Forest Ecology and Management 304 (2013) 233–242

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Forest Ecology and Management

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Complementarity in mixed-species stands of Abies alba and Picea abiesvaries with climate, site quality and stand density

0378-1127/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.foreco.2013.04.038

⇑ Corresponding author at: Chair of Silviculture, Faculty of Environment andNatural Resources, Freiburg University, Tennenbacherstr. 4, 79108 Freiburg, Ger-many. Tel.: +49 7612038628.

E-mail address: david.forrester@waldbau.uni-freiburg.de (D.I. Forrester).

David I. Forrester a,b,⇑, Ulrich Kohnle c, Axel T. Albrecht c, Jürgen Bauhus b

a Chair of Silviculture, Faculty of Environment and Natural Resources, Freiburg University, Tennenbacherstr. 4, 79108 Freiburg, Germanyb Department of Forest and Ecosystem Science, The University of Melbourne, 500 Yarra Boulevard, Richmond, VIC 3121, Australiac Forest Research Institute of Baden-Württemberg, Wonnhaldestr. 4, 79100 Freiburg, Germany

a r t i c l e i n f o

Article history:Received 2 October 2012Received in revised form 18 April 2013Accepted 24 April 2013

Keywords:Competition indexCompetitive reductionIndividual tree modelPlant–plant interactions

a b s t r a c t

Interactions between plant species can be dynamic, changing spatially and temporally with variability inclimatic, soil and stand conditions. We examined how inter- and intra-specific interactions between Abiesalba Mill. and Picea abies (L.) Karst. varied with climate, site quality and stand density in the Black Forestof south-western Germany, using spatially explicit neighbourhood indices. The mixing response, a mea-sure of complementarity, was quantified as the increase in growth of individual trees in a mixed-speciesneighbourhood compared to a mono-specific neighbourhood. Both species benefited from growing inmixed-species neighbourhoods, but this complementarity effect (�60% to >200%) depended on climaticconditions, site quality and stand density. Complementarity increased for A. alba with increasing meanmaximum temperatures in August, those for P. abies increased with mean minimum temperatures inMay and site quality, and in each case the magnitude of the effect was amplified with increasing standdensity. Complementarity is often considered to become more important in less productive ecosystems,but this study showed that for the given pair of species, complementarity effects can increase as growingconditions improve. A simple model is proposed that describes how relationships between productivityand complementarity change depending on the resources limiting productivity.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Community composition and stand structure can both be influ-enced by species interactions (Brooker et al., 2008; Coates et al.,2009; Thorpe et al., 2010). These interactions can be influencedby spatial and temporal changes in resource availability and abioticconditions (Tielborger and Kadmon, 2000; Brooker, 2006; Forresteret al., 2011) leading to dynamic relationships between species.Adapting forest ecosystems to climate change and its conse-quences is one of the biggest current challenges in forestry, andmixed-species stands are being viewed as one of the most impor-tant adaptation and risk-reduction strategies (Reif et al., 2010).Determining when and how species interactions might be influ-enced and respond, is considered a priority to understand how cli-matic variability might influence biodiversity (Brooker, 2006), andwill facilitate the design of innovative silvicultural systems to min-imize potentially detrimental effects of climate change.

In this study, complementary interactions (e.g. competitivereduction and facilitation) are considered to occur if growth is

greater in the presence of inter-specific competition comparedwith intra-specific competition. Following from the stress-gradienthypothesis (Bertness and Callaway, 1994; Callaway, 2007), com-plementary interactions between species have often been thoughtto become more important as ecosystem productivity declines (e.g.Paquette and Messier, 2011) and growing conditions becomeharsher (e.g. Brooker et al., 2008). There is a large body of evidenceto support these trends, but there are also many exceptions. Recentconceptual models indicate that positive interactions may actuallybe strongest under moderate conditions(e.g. Maestre et al., 2009;Holmgren and Scheffer, 2010). This is because (i) the beneficial ef-fects of nurse plants for resources such as water or light undermoderate conditions might be outweighed by increased competi-tion for the same resources in harsh environments, (ii) even ifthe relative facilitation effect increases with increasing stress,which may even expand the environmental niche in which a spe-cies can occur, the absolute facilitation effect should be largest atmoderate conditions because under harsh conditions growth is al-ready very slow and the facilitative effect will not be large enoughto change this, and (iii) organisms are adapted to their local ecosys-tem, and under relatively productive conditions organisms can berelatively more sensitive than those from harsher conditions, andtherefore facilitation can play a significant role under productiveconditions (Holmgren and Scheffer, 2010).

234 D.I. Forrester et al. / Forest Ecology and Management 304 (2013) 233–242

In forests, it may be possible for complementary interactions toincrease with increasing ecosystem productivity when interactionsbetween species improve the capture or use efficiency of a re-source such as light. This is because, as water and nutrient avail-ability and hence ecosystem productivity increases, leaf areasand light interception increase (Smethurst et al., 2003), and the rel-ative importance of competition for light is likely to increase (Pret-zsch and Biber, 2010). Any interaction that improves light captureor use efficiency should become more important with increasingproductivity. This study tested the hypothesis that complementar-ity would increase with site quality for a pair of species with differ-ent shade tolerances that are most likely to interact in ways thatimprove light capture and use.

