ORIGINAL PAPER

Monica Musio Æ Klaus von Wilpert Æ Nicole H. Augustin

Crown condition as a function of soil, site and tree characteristics

Received: 10 October 2005 / Accepted: 13 April 2006 / Published online: 29 June 2006� Springer-Verlag 2006

Abstract One of the aims of this work is to describe howthe target variable ‘‘tree vitality’’ in terms of needle lossis affected by other explanatory variables. To describesuch a relationship in a realistic way, we use generalizedadditive mixed models (GAMMs) which allow to takespatial correlation of the data into account and inaddition allow the inclusion of explanatory variables aspredictors with the possibility of having non-linear ef-fects. The GAMMs are fitted in a Bayesian frameworkusing Markov chain Monte Carlo techniques. Data areavailable for two years 1988 and 1994. We select a set ofbest explanatory variables from a large set of variablesincluding tree-specific variables, such as species, age,nutrients in the needles and site-specific variables such asaltitude, relief type, soil depth and content of differentnutrients in the top soil. In the two models for 1988 and1994, different sets of explanatory variables were se-lected as best predictors. In both models, the effects ofexplanatory variables allowed a plausible interpretation.For example, the site-specific variables such as relief andsoil depth were significant predictors, since these factorsdetermine how well water and nutrient supply is bal-anced at a specific site. The selected sets of explanatoryvariables differed between 1988 and 1994, giving anindication of a possible change in the main causes offorest deterioration between 1988 and 1994. From the

set of nutrient variables measured in the soil and in theneedles, in 1988 altitude a.s.l. and magnesium supplywere among the explanatory variables, in 1994 a com-bination of Al in the soil and the N/K-ratio (in theneedles) was selected in the model. In 1988 altitude a.s.l.was among the most important predictors in the model.This is in contrast to 1994 where altitude was not se-lected. This may have to do with the fact that in the earlyphase of forest health monitoring (1988) one of the maincauses of forest deterioration was magnesium deficiency.Later on this may have changed to a combination of soilacidification and nitrogen eutrophication. Thus by usingan adequate model such as the GAMM, sets ofexplanatory variables for needle loss may be identified.By fitting two GAMMs, with different sets of ‘‘best’’predictors, at two time points 1988 and 1994, we candetect changes in these sets of ‘‘best’’ predictors overtime. This allows us to use the monitoring data with thetree vitality indicator crown condition/needle loss as atool for forest health management, which may involvedecisions about concrete counter measures like e.g. for-est liming.

Keywords Needle loss Æ Site variables Æ Tree nutrition ÆSoil chemistry Æ Levels of environmental monitoring ÆGeneralized additive mixed models Æ Spatial correlation

Introduction

Forest decline, which was observed since the beginningof the 1980s, has been caused by a combination of nat-ural and anthropogenic stress factors in most of CentralEurope. Apart from distinct ‘‘hot spots’’ like the OreMountains in the Czech Republic, indirect impacts ofacid and nitrogen depositions prevail rather than directacute smoke damages (Schopfer and Hradetzky 1984).According to that finding, the forest monitoringschemes, which started mainly in 1983 with a strongfocus upon crown condition (as defined as loss of needles/leaves and yellowing), were step-by-step complemented

Communicated by Hans Pretzsch

M. MusioDipartimento di Matematica ed Informatica,Universita di Cagliari, via Ospedale,72, 09100 Cagliari, Italy

K. von Wilpert (&)Forest Research Centre Baden-Wuerttemberg,Wonnhaldestr. 4, 79100 Freiburg/Br, GermanyE-mail: Klaus.Wilpert@forst.bwl.deTel.: +49-761-4018173Fax: +49-761-4018333

N. H. AugustinDepartment of Mathematical Sciences,University of Bath, Bath BA27AY, UK

Eur J Forest Res (2007) 126: 91–100DOI 10.1007/s10342-006-0132-8

by surveys on soil chemical conditions and nutrientsupply of trees. Thus, these schemes developed to com-plex environmental monitoring schemes, which allow theexamination of varying influencing factors on treevitality, such as deposition of acid and nitrogen andtheir after-effects in ecosystem reactions, changingweather conditions, site-specific factors and interactionsamong these factors.

The leading hypothesis on the causes of forest declinepostulates for the chronic type of the damages the fol-lowing chain of cause and effect: acidic deposition and asurplus of nitrogen availability cause an accelerated soilacidification and disequilibria in tree nutrition, whichlead to yellowing and loss of needles/leaves (Schopferand Hradetzky 1984; Ulrich et al. 1994; Ulrich 1995;Landmann and Bonneau 1995). In order to investigatesome aspects of this hypothesis, data from differentsurveys on crown condition, tree nutrition and soilchemical status were combined in this investigation.

We assume that the loss of needles/leaves is an inte-grating indicator for tree vitality and hence use it as theresponse variable in our investigation. Considering therather contradictory discussion concerning the inter-pretation and ecological meaning of needle loss, thisvariable is a good choice for pragmatic reasons since itwas a constant part of the actual forest monitoringscheme since the beginning in the 1980s. On the otherhand, Ellenberg (1995, 1997) stated that the loss ofneedles/leaves is a natural reaction of trees to act againstany kind of stress and therefore a differential diagnosis,which identifies single factors of this stress like anthro-pogenic air pollution, would be difficult.

In this context, the aim of this study is to identify astatistical model, which is able to deal with categoricaland continuous variables and allows to incorporate thedata from the different surveys on the crown condition,tree nutrition and soil chemical status. The model isrequired to incorporate non-linear effects of someexplanatory variables, e.g. age and to deal with spatialcorrelation. We include data from two different timesinto the analysis in order to show how the effects of theexplanatory variables can change with changing envi-ronmental conditions.

