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For Ecol Manage. 2010 January 25; 259(3): 614–623.

PMCID: PMC2982682

Institute of Forest Growth, Department of Forest and Soil Sciences, BOKU - University of Natural Resources and Applied Life Sciences, Vienna, 1190 Peter Jordanstraße 82 Vienna, Austria

Markus O. Huber: ta.ca.ukob@rebuh.sukram

Received 2009 July 31; Revised 2009 November 13; Accepted 2009 November 16.

Copyright © 2010 Elsevier B.V.

Open Access under CC BY-NC-ND 3.0 license

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Tree growth models are supposed to contain stand growth laws as so called “emergent properties” which derive from interactions of individual-tree growth and mortality functions. This study investigates whether the evolving tree species composition in a long term simulation by the distance-independent tree growth model PrognAus matches the species composition of the potential natural vegetation type which is expected to occur if one refrains from further management interventions and major disturbances, climate change, and changes in site conditions can be excluded. For this purpose the development of 6933 sample plots of the Austrian National Forest Inventory was predicted for 2500 years. The resulting species proportions, derived from volume per hectare of 15 tree species or species groups, were used to classify every sample plot according to potential natural forest types, following a classification scheme based on expert knowledge. These simulated potential natural vegetation types were compared with expert reconstructions of the sample plots of the Austrian National Forest Inventory. A total of 5789 plots were actually classified with the scheme; in 33% of the cases the classification on the basis of the PrognAus-simulations was identical with the classification by the Austrian National Forest Inventory. A predominantly correct classification was achieved for the subalpine *Picea abies*-type and the *Fagus sylvatica*-type although PrognAus showed a tendency to overestimate the proportion of *F. sylvatica* and *P. abies*. Weaknesses in the ability to simulate forest types dominated by *Quercus* spp., *Acer* spp., and *Pinus sylvestris* were identified. This shortcoming might be caused by the mortality model which allows a larger diameter at breast height for *F. sylvatica* or by the ingrowth model whose terms for the consideration of inter-specific competition may lead to a disadvantage of *Quercus* spp., *P. sylvestris*, and *Abies alba*. Moreover, the ingrowth model might be influenced by management effects and the effect of selective browsing.

Tree growth models predict the development of each individual tree within a forest stand. These models are well accepted tools to support planning and decision making in sustainable forest management, especially in uneven-aged mixed species stands where traditional yield tables cannot be used (Hasenauer, 2006).

When growth functions are defined at the individual-tree level, stand growth is derived from the aggregation of individual-tree parameters. Hence tree growth models are supposed to contain stand growth laws, the so called “emergent properties” which derive from interactions of the individual-tree growth and mortality functions at the stand level. Numerous studies on the validation of tree growth models focused on such “emergent properties”, e.g. Reineke’s maximum stand density (e.g. Pretzsch et al., 2002; Monserud et al., 2005).

Odum (1969) defined succession as the directional process of plant community development which finally culminates in a stabilized ecosystem, the “climax” stage. Clements (1936) earlier described the “climax” as the stable species composition evolving under the ruling climate. This “monoclimax theory” has been questioned because scientists were aware of disturbances and their central role in succession. The successional process is frequently interrupted by disturbances and therefore has to start anew at some point, but still remains a never ending process. For a more detailed recapitulation of that controversy see Oliver and Larson (1996). However, the response to the question whether there exists a climax stage in the development of species composition strongly depends on the applied spatial scale, the disturbance-extent, and the disturbance-interval (White and Jentsch, 2001). According to Connell and Slatyer (1977) the species composition of the climax stage will remain constant (i) if it is only interrupted on a small scale (i.e. only individual trees die and are replaced) and (ii) if an individual tree is more likely to be replaced by an individual tree of its own species. Both assumptions apply to the tree growth model PrognAus because it does not account for climate change and changes in site conditions, and disturbances are limited to the individual-tree level. Tüxen (1956) defined the “potential natural vegetation” (PNV) as the species composition which would exist under the given site conditions without anthropogenic influence. The PNV was often misinterpreted as the species composition evolving in the “final stage” of the successional process which would start if the management refrains from further interventions. However, this will never occur because the present site conditions will not remain constant during the successional process. The PNV should rather be interpreted as the species composition associated with the present site conditions as if both would be the result of a successional process (Kowarik, 1987).