A second hypothesis was that complementarity would also beinfluenced by climatic variables such as temperature and precipita-tion. Many studies have shown that strategies for coping with cli-matic variability vary between species (Backes and Leuschner,2000; Leuschner et al., 2001; Leuzinger et al., 2005; Weber et al.,2007), however this is usually shown for mono-specific stands.Studies comparing responses by different species in mixtures(Wullschleger et al., 2001; Raftoyannis and Radoglou, 2002), haverarely compared the response of a given species in mixture to itsmonoculture (Pretzsch et al., 2013) and hence the effect speciesinteractions might have had on the response. This distinction isimportant because an individual species’ ability to cope with cer-tain environmental conditions probably depends on the speciescomposition, structure and stand density of the forest in which itis growing. Literature reviews have identified major knowledgegaps relating to how a trees response is affected by the neighbour-ing trees and species (Geßler et al., 2004, 2007).

Stand density can also influence species interactions (Huntet al., 1999; Garber and Maguire, 2004; Amoroso and Turnblom,2006; Condés et al., 2013) and often varies spatially and temporallywithin forests. For example there are many cases where eucalyptgrowth has been increased when planted in mixtures with nitro-gen-fixing acacia trees (Forrester et al., 2006). However, there arealso examples where very high densities, e.g. 1300–20,000 acaciatrees ha�1 in addition to about 1000 eucalypt trees ha�1, had netcompetitive effects on eucalypt growth, even though soil nitrogenincreased with acacia density (Hunt et al., 1999). Therefore, to

Table 1Site and stand information of the six study sites.

Study sites

Ta220 Ta2

Latitude, longitude 47�580N,8�530E

48�8�1

Elevation (m a.s.l.) 830 720Parent material Limestone SanMean daily max. temp. in June (�C)a 21.2 20.Mean daily min. temp. in January (�C)a �4.8 �4Mean daily temp. (�C)a 7.1 6.7Annual rainfall (mm)a 941 177Daily hours of sunshine (month�1) 144 138Slope Level SteAspect NA SouAverage age (A. alba/P. abies) 103/91 120Mean dominant height (m) during study period (A. alba/P.

abies)b32.8/34.6 27.

SIA.alba (m3 ha�1 year�1)c 12.5 7SIP.abies (m3 ha�1 year�1)c 11 6Pre-treatment volume(m3 ha�1) 598–707 524Species volume (%) at installation; fir/spruce/beech 79/17/4 38/Trees ha�1 at installation; fir/spruce/beech 238/55/27 238

a 1950–2007.b Tallest 100 trees ha�1 (tallest 50 ha�1 A. alba and 50 ha�1 P. abies).c SI = site index, the mean annual increment of monocultures expected at age 100 yea

examine the effects of a given factor (e.g. site quality or climate)on species interactions in forests, it is necessary to separate the ef-fects of stand density from that of species identity. This studyadopted an approach using neighbourhood indices and then usedit to examine how the balance between inter- and intra-specificinteractions changed with climate, site quality and stand densityin six mixed-species stands of Abies alba Mill. and Picea abies (L.)Karst. in the Black Forest, Germany. Whereas there have been anumber of studies analysing interactions between P. abies and Fa-gus sylvatica (e.g. Pretzsch and Schütze, 2009; Pretzsch et al., 2010),few studies have investigated interactions between P. abies and A.alba (Vallet and Pérot, 2011). Information about this species com-bination is likely to be important. The two species occur together inmixed mountain forests in central and southern European moun-tain ranges, and as A. alba is seen as a species that may replace P.abies on certain sites in a warmer and drier climate (Kölling,2007) there may eventually be more mixed stands of these species.

2. Methods

2.1. Site description

The experimental plots are located at six sites in Baden-Würt-temberg, Germany, covering the major natural range of A. alba (Sil-ver fir) in the Black Forest (Schwarzwald; sites: 221–223, 225), theSwabian Forest (Schwäbisch-Fränkischer Wald; site 224), and thesouth-western Swabian Alp (Südwest-Alb; site 220). The sites spanthe north–south extent of A. alba in this mountain range. Site andstand information is provided in Table 1 and Fig. 1. The climate istemperate to cool-temperate and annual precipitation ranges fromabout 900 to 1900 mm across the sites, with winter maxima at thehigh precipitation sites and summer maxima at the low precipita-tion sites.

The experimental plots were about 50 m � 50 m to 60 m �60 m in size and were established between 1979 and 1981 in 85-to 125-year-old stands dominated by A. alba and P. abies, in whichthere had been no harvesting for the previous 10 years. In additionPinus sylvestris, and F. sylvatica were present in the stands at lowdensity. Whereas P. silvestris was only present as scattered individ-

21 Ta222 Ta223 Ta224 Ta225

260N,40E

47�440N,7�580E

47�440N,8�10E

48�560N,9�340E

48�460N,8�260E

1020 1020 520 700dstone Gneiss Granite Sandstone Sandstone

6 19.9 19.7 22.5 20.6.1 �5.2 �5.6 �3.8 �3.7

5.8 5.5 7.8 7.03 1850 1827 1130 1535

136 137 140 133ep Moderate Moderate Moderate Moderateth South Northeast South Northwest/126 95/92 116/107 108/103 98/91

8/31.1 31.9/30.1 26.2/34.1 31.4/32.8 29.9/32.8

12 7 11 1110 10 9 10

–602 460–580 452–625 468–656 463–57862/- 61/24/16 33/47/20 42/58/- 52/46/2/222/- 270/68/335 158/139/334 157/225/- 251/131/27

rs.

