e c o l o g i c a l m o d e l l i n g 2 1 5 ( 2 0 0 8 ) 180–189

avai lab le at www.sc iencedi rec t .com

journa l homepage: www.e lsev ier .com/ locate /eco lmodel

Modeling radial growth increment of black alder (Alnusglutionsa (L.) Gaertn.) tree

Jana Laganisa,∗, Aleksandar Peckovb, Marko Debeljakb

a Laboratory for Environmental Research, University of Nova Gorica, Vipavska 13, Nova Gorica, Sloveniab Department of Knowledge Technologies, “Jozef Stefan” Institute, Jamova 39, Ljubljana, Slovenia

a r t i c l e i n f o

Article history:

Published on line 8 April 2008

Keywords:

Wetland forest

Black alder

Forest growth model

Feature selection

Machine learning

STELLA model

a b s t r a c t

Nowadays it is extremely important to understand ecosystem function and its dynamics to

predict future changes and consequently to perform appropriate measures. Hydromeliora-

tions and subsequent decrease in groundwater table are thought to be a major reason for

a decline in the vitality of black alder (Alnus glutinosa (L.) Gaertn.) wetland forests in North-

eastern Slovenia. In this study radial increments of trees were used as indicators of black

alder forest function and its disturbances. The aim of the study was to build a model of

annual radial increments of black alder trees, to use this model to identify environmental

attributes that most importantly affect ecosystem’s function and to predict changes in the

forest function under different scenarios of environmental conditions in the future. The

model was induced with a machine learning algorithm CIPER and it was based on the data

about site conditions and applied management measures in the past 35 years. Groundwa-

ter levels in combination with the duration of sun radiation were identified as the most

important environmental attributes affecting annual radial increments. Radial increments

were the lowest in very wet and cloudy years. On the other hand, radial increments were

decreased under drought stress as well. Changes in groundwater level and in duration of sun

radiation, as well as increased oscillations of groundwater level, all cause important increase

in oscillations of modeled radial increments, indicating higher stress. Radial increments

were further negatively affected by late white frosts in the spring.

1. Introduction

The understanding of ecosystem function and reconstructionof ecological niche are especially important in this period inwhich we have to carefully balance between different needs

and interests and in which we expect important changes ofclimate conditions. An important property of forest ecosys-tems is that they mark annual radial growth increments. Asgrowth is dependent on ecosystem’s well-being and function

∗ Corresponding author at: University of Nova Gorica, Laboratory for EnvTel.: +386 533 15 328; fax: +386 533 15 296.

E-mail addresses: jana.laganis@p-ng.si (J. Laganis), aleksandar.peck0304-3800/$ – see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.ecolmodel.2008.02.018

© 2008 Elsevier B.V. All rights reserved.

in individual years, radial increments can be regarded as reli-able indicators of ecosystem function.

Black alder (Alnus glutinosa (L.) Gaertn.; f. Betulaceae) is adeciduous tree species with many special ecological prop-erties as well as of an economical importance. Its most

ironmental Research, Vipavska 13, SI-5001 Nova Gorica, Slovenia.

ov@ijs.si (A. Peckov), marko.debeljak@ijs.si (M. Debeljak).

important ecological properties are adaptations to highgroundwater level, nitrogen fixation through symbiosis withactinomycetes Frankia, fast growth and short lifetime, andlight pretentiousness. In the stands under study it is also

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e c o l o g i c a l m o d e l l i n

eported to be resistant to white frosts, diseases and herbi-ores (Nemesszeghy, 1986; Brus, 2005).

