the output variables of the model, like the total cover in the different height classes in a cell, to developmental stages. Note that this assignment is only used to evaluate the model, because developmental stages are not directly included in the model. According to Korpel (1995), Table 1 shows the assignment of Table 1 Assignment of developmental phases to different combinations of percentage cover (F1–F4) in the four height classes within a grid cell

F1 F2 F3 F4

Growing-up stage (%)

Optimal stage (%)

Decaying stage (%)

10–70 20–50 20–50 20–80

0–10 0–10 0–10 85–100

20–80 0–50 0–20 0–50

combinations of certain cover values in the different height classes to the three developmental stages ‘growing-up’, ‘optimal’, and ‘decaying’. However, the scale of a single grid cell (corresponding to the size of a single large tree) is too small to assign developmental stages, which are used to characterise larger forest areas. Therefore, we apply a kind of weighted moving average over a cell and its eight neighbour cells (Fig. 3). First, we preliminarily assign to each of the nine cells a developmental stage according to Table 1 (Fig. 3B). Next, we achieve a sort of smoothing for the focal cell (Fig. 3C). We have to distinguish between three cases: (1) In the nine cells, all three stages appear in the same proportion. Then we make the interim stage of the focal cell its final stage, too. (2) One stage is predominant in the nine cells. Then this stage is assigned as the final stage to the focal cell. (3) Two preliminary stages predominate. If now or in the time step before the preliminary or final stage the focal cell belonged to one of these stages, we take this as the final stage of the focal cell. Otherwise we randomly choose one of the predominating preliminary stages as the final stage of the focal cell. 2.9. Simulation 2.9.1. Initial conditions To assign an initial configuration to the forest we choose cover values for each cell, each height

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Fig. 3. Evaluation of BEFORE regarding developmental stages. The state variables of BEFORE are the percentage cover (F1–F4) in the four height classes of each cell (A). According to Table 1, these cover values are mapped to developmental stages (B) and then the specific moving average described in the text is applied (C).

class and additional state variables (F1, F2, A3, D3, A4 and Cro). We tried to mimic three configurations: (1) afforested, homogeneous forest; (2) homogeneous managed forest; (3) natural forest, i.e. the proportion of the three developmental stages was chosen according to Korpel (1995), but no specific spatial structure was assumed. Depending on the initial configuration, the model forest takes different times to reach quasi-stationary dynamics irrespective of the initial condition (Neuert, 1999). When presenting the results describing the quasistationary dynamics, we refrain from describing the initial conditions in more detail (see Neuert, 1999). 2.9.2. Scheduling The light factor LF and the mortality rates are used unchanged during one entire time step. All state variables are updated immediately after a model rule has been applied, but this does not introduce any ordering effects except for windfalls (see below) because light factor and mortality rates are only updated at the end of each time step. First, the processes of growth, mortality and competition are computed in every cell from top to bottom. In the case of a closed upper crown canopy, we start with R1 describing competition. Otherwise gaps in the upper crown canopy are closed according to rules R2 and R3. Then rules R4 and R5 are executed, specifying the growth of the lower crown canopy, the juveniles and seedlings. The mortality and ageing rule R7 is the final rule processed in each height class.

Next, the rules describing storm effects are applied to all cells. To take the wind direction into account, the grid is processed from the main wind direction, i.e. north, east, south, or west. In this way, BEFORE can mimic the generation of windfall aisles which may occur after strong or extreme storms (Fig. 2). Now, rule R8 resumes the results of the growing process by updating the light conditions and mortality rates of each cell. Finally, R6 performs regeneration. 2.9.3. Simulated area and time horizon Unless stated otherwise, the results presented in the following were obtained from a model forest of 54  54 cells or ca. 60 ha. To avoid edge effects from the open boundary (light exposure and resistance to storms), which can be detected up to eight cells (ca. 100 m) from the edges, only the inner forest area was evaluated (corresponding to an area of 38  38 cells or ca. 30 ha). The simulation was run for 1000 time steps, corresponding to 15 000 years. 2.10. Parameterisation and calibration The model parameters are estimations based on observations in the literature and on our own observations (Table 2). However, the evidence supporting one of the estimated parameters EpKipp, describing the influence of gaps in the canopy to the susceptibility to windfall in the neighbour cell was limited. Therefore, EpKipp had to be determined by calibration. Using the reference values for the other