1980 1990 2000 2010

0

20

40

60220221222223224225

Basa

l are

a (m

2 ha−1

)

Measurement Year

Fig. 1. Stand basal area in each plot at each site at each measurement time.

D.I. Forrester et al. / Forest Ecology and Management 304 (2013) 233–242 235

uals, F. sylvatica admixtures comprised more substantial propor-tions in the stands’ standing volume at the beginning of the exper-iment (220: 0–9%, 222: 12–26%, 223: 14–26%, 225: 0–6%). NaturalF. sylvatica regeneration was found among the A. alba –P. abiesregeneration occurring during the observation period at sites220, 222, 223 and 225.

A wide range of growing conditions was created over time byapplying four different harvesting regimes to four plots at each ofthe six sites including a control as well as short, medium and longregeneration periods. These included a range of densities as wellas trees that experienced anything from only intra-specific competi-tion to only inter-specific competition. The range of stand basal areais shown in Fig. 1. Additional information about the sites and man-agement are provided in Weise (1995) and Puettmann et al. (2009).

2.2. Data collection

Tree diameters (at 1.3 m) were measured at approximately 5-year intervals between 1979 and 2007, stem positions of all over-storey trees were mapped.

Precipitation and mean daily maximum and minimum temper-atures were obtained from the German Weather Bureau (Deut-scher Wetterdienst; DWD). Site quality was quantified bycalculating site indices (SI) separately for A. alba (SIA.alba) and P.abies (SIP.abies) using age and dominant height data collected whenthe experiments were installed. Dominant height was calculated asthe height of the mean basal area tree of the 100 largest trees (bydiameter) ha�1. These data were used to estimate expected heightand mean volume increment at age 100 years based on yield tablesused by the state forest service in the research region for A. alba(Hausser, 1956) and P. abies (Wiedemann, 1942). If fewer than100 trees ha�1 were present for a species in a stand, site indexassessment was based on the height of the mean basal area tree.Site index was highest for a site located on a plateau, lowest onthe steepest site, and for intermediate sites it was lower on siteswith northerly aspects than those with southerly aspects (Table 1).

2.3. Competition indices

The competition experienced by each tree was described as afunction of the size, proximity and species identity of its neigh-bours using a simple summation equation:

NIi ¼Xn

j¼1

sizeaj

distancecij

ð1Þ

NIi is the neighbourhood experienced by the focal tree (i), from nneighbours (j), size is tree size quantified as tree basal area (cm2),and distance is the distance (m) between stem centre of the focaltree (i) and the jth neighbour. The importance of neighbour sizeand distance are controlled using the exponents a and c,respectively.

Trees were considered to be neighbours when their tops werecontained within an inverted cone with an opening angle of h orig-inating from two thirds of the focal trees’ height. This is a commonconcept for defining competition, when light is considered a majorlimiting resource (Biging and Dobbertin, 1992; Pretzsch, 2009, p.293). Optimal values of a, c and h for each species were determinedusing least squares where the R2 of the relationship between theperiodic annual basal area increment (PAI) and NI (both ln + 1transformed) was regressed against each of these constants usingthe method described by Vanclay (2006) and Forrester et al.(2011) in Simile v4.7 (Simulistics, www.simulistics.com). The NIi

were recalculated along a continuous range of values of the givenconstant until the maximum R2 was found. All trees within a plotbuffer of 10 m were considered competitors of focal trees but notas focal trees themselves. This buffer size was based on the treeheights and optimal h values to avoid edge effects from outsidethe plots. Similarly, trees that belonged to the regeneration cohort(tree basal areas less than 500 cm2) were considered competitorsbut not focal trees.

2.4. Growth models

To separate the effects of stand density and species, PAI wasmodelled as a function of tree diameter (cm) at the start of the rel-evant 5-year growth period, species-specific neighbourhood indi-ces (NI; see below), age, climatic variables and SI. To examinewhether species interactions were influenced by climate or SI,interactions between NIs and climate or SI were also included inthe model. Each climatic variable is the 5-year mean for the monththat was most highly correlated with basal area PAI. These were 5-year mean daily maximum temperature in August, mean dailyminimum temperature in May and precipitation during May, eachcorresponding to the relevant 5-year growth period. The neigh-bourhood indices were divided into their inter-specific and intra-specific components (e.g. NIA.alba, NIP.abies, NIF.sylvatica) (Forresteret al., 2011). A separate model was fitted for A. alba and P. abies.Growth models were not constructed for F. sylvatica because itwas not present at two sites, and at the others it contributed lowproportions of stand volume and basal area (Table 1). Competitionfrom F. sylvatica (NIF.sylvatica) was included in growth models for A.alba and P. abies. The starting models that included all of theseindependent variables took the form of the following equation:

