Evidence of elevation-speciﬁc growth changes of spruce, ﬁr, and beech in European mixed mountain forests during the last three centuries

: In Europe, mixed mountain forests, primarily comprised of Norway spruce ( Picea abies (L.) Karst.), silver ﬁr ( Abies alba Mill.), and European beech ( Fagus sylvatica L.), cover about 10 × 10 6 ha at elevations between (cid:2) 600 and 1600 m a.s.l. These forests provide invaluable ecosystem services. However, the growth of these forests and the competition among their main species are expectedtobestronglyaffectedbyclimatewarming. Inthisstudy,weanalyzedthegrowthdevelopmentofspruce,ﬁr,andbeech in moist mixed mountain forests in Europe over the last 300 years. Based on tree-ring analyses on long-term observational plots, we found for all three species ( i ) a nondecelerating, linear diameter growth trend spanning more than 300 years; ( ii ) increased growth levels and trends, the latter being particularly pronounced for ﬁr and beech; and ( iii ) an elevation-dependent change of ﬁr and beech growth. Whereas in the past, the growth was highest at lower elevations, today’s growth is superior at higher elevations. This spatiotemporal pattern indicates signiﬁcant changes in the growth and interspeciﬁc competition at the expense of spruce in mixed mountain forests. We discuss possible causes, consequences, and silvicultural implications of these distinct growth changes in mixed mountain forests. interspéciﬁque aux dépens de l’épicéa dans les forêts mixtes de montagne. Nous discutons des causes possibles, des con- séquences et des implications sylvicoles de ces changements marqués dans la croissance des forêts mixtes de montagne. [Traduit par la Rédaction] Mots-clés : changement climatique, changement dans la compétition, dominance du hêtre, tendances de la croissance, perte relative d’épicéa commun.