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Table 2 List of model parameters Para-meter

Description

Range

Source

Reference value

M1

Mortality rate of seedlings (per 15 years)

1

1

M2 M3 M4

Mortality of juveniles (per 15 years) Mortality in lower canopy (probability) Mortality in upper canopy (probability)

0.4–1 0–0.4 0–0.002

agemax

Maximum age (years)

150–350

L4

Measure of additional light by gaps in height class 4 Measure of additional light by gaps in height class 3 Main wind direction Probability of a storm occurring Probability of a tree being knocked down by a normal storm Probability of a tree being knocked down by a strong storm Probability of a tree being knocked down by a extreme storm Modifies the probability of a tree being knocked down by a storm Probability of trees of height class 3 emerging from height class 2 Maximum length of time spent in height class 3 Maximal regeneration rate of seedlings

0.001–0.02

Burschel and Schmaltz, 1965a,b, Peters, 1992, Watt, 1923 Estimated Estimated estimated according to Jenssen and Hofmann, 1997 Assmann, 1961, Fro¨ hlich, 1925, Holm, 1995, Peters, 1992, Remmert, 1988 Estimated

0–0.003

Estimated

0.002*

SW 1 0–0.002

SW 1 0.001*

0.003–1

Wagner, 1907 Wagner, 1907 Estimated according to Wagner, 1907 Estimated according to Faille et al., 1984a,b Estimated

0.004

0.001–50

Estimated

19*

0.7–1

Estimated according to Assmann, 1961, Kennel, 1966, Korpel, 1992 Estimated

1

L3 HWR pwind pKipp1 pKipp2 pKipp3 EpKipp Wmax D3max (years) Smax (per 15 years)

0.002–0.02

60–90 1

Assmann, 1961, Knapp and Jeschke, 1991

1 0.03 0.001 300

0.008*

0.002

6 1

Asterisks depict parameters which have a strong influence on the model results.

parameters, EpKipp was changed until the model forest reproduced the mean values of the proportional areas of the three developmental stages observed by Korpel (1995) in real natural forests (Table 3). Note that for this calibration no assumption had to be made about the existence of local cycles of developmental stages, the length of these cycles, or the spatial structure of the forest, including typical patch sizes. Table 3 Mean proportions of the developmental phases in natural beech forests (Korpel, 1995) Phase

Frequency (%)

Growing-up Optimal Decaying

34–43 20–22 42–45

3. Results 3.1. Microanalysis: dynamics of a small patch If the model forest is visualised regarding developmental stages (as described in Section 2.8 and Fig. 3), it shows a characteristic shifting mosaic of small patches being in different stages (Fig. 4A). Only after extreme storm events does this typical mosaic disappear and forest structure is more homogeneous (Fig. 4B). It takes about 100 years after an extreme storm event until the characteristic mosaic of Fig. 4A is re-established. To understand the emergence of the patchy forest structure, we analyse and demonstrate the behaviour of the model at the level of individual trees. For this ‘microanalysis’ (Auyang, 1998), we monitor the fate of an east–west transect of six forest cells (86 m long

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Fig. 4. Texture of different developmental stages (determined with the protocol described in Fig. 3) produced by BEFORE. The left column (A) shows the state of the forest in three consecutive time steps for a situation where no extreme storm event occurred. The right column (B) shows a sequence of four states just after an extreme storm event occurred. The size of the model forest is 54 times 54 cells, corresponding to 64 ha.

and 14 m wide). To visualise the state of the cells in a similar way to the profile diagrams in forestry, the state variables of the upper and lower canopy are visualised by icons representing trees (Fig. 5). The transects are taken from the same model forest as presented in Fig. 4. The initial situation of Fig. 5A (upper panel) shows a largely closed upper canopy, a sparsely filled lower canopy and also sparse cover in the two lower height classes. This situation largely corresponds to the