ytijk ¼ Xtijkbþ Zi;jkbi þ Zij;kbjk þ Zijkbijk þ etijk ð2Þ

etijk ¼ qet�1ijk þ etijk; ð3Þ

With random effects:

biidi�Nð0;r2

i Þ; biidij�Nð0;r2

ijÞ; biidijk�Nð0;r2

ijkÞ; eiidtijk�Nð0;r2Þ

where ytijk is the dependent variable, ln (PAI); Xtijk the independentvariables’ matrix (fixed effects matrix); Zijk the random effects ma-trix; b, b the parameters’ vector of fixed and random effects; t theindex for time of measurement; i the index for site; j the indexfor plot; k the index for tree; etijk the error component; q the auto-correlation coefficient; etijk is the within group error vector.

Table 2Parameter estimates of variables used to calculate the neighbourhood indices (see Eq.(1)) for each focal tree species (i), and R2 of the relationship between PAI and NI.

Species a c h (degrees) R2

A. alba 0.50 1.2 94 0.28F. sylvatica 0.51 0.9 102 0.40P. abies 0.60 1.1 86 0.33

236 D.I. Forrester et al. / Forest Ecology and Management 304 (2013) 233–242

Tree PAI was log-transformed so that relationships were linearand age was also tested in squared form to allow for any non-linearrelationships. Variogram plots were examined to ensure that therewas no spatial dependency, such as microsite effects, within theplots, and this was found to be true in all cases.

The mixed models based on Eqs. (2) and (3) were fitted as hier-archical mixed-effects models in R 2.15.2 (R Core Team, 2012). Therandom effects were Tree nested within Plot nested within Site toaccount for spatial correlation within the residuals, owing to thehierarchical structure of the dataset. Initially all fixed effect candi-date predictors were included in the models in Eqs. (2) and (3).Then all non-significant (P > 0.05) variables were removed in orderof decreasing P-value. Residual and normal quantile plots werevisually assessed to ensure that the residuals were centred at zero,approximately normally distributed and with constant varianceboth within and across groups. Random effects for each level ofnesting were considered significant when 95% confidence intervalsof the standard deviation did not contain zero. The normality of therandom effects were assessed at each level of nesting using normalquantile plots, and plots of the random effects were examined toensure that there was no spatial clustering. The structure of thevariance–covariance matrix was specified as general symmetricpositive-definite (data/results for covariance not shown). Serialautocorrelation resulting from the repeated measures for each treewas accounted for by including a first order autoregressive correla-tion structure with the same nested structure as used for the ran-dom effects.

2.5. Mixing response

The size and direction of the species interactions, or the ‘‘mixingresponse’’ was quantified as the absolute (Eq. (4)) or relative (Eq.(5)) increase in growth of trees experiencing only inter-specificcompetition compared to those only experiencing intra-specificcompetition.

Absolute mixing response

¼ Modelled PAINIinter

NIintra ¼ 0

� ��Modelled PAI

NIinter ¼ 0NIintra

� �ð4Þ

Relative mixing response

¼Modelled PAI

NIinter

NIintra ¼ 0

� ��Modelled PAI

NIinter ¼ 0NIintra

� �

Modelled PAINIinter ¼ 0

NIintra

� � ð5Þ

The relative mixing response is analogous to the relative yield,an index that is often used to quantify mixing effects (Harper,1977), and could also be considered a measure of complementar-ity. Relative yield is the ratio of yield of a given species in mixtureto monoculture. Here, mono-specific neighbourhoods are used as areference. Similar equations to this mixing response have been

Table 3Means and standard deviations of diameters (at 1.3 m), basal area PAI and NIs for A. alba

Site Diameter Basal area PAI (cm2 year�1) A. alba fo

A. alba P. abies A. alba P. abies NIA.alba

220 43.9 (9.1) 44.1 (7.2) 37.7 (28.8) 31.9 (17.2) 24.6 (13.6221 37.7 (7.0) 39.4 (6.8) 27.8 (19.9) 22.3 (12.5) 11.8 (7.7)222 49.2 (11.5) 46.6 (8.6) 44.3 (28.7) 36.2 (21.6) 23.7 (18.1223 49.7 (8.9) 49.0 (8.2) 39.7 (13.3) 27.3 (15.9) 11.6 (9.6)224 40.9 (8.6) 40.3 (7.4) 35.2 (25.6) 24.6 (15.6) 13.4 (7.8)225 39.2 (8.9) 45.6 (8.4) 25.3 (17.7) 27.7 (19.1) 11.9 (7.3)

used to separate ‘complementarity’ from ‘selection’ effects in bio-diversity experiments (Loreau and Hector, 2001), but without thesame control for stand density.