Introduction
In temperate Europe, mixed mountain forests of Norway spruce (Picea abies (L.) Karst.), silver fir (Abies alba Mill.), and European beech (Fagus sylvatica L.) connect the lowland beech forest communities with the spruce-dominated alpine forest types. Whereas forests in the lowlands were exploited much more intensively and were mostly converted to age-class systems by clear-cutting, forests located at higher elevations were often managed less intensively or were left in a more natural state compared with lowland forests (Magin 1959). The main reasons were that the productivity of mountain forests decreases with elevation, mountain forests are less accessible for logging, and mountain forests are highly relevant for protection against gravitational hazards such as avalanches, landslides, or rockfalls and other watershed services (Bebi et al. 2001).
We analyzed a species combination that covers an area of about 10 × 10 6 ha of mixed mountain forests in Europe (Hilmers et al. 2019). Norway spruce, silver fir, and European beech have coexisted for thousands of years in mixture without active management or with close-to-nature forestry across this region (Magin 1959;Preuhsler 1979). Although mixing proportions can favour one of the three species, in the long term, none of the three species are outcompeted. Here, we examine probable reasons for this balanced coexistence. We used increment records covering the last 300 years for revelation of the spatiotemporal growth response to changing environmental conditions. Based on the results, we will be better able to manage the balanced and successful interaction among the three species.
One precondition of a potential coexistence is the overlap of fundamental ecological niches among species (Hutchinson 1957). At elevations of 600-1600 m above sea level (a.s.l.), the climate envelopes of the three species intersect. Silver fir occurs with 500-1500 mm annual precipitation and 3-12°C mean annual temperature, and European beech occurs with 450-1500 mm annual precipitation and 3-12.5°C mean annual temperature; both species are present from the lowland to the montane zone where they are limited by temperature. Norway spruce is better adapted to a cold climate and occurs with 450-1250 mm annual precipitation and -2.5-8.5°C mean annual temperature (Kölling 2007).
Another precondition of coexistence is similar fitness (competitive ability) in the presence of competitors; this enables a common real niche. Similar light ecology across the species is an important feature in this context. All three species are shade tolerant, so none of them will be easily outshaded by the others in the long term. There is a ranking in light requirement, with spruce being more light demanding than fir and fir more than, or very similar, to beech, but the differences seem relatively small compared with tree species that demand more light such as Scots pine (Pinus sylvestris L.) or European larch (Larix decidua Mill.) (Valladares and Niinemets 2008). The minimal light requirements of shade leaves or needles in relation to light above canopy (100%) amounts to 3% for Norway spruce, 1.5% for silver fir, and 1.0% for European beech (Ellenberg and Leuschner 2010, pp. 103-105). Other authors (Burschel and Huss 1987, p. 171;Mitscherlich 1971, p. 76) rank fir and beech even more equally, which underpins their similar light ecology.
Norway spruce has proven to be more drought susceptible than beech and fir (Zang et al. 2014), although spruce foliage is xeromorphic. Both spruce and fir conifers reflect an isohydric strategy (Lyr et al. 1992), reducing stomata conductance at early stages of soil drought. Hence, xeromorphism of needles may be a feature to preserve water in the tree, once the stomata have closed. Under nonlimiting water supply, the lower leaf-level transpiration rate of spruce and fir is counteracted by higher leaf biomass and leaf area index at the stand level relative to beech (Ellenberg et al. 1986;Lyr et al. 1992). By contrast, beech displays an anisohydric strategy, with the stomata being less sensitive to soil drought, allowing for less limited carbon gain and stem and root growth during prolonged time spans under drought than in spruce and fir (Leuschner 2009;Nikolova et al. 2009). However, the hazardous behaviour of the anisohydric beech can be beneficial when water is abundant or under moderate drought stress, while leading to tree mortality under the impact of extreme water shortage (e.g., Klein 2014). Again, with increased atmospheric carbon dioxide (CO 2 ) concentration, the isohydric spruce and fir may limit risk of carbon starvation, following stomatal closure under drier conditions.
There are many more structural and functional traits such as crown plasticity (Jucker et al. 2015;Forrester and Albrecht 2014), rooting depth (Rothe 1997;Schmid and Kazda 2002), litter decomposition (Rothe and Binkley 2001), and browsing pressure (Ammer 1996) that prevent any one of the three species from becoming a permanent winner or loser, and despite their effects changing with climate and growing conditions, the balance among the tree species is maintained. That is, the potential damages are rather equally distributed, with the late frost and ozone susceptibility of fir and beech (Larsen et al. 1990;Matyssek et al. 2010), the high sensitivity to smoke damage and acid deposition of silver fir (Elling et al. 2009), and the high risk of bark beetle infestation (Wermelinger 2004) and snow and storm damage (Spiecker 2000) of Norway spruce. This temporal, spatial, and functional complementarity and risk distribution may contribute to the overyielding of Norway spruce and European beech Rothe 1997), Norway spruce and silver fir (Jensen 1983;Pretzsch et al. 2010;Vallet and Pérot 2011), and Norway spruce, silver fir, and European beech (Pretzsch and Forrester 2017;Mina et al. 2018). Hilmers et al. (2019) found that in terms of stand growth, mixed mountain forest ecosystems are rather resilient against disturbances such as acid deposition, climate warming, and ozone. Increment losses of one species can be counteracted and compensated by the other species. However, acid deposition, late frost and ozone impact, or increasing frequencies of extreme drought events and bark beetle attacks can compromise the contribution of fir, beech, and spruce, respectively (Bircher et al. 2016;Lindner et al. 2010). So, external negative effects on one of the three species can weaken its competitive ability, change its functional role, and change its growth contribution in favour of the other two (Bosela et al. 2019;Hilmers et al. 2019).
Mixed mountain forests in Europe are severely exposed to warming temperatures with no significant changes in precipitation (Auer et al. 2007, Bircher et al. 2016). In addition, increasing natural disturbances such as windstorms or bark beetle outbreaks are to be expected (Seidl et al. 2017). Further changes in the climate system could fundamentally alter the composition and structure of mountain forests (e.g., because of climate-induced shifts in species' niches) (Hanewinkel et al. 2013;Thom et al. 2017;Obojes et al. 2018). Previous research has shown that climate warming has increased the growing season length and productiv-ity of mountain forests (Oberhuber 2004;Jolly et al. 2005), generally above the elevational zone where mixed forests occur. It is less clear how climate change will influence mixed-species forests below the high alpine zone. For example, if beech benefits from higher temperatures at elevations between 600 and 1000 m, this may reduce the competitiveness of Norway spruce and silver fir. Any changes in the fitness and growth of one of the three species can be caused either directly by improved or reduced external growing conditions or indirectly by a strengthening or weakening of the competitors. Nonetheless, if water becomes increasingly limiting, the effects of climate change might become negative (Pichler and Oberhuber 2007;Allen et al. 2015).
Based on what is known about the three dominant tree species in mixed mountain forests, we can hypothesize how their relative growth may change across an elevation gradient in response to a changing climate. For example, Norway spruce may profit at the cold margin of its niche under increasing temperatures. In other words, areas at higher elevations where temperature was previously limiting may benefit Norway spruce more than European beech and silver fir, particularly when temperatures are still too cold for optimal growth of the latter two species. Based on the same reasoning, it follows that the smallest benefit for spruce should be at the lower elevations as temperature becomes suboptimal. At low elevations of the mixed mountain forest zone, the competitive pressure on Norway spruce may increase because of accelerating fir and beech growth and growth recovery of silver fir and European beech from sulfur dioxide (SO 2 ) pollution and ozone (O 3 ) damage, respectively (Elling et al. 2009;Uhl et al. 2013). The growth of silver fir and European beech at the higher elevations may also be enhanced by climate warming, especially on sites with sufficient water and nutrient supply and where temperature, late frost, and the length of the growing season were limiting their growth in the past.
We analyzed the growth changes of Norway spruce, silver fir, and European beech at 28 sites located across the European mountain regions. Climate warming in these regions is often coupled with sufficient water supply, but local variation in water supply and soil conditions may modify the general response pattern previously hypothesized. Based on the aforementioned considerations about elevational-dependent climate change effects in mixed mountain forests, we developed the following questions.
(i) How did the growth of the three tree species develop during the last three centuries?
(ii) Were there species-specific changes in the growth trends during this time period?
(iii) Were there elevational-dependent changes in the growth trends during the last three centuries?

Observational plots, site conditions, and sample sizes
For the increment cores sampling, we selected 28 fully stocked, unthinned, or slightly thinned long-term research forest stands distributed across Europe ( Fig. 1; Table 1). We included only fully stocked, unmanaged reference plots where growth was scarcely affected by human activities and that reflected natural dynamics and climate variations.