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optimum stage of development (‘Hallenwald’). The positive effect of light for the growth of the lower height classes is obvious: the gaps in the upper canopy of the two cells 3 and 4 lead to higher cover in the lower height classes. Additional light due to the gaps in the lower canopy of the right neighbour (cell 5) causes the even stronger cover of the lower height classes in this cell. In the next two time steps, we have normal storm events (of strength pKipp1) and at first a westerly wind. The giant beech in cell 1 is knocked down by the first storm and hits the upper and lower canopy of the three neighbour cells (cells 2, 3, and 4; middle panel). Some of these trees die, others lose parts of their crown (cell 4). Note the increased cover in the lower height classes in the cells affected by the wind-throw. In the next time step (lower panel in Fig. 5B), the wind direction changes to south-west. Again, trees are knocked down by the storm. At this point, the positive effect of diffuse and oblique light becomes apparent: the juveniles of the cells 3 and 4 (having the same light conditions in their upper canopy with one 2/8 beech and two 1/8 beeches, respectively) differ only because of the additional light reaching cell 3. The initial situation of Fig. 5B shows the same transect as before, but 150 years later. An extreme storm from the east has just knocked down a large proportion of the upper canopy. Almost the whole forest area is at the stage of decay (cf. Fig. 4B). Owing to the good light conditions, the two lower height classes are almost fully occupied and some juveniles grow into the lower canopy within the next time step. Here, the transition to individual-based modelling can be seen: depending on the degree of cover in the class of juveniles and on the amount of light available (rule R4) a certain number of canopy trees emerge as individuals with specific characteristics (e.g. age) out of the thicket of unspecified juveniles. After two more time steps, the trees can reach the upper canopy. In these time steps, there are only normal storms (of strength pKipp1) which have almost no influence on the just rejuvenated forest. Due to the extreme storm event in the beginning of this time series, the local dynamics of the forest are closely synchronised. Speaking of local dynamics we think of an area of ca. 40  40 m2, corresponding to one cell with its eight direct neighbours. It takes about seven time steps (ca. 100 years) until the effect, or ‘echo’, of

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Fig. 5. Profile diagrams from the interior of the forests shown in Fig. 4, i.e. the left column (A) shows a sequence of three states in a ‘normal’ period, the right column (B) a sequence of four states just after an extreme storm has occurred. The profile diagrams show a transect six cells wide (corresponding to 85.71 m) and one cell deep (14.29 m).

the extreme storm event is ‘forgotten’, i.e. no longer detectable in the forest structure and dynamics. 3.2. Regional cycles in forest structure The cyclic development of local stands is also detectable to some degree at the scale of the entire forest. In the following we average state variables characterising grid cells over the entire forest and discuss the emerging cycles of these mean values; it must, however, be kept in mind that forest structure is very patchy (Fig. 4) and therefore the spatial variance of the state variables at each time step very high. In Fig. 6, time series of state variables averaged over the entire model forest are shown: cover in the upper canopy and in the seedling height class, and proportion of the area being in the optimal stage. In addition, the upper panel in Fig. 6 shows the occurrence of strong and extreme storm events. In all other time steps, normal storms occur. The time series exhibit consid-

erable variation, which is more or less cyclic. A simplified but consistent explanation of these cycles in the model is as follows: A decrease in the cover in the upper canopy causes an increase in cover in the lower height classes. After some time, these new cohorts reach and close the upper canopy, and the cover in the lower height classes decreases. The period defined as the time from one maximum to the next of, for example, the times series of cover in the upper canopy varies between 100 and 405 years, with a mean of 240 years and standard deviation of 80 years. A Fourier analysis of the time series reveals a main period of 290 years. Both values for this mean period are independent of forest size if the inner forest area is larger than about 30 ha. The period values are of similar magnitude to the mean duration of a stand development cycle (260 years) and the maximum age of 345 years (agemax þ 45 years; see rule R7). The mean period increases with increasing agemax (not shown), although more pronounced is the effect of