Homogenous forests of black alder in the lowlands ofortheastern Slovenia are among the last remnants ofatural wetland forests of this species in central Europe

Nemesszeghy, 1986). The area of these forests was signif-cantly reduced in the 19th century. Severe decline in theitality of stands in the studied area was observed in theiddle of the last century (Wraber, 1951; Nemesszeghy, 1986;

evanic, 1993) as well as in other black alder floodplain forestsn Europe (Pretzell et al., 1997). This decline was attributedo a decrease in groundwater table (Pretzell et al., 1997) andhanged hydrological conditions due to extensive hydromelio-ations and regulations. The importance of groundwater levelnd hydrologic regime for wetland trees was also confirmed inhe studies of Keeland and Sharitz (1997). Despite the appar-ntly clear causal relationship between the groundwater levelnd stand vitality, studies performed until now did not suc-eed to prove changes in groundwater level as a major reasonor forest decline (Levanic and Kotar, 1996; Kosir, 1987; Levanic,993; Cater, 2002). In order to continue with this discussione conducted a case study research in a black alder floodplain

orest of Polanski Log.Radial growth of trees is influenced by a complex of

nvironmental parameters (attributes) that take place on aarticular site. These attributes include water availability, cli-ate conditions and soil fertility (Whitehead, 1998). Radial

rowth of trees responds very dynamically to a current com-ination of environmental attributes (Waring, 1987). For thateason we considered radial increments as indicators of func-ion and disturbances of black alder wetland forest ecosystemn individual years.

The main goal of this study was to construct a reliable sim-lation growth model of black alder forest stand. This modelas used to identify the set of the most important attributes

hat affect growth and development of the stand under studynd to predict changes in the function of these stands underuture climate change scenarios.

. Materials and methods

.1. Study site

.1.1. Site descriptionhe forest of Polanski Log covers the area of 414 ha on the

eft side of the Ledava River. The most common tree speciesn these stands is black alder (85%), followed by ash (12%)nd oak (3%) (Nemesszeghy, 1986). Long-term presence of sta-le alder forests was proved in a research of subfossil woodCuliberg, 1989). These stands can be classified as black alder’sest sites and as a climax community. Whereas heights up to0 m are reported for black alder in other countries (McVean,953; Dawson and Funk, 1981; Brus, 2005; Krstinic et al., 2002;eatherstone, 2003), they surpassed the height of 34 m in thetand under study (Nemesszeghy, 1986; Laganis, 2007). Trees

n individual plots are even-aged.

Black alder represents 95% of trees in the selected standForest Management Plans, 1971–2011). With 69 years itlready surpassed its maturity and it was cut down in Jan-

5 ( 2 0 0 8 ) 180–189 181

uary 2005. The latitude of the research site is 46,595 and itslongitude is 16,358. The area is flat and it is about 190 m abovethe sea level.

2.1.2. Climate and soil conditionsThe selected site lies in a Panonic-type of climate with dry andhot summers and cold winters. Mean annual temperature is9–10 ◦C. Important for the vegetation are negative impacts offrequent late frosts in the spring (until April) and early whitefrosts in the autumn (Wraber, 1951), despite they were notreported to cause important damage in black alder stands(Silvicultural chronicles).

The average amount of precipitation is only about 800 mm(Wraber, 1951), a bit less than 60% of which occurs duringthe growing period (Ziberna, 1992). Severe droughts duringthe summer and relatively poor physical and chemical soilproperties prevent higher agricultural productivity in this area(Wraber, 1951). The amplitude between the minimum andmaximum groundwater level was found to be about 1.5 mbetween the years 1953 and 1993 in about 7-km distant well(Smolej, 1995), which is of a similar distance from the LedavaRiver as is the selected stand.

The most important attributes that affect structure andfunction of these forests are hydrological conditions of soilwater and water regime. Soil water is standstill or it flowsvery slowly through a gravely substrate (Wraber, 1951; Levanic,1993). In our stand the groundwater level was relatively closeto the surface (0–80 cm) during measurements (September2004–January 2005). In some cases the stand was partly over-flown.

This flat area has gravelly to sandy siliceous grounding,covered with fertile, clayey alluvium (intrazonal type of soil,hypogleic eugley; Wraber, 1951; Kalan, 1988). This alluviumvaries in depth but in general it is relatively shallow (Wraber,1951; Levanic, 1993). A shortage of limestone is a reason forpoor physical and chemical soil properties (Wraber, 1951).Ascendant groundwater flows toward the surface (upward) areprevailing during the vegetation period and they bring plentyof mineral nutrients to the upper soil layers (Kalan, 1988).Nitrogen is reported to be abundant (Levanic, 1993; Kalan,1988).