The present study investigates if the evolving tree species composition in a long term simulation by the distance-independent tree growth model PrognAus matches the species composition of the PNV-type which is expected to occur if major disturbances, climate change, change in site conditions, and management interventions are excluded.

In 1981 the Federal Research and Training Center for Forests, Natural Hazards and Landscape (BFW) established a permanent inventory for the whole of Austria. The sampling design consists of 5500 clusters with a grid distance of 3.89 km and every cluster consists of a square of 200 m length. Each of the 4 corners of this square is used as the centre of a permanent sampling plot. The site characteristics (e.g. elevation, azimuth, soil group, soil moisture class, soil depth, etc.) were assessed within a 9.77 m radius of each centre and the sample trees were selected (i) by angle count sampling according to Bitterlich (1984) with a basal area factor of 4 m^{2} ha^{−1} for trees with a diameter at breast height (dbh) > 10.4 cm and (ii) within a circle with 2.6 m radius for trees with 5 cm $\le $ dbh $\le $ 10.4 cm. If the site factors were found to be inhomogeneous, the sampling plot was divided into sub-plots and the site characteristics were separately assessed for each sub-plot. From 1981 to 1996 every fifth cluster, and since 2000 one third of the clusters were remeasured every year. In the first period (1981–1985) tree height and the height of the living crown were measured for every tree, but in subsequent periods these parameters were only measured for the ingrowth trees and a subsample of the “old” trees (Schieler and Hauk, 2001). Thus unmeasured tree heights had to be estimated using height increment equations, estimated on the basis of the subsample of the respective period.

In the period 2000–2002, for every sample plot a PNV-type was reconstructed on the basis of the present site conditions and expert knowledge in vegetation science (Schieler and Hauk, 2001).

The individual-tree growth model PrognAus comprises several statistical models which were all parametrized with data from the ANFI for various tree species and a simulation interval of 5 years.

The tree growth prediction utilizes (i) the basal area increment model of Monserud and Sterba (1996) (for coefficients see Hasenauer, 2000), (ii) the crown ratio model of Hasenauer and Monserud (1996), and (iii) the height increment model of Nachtmann (2006). These models are functions of tree size variables (e.g. dbh, crown ratio, tree height), site variables (e.g. elevation, slope angle, dummy variables for Austrian growth districts, etc.) and distance independent competition variables (i.e. basal area of larger trees, BAL, according to Wykoff, 1990 and crown competition factor, CCF, according to Krajicek et al., 1961). The height increment model, based on the Evolon-model by Mende and Albrecht (2001), has a site specific saturation value and thus is convenient for long term growth simulation.

The probability ($P$) of mortality in a 5-year period is predicted using the logistic function according to Monserud and Sterba (1999) (for coefficients see Hasenauer, 2000):

$$P={(1+{e}^{({b}_{0}+({b}_{1}/dbh)+{b}_{2}\times CR+{b}_{3}\times BAL+{b}_{4}\times dbh+{b}_{5}\times db{h}^{2})})}^{-1}$$

(1)

where $dbh$ means diameter at breast height, $CR$ means crown ratio, $BAL$ means basal area of larger trees, and ${b}_{0}$–${b}_{5}$ are species-specific coefficients. The coefficients ${b}_{4}$ and ${b}_{5}$ are only significant for *Picea abies*; this means that large trees of all other species never die, a fact which obviously leads to an unreliable long term simulation. Therefore, the coefficients ${b}_{4}$ and ${b}_{5}$ of the *P. abies* model were used for the other species in order to get the expected U-shaped mortality rate over dbh which cares for age-related rather than competition-related mortality, and thus prevents from implausible tree dimensions.

For the present study the mortality model was used deterministically. This means that the probability of mortality for an individual tree was used as a mortality rate:

$$Nre{p}_{t+5}=Nre{p}_{t}\cdot (1-P)$$

(2)

where $Nre{p}_{t+5}$ is the number of stems per hectare represented by the respective individual sample tree at the end of the simulation interval of 5 years, $Nre{p}_{t}$ is the number of stems per hectare represented by the respective individual sample tree at the beginning of the simulation interval of 5 years, and $P$ is the probability of mortality for the respective individual sample tree.