Tree measurement protocol and core sampling
Increment cores were collected from about 20 dominant trees of each species per plot. To avoid damaging the trees on the plots, we sampled in most cases in the buffer zone of the plots, which were also fully stocked, unthinned, or just slightly thinned.
We sampled only trees of Norway spruce, silver fir, and European beech. The stem diameter at breast height (DBH; breast height = 1.3 m; in millimetres) was measured using a tape, and the height and height to the crown base (in decimetres) were measured using a Vertex hypsometer (Haglöf Sweden AB, Långsele, Sweden). The height to crown base was defined as the distance from the ground to the lowest living primary branch.
From each tree, we took two 5.15 mm cores at breast height, in the northern and eastern directions, with a standard increment borer, attempting to hit the centre of the stem to cover as many growth rings as possible. The increment cores were air-dried, mounted and glued on wooden supports, and subsequently sanded using sandpaper with progressively finer grit.
We applied a careful visual procedure for making sure that the sampled trees were not only dominant at the time of sampling, but also in the past. First, if longer suppression phases were clearly discernible on the wood sample immediately after coring in the field, the sample was not included in this study, and an alternative tree was selected. Second, after the growth ring widths were measured, we plotted the empirical growth curves for visual examination. About 5% of the trees were excluded at that stage because their growth curves showed depression phases of 10 years or more.
We tried to reduce the potential sampling bias (Cherubini et al. 2002;Nehrbass-Ahles et al. 2014) by applying the following criteria when selecting the sample trees. Most of the trees were sampled on long-term observation plots, so that their growth and social position in the last 50-100 years were documented. Based on this documentation, we sampled only trees that were dominant throughout this observation time. We sampled only trees with crown ratios (crown length/tree height) >0.5, as long crowns indicate a probably continuous dominance of the trees in the past. To avoid sample trees with suppression phases in the more distant past, we excluded all trees with longer low-growth phases as described by Pretzsch (2009, pp. 587-588). Such low-growth phases were either already visible on the increment cores during the sampling procedure in the forest or became visible when plotting growth rates over age after ring analyses in the tree-ring laboratory.

Tree-ring analyses and overview of tree-ring data
Tree-ring widths were measured to the nearest hundredth of a millimetre using a digital positioning table (Kutschenreiter and Fig. 1. Location of the 28 observational plots (black dots) in mixed mountain forests of seven countries where increment cores of Norway spruce, silver fir, and European beech were sampled for this study. The study covered mountain forests in Bosnia and Herzegovina, Bulgaria, Germany, Serbia, Slovakia, and Switzerland. See Tables 1 and 3 for descriptions of plot data. Map layers were compiled using QGIS version 3.12.3 (QGIS Development Team 2020). Johann; Digitalpositiometer, Britz and Hatzl GmbH, Austria). We measured the annual ring widths on each core and cross-dated the individual tree-ring width time series. The radial increments, ir, of the two cores of a tree (ir 1 and ir 2 ) were added to obtain a representative time series of diameter increment, id, for each tree (id = ir 1 + ir 2 ). For those trees with cores that did not reach the pith, the age was estimated from the sum of the number of growth rings of the core (NGR core ) and an estimate of the missing number of growth rings (NGR missing ) by applying the equation Age = NGR core + NGR missing . The number of missing rings was estimated by dividing the last known diameter by the mean diameter increment of the first 30 years. Table 2 and Supplementary Table S1 1 provide an overview of the tree-ring data used for this study.

Linearity of diameter growth over age
To test past tree diameter growth over age for linearity versus nonlinearity, we used the following simple model: which is equivalent to (1b) ln(D) ϭ a 0 ϩ a 1 × ln(AGE) with a 0 ϭ ln(k) where D is tree DBH (in millimetres), AGE is tree age (in years), k is a scaling parameter, and a 1 is the exponentwhich is most crucial for our research question. When a 1 = 1, eq. 1 describes linear growth. When a 0 < 1 or a 1 > 1, the equation describes nonlinear growth, with decreasing or increasing growth rates, respectively. We chose this simple model because more complex (e.g., sigmoid) patterns could be ruled out after visual data inspection. This concept was applied to the full data set, but separately for each tree species, by way of a mixed linear regression model as follows: ( The fixed-effect parameters a 0 and a 1 have exactly the same meaning as in eq. 1b; if a 1 is not significantly different from 1, we would assume a linear growth process. The indexes i, j, and k in eq. 2 refer to the levels of plot, tree on plot, and single observation, respectively. To account for autocorrelation, random effects b and c were applied on the levels of plot and tree on plot. Whereas the random effect b relates to the intercept a 0 , the random effect c refers to the slope a 1 . All random effects were assumed to be normally distributed with an expected mean of 0. The decision to accept the full random-effect model as shown in eq. 2 or potentially simpler subforms was made based on the Akaike information criterion (AIC) (Burnham and Anderson 2004). The uncorrelated remaining errors are ijk .