2.1.3. HistoryAccording to the Forest Management Plans (1959–1968) andreports of Wraber (1951) large part of the area was uncrossablein the 18th century due to high water levels. The landscapewas covered by oak and alder forests. Several meliorationsperformed after the year 1814 drained the area, large extentsof forests were cleared to obtain new agricultural surfaces(Levanic and Kotar, 1996; Nemesszeghy, 1986) and large partof remaining forests was endangered due to a decrease in thegroundwater level (Wraber, 1951) and changes in the rhythm offlooding (Levanic, 1993). Smolej (1995) reports that between theyears 1953 and 1992 (40 years) groundwater level decreased for60 cm. The area became less appropriate for black alder (Brus,2005) and forests remained only on soil, which were inappro-

priate for agriculture due to high groundwater or low fertility(Nemesszeghy, 1986).

In 1980 a reservoir at Radmozanci was constructed andthe riverbed of the Ledava River was deepened. As a result a

i n g

182 e c o l o g i c a l m o d e l l

further decrease of groundwater level took place, the naturalflooding in the spring was halted (Kalan, 1988; Cater, 2002) andan artificial flooding in the summer was introduced (Levanic,1993; Levanic and Kotar, 1996).

2.2. Methods

2.2.1. DatasetDataset (attributes) required for the model construction andvalidation consisted of the data on the radial growth of eighttrees in the selected forest stand, attributes describing mete-orological and hydrological conditions and attributes on theforest management measures performed in the selected for-est stand. All three types of attributes were available for thepast 35 years before the final clear-cut of the selected stand.

During the felling we obtained tree disks from eight neigh-boring trees from the dominant social layer. Neighboring treeswere chosen to minimize differences in site conditions andmanagement measures. About 5-cm-thick tree disks weretaken at the trunk height of 1.3 m. After air-drying, sand-ing and polishing they were prepared for dendrochronologicalanalysis. Radial increments were measured to the nearest0.01 mm using a LINTAB measuring stage and a dissectingstereomicroscope Olympus SZ-CTV (SZ-60) with video display.Measurements were done in two different directions on eachtree disk and the average value was used in the calculations.

Meteorological attributes were obtained from the nearestpermanent meteorological station. As the area is flat the datafrom about 5 km distant Meteorological Station Lendava wereconsidered to be valid for our stand. Among meteorologi-

Table 1 – The selected attributes for CIPER and corresponding re

Age (−0.619) maxL 5–7 (0.200)

thinn (−0.398) maxL 5–9 (0.192)thinn y-1 (−0.149) minL 4 (−0.533)thinn y-2 (0.075) minL 5 (−0.609)maxgw 7 (0.205) minL 7 (−0.613)maxgw 4–7 (0.062) minL 8 (−0.582)maxgw 8–10 (0.016) minL 9 (−0.641)maxgw 4–10 (0.055) minL 4–7 (−0.665)mingw 7 (0.177) minL 8–10 (-0.645)mingw 4–7 (0.082) minL 4–10 (−0.684)mingw 8–10 (0.046) minL 4–6 (−0.627)mingw 4–10 (0.062) minL 5-7 (-0.683)avergw 7 (0.194) minL 5–8 (−0.690)avergw 4–7 (0.064) minL 4–9 (−0.668)avergw 8–10 (0.017) minL 12–2 (−0.548)avergw 4–10 (0.026) averL 5 (−0.553)maxL 5 (−0.282) averL 4–7 (−0.600)maxL 7 (−0.086) averL 8–0 (−0.553)maxL 4–7 (−0.092) averL 4–10 (−0.658)maxL 8–10 (−0.150) averL 4–6 (−0.613)maxL 4–10 (−0.058) averL 4–9 (−0.635)

Numbers refer to the month(s) of the year the attribute refers to (e.g. 12–2February of the current year; 4–7 refers to the period between current Apmaximum values respectively; thinn: thinning (m3/stand) before the currduration of sun radiation (h); prec: precipitation (mm); ETo: potential evapand potential evapotranspiration (mm); T: temperature; cumT > 0: cumulatwith the minimum temperature below 0 ◦C; d-minT > 25: number of dayswith white frost; d-snow y-1: number of days with snow in the previous w