The ingrowth model according to Ledermann (2002) consists of sub-models for a direct prediction of (i) the probability of ingrowth and (ii) the number of ingrowth trees for a 5-year period within a circle with a radius of 2.6 m. Additionally Ledermann (2002) developed (iii) sub-models for the probability that the ingrowth tree belongs to a certain species, and species-specific sub-models to estimate (iv) the dbh and (v) the height of every ingrowth tree. The sub-model (iii) was developed for (1) *P. abies*, (2) *Abies alba*, (3) *Larix decidua*, (4) *Pinus sylvestris*, (5) *Pinus cembra*, (6) *Fagus sylvatica*, (7) *Quercus* spp., (8) *Fraxinus excelsior*, (9) *Acer* spp., (10) *Carpinus betulus*/*Tilia* spp., (11) *Alnus* spp., (12) *Betula* spp./*Sorbus* spp., and (13) *Populus* spp./*Salix* spp. Note that Ledermann (2002) built groups for all the previously mentioned species separated by a slash because the individual models for these species did not differ significantly. Therefore, these species can only be dealt with as species-groups. In addition, in the present study the model for *P. sylvestris* was used for (14) *Pinus nigra* and the model for *Acer* spp. was used for (15) *Ulmus* spp. Thus only these 15 tree species or species-groups are used in the PrognAus-simulations. Some of the coefficients in model (iii) were corrected according to Ledermann (personal communication) because these have been misprinted in the original article.

The ingrowth model was used deterministically. The total number of ingrowth trees per hectare ($Nre{p}_{Tot}$) within a circle with 2.6 m radius was calculated as follows:

$$Nre{p}_{Tot}={P}_{Ingr}\cdot {N}_{Ingr}\cdot \frac{10000}{2\text{.}{6}^{2}\cdot \pi}$$

(3)

where ${P}_{Ingr}$ is the probability of ingrowth, predicted by sub-model (i), and ${N}_{Ingr}$ is the number of ingrowth trees, predicted by sub-model (ii). The ingrowth-tree-species-distribution was calculated as follows:

$${S}_{i}=\frac{Ps{p}_{i}}{\sum _{i=1}^{15}Ps{p}_{i}}$$

(4)

where ${S}_{i}$ is the proportion of species $i$, and $Ps{p}_{i}$ is the probability, predicted by sub-model (iii). $Nre{p}_{Tot}$ was then distributed to the 15 tree species or species groups ($Nre{p}_{i}$) as follows:

$$Nre{p}_{i}=Nre{p}_{Tot}\cdot {S}_{i}$$

(5)

This means that, in every period, 15 “trees” (i.e. 15 data-records) grow in and the sum of the stem numbers represented by these 15 “trees” equals $Nre{p}_{Tot}$ according to Eq. (3).

The only model which was not used deterministically is sub-model (iv) of the ingrowth model. It is a transformation of the probability density function of the Weibull-distribution. A uniformly distributed random number $\ge 0$ and $<1$ is utilized to attribute a Weibull-distributed dbh to each ingrowth tree.

The tree volume was calculated according to Pollanschütz (1974) for trees with a dbh $\ge $ 10.5 cm and Schieler (1988) for trees with a smaller dbh.

PrognAus is very reliant on the competition variable BAL because it is incorporated as explanatory variable in some of the models mentioned above. Ledermann and Eckmüllner (2004) showed that the resolution of the competition variable BAL changes during the course of the growth projection, and that this leads to biased simulation results. As a solution for this problem Ledermann and Eckmüllner (2004) introduced the “tree record splitting method”: if the basal area represented by the sample tree (i.e. tree record) exceeds a certain threshold then the tree record is to be copied certain times and the represented stem number is to be partitioned. Both the basal area threshold and the number of record-copies depends on the sampling method which was used for sampling the data used for the parameterization of the model using BAL as explanatory variable. For PrognAus
Ledermann and Eckmüllner (2004) recommend to use a threshold of 5.33 m^{2} ha^{−1}, and to duplicate the tree record. In this way trees representing more than 5.33 m^{2} ha^{−1} are split into two tree records, each representing half of the original stem number (and thus basal area per hectare).

In order to find the point in time from which the species composition can be assumed to be in a steady state, 10 sample plots from each of the 18 PNV-groups were randomly selected and the development of these plots was simulated with PrognAus for 3000 years, starting with individual sample tree data of the ANFI for the period 2000–2002. For all 15 tree species or species-groups the respective proportions of volume per hectare were calculated. For all tree species with a respective proportion $\ge 1$% after 1500 years, the proportion range ${R}_{\%}$ (i.e. the difference between the maximum proportion and the minimum proportion) within the periods 1000–1500, 1500–2000, 2000–2500, and 2500–3000 was calculated for all 180 sample plots. It was decided to simulate for a minimum of 1000 years (i.e. approximately the maximum possible lifespan for an individual tree) to make sure that no individual trees of the tree population resulting from management influences were left. Fig. 1 shows boxplots for the distribution of the maximum variation of the species proportion (i.e. the maximum value of ${R}_{\%}$ over all 15 species within the respective period) over the 180 sample plots for the respective periods.