Data and statistical method

The data

The response variable and a broad set of descriptivecategorical site-specific variables as well as data on treenutrition are available from the ‘‘ImmissionsokologischeWaldzustands—Erfassung (IWE)’’, a combined surveyof crown condition in terms of needle loss and treenutrition. The IWE was performed every 6 years since1983. We used the data of 1988 and 1994 because theseprovided the best co-incidence in time to the ‘‘BodenZustands Erfassung (BZE)’’, a soil chemical survey,which was performed between 1989 and 1992.

The soil chemical data (BZE)

The BZE data are on the chemical soil condition of thehumus layer and the mineral soil. The soil chemical dataallow judgments about the acidification status, the po-tential phytotoxic effects (e.g. of ionic aluminium) andthe ability of the soil to serve as a stable stock ofnutrients. The upper soil, where the intensive rootingzone is located, is represented in the BZE by the depthlayers 0–5, 5–10 and 10–30 cm. In the following, weconsider only the chemical status of the uppermostrooting zone at 0–5 cm depth (Mg-, Ca-, P-, K-, N-, Al-,Fe-content and pHKCl). Preparation of soil samples andtheir analyses were performed according to the BZEmanual (BML 1990).

The needle loss and tree nutrition data (IWE)

Since the aim of the IWE survey is to elucidate thecausal background of forest deterioration, it contains abroad set of explanatory variables potentially influenc-ing the defoliation of trees. The degree of defoliation wasconsidered as an integrating indicator of tree vitality. Inorder to simplify the statistical models, we categorizedthe needle loss, which is assessed usually in 5% classes toa binary needle loss class (NLC) taking the value 0 if thedefoliation is slight (0–20%) and the value 1 if it ismoderate or severe (25–100%). This response and thedescriptive site variables are shown in Table 1, onlypresenting the variables, which were finally used in themodels. The IWE material is restricted to dominant andsubdominant trees in order to exclude effects of standsociology from the analysis. All assessments and mea-surements have been performed at two single trees,which have been felled at about 800 sampling points in a4 · 4 km grid, respectively. Between 1988 and 1994 thecriteria for tree sampling had been changed: in 1988,from the collective of dominant (subdominant) trees inthe sample the mostly damaged (‘‘minus tree’’) and abelow-average damaged tree (‘‘plus tree’’) were selected,whereas in 1994 two trees with medium damage hadbeen sampled. This change in the inventory design canprovoke a biased comparison between the two cam-paigns. The ‘‘minus trees’’ were too extreme by repre-senting the worst trees and not the whole collective.Thus, they did not spatially differentiate in the NLC.The collective of the ‘‘plus trees’’ was more comparableto the trees of 1994 in their range of NLC (Musio et al.2005). Hence, in order to reduce this problem in com-parability, the material was restricted in 1988 to the‘‘plus trees’’. Needles for analysis of nutrient contentwere collected at main branches of the seventh whorl.We used in this analysis only needles from the first agegroup, which show most expressive reactions on varyingavailability of nutrients as being caused by soil acidifi-cation (von Wilpert 2003). Preparation of the needlesamples and their analyses were performed according tothe BZE manual (BML 1990). The analyses provided

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data on the content of all important macro-nutrients(Mg, Ca, K, N, P, Mn, Zn). In order to characterizenutrient imbalances between nitrogen and alkaline ca-tions, the ratios N/K, N/Mg and N/Ca were checked inthe analysis as potential predictors. The IWE data fromthe campaigns 1988 and 1994 contain only data for thetree species spruce (Picea abies, L. Karst) and fir (Abiesalba, Mill.).

In order to judge the comparability of the IWE sur-veys of the two years in terms of defoliation intensity weuse a different source of data: the consistent time seriesof needle loss in the monitoring scheme of the yearlycrown condition survey ‘‘Terrestrische WaldschadensInventur’’ (TWI). Figure 1 shows that the defoliationintensity was very similar at the two time points, 1988and 1994. For fir the mean needle loss across the wholeof Baden-Wuerttemberg was around 32% and forspruce it was around 21%.

How the data from the two surveys (IWE and BZE)were matched

Since the BZE survey was carried out between 1989 and1992, the BZE soil nutrient data were matched with theIWE data of the two years, 1988 and 1994. This is jus-tified by the fact that the ongoing processes in the soil(measured in the BZE) happen at a much slower ratethan the processes in the tree (measured in the IWE).

A problem for the statistical performance of theresulting models was the fact that we had to restrict thematerial to the coinciding sampling locations of the BZEand the IWE had been performed. Thus the number ofobservations with matching locations was only 107 in1988 and 194 in 1994.

The statistical method

Our data analysis problem requires a tool for adequatelymodelling the relationship between the response variableNLC and the potential predictors, of which some mayhave non-linear effects. In addition, we need to take thespatial correlation of the data into account. Since not