3. Results

3.1. Neighbourhood indices and tree growth

Neighbourhood indices accounted for 28%, 40% and 33% of thevariability in periodic increment of individual tree basal area forA. alba, F. sylvatica and P. abies, respectively (Table 2). The optimalangle h of the inverted cone for determining neighbours of focaltrees was 86, 94 and 102 for P. abies, A. alba and F. sylvatica, respec-tively. The differences in h suggest that trees have to be closer toP. abies than to F. sylvatica before they influence the growth ofthose species, which may reflect lower crown-length-to-crown-width ratios and greater crown plasticity of F. sylvatica. Values ofa and c were important for all species (–0 or 1) and show thatthe influence of neighbours increases with their size at a greaterrate (a) for P. abies and decreases as the distance to the neighbourincreases at a greater rate (c) for A. alba.

3.2. Growth models

The neighbourhood indices were significant in the final tree ba-sal area PAI models for both A. alba and P. abies (Tables 3 and 4,Fig. 2). There was a significant interaction between NIP.abies andmean maximum temperature in August in both models, and theP. abies model also contained interactions between NIP.abies andboth mean minimum temperature in May and SIP.abies. The randomeffects of Site, Plot and Tree were also significant in the models foreach species. Accounting for serial autocorrelation lowered the AICvalues from 2495 to 2344 for A. alba and from 1507 to 1498 for P.abies. The autocorrelation coefficient for A. alba indicated a highercorrelation (rho = 0.51) than that for P. abies (rho = 0.22). A lag ofone period was suitable for both models.

3.3. Mixing response

The effects of the interactions on basal area PAI in each growthmodel are shown in Figs. 2 and 3. For A. alba, basal area PAI wasusually greater in mixed-species neighbourhoods than in mono-specific neighbourhoods, except at the lowest mean maximum Au-gust temperatures (Fig. 2a). The interaction between inter-specificcompetition (NIP.abies) and mean maximum August temperature

(n = 1311) and P. abies (n = 892) focal trees.

cal trees P. abies focal trees

NIP.abies NIF.sylvatica NIA.alba NIP.abies NIF.sylvatica

) 9.1 (10.9) 4.5 (2.9) 35.6 (24.7) 35.7 (25.5) 13.5 (8.3)17.2 (10.0) 39.0 (23.5) 19.7 (12.4)

) 8.8 (7.4) 14.1 (9.2) 21.4 (13.1) 28.1 (16.8) 13.9 (8.1)23.1 (17.8) 11.6 (9.4) 34.2 (18.9) 17.7 (11.8) 11.7 (6.2)15.6 (9.8) 48.5 (26.1) 24.1 (15.9)13.7 (8.1) 5.6 (4.2) 27 (17.9) 20.8 (12.1) 10.9 (4.4)

0 20 40 60 800

20

40

60 (a) A. alba Mix: max.T = 19.6Mix: max.T = 21.9Mix: max.T = 24.1Mono

Basa

l are

a PA

I (cm

2ye

ar−1

)

0 50 100 150

(b) P. abies MixMono: max.T = 19.6Mono: max.T = 21.9Mono: max.T = 24.1

0 50 100 150

0

20

40

60 (c) P. abies Mix: min.T = 3.6Mix: min.T = 5.7Mix: min.T = 7.8Mono: min.T = 3.6Mono: min.T = 5.7Mono: min.T = 7.8

Basa

l are

a PA

I (cm

2ye

ar−1

)

Neighbourhood index0 50 100 150

(d) P. abies MixMono: SIP.abies = 6Mono: SIP.abies = 8.5Mono: SIP.abies = 11

Neighbourhood index

Fig. 2. Influence of intra-specific and inter-specific neighbourhood indices (NI) on A. alba (a) and P. abies (b–d) basal area PAI with varying levels of 5-year mean maximumtemperature in August (a and b), 5-year mean minimum temperature in May (c), and SIP.abies(d). Graphs were produced using the models shown in Table 4. For each graph allclimatic variables, diameter, age and SI are held constant at their mean values, except for the variable indicated in the legends, which span the range found in this data set.Growth responses to inter-specific NIs are indicated as ‘‘Mix’’ and are calculated with zero intra-specific competition, while growth responses to intra-specific NIs areindicated as ‘‘Mono’’ and are calculated with zero inter-specific competition.

D.I. Forrester et al. / Forest Ecology and Management 304 (2013) 233–242 237

(Table 4) resulted in increasing absolute and relative mixing re-sponses with increasing mean maximum temperatures, and thiseffect increased with increasing NI (Fig. 3a and b). In contrast P.abies only grew better in mixed-species neighbourhoods underlower mean maximum August temperatures, higher mean mini-mum May temperatures, and higher SIP.abies (Figs. 2 and 3). Themagnitude of these absolute and relative responses of P. abies,whether positive or negative, increased with increasing NI(Fig. 3). Basal area PAI of both species declined with increasingmean May precipitation, however, unlike maximum and minimumtemperature, there were no interactions between precipitation andinter- or intra-specific competition for either species.

These tree-level responses were aggregated to the stand levelusing the mean stand conditions in terms of diameter, stand den-sity (trees ha�1), age, NIA.alba and NIP.abies, and with zero NIF.sylvatica.Fig. 4 shows the combined effect of the growth response of bothspecies on total stand basal area increment. These are constructedusing the models for each species (Table 4), and summing them to-gether to give the stand total.