Tukey-boxplots of the maximum variation in the species proportion within 4 consecutive 500-year simulation periods. The first period begins after 1000 simulation-years. The maximum variation was calculated as the maximum value over all tree species of **...**

Obviously the maximum variation in the species proportion decreases with time. After 2500 years the median of the maximum variation is less than 2.5%, and after 3000 years the median is less than 1.7%.

For the present study only undivided sample plots in non-protection forests were used (in total 6933 plots). As a compromise between desired accuracy, required computing time, and data quantity, it was decided to simulate the development of all 6933 sample plots of the ANFI for 2500 years, based on the individual tree and site specific data collected in the period 2000–2002. The steady state species proportion (${P}_{s}$) was then calculated for all tree species and sample plots on the basis of the stand volume per hectare in the last 500 simulation years:

$${P}_{s}=\frac{{\overline{V}}_{s}}{{\overline{V}}_{t}}\times 100$$

(6)

where ${\overline{V}}_{s}$ is the arithmetic mean volume [m^{3} ha^{−1}] for the respective species and ${\overline{V}}_{t}$ is the arithmetic mean volume m^{3} ha^{−1}] for the total stand.

Starlinger (unpublished, cited in Lexer, 2001) roughly described species proportions for different PNV-types. Table 1 shows the species proportions for 18 PNV-types and the number of sample plots expected by the ANFI for each of these PNV-types.

Number of sample plots (*N*) expected by the Austrian National Forest Inventory for each of the 18 potential natural vegetation types and the range of species proportions for the respective type according to Starlinger (in Lexer, 2001).

Every sample plot was classified according to its steady state species proportion, based on the PNV-type classification scheme in Table 1.

The scheme by Starlinger (in Lexer, 2001) does not consider all possible combinations of species proportions. That led to non-classified sample plots. For non-classified sample plots a hierarchical cluster analysis (average linkage method and Euclidean distance measure) using function hclust in R (R Development Core Team, 2009) was applied to find sample plots with similar species proportions.

The share of concordant classifications in the total of all classified sample plots was calculated, as it is a very simple index of agreement. Another common measure of the agreement between two examiners is the *kappa-statistic* ($\kappa $, c.f. Le, 2003, pp. 118–120) which accounts for random success in correct classifications. It takes on a value of 1 with perfect agreement and has a value close to zero when the observed agreement is approximately the same as would be expected by chance. $\kappa $ was calculated both overall and by catergory.

The maximum value of the simulated diameters at breast height was 166 cm, and the maximum value of the simulated tree heights was 50 m.

Fig. 2 shows the simulated development of the volume per hectare for one ANFI-plot, as an example for the wave form of the volume curve simulated by PrognAus. The arithmetic mean of the stand volume per hectare in the last 500 simulation years (marked as dashed rectangle) was used to calculate the steady state species composition, which is the focus of the given study. The maximum value (over all sample plots) of the mean volume in the last 500 simulation years was 640 m^{3} ha^{−1}.

Table 2 shows the number of sample plots for the PNV-types simulated by PrognAus and classified according to their steady state species proportion, in comparison to the expected PNV-types of the ANFI. Eighty-three percent (5789 plots) were actually classified by using the scheme in Table 1, of which only 33% (1887 plots) were correctly classified. The overall kappa was 0.183. Table 2 shows the kappa statistics by category. A predominantly correct classification (71% and 81%, respectively) was only achieved for the subalpine *P. abies*-type (03, $\kappa =0.820$) and the *F. sylvatica*-type (07, $\kappa =0.955$). For 227 sample plots of the subalpine *P. abies*-type (03) according to the ANFI, and 58 sample plots of the montane *P. abies*-type (04) according to the ANFI, the PrognAus-simulations resulted – correctly – in *P. abies*-types, but it was not able to separate between the montane- and the subalpine-types (in Table 2 these plots were counted to the correct classifications). The rare *L. decidua*-type (02), the *Quercus*-types (08, 09, 10, and 11) the *Alnus incana*-type (17), and the *Pinus*-types (11, 21, 22, and 23) did not show up in the PrognAus-simulations. The *Quercus* spp.–*Carpinus betulus*-type (08) showed up only once and the *Acer pseudoplatanus*-type (13) three times, but never for sample plots where the *A. pseudoplatanus*-type was expected according to the ANFI. According to PrognAus just 3 PNV-types (*F. sylvatica* (07), subalpine *P. abies* (03), and *P. abies–A. alba–F. sylvatica* (06)) comprised 79% of all sample plots. In contrast ANFI allocates 59% of all plots to these PNV-types.