accounting for spatial correlation may lead to biasedvariance estimates and hence biased conclusions. Acommon way to solve this problem is to use a general-ized linear mixed model (GLMM) where the presence ofa spatial effect explicitly acknowledges for correlationbetween close observations (see Zeger and Karim 1993,Diaz-Avalos et al. 2001, Besag et al. 1991 for an appli-cation in forestry). However, GLMM in its originalform assumes that the relationship between the predic-tors and the response is described with a defined math-ematical function (i.e. straight line, polynomial).Augustin et al. (2005b) compares the GLMM method-ology to other methods in the context of a forestryexample. Generalized additive mixed models (GAMM)enable to relax this assumption by replacing a definedfunction with a non-parametric smoother (see Fahrmeirand Lang 2001, Musio et al. 2005 and Augustin et al.2005a for applications in forestry) and offer a flexibleand realistic tool to deal with spatially correlated datalike ours, in which the relationship between the NLCand the continuous predictors cannot be easily defined.Below we give a short description of the main features ofthe GAMM; more details on the theoretical aspects ofthis method can be found in Augustin et al. (2005a)where a similar methodology is applied solely to theIWE data of Baden-Wuerttemberg. The GAMM tech-nique assumes that given a set of continuous explana-tory variables (a1,..., an), and a set of further categoricalexplanatory variables, z = (z1,..., zp), the observed re-sponse y belongs to the exponential family with themean l linked to the predictor g by

l ¼ hðgÞ and

g ¼ b0 þ f1ða1Þ þ � � � þ fnðanÞ þ b1z1 þ � � � þ bpzp

þ fspatðx; yÞ;ð1Þ

where b0 is the intercept, f1,...,fn are smooth functions ofcontinuous explanatory variables (for instance the age),bj are parameters of the explanatory variables zi (forexample the relief type) and fspat is a smooth bivariatefunction of the coordinates x and y of the centroids ofeach growth region the observation refers to. Here theresponse variable is binary, NLC [slight needle loss (0)

Table 1 Response anddescriptive variables from thedataset of the IWE used in thefinal models

Parameter Code Description Type

Response Needle loss 0–100 Percentage of referencetree (5% classes)

Continuousbinary

Needle loss class 0 Needle loss 0–20%NLC 1 Needle loss 25–100%

Explanatoryvariables

Tree species 1 Spruce Binary2 Fir

Relief type 1 Plateau, upper and middle slope Categorical2 Footslope and valleys

Soil depth 1 Shallow (<30 cm) Categorical2 Average (<60 cm)3 Deep (>60 cm)

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and severe needle loss (1)]. In this case, we assume aBernoulli (p) distribution for our response variable,where p is the probability relating to needle loss. So l ofthe general notation above is in this particular case theprobability for moderate/severe damage, p. This prob-ability may be linked to the linear predictor g using anumber of link functions including the logit, the probitand the log–log. We use the probit link function since ithas computational advantages when the GAMM is fit-ted in a Bayesian framework (see below and Albert andChibs 1993). The probit link function, U-1, is the inverseof the cumulative density function of the normal distri-bution. Thus, the link between the probability of dam-age and the linear predictor is

/�1ðpÞ ¼ g or p ¼ /ðgÞ:

We fit the GAMM in a Bayesian framework. Byassuming that the observed data and the parameters arerandom variables, the Bayesian approach provides acohesive framework for combining complex models andexpert opinions (see Banerjee et al. 2004 for an appli-cation of Bayesian statistics in the analysis of spatialdata). Bayesian statistics have gained recently consider-able popularity, as many complex problems, involvingthe analysis of large datasets, have become computa-tionally feasible by using a Bayesian approach. This al-lows us to use Markov chain Monte Carlo (MCMC), asimulation technique, in cases where exact likelihoodevaluations are not possible. MCMC has made it pos-sible to fit complex and more realistic Bayesian modelsto large datasets. Among the benefits of the Bayesianapproach are a more natural interpretation of the sta-tistical conclusions. For instance, it allows a directinterpretation of the parameter intervals (called confi-dence intervals) that can be directly regarded as having ahigh probability to contain the unknown parameters.

In a Bayesian context, the unknown functions f1,...,fn,fspat and the parameters bj of the linear part are con-

sidered as random variables and have a prior probabilityreflecting the researchers ‘‘prior’’ belief about theparameters of the model without knowledge of the data.

We assumed the following priors:

• non-informative priors on the fixed effects parametersbj, which reflect a prior ignorance;

• Bayesian P-splines for the smooth function of con-tinuous explanatory variables f1,...,fn, (Lang andBrezer 2004);

• since we were interested in separating the effect of theten main forest growth regions of Baden-Wuerttem-berg (Rhine valley, Odenwald, South, Middle, Northof the Black Forest, East and West of the Neckarvalley, Baar/Wutach, Swabian Alb, Pre-alpine glaciallandscape), we modelled the spatial effect, fspat, as atwo-dimensional P-spline, where the estimation wasbased on the coordinates of the centroids of the regionwhere an observation belongs to (Lang and Brezer2004). This is an informative prior because it assumesspatial correlation.

Estimation of functions and parameters was based onthe posterior distribution which refers to the probabilitythat a model is true after observed data have been takeninto account. Since the posterior was intractable ana-lytically, inference was carried out using the simulationmethod MCMC; with the aim to take a sample from theposterior without being forced to compute it explicitlyand thus reducing computing effort (see Gilks et al. 1996for an introduction to MCMC techniques).

Model selection

Having combined the BZE and IWE data, we had alarge set of potential explanatory variables to consider.

Tree-specific variables: age, species and nutrients inthe needles (Ca, Mg, K, P, Mn, N/Ca, N/Mg, N/P,N/K).

Site-specific variables: altitude, x and y coordinates,relief, trophic class, soil depth, humus form, soil waterbudget, social class of the tree, exchangeable elementpools and pH-values in the soil at 0–5 cm depth (Mg,Ca, P, K, N, Al, Fe and pHKCl which we will denote inthe formula as MgS, CaS, PS, KS, NS, AlS, FeS andpHKClS).