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Fig. 6. Cyclic dynamics of variables characterising the entire forest. Upper panel: regime of storm events. In years without strong (strength 2) or extreme (strength 3) storm events, normal storm events occur. Middle panel: time series of total cover in the upper canopy (F4) and the seedlings height class (F1), averaged over the entire forest. Lower panel: time series of the percentage area of the forest in the optimal developmental stage (‘Hallenwald’).

storms on the regional cycles: again, variations of the parameters pKipp2 and pKipp3 describing the severity of strong and extreme storms have only little influence. They cause variations of the mean period of maximal 20 years. By contrast, the normal storms occurring regularly have a much stronger impact. Doubling pKipp1 compared to its reference value reduces the mean period to just 180 years. With pkipp1 ¼ 0 storms occur in only 11% of the time steps. In this case, the mean period equals the mean duration of a stand development cycle (260 years). Since this cycle is not regularly interrupted by storms, it completely determines the forest structure and dynamics. On the other hand, with pkipp1 ¼ pkipp3 , we have extreme storms occurring in almost every time step. No upper canopy can emerge (mean of F4 approaches zero) in this scenario and the mean period decreases. 3.3. Synchronisation and desynchronisation The mosaic pattern typical of natural beech forests and reproduced by BEFORE indicates that stand

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Fig. 7. Dynamics of the percentage area in the optimal stage for different model scenarios. (a) Reference model; (b) no storms occur; (c) no storms occur, and there is no neighbourhood interaction ‘light’; and (d) no neighbourhood interaction ‘light’, but storms occur.

development is synchronised at the local scale (corresponding to few grid cells), whereas at the regional scale (corresponding to the entire forest) it is desynchronised. Here synchronisation means that each cell of the whole area under consideration is nearly of the same developmental stage. Fig. 4 shows that this synchronisation is only a local process. To identify the synchronising and desynchronising processes, scenarios were analysed in which different processes were deactivated. To compare the scenarios we always used the same time series of storm events. Fig. 7A shows the reference case with its characteristic cyclic fluctuation. Due to the highly uniform initial distribution afforested, homogeneous forest the optimum stage only occurs after 100 years of simulation. In the scenario of Fig. 7B, no storms occur (pwind ¼ 0, rule R9). As a result, the percentage of optimal stage cycles between almost 0 and 100%, which means that the forest dynamics are entirely synchronised. Obviously, with pwind ¼ 1, the frequently occurring normal storms (pKipp1) determine forest structure to a large degree. They act locally by damaging only few

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cells at once and thus have a desynchronising effect at the scale of the entire forest. In the scenario in Fig. 7C, both storms and the neighbourhood interaction ‘light’ were deactivated: gaps in the two upper height classes only benefit trees in lower height classes of the same cell, but not trees in neighbour cells (i.e. no diffuse and oblique light; note that for this scenario, the light input of the cell in focus had to be increased by a factor of 2.5 because otherwise the lower height classes would have received so little light that no developmental cycles would have emerged). In this scenario, the forest-wide synchronisation of Fig. 7B completely disappears. Each cell in the model forest has its own dynamics and is no longer influenced by neighbour cells. Consequently, no spatial structure can emerge. The assignment of developmental stages now indicates that the entire forest is at the optimal stage, but this is an artefact of the moving average in the assignment of developmental stages. Diffuse and oblique light is thus in our model a decisive mechanism for local synchronisation. Ironically, storms are synchronising at the local scale. This becomes clear in the scenario of Fig. 7D, where again no neighbourhood interaction ‘light’ occurs, but now storms are activated again. The resulting dynamics are very similar to those of the reference case (Fig. 7A). The synchronising effect of storms at the local scale is due to the damage of the windfalls. This damage ‘spreads’ into the neighbourhood so that the state and, in turn, the dynamics of neighbouring cells become partly synchronised.