Moreover, 17% (1144 plots) could not be classified according to Starlinger (in Lexer, 2001). Four distinct clusters were selected (data not shown) and the arithmetic means of the species proportions within the sample plots in these clusters were calculated. Cluster C1 ($n=14$) represents a forest type dominated by *L. decidua* with *P. cembra*; however, the proportion of *Alnus* spp. is too high to classify the cluster as the *L. decidua–P. cembra*-type (01). Cluster C2 ($n=363$) represents a forest type dominated by *P. abies*; however, the proportion of deciduous tree species is too high to classify the cluster as one of the *P. abies*-types (03, 04, and 05) and the proportion of *F. sylvatica* and *A. alba* is too low to classify the cluster as the *P. abies–A. alba*-type (05) or the *P. abies–A. alba–F. sylvatica*-type (06). Cluster C3 ($n=11$) represents a forest type dominated by *A. alba*, *P. abies*, and *Fraxinus* spp.; however, the proportion of deciduous tree species is too high to classify the cluster as the *P. abies–A. alba*-type (05) and the proportion of *F. sylvatica* is too low to classify the cluster as the *F. sylvatica*-type (07). Cluster C4 ($n=756$) represents a forest type dominated by *P. abies* with admixed *Fraxinus* spp.; however, the proportion of *Quercus* spp. is too low to classify the cluster as the *F. sylvatica*-type (07) and the proportion of *P. abies* and *A. alba* is too low to classify the cluster as the *P. abies–A. alba–F. sylvatica*-type (06).

The average species proportions calculated for sample plots of the same PNV-type as simulated by PrognAus are provided in Table 3; the number of sample plots for the respective groups are shown in Table 2 (second column from the right). It can be seen that the proportion of *A. alba* is small in the *P. abies–A. alba–F. sylvatica*-type (06) and the *F. sylvatica*-type (07); i.e. in those places where one would expect a large proportion of *A. alba*. *P. sylvestris* is present in all PNV-types, but only in very small proportions, except for the *L. decidua–P. cembra*-type (01). *Quercus* spp. are also underrepresented in the PNV-types simulated by PrognAus. The only sample plot classified as *Quercus* spp.–*C. betulus*-type (08) shows a species composition dominated by *C. betulus*/*Tilia* spp. instead of *Quercus* spp. Moreover, the *A. pseudoplatanus*-type (13), where *Acer* spp. should be the dominant tree species, is dominated by *F. sylvatica*.

Average species proportions (mean $\pm $ standard deviation) calculated over all sample plots using the same PNV-types as simulated by PrognAus. For PNV-type 08 no standard deviation is provided because there is only one plot in this group. “ **...**

If one calculates the average species proportions for sample plots of the same PNV-type as expected by the ANFI (Table 4, the number of sample plots for the respective groups are provided in the last row of Table 2), the rather high proportion of *F. sylvatica* for all types which should be dominated by deciduous tree species is clearly visible. Moreover, the proportion of *A. alba*, *P. sylvestris*, *Quercus* spp., and *Acer* spp. is very low and the proportion of *Fraxinus* spp. and *Alnus* spp. is rather high.

Fig. 3 shows that the proportion of coniferous tree species increases with increasing elevation of the sample plot. However, several sample plots between 200 and 600 m a.s.l. show a high proportion of coniferous species too.

The given study investigates the evolving tree species compositions in long term simulations by PrognAus. For this purpose the stand development had to be simulated for a period of 2500 years; therefore, it is relevant that the tree dimensions simulated by PrognAus remain within a biologically plausible range. The maximum values of the simulated tree dimensions show that this is the case.

The age of individual-trees in simulations by PrognAus cannot be given (unlike to other individual tree simulators, e.g. BWINPro, see Nagel and Sprauer, 2009) because the age of the tree at the time of ingrowth is unknown, and individual-tree mortality is not a discrete event.