Different competing models were compared using thedeviance information criteria (DIC) (Spiegelhalter et al.2002), which combine a Bayesian measure-of-fit with ameasure of model complexity. The DIC criteria can beconsidered as an extension of the Akaike informationcriteria (AIC) for complex random effect models inwhich the number of parameters is not actually defined.As the AIC, the DIC does not allow to identify the‘‘correct’’ model, but permits to compare a collection ofalternative models. The lower the DIC the better is themodel. The model with the lowest value of the DIC waspreferred.

10

15

20

25

30

35

40

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

year

mea

n d

efo

liati

on

[%

]

20.4% 21.1%

32.6%

31.6%

Abies alba

Picea abies

Fig. 1 Development of the mean defoliation, data from thesystematic 4 · 4 km grid of the annual crown condition survey(TWI) for fir (Abies alba, Mill) and spruce (Picea abies L. Karst.).Vertical reference, time of the IWE campaigns

94

We use the publicly available software package Ba-yesX (http://www.stat.uni-muenchen.de/�lang/bayesx)to fit the models.

Results and discussion

Having the commonly assumed processes of forestdeterioration in mind, all sensible combinations of theset of potential predictors as defined above were con-sidered. These processes include for example soil acidi-fication (Ulrich et al. 1994; Ulrich 1995), effects ofphyto-toxic reaction products of acidification (Rost-Siebert 1988; Sverdrup and Warvinge 1993; Cronan andGrugal 1995), nutrient shortage, e.g. Mg-deficiency(Zech and Popp 1983; Evers 1994) or nutrient imbal-ances attributed to nitrogen surplus (Evers et al. 1968;Hildebrand 1994; Mohr 1994), which were discussed tobe main processes causing forest decline and needle loss.Besides these, ‘‘new’’ stress factors ‘‘natural’’ site- andtree characteristics were tested as potential predictors,such as soil depth, relief form, humus form, altitudea.s.l., tree species and age.

The mean percentage of damaged trees (NLC = 1)was in 1988 27% and in 1994 40%, which partly couldbe caused by the different sampling design between 1988and 1994. But the absolute level of NLC is not a veryimportant aspect here since we are mainly concernedwith assessing the strength and type of association be-tween NLC and the set of predictors. Following the DICcriterion, we identified as ‘‘best models’’ for the 1988data:

g ¼ b0 þ fageðageÞ þ faltitðaltitudeÞ þ fMgðMgÞþ b1 species2 þ b2relief2þfspatðx;yÞ: ð2Þ

The model selected for 1994 was

g ¼ b0 þ fageðageÞ þ fAlSðAlSÞ þ fNKðN=KÞþ b1 species2 þ b2 relief2þ b3 soildepth2 þ b4 soildepth3 þ fspatðx;yÞ; ð3Þ

where we coded the categorical predictors according toTable 1, with the first category used as reference.

In both models explanatory variables of soil-, site-and tree characteristics as well as nutritional variablesare present, indicating that the main processes of forestdecline are indeed contributing in a complex way to thedefoliation status. But different sets of predictors wereselected for the two years.

Regarding the categorical predictors, in the model of1988, tree species and relief type (Table 2) were included.The resulting parameters allowed a sensible interpreta-tion in each case.

Concerning the effect of tree species, which is signif-icant in models 2 and 3, we see clearly that fir trees havea higher probability of damage than spruce. The pos-terior mean for fir (species 2) and the whole 95% con-fidence interval lie in the range of positive values

(indicating a significantly increased probability for nee-dle loss). Note that we interpret an effect as to be sta-tistically significant if the 95% confidence interval doesnot include zero. The posterior mean for the effect ofrelief type indicates a decreased, but not statisticallysignificant, probability for needle loss at foot slopes andvalleys (relief 2) with the main proportion of the 95%confidence interval being in the negative range. Thiscorresponds to increased amounts of exchangeablealkalinity in the soil, as described by Zirlewagen (2003)and Zirlewagen and von Wilpert (2004) at foot slopes ofthe mountainous landscape of the Black Forest.

In 1994, in addition to these two explanatory vari-ables with effects comparable to the model of 1988(Table 3), soil depth was included into the model.

The upper classes of soil depth (30–60 and >60 cm)provided a clear mitigating effect on the probability forneedle loss as compared to the reference class with a soildepth <30 cm. This finding is also plausible, since indeeper soils the shortage in water and nutrient supply isless probable than in shallow soils. Thus, trees in deepersoils appear to be less exposed to site-specific stressfactors.

In both models, for 1988 and 1994, three continuousvariables were selected. In both models age was con-tained as an important explanatory variable (Figs. 2, 5).Additionally variables describing site, soil and/or nutri-tional characteristics, were selected. In 1988, the effect ofage is a clearly increasing function, indicating anincreasing probability for needle loss with increasingage.

The effect of age is significantly in the negative rangebelow ca. 90 years, and above 120 years it contributesincreasingly to the probability of needle loss. Thisincreasing effect of age was found in most investigationson forest decline and also was included into the meth-odology of some inventory schemes by including onlytrees with an age >40 years (Evers and Schopfer 1988).

It is well known that there is some relationship be-tween altitude and needle loss. Schopfer and Hradetzky

Table 3 Posterior mean parameters of fixed effects for the 1994model

Variable Mean 2.5% Quant. 97.5% Quant.

Constant 1.03479 �0.13291 2.43506Species2 0.72161 0.09524 1.34914Relief2 �0.36585 �0.78573 0.02683Soildepth2 �0.63267 �1.22583 �0.06770Soildepth3 �0.54109 �1.26870 0.13782

Table 2 Posterior mean parameters of fixed effects for the 1988model

Variable Mean 2.5% Quant. 97.5% Quant.