Maximum August temperatures had a positive influence on thegrowth of both species in mono-specific neighbourhoods (Fig. 4a–c). However, the mixing response increased with maximum Augusttemperature for A. alba and decreased for P. abies; as temperatureincreases, the A. alba mixture line bends upwards while the P. abiesline bends downwards (Fig. 4a–c). The net effect is that the total

basal area increment of mixtures is more than would be expectedif inter- and intra-specific competition were equal. The responsesto mean minimum May temperature and SIP.abies are both drivenby P. abies because interactions between each of these variableswith NI were not significant in the A. alba model. Hence mixing ef-fects increase with increasing minimum May temperatures(Fig. 4d–f) and SIP.abies (Fig. 4g–i) because of the response by P.abies; the slight upwards bend in the A. alba line occurs regardlessof minimum May temperatures and SIP.abies, and simply results be-cause in most stands A. alba grows better in mixed neighbourhoodsthan in mono-specific neighbourhoods.

The effect of stand density on the mixing response is shown inFig. 4j–l. At low densities there are only weak interactions betweenspecies, but these interactions become more intense as density in-creases. Despite these density effects, total modelled stand basalarea increments were similar at each density because the increaseddensity resulted in more intense competition and lower individualtree growth rates.

4. Discussion

Both species benefited from growing in mixed-species neigh-bourhoods compared with mono-specific neighbourhoods, but thiscomplementarity effect depended on climatic conditions and stand

19 20 21 22 23 24 25

−20

−10

0

10

20

max.T (.oC)

Low NIMedium NIHigh NI

(a) A.alba

19 20 21 22 23 24 25

−50

0

50

100

150

200

250

max.T (.oC)

(b) A.alba

19 20 21 22 23 24 25

−20

−10

0

10

20

max.T (.oC)

(c) P.abies

19 20 21 22 23 24 25

−50

0

50

100

150

200

250

max.T (.oC)

(d) P.abies

3 4 5 6 7 8

−20

−10

0

10

20

min.T (.oC)

(e) P.abies

3 4 5 6 7 8

−50

0

50

100

150

200

250

min.T (.oC)

(f) P.abies

5 6 7 8 9 10 11 12

−20

−10

0

10

20

SIP.abies

(g) P.abies

5 6 7 8 9 10 11 12

−50

0

50

100

150

200

250

SIP.abies

(h) P.abies

Abso

lute

resp

onse

(cm

2ye

ar−1

)

Rel

ativ

e re

spon

se (%

)

Fig. 3. The influence of climatic variables and SIP.abies on the absolute (left side) and relative (right side) mixing responses of A. alba (a and b) and P. abies (c–h) at low (L),medium (M) and high (H) stand densities (based on NI). Absolute and relative responses were calculated using data from Fig. 2 and Eqs. (4) and (5).

238 D.I. Forrester et al. / Forest Ecology and Management 304 (2013) 233–242

density. This study indicates that the direction and magnitude ofinteractions between A. alba and P. abies can change with climaticvariables such as temperature. Also, growth and complementarityeffects in mixed-species forests sometimes improved as growingconditions improved, which is contrary to the stress-gradient

hypothesis, but consistent with more recent conceptual modelsabout facilitative effects along environmental gradients (Holmgrenand Scheffer, 2010).

Temperature increased the growth of both species in mono-spe-cific neighbourhoods. However, while higher mean daily maxi-

Table 4Parameter estimates (Eq. (2)) and their standard errors for models describing the (ln)basal area PAI of A. alba and P. abies. For the A. alba model AIC = 2344, the number ofobservations was 1311, etijk = 0.60 and rho = 0.51. For the P. abies model AIC = 1498,the number of observations was 892, etijk = 0.47 and rho = 0.22. prec. is 5-year meanmonthly precipitation in May (mm month�1), max. T is the 5-year mean dailymaximum temperature in August (�C), min. T is the 5-year mean daily minimumtemperature in May (�C). sd is standard deviation.

Parameter A. alba P. abies

Estimate se Estimate se

Diameter 0.037207 0.0035206 0.03802637 0.0045352NIA.alba �0.026137 0.0026111 �0.00680108 0.0016952NIP.abies �0.130855 0.0283612NIF.sylvatica �0.040291 0.010893 �0.01659403 0.0059787prec. �0.002681 0.0005257 �0.00396846 0.000603min. T 0.15723925 0.0565479Age 0.152435 0.0273016 0.07707186 0.0220177Age2 �0.000678 0.0001160 �0.00053762 0.0000941NIP.abies �max. T 0.005238 0.0013177 0.00166916 0.0004331NIP.abies �min. T �0.00292038 0.0010733NIP.abies � SIP.abies �0.00308709 0.0006224

Estimate Lower Upper Estimate Lower Upper

sdi 0.1897 0.0811 0.4434 0.4679 0.2316 0.9451sdij 0.0976 0.0354 0.2686 0.1711 0.0920 0.3179sdijk 0.2659 0.1546 0.4573 0.2854 0.2256 0.3611