Temporal trends in diameter growth
The analyses with eq. 2 indicated linear diameter growth over age; therefore, we used the following mixed linear model for investigating temporal trends concerning the level and the steepness of the diameter-age relationship: Except for the fixed effects and their parameters (a 0 , a 1 , a 2 , and a 3 ), the notation of this model is exactly the same as for eq. 2. The fixed effect DYEAR (abbreviation for "DBH-year") indicates the calendar year when a given tree had a DBH for the first time (i.e., when the height of 1.3 m was reached). A significant estimate of a 2 would indicate that there was a temporal trend of the diameterage relationship's level, whereas a significant value of a 3 would indicate a temporal trend in the slope. As with the model in eq. 2, the AIC was applied for deciding between the full set of random effects and simpler subsets.

Temporal growth trends and elevation
For testing the combined influence of age, DBH-year, and elevation, we formulated a mixed linear regression model, which can be seen as an extended combination of eqs. 2 and 3: Again, the meaning of the notation is the same as in eqs. 2 and 3; the only new variables were the fixed effect ALT and deMARTONNE, which stand for a given plot's elevation above sea level in metres and the de Martonne aridity index (de Martonne 1926), respectively.
The fixed effects in this model cover the main effects ln(AGE), DYEAR, ALT, and deMARTONNE and all of their two-way interactions. When fitting the model, nonsignificant interactions were removed and the model was refitted, but if an interaction was significant, the contributing main effects were kept in the model even when not significant, following a protocol suggested by Zuur et al. (2009). The decision about the random effects to be kept in the model was made in the same way as described for eqs. 2 and 3. The model was fitted for each species separately. To avoid conver- gence issues with this model, DBH-years earlier than 1600 were omitted from the data. Mixed-effect models were computed using the R package nlme (Pinheiro et al. 2018; R Core Team 2018). Figure 2 provides an overview of all trees' diameter-age trajectories in a double logarithmic coordinate system. Visually compared with the reference lines, which represent an exponent a 1 = 1 (cf. eqs. 1a and 1b), the trajectories suggest a generally linear growth pattern. The growth trajectories in the upper right corner of the graphs were derived from very old stands. They cover several hundred years but appear short in the graphs because of the logarithmic scale.

Linearity of diameter growth over age
As shown in Tables 3-5, the estimates of the fixed effect a 1 for spruce, fir, and beech were 0.9804 (standard error (SE) 0.0945), 1.0597 (SE 0.0843), and 1.0559 (SE 0.0731), respectively. For all three species, 1 was within a 1 ± 1.96 × SE. This indicates no significant deviation from linear diameter growth over age for each of the three tree species as illustrated in Fig. 3. As there were linear relationships, the slope of the diameter-age lines shown in the right panel of Fig. 3 results from e a 0 . We thus obtained mean diameter growth rates of 4.31, 2.81, and 1.96 mm·year -1 for spruce, fir, and beech, respectively.

Temporal trends in diameter growth
The results obtained by fitting the regression model from eq. 3 are listed in Tables 6-8. All fixed-effect parameters were significant with p < 0.0001, indicating clear temporal trends, with all tree species exhibiting a similar pattern. For all species, we found positive main effects of age and DBH-year and a slight negative effect of the interaction between DBH-year and age. For all species, this leads, over the past 300 years, as Fig. 4 shows, to a pronounced increase of the diameter-age relationship and a slight increase of the slope. Figure 5 compares the species-wise results directly. The aforementioned trends steepen the diameter-age relationship from 1700 to present. They were strongest for silver fir and European beech and least pronounced for Norway spruce. This means that, given increasing growth levels and slopes for all species, the age trends among the species were spruce Ͼ Ͼ fir > beech in 1700 but have changed to rather similar trends (spruce Х fir Х beech), indicating more similar growth vigour in 1800 and 1900.