Constant �1.26191 �2.27866 �0.34141Species2 2.10919 1.18173 3.09054Relief2 �0.23751 �0.74814 0.30176

95

(1984) stated that in and above the meteorologicalinversion layer in mountainous regions the intensity ofyellowing and needle loss is at a maximum because ofthe over-above high acid input from rain and fog pre-cipitation there. They called that phenomenon as thehigh elevation forest disease. This theory is supported bythe fact that also in our model for 1988 altitude wasselected as an important explanatory variable for needleloss (Fig. 3), which provides a significantly positive ef-fect on needle loss above the altitude of about 900 ma.s.l. That is the average situation of the inversion layer.

The effect of the magnesium content of recent needles(seventh whorl) is a clearly decreasing function (Fig. 4).This is in accordance with the finding that at soils uponcrystalline bedrocks, which provide poor magnesiumsupply from bedrock composition, magnesium defi-ciency was one of the leading factors of forest decline(Zech and Popp 1983; Feger and Raspe 1992; Evers1994).

It is evident that a significantly increasing effect of themagnesium supply on the probability of the needle loss

is found below the threshold for sufficient magnesiumsupply as indicated by Evers (1985) on the basis ofneedle analyses and fertilization trials. In the range ofhigh magnesium supply a slight protection effect againstneedle loss can be observed.

In 1994, the age was included even with the highestweight into the model (Fig. 5). But the effect of age hada different shape, it was not as linear as in the 1988model. We found a slight positive effect at ages above80 years, very young trees experienced a significantlyreduced probability for needle loss.

The effect of exchangeable aluminium in the upper-most layer of the mineral soil (0–5 cm) was included intothe model for 1994 by a significantly increasing function(Fig. 6). Above the threshold of about 120 lmolc g

�1

the exchangeable aluminium stock has a significantlyincreasing effect on the probability of needle loss.

The exchangeable aluminium stock is an indicator forthe acidification status of soils. In the BZE material, thecorresponding base saturations to the range of Al con-

2.8

1.63

0.46

-0.71

-1.88

40 75.5 111 147 182

Effect of age,1988

age [year]

s(ag

e)

Fig. 2 Non-linear effect of age in 1988 (bold solid line). Shown arethe posterior means together with 95 (thin dashed lines) and 80%(thin solid lines) pointwise credible intervals

3.06

1.95

0.83

-0.28

-1.39

200 440 680 920 1160

Effect of altitude, 1988

altitude [m]

s(al

titud

e)

Fig. 3 Non-linear effect of altitude in 1988 (bold solid line). Shownare the posterior means together with 95% (thin dashed lines) and80% (thin solid lines) pointwise credible intervals

3.08

1.42

-0.25

-1.92

-3.59

0.37 1.01 1.65 2.28 2.92

Effect of Mg, 1988

Mg [mg/g]

deficient sufficient high

s(M

g)

Fig. 4 Non-linear effect of the magnesium content in needles of thefirst age class, seventh whorl in 1988 (bold solid line). Shown are theposterior means together with 95% (thin dashed lines) and 80%(thin solid lines) pointwise credible intervals. Nutritional classesaccording to Evers (1985)

3.88

1.98

0.07

-1.84

-3.75

44 84.3 125 165 205

Effect of age,1994

age [year]

s(ag

e)

Fig. 5 Non-linear effect of age in 1994 (bold solid line). Shown arethe posterior means together with 95% (thin dashed lines) and 80%(thin solid lines) pointwise credible intervals

96

centrations >120 lmolc g�1 were in the average 7.8%

and to the range of Al concentrations <50 lmolc g�1

51.4%. This indicates that the posterior effect above Alconcentrations of 120 lmolc g

�1 in Fig. 6 is character-ized by a predominance of Al at the exchanger surfacesof the soil. Such high Al-saturation at exchanger sur-faces makes the appearance of ionar Al in the soilsolution probable (Ulrich 1992), which is a stress factorfor roots (Rost-Siebert 1983, 1988; Sverdrup andWarvinge 1993). In contrast, below Al concentrations of50 lmolc g

�1, base saturations are so high that they cancompensate the stress inducing effect of Al (Sverdrup1995).

In the model for 1994 also a component of treenutrition was included by the ratio of nitrogen andpotassium in the needles (Fig. 7). This ratio (N/K) isusually interpreted as an indicator for tree nutrition indisequilibrium caused by a surplus of nitrogen, whichsubsequently leads to an uptake concurrence betweennitrogen and potassium.

The threshold between a harmonic and a disequili-brated ratio among N- and K-supply is conventionallyassumed at 3.0 (Huttl 1991). This is due to the fact thatan uptake concurrence does exist between nitrogen,especially ammonium, and potassium because both ele-ments are taken up by the same ion channels (Mohr1994; Mengel 1991). The contribution of the N/K-ratioindicated in the model for 1994 a sharp increase above 5,which is far in the disequilibrated range. But note thatthis increase is not significant at the 95% level.

The credible regions for the spatial effect, fspat , fittedfor the ten growth regions in Baden-Wuerttemberg toboth models 1988 and 1994 are similar. The spatial effectcan be thought of as a residual effect, which should havea mean of zero if the other explanatory variables in themodel are sufficient in explaining the observed spatialvariation in needle loss. We see that this is the case foreight of the ten growth regions, where the posteriormean of the spatial effect is situated within the 95%

confidence interval (Fig. 8). The sole exceptions are thetwo growth regions Southern and Middle Black Forest,where the spatial effect is strictly positive (outside the95% confidence interval).

This indicates that the deterministic part, i.e. the in-cluded explanatory variables, of both models explainsnot all of variation of the measured NLC. Thus, the‘‘spatial effect’’ compensates the lack of deterministicexplanation with apparent positive values.