Fig. 2 shows the simulated volume development for one sample plot as an example, but the graphs for the other plots look rather similar. The wave-like volume development is caused by overlapping bell-shaped volume curves of consecutive tree generations. At the time of the maximum volume, for this plot around the year 100, the simulated stand is still even-aged (the volume curves of the first two generations do not overlap at this time). In the further development the volume approaches a steady state.

PrognAus simulates the development of a forest stand based on a sample. This means that, since PrognAus is a distance-independent tree growth model, it does not simulate single trees of the stand but rather sample trees with their represented stem number per hectare. For the given study the simulations were initialized with individual-tree data collected by the ANFI in the period 2000–2002; thus, in the simulations carried out for this study the size of the simulated sample plot is equal to the size of the sample plot used by the ANFI (i.e. a combination between a variable radius sample plot and a fixed radius sample plot) until the last tree sampled in this way is deleted from the tree list (because it represents less than 0.01 trees per hectare, which is the general threshold for the deletion of tree records used by PrognAus). All other trees were generated by the ingrowth model which has been parameterized with data sampled by using sample plots with a fixed radius of 2.6 m. This means that every generated ingrowth tree represents 471 trees per hectare. In this way it may occur that only one sample tree dominates the entire plot; this would lead to biased results in terms of stand characteristics. However, this can be avoided by applying the tree record splitting procedure (Ledermann and Eckmüllner, 2004) which can be understood as an enlargement of the sample plot size (Ledermann, 2003).

The percentage of 33% correctly classified PNV-types seems rather low. According to Monserud (1990) the overall-kappa of 0.183 indicates a “very poor” degree of agreement. Forest types dominated by *Quercus* spp. or *P. sylvestris* did not show up in the present simulation results and the *F. sylvatica*-type dominates the PrognAus-simulations. The category-specific-kappas indicate that PrognAus simulates the *F. sylvatica*-type ($\kappa =0.955$, “excellent” agreement) and the subalpine *P. abies*-type ($\kappa =0.820$, “very good” agreement) well. Several reasons might help explain these results:

(a) *Conceptual and structural specifics of the model-approach*:

Firstly, the probability of mortality at crown ratios higher than 0.2 is lower for *F. sylvatica* than for *P. abies* and “Other broadleaf species”, and with increasing BAL the probability of mortality is increasing faster for the latter species than for *F. sylvatica*. At crown ratios higher than 0.5 only *L. decidua* has a lower probability of mortality than *F. sylvatica* (Fig. 4). This means that *F. sylvatica* has a higher chance to survive the critical phase of youth and can grow to a larger dbh which leads to a larger tree volume and therefore a higher proportion in volume per hectare of the total stand.

Probability of mortality modified after Monserud and Sterba (1999) (for coefficients see Hasenauer, 2000) over the diameter at breast height for *Fagus sylvatica*, *Picea abies*, *Larix decidua*, and “Other broadleaf species” at a BAL of 0 (left), **...**

Secondly, according to Ledermann (2002) the probability of ingrowth of *F. sylvatica* is independent of the stand density (CCF), whereas for all other species, except *A. alba* and *C. betulus*, this probability is decreasing with increasing CCF. Ledermann (2002) provides the explanation that regeneration of *F. sylvatica* can be found in stands with rather low CCF and even in clearcuts, whereas other shade tolerant species (e.g. *A. alba*) show no such regeneration. However, these model characteristics may result in *A. alba* and *C. betulus* being the only species which are able to out-compete *F. sylvatica* in terms of ingrowth in the case of increasing CCF if site conditions are not considered. The fact that *F. sylvatica* is a highly competitive species was shown by Sterba and Eckmüllner (2008). Their study revealed that *F. sylvatica* actually invades secondary conifer forests rather fast if forest management permits natural regeneration.