Temporal growth trends and elevation
For Norway spruce, the growth trend did not change with elevation ( Fig. 6; Table 9). Although elevation as a main effect had no significant (p = 0.9102) influence on the level of the diameter-age relationship, there was a significant positive interaction of elevation with ln(AGE). However, this was counteracted by a significant negative interaction of elevation with deMARTONNE. We could not identify any elevation-dependent changes in growth during the last 300 years for Norway spruce. The de Martonne aridity index had a significant negative effect on the diameter-age relationship. This was counteracted by a significant positive effect of the interaction of deMARTONNE with ln(AGE) and DYEAR. Whereas in the past (DBH-year 1700) Norway spruce trees showed higher growth with lower de Martonne indices, this trend was reverted to higher growth with higher de Martonne indices for trees with a DBH-year of 1900. Our results suggested large differ- Fig. 2. Trajectories of stem diameter at breast height (DBH) and tree age for the 382 Norway spruce, 679 silver fir, and 660 European beech trees during the last few centuries, in double logarithmic representation. Most trees show a linear increase in stem diameter with progressing age (reference lines ln(D) = a 0 + a 1 × ln(AGE) with a 0 = 1 and varying a 0 ) and no asymptotic growth curve pattern. [   ences in growth with fluctuating de Martonne indices at the same elevation ( Supplementary Fig. S1 1 ). Silver fir showed elevation-related trends ( Fig. 7; Table 10). Although elevation significantly (p < 0.0001) reduced the level of the diameter-age relationship, this was counteracted by a significant positive interaction of elevation with DYEAR and ln(AGE). This means that there was an elevation-related differentiation of the general growth trend towards increasing growth with increasing DBH-year. Our model suggested that in the past (DBH-year 1700), growth of silver fir was highest at low elevations and lowest at high elevations. This behaviour of silver fir changed from 1700 to present. Regarding the de Martonne aridity index, our results showed a significant negative effect on the diameter-age relationship. This was counteracted by a significant negative interaction of deMARTONNE with DYEAR and ln(AGE). Whereas in the past the growth of silver fir became higher as the de Martonne index increased, this trend was nonexistent or even reverted for trees with a DBH-year of 1900 ( Supplementary Fig. S2 1 ).
Similar results were found for European beech ( Fig. 8; Table 11). We detected a contrasting trend for elevation and its interactions with other variables. Whereas the significant effect of elevation (p < 0.0001) suggested a general trend towards lower growth with higher elevations, this was counteracted by positive interactions of elevation with ln(AGE) and DYEAR. As Fig. 8 shows, the model suggested higher growth with decreasing elevation for trees with a DBH-year of 1700. This elevation-related ranking, however, changed strongly with time. For trees with a DBH-year of 1900, the initial trend totally reverted; trees at higher elevations showed clearly higher growth rates. The elevation effects took place inside the general pattern of increasing growth with increasing DBHyear. The de Martonne aridity index had a significant (p < 0.0001) increasing influence on the level of the diameter-age relationship. This was counteracted by a significant negative interaction of deMARTONNE with ln(AGE). The interaction of deMARTONNE with DYEAR showed no significant effect. We could not find any changes of the growth of European beech in the last 300 years that were dependent on the de Martonne index ( Supplementary  Fig. S3 1 ).

Integrated view on the revealed growth patterns
The tree-ring analyses revealed that the relative competitiveness and fitness among the three species are changingthe balance of the past due to the interactions described in section 1 might be compromised. According to theory (von Bertalanffy 1951; Zeide 1993) and empirical findings (Assmann 1961;Kramer 1988;Weiner and Thomas 2001), the diameter-age curves of trees should show an asymptotic development of their course at advanced tree ages of 100-300 years. Although most of our sampled trees were at least 300 years old (see Supplementary Table S1 1 ), their diameter-age trajectories are still increasing linearly (Figs. 2  and 3). This phenomenon applies on average for all three species and suggests a large-scale change of the environmental conditions in the last decades. Obviously, the environmental conditions changed in a way that was, on average, beneficial for the growth of all three species and delayed the normal age-related ontogenetic drift and downturn of tree growth (Evans 1972). This general trend was an overarching pattern, but the three species differed in the strength of this trend and its occurrence at different elevations.
During the last 300 years, the mean growth rates, as well as the age trend of the three species, increased significantly (Fig. 4). Trees with an age of 75 years in 1700 grew much more slowly and followed a flatter age trend than trees with an age of 75 years in 1800 or 1900. Whereas this overall pattern was similar for all species, they differed in the extent of this temporal shift of their diameter-age curves. The shift was lowest for Norway spruce and strongest for European beech (Fig. 5). This species-specific shift results in a remarkable change of the relative growth velocity of the three species. Three centuries ago, Norway spruce was clearly ahead of silver fir and European beech. This relationship has changed continuously and now favours silver fir and especially European beech. The trees with a DBH-year of 1900 follow rather similar diameter-age trajectories independent of the tree species. This change in the relative growth strength among the tree species is not the result of an absolute decrease of the growth and productivity of Norway spruce but a result of a lower increase of the growth and productivity compared with the other two, more successful species.
The analysis of growth trends at different elevations reveals an interesting elevation-specific change of growth behaviour for silver fir and European beech (Fig. 8). In stands with a DBH year of 1700, the growth rates were initially higher at lower elevations, but this trend later reversed in direction. In DBH-year 1800 or 1900, the growth was generally higher, but even the ranking of the growth at different elevations changed towards a superiority of the growth of silver fir and European beech at high elevations. This may suggest that the growing conditions for both species generally improved, but at higher elevations even more than at lower elevations (Fig. 8, middle and upper curves).
We sampled only dominant trees. In their very early juvenile phase, they might have been in sit-and-wait positions in the understorey of the stands. But based on the increment cores, we included only individuals without suppression phases during the last centuries. Thus, the sample trees represent the survivors of the population in the long term that had no long-term strong shading and only normal lateral interspecific competition by neighbouring trees. This means that their growth provides a good indication of responses to environmental conditions and relative growth levels and trends of the three species in the overstorey of mixed mountain forests. As the dominant trees represent the majority of the stand growth in mixed mountain forests (Magin 1959;Preuhsler 1979), the sampled trees may also indicate the growth trend and relative contribution of the species to the growth at the stand level.