Conclusion

Our study is based on observational data rather thanexperimental data. Hence, results only allow inferenceon the association between the response and the pre-dictors, rather than causation. In addition, we havecarried out model selection, but as it is commonplace inmost statistical applications, inference from the model isbased on the assumption that the fitted model was pre-specified. Ignoring the uncertainty about the modelselection process may lead to unjustifiable confidence inparameter estimates (Chatfield 1995). It is possible toaccount for uncertainty due to the model selectionprocess, and this can be easily done for relatively simplemodels, which just include linear effects, see e.g. Hoetinget al. (1999) and Augustin et al. (2005c). Since theBaysian GAMMs fitted here are quite complex, due tonon-linear effects of predictors and the presence of aspatial effect, it is beyond the scope of this paper toaccount for such model selection uncertainty.

Since we take the spatial correlation in our data intoaccount, our analysis allows to select a set of ‘‘best’’explanatory variables for the defoliation elucidating therelationship between the defoliation and the selectedexplanatory variables which are not easily detected withtraditional methods. The advantage of the BayesianGAMM used here is to provide a map of the spatialrandom effect, fspat. This points to areas, where the

3.09

2.06

1.03

-0.01

-1.04

1.09 2.56 4.03 5.5 6.97

Effect of N/K,1994

N/K

harmonic disequilibrated

3.0

s(N

/K)

Fig. 7 Non-linear effect of the N/K-ratio in needles of the first ageclass, seventh whorl in 1994 (bold solid line). Shown are theposterior means together with 95% (thin dashed lines) and 80%(thin solid lines) pointwise credible intervals

1.36

0.6

-0.16

-0.92

-1.68

0.1 55.1 110 165 220

Effect of Al (0-5cm), 1994

Al [µmolc/g]

s(A

l)

Fig. 6 Non-linear effect of the exchangeable aluminium content inthe uppermost mineral soil (0–5 cm) in 1994 (bold solid line). Shownare the posterior means together with 95% (thin dashed lines) and80% (thin solid lines) pointwise credible intervals

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deterministic part of the model could not significantlyexplain the variability of needle loss. In the case of theposterior means of fspat corresponding to the ‘‘regions’’lying in the positive range, as occurred at two smallgrowth regions of the Black Forest in both years in thisstudy, this indicates a lack of deterministic processknowledge and appropriate explanatory variables forthis area. A possible predictor missing in the modelmight be for example information on the delayed forestliming in the southern parts of the Black forest, thus thecompensating effect of the lime application being notfully developed at the time, when the survey had beenperformed. But since such interpretations are ratherspeculative, and lime application is not available in

terms of exact numbers at the single grid points of thesurvey, it could not been included into the models. It isremarkable that all explanatory variables contributingto the models for 1988 and 1994 in our study allowedplausible interpretations. The contribution of site vari-ables such as relief and soil depth can be interpreted asthe natural ability of sites to equilibrate the supply ofwater and nutrients, which is attached to deeply devel-oped soils and/or to the more protected situations in thelandscape like foot slopes or valleys (Zirlewagen 2003;Zirlewagen and von Wilpert 2004). The differing patternof continuous explanatory variables among the years1988 and 1994 allow to assess what disturbances were inthe foreground of forest deterioration at that timerespectively. The fact that among the most importantexplanatory variables for needle loss were in 1988 thealtitude a.s.l. and the magnesium supply suggests thatthe factors of the so-called high elevation disease wereactive at that time. There a latent magnesium deficiencyat mountainous regions with crystalline bedrocks con-taining few magnesium met over-above acid depositionscaused by the local meteorological circumstances of highprecipitation rates and the additional deposition by fogprecipitation (Zech and Popp 1983; Evers and Schopfer1988; Evers 1994; Gulpen and Feger 1998). Neverthe-less, these are mere speculations rather than firm con-clusions, since we have to bare in mind that for the 1988data we have the caveat that the sampled trees includedin the analysis are only the ‘‘plus trees’’. Also, in 1988 wehave fewer observations (N = 107) and hence lessinformation compared to 1994 (N = 194). In order toprotect forest soils from further acidification and toenhance the magnesium supply of forests, after 1983forest liming was performed in the state of Baden-Wuerttemberg using a dosage of 3–4 t ha�1 of dolomitepowder (von Wilpert and Lukes 2003). This forest lim-ing campaign covered the main area of the northern andmiddle part of the Black Forest and resulted in a sig-nificant increase of the supply of trees with Ca and Mgbetween 1983 and 1994 (von Wilpert 2000). Thus, thecomposition of the set of nutrient variables in our modelfor 1994 can be explained easily: the explanatory vari-able Mg in the needles, which was significant in 1988 wasnot significant in 1994 anymore. Instead, Als (Al in thesoil) and N/K (in the needles) were significant in 1994.Als can be interpreted as an indicator for soil acidifi-cation, and the N/K-ratio can be regarded as indicatorfor increasing eutrophication caused by a surplus ofnitrogen deposition. A surplus of nitrogen availabilitycauses uptake antagonisms, especially to potassium(Hildebrand 1994; Mohr 1994).