Thirdly, the ingrowth model according to Ledermann (2002) contains dummy variables to account for inter-specific competition. Thus the probability of ingrowth of *Quercus* spp. is reduced if *C. betulus* is present in the species composition. However, the probability of ingrowth of *C. betulus* is increased if *Quercus* spp. are present in the species composition. This one-sided competition may be responsible for the relation between these species in the PrognAus-simulations. Table 4 shows higher proportions for *C. betulus* than for *Quercus* spp. for PNV-types 08, 09, 10, and 11. The only sample plot classified as PNV-type 08 in Table 3 is also dominated by *C. betulus*. The model also includes dummy variables to account for the one-sided impact of *P. abies* upon *P. sylvestris* and *F. sylvatica* upon *A. alba*. Although ecologically plausible (cf. Ellenberg, 1996; Mayer, 1974), this may prevent *Quercus* spp., *P. sylvestris* or *A. alba* from dominating the species composition in those sample plots where the site characteristics are also favourable for *C. betulus*, *P. abies* or *F. sylvatica*, respectively. A study by Schodterer (2007) showed that in the Burgenland region in eastern Austria the percentage share of *Quercus* spp. in the height class 10–30 cm is 22% but only 7% in the height class 200–500 cm, whereas the respective percentage share for *C. betulus* are 12% and 25%. This makes it very obvious that *Quercus* spp. are at a disadvantage. Coppicing which is still a common management practice in the east of Austria benefits *C. betulus* at the cost of *Quercus* spp.

Fourthly, the choice of a wrong growth district can have a strong effect on the simulation result. The use of growth district 1 (“Austrian part of the Bohemian Massif”) instead of growth district 2 (“eastern pannonic semiarid region”) causes a difference of 50% in the probability of *P. abies* at 400 m a.s.l. according to sub-model (iii) by Ledermann (2002). Thus, errors in the determination of the growth district might explain that several sample plots (e.g. two sample plots at 400 m a.s.l. with dry Cambisols or Luvisols in growth district 1, at the boarder to growth district 2) showed a steady state species composition dominated by *P. abies* instead of broadleaf species.

Fifthly, PrognAus seems to be stricter in the consideration of site characteristics for the estimation of a PNV-type than the ANFI. The sample plots of the *L. decidua–P. cembra*-type according to PrognAus are limited to elevations higher than 1700 m a.s.l. In contrast, the sample plots of the same PNV-type according to the ANFI can be found also at elevations down to 1200 m a.s.l. Moreover, PrognAus restricts the *Alnus glutinosa–Fraxinus* spp.-type to Fluvisols and Fibric Histosols, whereas the same PNV-type according to the ANFI can be found also on moist Cambisols or temporarily waterlogged (Stagno-gleyic) soils on unconsolidated sediments.

(b) *Data used for the parameterization of the ingrowth model*:

Schodterer (2007) indicated that *A. alba*, *Quercus* spp., and *Acer* spp. are affected by selective browsing. Ledermann (2002) pointed out that browsing would have no direct influence on the probability of ingrowth because ingrowing trees have already exceeded breast height by far (note the 5 cm dbh threshold) and the top bud is therefore out of reach of browsing animals. However, the fact that the proportion of those tree species affected by selective browsing decreases with increasing height (Schodterer, 2007) might also be reflected in the data used by Ledermann (2002) for the parametrization of the ingrowth model. If the PNV-type estimates of the ANFI do not take into account that the species-specific regeneration potential is influenced by browsing, the proportion of certain species is bound to be overestimated and must therefore differ from the simulation results achieved by PrognAus.

As for PNV-types dominated by coniferous species, the overestimation of the proportion of *P. abies* might account for (i) the fact that most of the sample plots which one would have expected to be a PNV-type dominated by *L. decidua* were actually classified as subalpine *P. abies*-type (Table 2), and (ii) a high proportion of coniferous species in sample plots between 200 and 600 m a.s.l. (Fig. 3). A possible reason for an overestimation of *P. abies* is the influence of management which is surely reflected in the data used by Ledermann (2002) for the parametrization of the ingrowth model. Conifers, especially *P. abies*, have played a dominating role in forestry for more than 200 years (Johann et al., 2004). *P. abies* is the major tree species in Austria representing 54% of the overall forest area (Republic of Austria, 2008) and, due to its economical importance, it is often preferred by the management, even on sites where it would not be the major species in terms of PNV. In this context broadleaf species were actually removed systematically by precommercial thinning to favour *P. abies*. All sample plots between 200 and 600 m a.s.l. and a high proportion of coniferous species show rather similar soil characteristics: wet soils, soils affected by stagnant moisture, and nutrient-poor soils. Also at these sites management might have favoured *P. abies* instead of broadleaf species which might be more appropriate for such soils.