Significant growth changes of Norway spruce, silver fir, and European beech during the last three centuries
Several studies suggest that the effects of climate warming are strongest at northern latitudes and higher elevations where the temperature and length of the growing season have been limiting growth. This applies especially for moist forest ecosystems where water limitation plays a minor role. Most studies on growth trends at high elevations have so far been based either on scenario analyses with simulation models (Nogués-Bravo et al. 2007;Theurillat and Guisan 2001) or on heating experiments (Saxe et al. 2001;Schindlbacher et al. 2011). Evidence based on long-term surveys combined with tree-ring analyses reaching back several hundred  (Kräuchi et al. 2000).
In the study area, all three species, on average, show an increasing growth trend. This corresponds with growth trends revealed for lowland forests in many parts of Central Europe (Kauppi et al. 2014;Pretzsch et al. 2014;Spiecker 2000). Compared with the findings in the lowland and boreal areas, the acceleration in the mixed mountain forests is even stronger. The diameter growth curves showed no asymptotic turn towards a final diameter, even for very old trees. Although we included only trees that did not show distinct suppression phases in their ring patterns in the past (see section 2), the persistent growth may partly be a sampling effect. At present, the sample trees are dominant, but some might have been subdominant and slow growing in the past and, as a consequence, persistently growing even until high ages as shown by von Guttenberg (1915). In addition, the growth of the tree in advanced ages may be accelerated by changed environmental conditions.
We hypothesize that the increased temperature and extended growing season, the fertilizing effect of nitrogen deposition, and the elevated CO 2 concentration may contribute to this general pattern. Rising temperature alone, as a main factor, is rather unlikely (Fig. 9). An increase in temperature by 2°C as assumed in the niche diagram (grey hatched stripes from positions 1, 2, and 3 in Fig. 9) would leave the growth of Norway spruce at higher elevations (position 1) rather unmodified but would strongly reduce it at middle (position 2) and lower (position 3) elevations of our study area. This differs considerably from the general positive pattern that we found. For European beech and silver fir, a temperature increase of 2°C would strongly increase growth at the higher and middle elevations but would cause no changes at the lower elevations. Again, this does not correspond with the expected pattern, as we found an increase at all elevations. Consequently, temperature changes may be only one of several important factors. Fig. 3. Mean growth trend for Norway spruce, silver fir, and European beech during the last few centuries in double logarithmic and linear representation based on the statistical model from eq. 2. On average, there was no declining increment trend with age, which would mean a turn towards an asymptotic diameter. The trend is linear for all three species, with the following ranking regarding the steepness of the slope: silver fir > European beech > Norway spruce.