We use the novel GAMM methodology applied in aBayesian framework (Fahrmeier and Lang 2001), whichhas several advantages over traditional methods, such aslinear regression, traditionally used for these types ofdata. It is possible to model any type of response vari-able following a distribution of the exponential family.This includes binary data (e.g. healthy/damaged) andordered categorical data (e.g. low/medium/high). The

1

2

3.1

3.2

3.3

4.14.2

5

6

7

spatial effect in the model is significantly negative

spatial effect in the model is not significant

spatial effect in the model model is significantly positive

not included into the analysis

Legend:

1 = Rhine valley

2 = Odenwald3 = Black-Forest (3.1 south, 3.2 middel, 3.3 north)

4 = Plane and hilly region of the Neckar valley (4.1 east, 4.2 west)

5 = Baar - Wutach

6 = Swebian Alb7 = Pre-alpine glacial landscape

Growth regions:

1994 and 1988

Fig. 8 Non-linear posterior effect of the non-parametric smoother,the bivariate function fspat(x,y) where x and y are the coordinates ofthe centroid of each growth region for 1988 and 1994. Shown arethe posterior means. Grey colour indicates that the 95% credibleregion contains zero

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method deals with spatial correlation, rather thanignoring it, which may lead to biased results. In additionthe method allows the inclusion of non-linear effects ofexplanatory variables and this makes the models morerealistic. Thus, we have successfully identified sets ofexplanatory variables for explaining the probability ofneedle loss for the two years, 1988 and 1994. These twosets indicate a possible change of the main causes offorest deterioration. Thus, this technique allows us touse crown condition indeed as an early warning indica-tor, which can be interpreted in such a differentiatingway that concrete counter-measures like e.g. forest lim-ing can be planned on this basis. The aim of our studywas to demonstrate that the crown condition in terms ofneedle loss is an informative indicator of the healthstatus of trees instead of an unspecific tree reaction;which allows little differentiating interpretation, likeEllenberg (1995, 1997) stated in his criticism. The foundassociations and interpretations on the possible causesof crown condition in this study confirm the results ofthe international cooperative programme on assessmentand monitoring of air pollution effects on forests (ICPforests) in principle. There it was stated that 30% ofvariation in defoliation could be assigned to stand age,soil type, precipitation, ozone- and sulfur deposition andfoliar chemistry (De Vries et al. 2002). These findings ofICP forests were based upon level II case studies, whichare not representative in space, at least at a nationalscale. The advantage of the approach in this study is theconsequent use of data with a relatively high spatialresolution. Figure 8 shows that the models fit quite well,in most of Baden-Wuerttemberg. The variation of crowncondition could adequately be explained using the se-lected explanatory variables. An important preconditionfor this was the availability of data on the soil chemicalstatus at the same scale as the tree nutrition data pro-vided by the IWE scheme. The latter is a special featureof the monitoring scheme undertaken in Baden-Wuert-temberg and not part of the international level I-moni-toring scheme.

Acknowledgments The work was supported by the BMBF-researchproject number 0339985. We thank Edgar Kublin for his helpfulcontributions. Moreover, we are grateful for the quick and helpfulsecond review.

References

Albert J, Chibs S (1993) Bayesian analysis of binary and poly-chotomous response data. J Am Stat Assoc 88:669–679

Augustin NH, Lang S, Musio M, von Wilpert K (2005a) A spatialmodel for the needle losses of pine trees in the forests of Baden-Wuerttemberg: an application of Bayesian structured additiveregression. J R Stat Soc C (Appl Stat). Invited for resubmission

Augustin NH, Kublin E, Metzler B, Meierjohann E, von Wueh-lisch G (2005b) Analysing the spread of beech canker. ForestSci 51(5):438–448

Augustin NH, Sauerbrei W, Schumacher M (2005c) The practicalutility of incorporating model selection uncertainty into prog-nostic models for survival data. Stat Model 5:95–118

Banerjee S, Carlin BP, Gelfand AE (2004) Hierarchical modellingand analysis for spatial data. Chapman & Hall, London

BML (1990) Bundesministerium fur Ernahrung, Landwirtschaftund Forsten (Hrsg.), Bund-/Landerarbeitsgruppe BZE:Bundesweite Bodenzustandserhebung im Wald, Arbeitsanlei-tung. 147 S

Besag J, York J, Mollie A (1991) Bayesian image restoration, withtwo applications in spatial statistics (with discussion). Ann InstStat Math 43:1–59

Chatfield C (1995) Model uncertainty, data mining and statisticalinference. J R Stat Soc A 158:419–466

Cronan CS, Grugal DF (1995) The use of calcium/aluminium ra-tios as indicators of stress in forest ecosystems. J Environ Qual24:209–226

De Vries W, Forsius M, Lorenz M, Lundin L, Haussmann Th,Augustin S, Ferretti M, Kleemola S, Vel E (2002) Cause–effectrelationships of forest ecosystems: joint report by ICP forestsand ICP integrated monitoring. UN/ECE, Genova, pp 46

Diaz-Avalos C, Peterson DL, Alvardado E, Ferguson SA, BesagJE (2001) Space–time modelling of lightning-caused ignitions inthe Blue Mountains, Oregon, Canada. J Forest Res 31:1579–1593

Ellenberg H (1995) Neuartige Waldschaden? Okologische Kritik anden Untersuchungsmethoden. AFZ 50(15):796–797

Ellenberg H (1997) Sogenannte, ‘‘Blattverluste’’ = kein sicheresMaß fur Waldschaden. SDW: Unser Wald (1):4–6

Evers FH (1985) Nomograms for classifying the nutrition supply ofneedles and leaves. Internal technical paper at the Forest Re-search Institute, Freiburg

Evers FH (1994) Magnesiummangel, eine verbreitete Erscheinungin Waldbestanden: Symptome und analytische Schwellenwerte.Mittl. d. Vereins f. Forstl. Standortskartierung. u. Forstplanzenzuchtung 37:7–15

Evers FH, Schopfer W (1988) Ergebnisse der BelastungsinventurBaden-Wurttemberg 1983. Mitt. der Forstl. Vers. u. Fors-chungsanst 188