D.I. Forrester et al. / Forest Ecology and Management 304 (2013) 233–242 239

mum temperatures (in August) increased mixing effects on A. alba,they decreased mixing effects on P. abies. This probably relates tointer-specific differences in growth responses to temperature andto its influence on evaporative demand and soil water availability.For example, A. alba can develop deeper root systems than P. abies(Köstler et al., 1968), which may improve access to and uptake ofsoil resources. If water availability declines as temperature in-creases, the better ability of A. alba to access water would be acompetitive advantage, increasing its mixing response whilereducing the mixing response of P. abies. The mixing response ofP. abies also increased with increasing mean minimum tempera-tures in May and may relate to its influence on early and late sea-son growing conditions. Our finding is also supported byretrospective analyses of the tree growth response to climatic var-iation. In the Black forest region, radial growth of P. abies, particu-larly at higher altitudes, is more likely affected by drought thanthat of A. alba (van der Maaten-Theunissen et al., 2013).

Both species often grew better in mixed-species neighbour-hoods than in mono-specific or less diverse neighbourhoods. Basedon the data from this experiment we cannot examine the mecha-nisms driving the complementarity effect in these mixtures, andcan only speculate that a possible driver was improved light inter-ception or efficiency due to contrasting crown physiologies, crownarchitectures and stratification. A. alba is more shade tolerant thanP. abies (Grassi and Bagnaresi, 2001; Stancioiu and O’Hara, 2006)and stratified canopies were observed in this study such that the50 largest-diameter P. abies trees ha�1 were usually taller thanthe same cohort of A. alba trees. Increases in productivity withincreasing diversity have been linked to higher light absorptionby more structured canopies (Naeem et al., 1994, 1995) and varia-tion in traits such as shade-tolerance can be important contribu-tors to increased productivity in mixtures (Zhang et al., 2012).

The mixture effects shown in the models (Figs. 2 and 3) are atthe individual tree level. At the stand level the net effect of re-sponses by each species meant that the growth of 1:1 mixtureswas about 10% greater than what would be expected when inter-and intra-specific competition are equal, averaged across all standsin Fig. 4. A. alba also grew better (14.5%) in 1:1 mixtures with P.abies in France, when averaged across a wide range of site qualities,whereas there was no mixing response by P. abies (Vallet and Pérot,2011).

Complementarity is often considered to become more impor-tant as ecosystem productivity declines (Paquette and Messier,2011) and growing conditions become harsher (Brooker et al.,2008), e.g. in accordance with the stress-gradient hypothesis (Bert-ness and Callaway, 1994; Callaway, 2007). Contrary to this ecolog-ical theory, in this study complementarity in terms of mixtureresponses was only weakly (but positively) related to site quality,and increased with minimum (P. abies) or maximum (A. alba) tem-peratures. Similarly, some of the largest reported facilitative effectsof mixing nitrogen-fixing species with Eucalyptus species were onvery fertile sites in Hawaii (Binkley et al., 2003; Forrester et al.,2006). This is consistent with more recent conceptual modelsshowing that positive interactions may actually be more promi-nent under moderate environmental conditions (Maestre et al.,2009; Holmgren and Scheffer, 2010).

These seemingly contrasting trends of increasing versusdecreasing levels of complementarity with increasing productivitymay be explained using the concept depicted in Fig. 5. Here we as-sume that the direction of these mixture effects will be determinedby (1) how the growing conditions change along the gradient inproductivity or as stands develop, and (2) by the type of speciesinteraction, in terms of the resource that it influences, e.g. im-proved nutrient availability via faster litter nutrient cycling, or re-duced competition for light due to canopy stratification (see Fig. 5).To interpret these trends, it is also pertinent to consider that onlower quality sites, below-ground resources (water and nutrients)are expected to limit growth relatively more than light, but as theavailability of below-ground resources (and site quality) increase,the relative importance of competition for light probably increasesin forests (Pretzsch and Biber, 2010). That is, as site quality in-creases, stands have higher leaf areas because the increased nutri-ent and water availability enables trees to build and maintainhigher leaf areas (Smethurst et al., 2003; Hubbard et al., 2010),which increases competition for light. Fig. 5 ignores the case whereone species is significantly more dominant than another so that theformer grows larger in mixtures simply because it benefits fromthe slower growth and less intense competition from the formerand not due to any species interaction per se. For example mixingeffects of F. sylvatica can also increase with site quality as intenseintra-specific competition is replaced with less intense inter-spe-cific competition from species such as P. abies (Pretzsch et al.,2010).

Complementarity, or mixing effects, also increased with standdensity, for both species (Fig. 4j–l). Increasing or decreasing com-plementarity effects with increasing stand density have been re-ported in other studies (Hunt et al., 1999; Garber and Maguire,2004; Amoroso and Turnblom, 2006; Condés et al., 2013). At lowdensities any species interactions, whether positive or negative,will probably be weaker, and hence complementarity may initiallyincrease with stand density, as was the case in this study. At veryhigh densities, which did not appear to occur in this study, intensecompetition may outweigh any complementarity effects (Huntet al., 1999). These density effects may also be explained usingthe conceptual model of Fig. 5 because stand density can also influ-ence which resource is most limiting for growth (x-axis of Fig. 5).So if species interactions improve light capture and light becomesan increasingly growth limiting resource with increasing standdensity, complementarity effects should increase with increasingstand density, at least until density is so high that competition out-weighs any complementarity effects.