Fig. 8. Percentage area of the forest in the three different developmental stages, depending on the inner area of the model forest. The percentage values are averages over 15 000 years (1000 time steps).

recorded for forests of different size (Fig. 8). Note again that only the interior of the forest was evaluated (ignoring a boundary of eight cells). From an inner area of about 40 ha on, the percentage of the developmental stages corresponds to that described for real undisturbed forests (Table 1). This inner forest area corresponds to an entire forest area of about 70 ha (about 60  60 cells). However, the mosaic pattern also emerges in smaller forests, although for forests smaller than 20 ha (where the inner area is only 23% of the total area) edge effects are so dominating that we can no longer speak of a regional forest structure typical of natural beech forests. Nevertheless, even very small unmanaged beech forest will show a high structural diversity at small scales (Fig. 9), because the processes of synchronisation and desynchronisation are still active.

3.4. Effect of forest size on forest structure 3.5. Validation To assess the effect of forest size on forest structure, the mean values (with respect to simulation time) of the percentage area of the three developmental stages is

When designing BEFORE, a model structure was chosen which in principle allows two patterns to

Fig. 9. Forest structure of a small model forest for three consecutive time steps (forest area: 22  22 grid cells, corresponding to 9.88 ha total area, and 0.73 ha inner area).

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emerge but which were not hard-wired into the model rules: the mosaic pattern of patches of different developmental stages, and the local cycles of the developmental stages. The question was whether the processes built into the model are sufficient to reproduce these two patterns. The results show that indeed they are: in every time step, the same type of mosaic pattern as observed in natural forests (Korpel, 1995; Leibundgut, 1982; Remmert, 1988; Peterken, 1996) is produced. Though we used the overall mean of developmental stages to calibrate the parameter EpKipp, the mosaic pattern itself is an independent model result. Moreover, the size of the mosaic patches generated by BEFORE (on average 0.3 ha) corresponds to the values observed (0.1–2 ha; Remmert, 1988) (Fig. 4). Furthermore, BEFORE reproduces the local cycle of developmental stages. The ‘normal’ sequence of stages (growing-up, optimal, decaying, growing-up, etc.) is interrupted only in 11.75% of all time steps. The initial situation of Fig. 5A (upper panel) shows a largely closed upper canopy, a cases: in 8.52% of all cases, storm effects turn the growing-up stage directly into the decaying stage, preventing the formation of the optimum stage. Only the remaining 3.23% constitute a genuine violation of the sequence of stages. Also, the average time the cells spend in each developmental stage closely corresponds to the observed values (Table 4). All in all, BEFORE reproduces the main structures and dynamics of natural beech forest both qualitatively and quantitatively and thus seems to capture the essential structural elements and processes of these forests. Therefore, BEFORE can be used to analyse in more detail the spatiotemporal dynamics of natural beech forests over large areas and long time horizons.

Table 4 Comparison of simulated and observed (Korpel, 1995) mean lengths of the developmental stages Mean time spent in the development phases in years

Growing-up Optimal Decaying

Model

Korpel

105 45 120

85–100 40–50 95–110

363

3.6. Sensitivity Small changes to the parameters do not lead to modifications of the model forest structure (for details see Neuert, 1999). Nevertheless, we can distinguish between parameters with a greater and with a smaller influence on model results. Here, the model results considered are the percentage area of developmental stages (averaged over the whole simulation run) and the time series of the total cover of the four height classes. For example, normal storm events (described by parameter pKipp1) affect model results much more than the stronger storm events do (pKipp2 and pKipp3). Hence, in the long run the frequently occurring normal storms (89% of storm events with strength pKipp1; rule R9) produce the typical stand structure of the natural forest, despite small periods after extreme storm events, where nearly the whole forest is in the decaying stage. On the other hand, increasing the proportion of extreme storm events means intensifying the irregularity of forest dynamics. Considering another group of parameter values, the basic mortality rates, we found that the rates of the two lower height classes have the greatest influence: reducing the mortality rate of height classes 3 and 4 first leads to an increase in cover in all four height classes. However, this includes the stronger, longer shading of the lower height classes, which increases the actual mortality rates via the reduced light factor LF (Rule R7). Thus, there is a regulation, i.e. a negative feedback, built into the model which makes it less sensitive to changes in the basic mortality rates. The parameter with the strongest influence on the forest structure is EpKipp, which describes the influence of gaps in neighbour cells on susceptibility to windfall. At the same time, EpKipp is the parameter we know least about. To describe the spatiotemporal dynamics of natural beech forests in more detail, windfalls and the effects of gaps on windfalls have to be studied empirically in much more detail. So far, very few studies on this topic exist.