A comparable study was carried out by Lexer et al. (2002) with the 3D-patch model PICUS v1.2 for 2800 ANFI plots, where 43% of the simulated steady state species compositions were correctly classified with Starlinger’s (in Lexer, 2001) scheme. The authors point out that both the estimated PNV-types of the ANFI and the species thresholds provided by Starlinger (in Lexer, 2001) are themselves some kind of models and therefore a possible source of error. The tendency of PICUS v1.2 to overestimate the proportion of *P. abies* at the expense of *F. sylvatica* and *A. alba* was not found in this study. PrognAus rather shows the tendency to generally overestimate the proportion of *F. sylvatica* (cp. Table 4) which results in the classification of 51% of the sample plots as the *F. sylvatica*-type. PICUS v1.2 (in Lexer et al., 2002) as well as PrognAus show weaknesses in their ability to simulate forest types dominated by *Quercus* spp. or *P. sylvestris*. However, when comparing PICUS v1.2 and PrognAus one has to consider that the model-drivers are different. The former model uses, among other things, very detailed soil characteristics (e.g. water holding capacity, C/N-ratio) which had not been measured by the ANFI and therefore had to be estimated from the available – more general – site characteristics (Lexer et al., 2002). The model-drivers used by PrognAus are directly available because the PrognAus-models were all parametrized with data of the ANFI (e.g. nominally scaled soil groups).

Comparable studies carried out with static vegetation models (i.e. models for directly estimating the PNV-type) and independent data (i.e. data not used in parameter estimation) show slightly better results. The simulations by Brzeziecki et al. (1993) for Switzerland corresponded in 46% with the expectations by experts. Lexer (2001) developed a logistic model for estimating PNV-types (also based on data of the ANFI) which achieved an overall concordance of 55% ($\kappa =0.406$, “fair”). However, also the static vegetation models show weaknesses in their ability to simulate PNV-types which were infrequent in the dataset used for parameterizing the model.

The forest types derived from the cluster analysis on the proportion of species in the sample plots which could not be classified using the scheme developed by Starlinger (in Lexer, 2001) seem ecologically plausible. The distribution of the clusters in the PNV-type estimates of the ANFI (Table 2) seems to indicate that type C1 reflects a transition from the *L. decidua–P. cembra*-type (01) to the subalpine *P. abies*-type (03); C2 might indicate a transition from *P. abies*-types (03, 04, 05, and 06) to types dominated by *Alnus* spp. and *Fraxinus* spp. (14, 15, and 17) while C3 seems to point to a transition from the *P. abies–A. alba*-type (05) to the *F. sylvatica*-type (07). Type C4 may reflect a forest type close to the PNV-types dominated by *F. sylvatica* (06 and 07) or *Quercus* spp. and *C. betulus* (08).

The steady state species composition evolving in long term simulations carried out with the distance-independent tree growth model PrognAus corresponds to the expected species composition in only 33% of the 5789 sample plots in the Austrian National Forest Inventory. The proportion of *F. sylvatica* and *P. abies* in the PrognAus-simulations seems to be too high, whereas the proportions of *Quercus* spp., *Acer* spp., *A. alba*, and *P. sylvestris* were underestimated. This may be due to the mortality model which allows higher diameters of *F. sylvatica* and thus a higher proportion of volume per hectare, and the ingrowth model whose terms for the consideration of inter-specific competition may lead to a disadvantage for certain species, even on such sites where they should be dominant according to the potential natural vegetation type estimated by the ANFI. Furthermore, the ingrowth model has been built to describe ingrowth under management and recent human influences rather than under unmanaged conditions.

The given study showed that PrognAus produces plausible results in terms of the potential natural vegetation type for sites where *F. sylvatica* or *P. abies* is expected to be the dominant tree species; thus, PrognAus can be considered a reliable tool to predict the development of the species composition at such sites. To correct the performance of PrognAus in terms of the other potential natural vegetation types it would be necessary to reparameterize the ingrowth model and the mortality model with data from unmanaged forest ecosystems.

This study was carried out in the framework of the research project EPIT-Emergent Properties of Individual-tree Models funded by the Austrian Science Fund (FWF, project P18044-B06). I want to thank Klemens Schadauer and all associates of the Austrian National Forest Inventory who provided the data. Many thanks to Thomas Ledermann for providing the source code of PrognAus, and to Sonja Vospernik who adjusted the code to the aim of the research project. I am grateful to Manfred J. Lexer for his permission to use his classification scheme and for various helpful comments on an earlier version of the manuscript. Many thanks are due to two anonymous reviewers for their very helpful suggestions.

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