Species-specific and elevation-dependent reaction pattern
Our study provides a model example for a reversing, elevationdependent growth response of species. Silver fir and especially European beech thrive at higher elevations because of improved growing conditions and lower competition by Norway spruce. Simultaneously, their growth hardly changes at lower elevations. Of course, elevation is just used as a proxy for mean annual temperature and length of the growing season in this region (Körner 2007). Especially in mountain forests with temperature limitations and short growing seasons, the extended length of the growing season (Menzel and Fabian 1999) may cause a long-term acceleration of tree growth (White et al. 1999).
However, there are other climatic trends (e.g., precipitation), which are not generally related to elevation. Thus, we were able to show that not only the elevation, but also the de Martonne aridity index, has a significant effect on the growth of Norway spruce. At the same elevation, Norway spruce showed clear differences in growth with fluctuating de Martonne indices (see Supplementary  Fig. S1 1 ). This finding makes it clear that there is a high regional variation in precipitation and aridity and that these variations must be considered when analyzing growth trends in mountain areas (Körner 2007). Figure 9 may contribute to a better understanding of the species-specific growth behaviour, especially the relative gain of silver fir and European beech compared with Norway spruce. Considering only the temperature changes, European beech and silver fir should mainly gain in growth under climate warming, whereas Norway spruce should mainly lose in growth. This change in the ranking among the species is in line with our findings. The growth increase of Norway spruce, despite detrimental mean temperature effects, might result from other positive effects such as extended growing season, fertilizing deposition, or increase of the atmospheric CO 2 concentration. In addition, at positions 2 and 3 in Fig. 9, the mixing of Norway spruce with European beech and silver fir may result in a competition reduc- Fig. 4. Changes of the level and the slope of the diameter growth curves for the three species during the last three centuries according to the results obtained by fitting the mixed linear model from eq. 3. DBH-years 1700, 1800, and 1900 (abbreviated as DYEAR in eq. 3) mean that the trees reached a height of 1.3 m in the years 1700, 1800, and 1900 and are 320, 220, and 120 years old at present (in 2020), respectively. tion or even facilitation compared with growth in intraspecific neighbourhoods (Pretzsch and Forrester 2017, pp. 146-148). Stands of Norway spruce cultivated beyond the natural niche (position 3) may be increasingly endangered by drought and by competition from silver fir and European beech. Temperature and precipitation measurements over the last decades showed a significant increase in temperature but no significant trend in annual precipitation in the mountain regions of Europe (e.g., Auer et al. 2007;Büntgen et al. 2011;Hilmers et al. 2019). The growth of beech increased because of this warming and the simultaneously high amount of precipitation at higher elevations (Fig. 8). This is in line with the work of Aertsen et al. (2014) and Tegel et al. (2014), who also discussed an increase in growth of beech. Nevertheless, beech faces challenging environmental changes, especially in mountainous areas. Environmental changes in the alpine regions are mainly characterized by acid and nitrogen depositions and O 3 pollution (Brang 1998;Flückiger and Braun 1999;Smidt and Herman 2004). Muzika et al. (2004), for example, found significant negative correlations between air pollutants (O 3 , nitrogen dioxide (NO 2 ), and SO 2 ) and the growth of beech and spruce in the Carpathian Mountains. In addition, there are natural influences due to climate change such as late frost events and drought stress (Dittmar et al. 2003;Jump et al. 2006;Bontemps et al. 2009), as well as biotic diseases such as fungal infestation (Cherubini et al. 2002). However, so far, the growth-accelerating effects of the climate warming seem to outweigh negative effects in mixed mountain forests (Tognetti et al. 2014).
For silver fir, our results (Fig. 7) are in line with several studies (e.g., Uhl et al. 2013;Büntgen et al. 2014;Bosela et al. 2018) that demonstrated an unprecedented increase in productivity of silver fir in Central European forests following the reduction in air pollutants since the 1980s in combination with a warmer, but not drier, climate in the Alps. However, a recent Europe-wide study on the growth of silver fir throughout the Holocene ) describes increasing radial growth in the Italian Alps and the Apennines until the turn of the millennium, but not beyond. Bosela et al. (2018) showed that silver fir populations in the southern parts of the Alps may have recently experienced a growth limitation due to drought. Silver fir populations close to the Mediterranean distribution limit already show a drought-induced growth depression, which will become even more critical in a warmer and drier future (Antonucci et al. 2019).
Remarkably, our results for spruce (Fig. 6) show a steady increase in growth rates since the 17th century, even at lower elevations (ϳ800 m a.s.l.); this is similar to the findings by Schurman et al. (2019). However, the increase was lower than for the other two species (Fig. 5). This suggests that in the mixed mountain forests of Europe, spruce, in relation to beech and silver fir, loses in the face of competition probably because of its lower adaptation to drought compared with the associated species and their increasing vitality and competitiveness. Cocozza et al. (2016) observed that the phenology of cambial cell production in spruce is highly variable and plastic with elevation, enabling this species to occupy sites with contrasting climatic conditions, namely high elevations and cold sites. However, further climate warming, natural disturbance events such as strong winds, bark beetle out- Note: Significant fixed-effect parameter estimates are in boldface type. Because of the different orders of magnitude in the parameter estimates, they are presented in scientific notation. "-" means that the particular component was excluded from the final model. breaks, and summer droughts will pose great challenges for spruce, especially in monolayered stands at low elevations (Lévesque et al. 2013;Zang et al. 2014;Seidl et al. 2017) and probably less seriously in mountain areas with cooler temperatures and higher precipitations. Hilmers et al. (2019) showed that the stand-level productivity of mixed mountain forests was stable, in terms of volume increments over the last 30 years. However, they also showed that the tree species involved (beech, spruce, and fir) showed remarkably different volume increments at the stand level. Spruce showed a significant decline in productivity, whereas silver fir showed significant productivity gains. Beech showed unchanged volume increments over several decades. In summary, the stand-level productivity remained rather stable because losses of one species were compensated by gains of the others.
Our results deal with the individual tree level and show that the mean increment, as well as the age trend of all three tree species, has increased steadily since the 17th century. Productivity at the stand level, however, is not only driven by the productivity of the individual trees, but also depends on stand structure (e.g., density and size distribution) (Forrester 2019). It is likely that the sampled dominant trees benefited more from the extended growing seasons and the effect of CO 2 fertilization (Kulakowski et al. 2011;Pretzsch et al. 2014) than the subdominant and suppressed individuals that were limited by light. It is possible that spruce trees from intermediate and suppressed social classes may have suffered significantly or even died from the competitive shift among the three tree species and thus the productivity of Norway spruce at a stand level may have decreased as reported by Hilmers et al. (2019).
The revealed growth trends may be overestimated because of a bias that may be caused by sampling dominant trees that were subdominant in the more distant past. Their growth trend may partly be an effect of a change from a subdominant and slowgrowing social position to a dominant and fast-growing social position within the population. We tried to reduce this potential sampling bias as described in section 2.1.2. Thus, the statements about the absolute growth trend of Norway spruce, silver fir, and European beech should be used cautiously and need further substantiation. However, the general findings of a positive growth trend, the relationships among the tree species, and the elevationspecific growth changes would hardly be modified by a biased sampling. Therefore, we think that, unlike the statements about the absolute trends, the relative changes of growth are well substantiated by our study.