4. Discussion The forest model BEFORE was developed to reconstruct the spatiotemporal dynamics of natural beech

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forests in central Europe. A model like this is needed because forest management, forest ecology and conservation are all paying growing attention to the natural dynamics of beech forests. BEFORE is a bottom-up simulation model which is built from a consideration of the basic entities of a forest, i.e. the trees, provides these entities with behavioural rules, and then checks the resulting structures and dynamics of the forest. The problem when structuring bottom-up models is that there are so many degrees of freedom that the model can all too easily become unwieldy, making it hard to parameterise, understand and test (Grimm, 1999, 2002). Patternoriented modelling is a general modelling strategy which aims to make the choice of model structure of bottom-up models less arbitrary, the model as complex as necessary (but not more so), and the model testable (Grimm, 1994; Grimm et al., 1996; Grimm and Berger, 2003; Wiegand et al., 2003). The idea is to identify patterns in the real system and then to provide a model structure which in principle allows these patterns to emerge in the model. A pattern is anything which is beyond random variation. It is important not to focus on only one pattern, because this would not sufficiently narrow down the model structure, but to try to reproduce multiple patterns simultaneously. As a result of the pattern-oriented modelling strategy, the model will finally be ‘structurally realistic’, i.e. contain the key structures and processes of the real system. Indicators of structural realism are independent predictions regarding properties of the system which were used neither during model development nor calibration.

virtual forester (see also ‘virtual ecologists’ in Berger et al., 1999; Grimm et al., 1999) assigned the stages according to the classification listed in Table 1. 4.2. Beyond verbal models: temporal variations The main limitation of verbal models of beech forest dynamics is that they cannot provide a dynamic picture. Verbal models are succinct integrations of decades of observations in natural forests and forest reserves. But due to the principle limitation of verbal models, which are still based on rather short observation periods, they can only describe snapshots of the spatial structure and the developmental cycle. BEFORE now shows that the verbal models are correct on average, but that natural beech forests exhibit considerable temporal variation. The mosaic pattern continuously changes because of neighbourhood interactions and the effects of storm events. The percentage of forest area in the different developmental stages varies considerably. For example, although on average 21% of the forest are in the optimum stage, in periods without extreme storm events this percentage fluctuates more or less regularly between 10 and 40%, and after extreme storms even between nearly 0 and 60%. A natural beech forest may thus be devoid of almost any optimum stage (or ‘Hallenwald’) for about 180 years, but this picture of the forest is within the normal range of fluctuation. We showed that the cyclic regional fluctuations in forest structure can be traced back to the local cycle of the developmental stages. 4.3. Limitations of developmental stages as indicators of naturalness

4.1. Capturing spatiotemporal dynamics BEFORE reproduces the mosaic structure of the stages observed in natural beech forests both spatially (patch size) and temporally (length of time of different stages) (Table 4). Neither the mosaic pattern nor the developmental stages are included into the model structure of BEFORE but emerge from local processes and neighbourhood interactions. This is an important part of the validation of this model. Note that the developmental stages are not state variables but characterise specific combinations of state variables within a grid cell. Very much like a real forester assigning developmental stages in a real forest, in BEFORE a

Developmental stages provided very useful patterns for designing and validating BEFORE. However, an important implication of the cyclic fluctuations in forest structure is that developmental stages are not ideal for characterising the ‘state’ of natural beech forests. Natural beech forests should instead be characterised by a range of possible states generated by the typical dynamics of the forest rather than by a single state. Moreover, the assignment of developmental stages in real forests is not an easy task: either assignment is based on rough qualitative assessments, which runs the risk that no two foresters will assign the same stages to a specific plot within a forest, or the assign-