Evers FH, Schopfer W, Mikloss J (1968) Die Zusammenhangezwischen Stickstoff-, Phosphor- und Kalium–Mengen und denC/N-, C/P- und C/K—Verhaltnissen der Oberboden vonWaldstandorten. Mitteilungen des Vereins fur Standortkundeund Forstpflanzenzuchtung, Nr 18

Fahrmeir L, Lang S (2001) Bayesian inference for generalizedadditive mixed models based on Markov random field priors. JR Stat Soc C 50:201–220

Feger KH, Raspe S (1992) Ernahrungszustand von Fichtennadelnund—wurzeln in Abhangigkeit vom Nahrstoffangebot im Bo-den. Forstw Cbl 111:73–76

Gilks WR, Richardson S, Spiegelhalter DJ (1996) Markov chainMonte Carlo in practice. Chapman & Hall, London

Gulpen M, Feger KH (1998) Magnesium- und Calcium-Ernahrungvon Hochlagenfichten: Vergilbungszustand und Reaktion aufunterschiedliche Dungung. Z Pflanzenernahrung Bodenkunde161(6):671–679

Hildebrand EE (1994) N deposition as a site factor for forest standsin Southwest Germany. Nova Acta Leopoldina NF70 288:418–424

Hoeting JA, Madigan D, Raftery AE, Volinsky CT (1999) Baysianmodel averaging: a tutorial (with discusssion). Stat Sci 14:382–417

Huttl R (1991) Die Nahrelementversorgung geschadigter Walder inEuropa und Nordamerika. Freiburger Bodenkundl Abh 28:440

Lang S, Brezger A (2004) Bayesian P-splines. J Comput GraphicalStat 13:183–212

Landmann G, Bonneau M (eds) (1995) Forest decline and atmo-spheric deposition effects in the French mountains. Springer,Berlin Heidelberg New York, p 461

Mohr H (1994) Stickstoffeintrag als Ursache neuartiger Wald-schaden. Spectrum der Wissenschaft 1(94):48–53

Mengel K (1991) Ernahrung und Stoffwechsel der Pflanze. G Fi-scher, Jena. 466

Musio M, Augustin N and von Wilpert K (2006) Geoadditivemodels for forestry defoliation data: a case study (in press)

99

Rost-Siebert K (1983) Aluminium—Toxizitat und—Toleranz anKeimpflanzen von Fichte (Picea abies Karst.) und Buche (Fa-gus silvatica L.). AFZ 26/vg27:686–689

Rost-Siebert K (1988) Ergebnisse vegetationskundlicher undbodenchemischer Vergleichsuntersuchungen zur Feststellungimmissionsbedingter Veranderungen wahrend der letzten Jah-rzehnte. Ber. Forschungszentr. Waldokosysteme Gottingen. B8,pp 158

Schopfer W, Hradetzky J (1984) Der Indizienbeweis: Luft-verschmutzung maßgebliche Ursache der Walderkrankung.FwCbl 103:231–248

Spiegelhalter DJ, Best N, Carling BP, van der Linde A (2002)Bayesian measure of model complexity and fit (with discussion).J R Stat Soc B 64:583–639

Sverdrup H (1995) Critical loads and the BC/Al-ratios as indicatorof soil acidification effects on tree growth. Kungl + Skogs ochLantbruksakademiens Tidskrift 134(11):77–98

Sverdrup H, Warvinge P (1993) The effect of soil acidification onthe growth of trees, grass, herbs as expressed by the(Ca + Mg + K)/Al ratio. Report in Ecology and Environ-mental Engineering 2. Lund, Lund University, Department ofChemical Engineering II, pp 42

Ulrich B (1992) Forest ecosystem theory based upon materialbalance. Ecological Model 63:163–183

Ulrich B (1995) The history and possible causes of forest decline incentral Europe, with particular attention to the German situa-tion. Environ Rev 3(3, 4):262–276

Ulrich B, Cronan CS, Wolters V, Schaefer M, Eichhorn J, WorrallJJ, Rapp C, Jentschke G, Gruber F, Roloff A, Godbold DL,Huttermann A (eds) (1994) Effects of acid rain on forest pro-cesses. Wiley-Liss, New York, p 419

von Wilpert K (2000) Neue Entwicklung in der Waldernahrung.Forstliche Versuchs- und Forschungsanstalt Baden-Wuerttem-berg. Jahresbericht 1999, pp 33–36

von Wilpert K (2003) Drift des Stoffhaushalts im Fich-ten—Dungeversuch Pfalzgrafen weiler. AFJZ 174(2/3):21–30

von Wilpert K, Lukes M (2003) Ecochemical effects of phonoliterock powder, dolomite and potassium sulfate in a spruce standon an acidified glacial loam. Nutrient cycling in agroecosys-tems. Kluwer, Dordrecht, vol 65, pp 115–127

Zech W, Popp E (1983) Magnesiummangel, einer der Grunde furdas Fichten- und Tannensterben in -NO-Bayern. ForstwissCentralblatt 102:50–55

Zeger SL, Karim MR (1993) Generalized linear models with ran-dom effects: a Gibbs sampling approach. J Am Stat Assoc86:79–86

Zirlewagen D (2003) Regionalisierung bodenchemischer Eigens-chaften in topographisch stark gegliederten Waldlandschaften.Freiburger Forstliche Forschung, Band 19, pp 154

Zirlewagen D, von Wilpert K (2004) Using model scenarios topredict and evaluate forest management impacts on soil basesaturation at landscape level. Eur J For Res 123(4):269–282

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