2 1 5 ( 2 0 0 8 ) 180–189

cal attributes we investigated monthly data on duration ofsun radiation (h), precipitation (mm), potential evapotranspi-ration (ETo; mm), the difference between precipitation andETo, number of days with white frost, number of days withsnow, maximum, average, and minimum monthly temper-atures (◦C), cumulative temperatures above 0 ◦C, above 5 ◦C,and above 10 ◦C, number of days with minimum temperatureabove 0 ◦C, below −4 ◦C, below −10 ◦C and above 25 ◦C, as wellas number of days with maximum temperature above 10 ◦Cand above 25 ◦C.

Groundwater levels were measured in about 7 km dis-tant well and the Ledava River levels were measured on apermanent measurement station Centiba, which is locatedabout 10 km downstream from the research site. We acquiredattributes on monthly minimum, average, and maximumLedava River levels and groundwater levels. Our stand islocated within the Ledava River’s catchment area and the Riverflows a bit more than 1 km away from our stand. Previousresearch confirmed a close link-up and synchronous fluctu-ations of Ledava River level and groundwater level in this area(Levanic, 1993). Groundwater levels showed poor agreementwith radial increments (e.g. Table 1) and they were not used inthe further work. Poor regression coefficients most probablyindicate that the sampling well was too far away and that itwas affected by some other hydrological regimes. At the sametime the data on this attribute were available for a shorter time

period (20 years).

The attributes on forest management measures per-formed in the selected forest stand in the past 35 years(Forest Management Plans, 1971–1980, 1981–1990; 1992–2001;

gression correlation coefficients in the parenthesis

averL 12–2 (0.422) ETo 4–10 (−0.072)

t-sun 4 (−0.362) maxT 6 (−0.297)t-sun 4–7 (−0.392) maxT 7 (−0.031)t-sun 4–10 (−0.383) maxT 4–10 (−0.073)t-sun 4–6 (−0.414) maxT 5–7 (0.130)t-sun 5–9 (−0.417) maxT 12–2 (0.049)t-sun 4–9 (−0.439) minT 4 (0.066)precip 7 (0.233) minT 8 (−0.126)precip 8 (0.114) minT 4–7 (0.066)precip 4–7 (0.155) minT 4–10 (−0.118)precip 8–10 (0.085) minT 4–6 (0.066)precip 4–10 (0.166) minT 4–9 (0.066)precip 4–9 (0.182) averT 4–7 (−0.020)prec-ETo 7 (0.226) averT 4–10 (−0.078)prec-ETo 8 (0.120) cumT>0 4–7 (−0.005)prec-ETo 4–7 (0.155) cumT>0 4–10 (−0.073)prec-ETo 8–10 (0.092) d-minT<0 4–7 (−0.198)prec-ETo 4–10 (0.162) d-minT>25 6 (−0.147)prec-ETo 4–9 (0.177) d-wf 4–7 (−0.399)ETo 4–7 (−0.054) d-wf 4–10 (−0.130)ETo 8–10 (−0.103) d-snow y-1 (0.141)

refers to the period between December of the previous year and theril and July); max, aver and min refer to the minimum, average andent season; gw: groundwater level; L: the Ledava River level; t-sun:otranspiration (mm); prec-ETo: the difference between precipitationive temperature above 0 ◦C in this period; d-minT < 0: number of dayswith minimum daily temperature above 25 ◦C; d-wf: number of daysinter.

e c o l o g i c a l m o d e l l i n g 2 1 5 ( 2 0 0 8 ) 180–189 183

Table 2 – A comparison of relative root mean square error (RRMSE) and indicators of the equation complexity of 12models chosen after the first selection

Model RRMSE Number of attributesin the equation

Equation sizea Equation degreea Equation lengtha

1 Jnj3 2m 0.7282 6 12 2 192 Jnj3 3s 0.7599 6 8 3 133 Jnj3 1s 0.7614 6 8 3 124 Jnj3 4m 0.76455 3 7 3 135 Jnj2 2 0.7685 5 11 3 196 Jly 4xl 0.7686 6 11 3 207 Jly 3al 0.772 6 12 2 108 Avg 3hxl 0.7746 6 5 7 149 Jnj2 3m 0.7748 6 11 3 19

10 Jnj1 4 0.7839 3 7 6 2211 Avg 3al 0.7887 4 4 3 712 Jnj2 2s 0.8060 5 6 3 10

equat

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sitivity analyses. We focused on determination of changes in

a The size of the equation is the number of polynomial terms in thelength is the sum of the exponents of the variables.