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ment is based on field data and a table such as Table 1, but gathering these data is so time-consuming that it has rarely been done for larger areas. Developmental stages are thus not suitable as a practical means to indicate the naturalness of a specific beech forest, for example in a forest reserve. Yet indicators of naturalness are badly needed because they would provide guidelines for natural forest management and characterising forest reserves. Fortunately, BEFORE is a bottom-up model which allows use to be made of all the details which are ignored and aggregated in the assignment of developmental stages. Therefore, Rademacher et al. (2001) analysed the age structure of the canopy and the distribution and abundance of very large or old trees. It turned out that these aspects of beech forests are better indicators of naturalness because they fluctuate much less than the percentage of developmental stages and are easier to assess empirically. 4.4. Agents responsible for forest structure BEFORE indicates that the number of processes generating the characteristic patterns of beech forests is rather small. Locally, dynamics in the vertical structure are governed by vertical light competition between trees of different height classes, which also includes negative feedback between mortality rates and cover. Lower mortality leads to higher cover which, in turn, increases mortality due to insufficient light conditions. Vertical light competition is a key process in forest dynamics which is probably included in virtually every forest model which aims to be structurally realistic. For example, in FORMIX3 (Huth and Ditzer, 2000, also in FORMIND, Ko¨ hler and Huth, 1998), a model of tropical rainforests, light competition is described in a similar way as in BEFORE, although FORMIX3 is more mechanistic by focusing on photosynthesis as driving process. The widely used gap models (Botkin, 1993) also include vertical competition for light. The second class of processes driving the spatiotemporal dynamics of natural beech forests are neighbourhood interactions, mainly by windfalls and by light conditions. The initial situation of Fig. 5A (upper panel) shows a largely closed upper canopy, a diffuse and oblique light, coming in through gaps in the canopy.

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These interactions partly synchronise the local dynamics on neighbouring sites. For example, if a windfall causes damage in neighbouring cells, in all these cells younger and smaller trees will simultaneously receive additional light. The same is true for diffuse and oblique light: additional light benefits not only the trees in the cell in focus, but also in the neighbour cells. All in all, the concept of forest dynamics presented by BEFORE is as follows: locally, the negative feedback between cover in higher height classes of the forest and growth and survival in lower height classes causes cyclic dynamics, oscillating between ‘Hallenwald’ and more complex vertical structures. Gaps in the canopy, created by the frequently occurring normal storms or by the death of older trees, cause ‘pulses’ of vitality affecting growth and survival. The effect of these pulses is not strictly local, but spreads into the immediate neighbourhood and leads to small areas which are at the same stage of development. If no storms occurred and only the neighbourhood interaction ‘light’ was present, the development of the entire forest would be synchronised. And indeed, many monospecific forests have areas at the same stage which are much larger than in central European beech forests (Jeltsch and Wissel, 1994). Storms, however, disrupt the local developmental cycles in beech forests and prevent regional synchronisation over the entire forest. 4.5. Pattern-oriented modelling and empirical knowledge BEFORE is the first rule-based forest model which includes vertical structure and detailed rules describing, for example, the effect of windfalls. Earlier rulebased forest models are less complex (Wissel, 1992; Jeltsch and Wissel, 1994; Ratz, 1995). The model of Wissel (1992), which addresses the same forest type as BEFORE central European beech forests ignores vertical structure and focuses on other processes than BEFORE. Wissel assumes locally, on grid cells, a cyclic succession which also includes stages of open area and other tree species than beech. BEFORE is based on different assumptions and focused on two, instead of only one pattern: the mosaic pattern as in Wissel (1992) and also on the patterns in the vertical structure of natural beech forests. This pattern-oriented