It is important to note that only six sites were used in this studyand even though these covered the latitudinal range of A. albastands along this mountain range, a greater number of standswould be required to make more general conclusions about the ef-fect of climate on the interactions between these species. Anotherdisadvantage of the data set used was that tree age ranged from 85

0.0

0.2

0.4

0.6

0.8

1.0 (a) max.T = 19.6 (b) max.T = 21.3 (c) max.T = 24.1

0.0

0.2

0.4

0.6

0.8

1.0 (d) min.T = 3.6 (e) min.T = 5.3 (f) min.T = 7.8

0.0

0.2

0.4

0.6

0.8

1.0 (g) SIP.abies = 6.0 (h) SIP.abies = 8.5 (i) SIP.abies = 11.0

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0 (j) 100 trees ha−1

Mix A. albaMix P. abiesMix TotalMono A. albaMono P. abiesMono Total

0.0 0.2 0.4 0.6 0.8 1.0

(k) 240 trees ha−1

0.0 0.2 0.4 0.6 0.8 1.0

(l) 400 trees ha−1

Basa

l are

a in

crem

ent (

m2

ha−1

year

−1)

Proportion of A. alba

Fig. 4. Basal area increment of A. alba and P. abies at varying levels of 5-year mean maximum temperature in August (�C) (a-c), 5-year mean minimum temperature in May(�C) (d-f), SIP.abies (m) (g-i) or stand density (j-l). All lines were calculated using the models described in Table 4, with average values for all variables except the variable noted.Thick lines indicate growth in mixtures and the corresponding thin lines show the expected growth in monocultures. Positive mixture effects occur when mixture lines bendupwards away from monoculture lines. Straight monoculture lines indicate no mixing effect and downward bending lines indicate that growth was poorer in mixtures than inmonocultures.

240 D.I. Forrester et al. / Forest Ecology and Management 304 (2013) 233–242

to 146 years and since age can significantly influence species inter-actions (Forrester et al., 2011) a greater range of ages and tree sizeswould enable more general conclusions.

Site indices had no significant influence on A. alba growth andonly a minor influence on P. abies growth, even when climatic vari-ables were removed (data not shown). Site indices calculated fromyield tables, as done in this study, depend on empirical relation-ships between height and age. However, shade tolerant speciessuch as A. alba can remain in the under storey for decades, therebydistorting height-age relationships and hence calculations of siteindex. Also, site indices indicate the net effect of factors such as soiland climate, but since yield tables predict site indices according tomonocultures, they do not take account of species interactions,which significantly influenced the growth of these stands. Thismay explain the minimal impact of site indices on growth whenspecies interactions were taken into account, and indicates the lim-itations of the use of yield-table-derived site indices for mixed spe-

cies stands, especially given that growth of P. abies in mono-specific neighbourhoods declined with increasing site index, whichwas derived using height-age data from these mixed stands (notmonocultures).

4.1. Management implications

Forest policies are encouraging more tree species diverse forestsin order to increase productivity and sustainability, to reduce vul-nerability to stress and disturbances, and to provide a wide rangeof ecosystem goods and services. This study shows that in termsof productivity, mixtures of A. alba and P. abies may actually beuseful systems for some sites, but may prove counter-productiveat others. This depends on the types of species interactions in themixture, and the site conditions.

This study, and the positive relationships between facilitativeinteractions and the success of forest restoration projects in mod-

Fig. 5. Conceptual relationship between growing conditions and the mixingresponse of a given species. Two examples are shown: (a) is the case found inthis study, where the species interactions may have resulted in a reduction incompetition for light. On low productivity sites, resources other than light limitgrowth (e.g. soil nutrients, soil moisture, harsh climatic conditions) so this type ofinteraction is not as useful. As growing conditions improve light becomes arelatively more growth limiting resource and any interaction that improves lightcapture or use efficiency should increase the mixing effect. In contrast (b) is a casewhere the mixing effect decreases as nutrient availability increases. Interactionsthat improve nutrient availability (e.g. accelerated rates of nutrient cycling) will bemore valuable on sites where those nutrients are limiting.

D.I. Forrester et al. / Forest Ecology and Management 304 (2013) 233–242 241

erate or better environments (Gómez-Aparicio, 2009), indicatesthat further work to examine the trends proposed in Fig. 5 mighthave considerable value for forest management. Furthermore,examining tree growth responses to climate may be of limited va-lue if this does not consider species interactions since many forestsare not mono-specific.

Acknowledgements

We thank the many people who have been involved in the plan-ning, establishment, maintenance and measurement of the fieldexperiments used in this study, including employees of the ForestResearch Institute of Baden-Württemberg and the Forest Districtswhere the field sites are located. Klaus Puettmann provided a for-matted version of the data. D.F. received an Alexander von Hum-boldt Fellowship to work on this project. We would also like tothank Andreas Brunner and three anonymous reviewers who pro-vided comments that improved the manuscript.

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