Relevance and perspectives
The study by Hilmers et al. (2019) about the stand growth of mixed mountain forests covered many of the plots that were also included in our study of the individual tree growth. Hilmers et al. (2019) showed that the stand growth in total has hardly changed over the last 30 years (Hilmers et al. 2019). Any growth decline or dropout of subdominant trees may have been compensated by the persevering growth of the dominant trees shown in our study. A temporal growth decline of silver fir due to SO 2 emissions in 1970-1990, for instance, was compensated by the growth of Norway spruce, which is more resistant to SO 2 pollution. Growth losses due to O 3 emissions may be compensated by the other two  species. The particular drought-sensitive and isohydric sit-andwait behaviour of Norway spruce might be counteracted by the anisohydric behaviour of European beech that continues growing unless water scarcity causes hydraulic failure (e.g., Klein 2014).
Our results suggest that this balance and growth stability due to tree species diversity may be compromised in the future. Especially at lower elevations, where Norway spruce grew optimally in the past, drought may reduce its contribution to stand growth in the future. One additional reason for this may be the relative loss in competitiveness compared with silver fir and European beech, which are better adapted to drought. We hypothesize that a key life-history trade-off will be how these three species trade off resources devoted to drought (future limiting factor) versus radiation (main limiting factor over thousands of years) and that this trade-off may shift with ontogeny. In addition, bark beetle outbreaks and storm damage can reduce the share of spruce in lowelevation forests.
The contradictory findings in this study that the increment cores of dominant trees of Norway spruce showed increasing growth but the stand growth of Norway spruce is decreasing on the same plots (Hilmers et al. 2019) may be explained by the decreasing abundance of Norway spruce in the stands. This decreasing abundance of Norway spruce may be a result of the growth trends that are more positive for silver fir and European beech and that may cause a relative competitive disadvantage for subdominant spruces. However, this is speculative and needs further research into the contribution of different species and size classes of individuals to the stand growth as recently pointed out by Torresan et al. (2020).

Silvicultural and ecological implications
The long-term growth trajectories of Norway spruce in relation to silver fir and European beech suggest a relative advantage of fir and beech at the expense of spruce. The growth reduction of spruce in relation to fir and beech means a loss of fitness. At lower elevations, Norway spruce is limited by drought events and bark beetle; at higher elevations, it is impaired by the growth acceleration of neighbouring silver fir and European beech in mixed mountain stands. Except in the high-montane and subalpine zone, silver fir and European beech will probably benefit from natural conditions (i.e., without silvicultural promotion) and gradually replace the role that Norway spruce had in the past. At lower elevations, Norway spruce will be restrained to cold sites where fir and beech may be limited by late frost. Norway spruce may also have a chance to establish under disturbances that cause abrupt opening of the previously dense canopy and exposure of the soil. In addition, spruce regeneration depends on nurse logs in some stand conditions (Stroheker et al. 2018). Where there is not yet impeding competition by already established fir and beech, spruce regeneration may benefit from its ability to quickly establish on open mineral soil and establish successfully, although the further development may be questionable because of the previously mentioned restrictions.
Norway spruce can be only partly replaced by silver fir. Forest management may be interested in keeping a significant portion of Norway spruce in mountain forests, for example, because of its high appreciation by forest industry and its contribution to ero- Note: Significant fixed-effect parameter estimates are in boldface type. "-" means that the particular component was excluded from the final model. Fig. 9. Temperature niches of Norway spruce, silver fir, and European beech according to Kölling (2007) and effects of climate warming (grey hatched stripes with arrows pointing to the right to warmer conditions) in mixed mountain forests in Europe. Positions 1-3 represent the constellation of the three species at high, middle, and low elevations, respectively. sion protection due to its canopy closure in the winter period when beech is leafless. Norway spruce can also be promoted on sites where silver fir may fail to regenerate because of browsing pressure (Kupferschmid 2018).
Although Norway spruce may have no future at lower elevations because of interspecific competition, warming, drought, and bark beetle damage, it may be promoted by silvicultural measures at higher elevations. Natural regeneration may be successful by opening the canopy of previously fully stocked stands in seed years. Planting may also be an option, for example, in combination with opening for skyline crane harvest operations. However, the strengthening of silver fir and European beech will require continuous promotion of Norway spruce after successful establishment, especially in lower and middle elevations.
Mountain forests in Europe provide diverse ecosystem services such as protection against natural hazards, wood, water purification, biodiversity, and recreation areas. The mixed mountain forests analyzed in this study fulfil many ecosystem services better than monocultures. Therefore, forest management should strive to keep them stable and even transform homogenous forest stands into selection forests or other kinds of forests with rich composition and structure.
The sustainability of mixed mountain forests in wood production and other ecosystem services is mainly based on the tree species diversity. Species diversity can mean risk distribution in view of abiotic and biotic disturbances, stability of growth, and permanent protection function (soil erosion, avalanches, and flooding). The weakening of one species by environmental change may be successfully compensated by promoting and transitioning to more suitable tree species such as sycamore maple (Acer pseudoplatanus L.) or European chestnut (Castanea sativa Mill.). Introduction of alien species such as Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) is quite controversial, as this will conflict with the objective of managing mountain forests less intensively or leaving them in a more natural state.

Conclusions
Tree-ring analyses revealed significant elevation-specific growth changes of Norway spruce, silver fir, and European beech in European mixed mountain forests during the last three centuries. The growth of Norway spruce lags behind that of fir and beech, especially at lower and middle elevations. However, for the maintenance of production, biodiversity, recreation, and essential protection services of mountain forests, silvicultural concepts should ensure the promotion of spruce on sites suitable for future climatic conditions while facilitating the establishment of other better adapted tree species where spruce might become at risk.
A potential silvicultural challenge in these forests may be to keep at least a minor portion of Norway spruce because of its significant provision of various ecosystem services. In particular, the mixed mountain forests with high portions of Norway spruce should be converted to more diverse stands by regulating the natural regeneration or by planting in favour of, for example, silver fir, European beech, sycamore maple, or Douglas-fir for stabilization of growth, productivity, and other ecosystem services.