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modelling strategy leads to a model which is considerably more complex than the model of Wissel (1992), but is also more realistic in that it captures essential structures and processes of real beech forests. The complexity of the structure of BEFORE also allows much more expert knowledge on the part of foresters to be integrated. This knowledge is expressed in probabilistic ‘if-then’ rules. BEFORE shows that empirical ‘if-then’ rules are sufficient to describe the essential processes driving the spatiotemporal dynamics of beech forests.

tion of the rule-based design of BEFORE with gap models, which are good at describing local community development, might be a good modelling strategy. Rules could be used to describe disturbances and their influence on parameters of the gap model both locally and on neighbouring sites. The lesson from BEFORE is that a rule-based, rather coarse description of disturbances and their effects may be sufficient in many cases. Very detailed descriptions of light regimes etc. as, for example, in SORTIE (Deutschman et al., 1997) may still be useful for many problems, but are not mandatory.

4.6. Effect of forest size on forest structure 4.8. Outlook Many forest reserves with beech forest in Germany are smaller than 10 ha, and the majority are smaller than 100 ha. The question arises whether these protected forests are useless because they are too small. Fig. 9 shows that even these small plots will develop a rich structure characteristic of natural beech forests. Thus, many small unmanaged plots of beech forests within larger but managed areas would benefit from the re-establishment of important elements of the natural biodiversity in the woodlands of central Europe. ‘Islands’ of small unmanaged forest areas within a naturally managed forest might therefore be a promising strategy for restoration. On the other hand, only reserves larger than 20– 30 ha are large enough to develop spatiotemporal dynamics which are independent of edge effects (assuming there are any edges) and which on average leads to percentages of the developmental stages corresponding to those in larger natural beech forests. But still, even these larger reserves would only be ‘sufficient’ with regard to the beech itself. Other species living in beech forest may have more complex, sometimes much larger area requirements. 4.7. Limitations of the modelling approach of BEFORE The general design of BEFORE can also be used for other monospecific, natural forests. However, it remains a moot point whether this design is also suitable for mixed species forests. In many cases, formulating rules to describe conditions under which certain tree species become established and dominate locally may be impossible. In such cases, a combina-

In Section 1, we listed the main questions to be addressed with BEFORE: How large should forest reserves be to allow natural spatiotemporal dynamics to emerge? How variable are the spatial and temporal patterns in natural beech forests? Further questions include: What are good indicators of the naturalness of a beech forest? How can beech forests be managed such that natural structures emerge and are maintained? The first two questions are tackled in this paper; the question of indicators is discussed in Rademacher et al. (2001). Now, the remaining question is whether BEFORE can really be used to develop strategies for forest management which would allow more natural structures and processes to emerge in managed beech forests. As far as the question of unmanaged ‘islands’ within managed forests is concerned, BEFORE can be used directly, as shown above. However, to really address questions of forest management, i.e. silviculture, the structure of BEFORE seems too coarse. Trees are distinguished by age, height and canopy size, but the main variable of interest to forest management is stem volume. Therefore, the question arises whether the coarse structure of BEFORE could be mapped to more detailed information about stem volume. The work of Rademacher and Winter (2003) shows that this is possible. The purpose of their work was to use BEFORE to keep track of coarse woody debris in natural beech forests. To this end, additional rules had to be introduced which describe the percentage and the decay time of lying and standing dead wood. Moreover, to be able to compare model results to empirical assessments of the amount of coarse woody

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debris, stem volumes of the trees in BEFORE had to be assessed. This proved possible by using yield tables for younger trees and by fitting the total amount of dead wood of the model to empirical values. Furthermore, model results were insensitive to those stem volumes which could only be roughly estimated, i.e. very old and large trees. The work of Rademacher and Winter (2003) suggests it should be possible to use BEFORE to compare different management strategies, which are simulated by simulating virtual foresters harvesting and, depending on their management strategy, regenerating the beech forest. In contrast to existing models for silviculture, which focus on shorter time periods of one or two decades, BEFORE could be used to study the consequences of forest management for forest structure for, e.g. a century or longer.

Acknowledgements We would like to thank Andreas Huth and two anonymous referees for their valuable comments on earlier versions of this paper.

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