002–2011) consisted of the mass of wood removed by precom-ercial thinning performed before the current growing season

nd before growing seasons 1, 2 and 3 years ago (thinning isommonly realized in the winter). Available were also the datan biomass of wood and biomass increments in each decade.

According to the results of Chmielewski and Rotzer (2001),ntonic et al. (1998/99) and the data from the Agency of theepublic of Slovenia for Environment (ARSO) we determinedhat the growing season extends between April and Octo-er. We investigated attributes for each month during thiseriod as well as attributes aggregated into groups: averagedr extreme values between April and June (4–6), between Maynd July (5–7), between July and August (6–8), between Maynd August (5–8), etc. Altogether we obtained 333 attributes,hich were tested for their effect on radial increments.

.2.2. Data analysiso identify the attributes that most importantly affectadial growth and to determine the relationship betweennnual radial increments and environmental and manage-ent attributes, the machine learning algorithm CIPER was

pplied.CIPER stands for Constrained Induction of Polynomial

quations for Regression (Peckov et al., 2006). This is anlgorithm for inducing polynomial equations from the dataTodorovski et al., 2004). The algorithm heuristically searcheshrough the space of possible equations for solutions that sat-sfy the given constraints. The output of CIPER consists of theolynomial equation that satisfies the complexity constraintsnd fits the data best (Peckov et al., 2006).

In the space of polynomials of arbitrary degree we canlways find a polynomial with error of zero on the trainingata. However, such equations can be very complex. To find anptimal trade-off between complexity of the model and welltting the data the CIPER uses Minimal Description Length

MDL) Principle as a search heuristic. The MDL Principle is aethod for inductive inference that provides a generic solu-

ion to the model selection problem (Peckov et al., 2006).CIPER beam search procedure starts with a constant poly-

omial. The equation is then refined with adding terms orultiplying terms with some attributes. Every term in the

ion; equation degree is the largest degree of any one term; equation

equation can be considered as a factor that influences the per-formance of the model. Only attributes that have significantinfluence on the performance of the model are included in theequation.

In CIPER the number of attributes that can be consideredat the same time is limited according to the number of theinitial data we have (in our case eight trees and the period of 35years, altogether 280 data for each attribute). Consequently wefirstly had to reduce the number of attributes for further workwith CIPER. We applied linear regression on the data aboutradial increments of eight trees and individual environmentalor management attributes. This way we reduced the numberof attributes from 333 to 84 (Table 1).

The selected 84 attributes were treated with CIPER algo-rithm. Fifty-two different combinations of 6–10 attributes weretested during the study. Each combination was run with differ-ent constrictions on the model complexity, which altogetherresulted in 124 experiments.

2.2.3. ModelingThe first selection among the models was performed accord-ing to the relative root mean square error (RRMSE), which isan indicator of the error of predictions. Twelve models werechosen among 124 experiments for a more precise study inSTELLA systems thinking software (Isee Systems) (Table 2).Selected equations were used to construct growth models ofradial increments of black alder trees under study. The select-ing criterion applied to these models was their behavior underchanging environmental conditions (data not shown). Theircomplexity, especially the equation degree, was considered aswell.

Models helped us to compare modeled and measured val-ues in individual years (e.g. Fig. 1) and changes in modeledradial increments under changing environmental conditions(e.g. Figs. 2 and 3). We run several simulations and several sen-

the modeled radial increments after increasing or decreasingvalues of individual attributes or attribute combinations for agiven percent (Fig. 3). In the presented graphs attribute valueswere changed for 25%.

184 e c o l o g i c a l m o d e l l i n g

Fig. 1 – Comparison of modeled and measured values ofradial increments (r-incr; mm).

Fig. 2 – Modeled values of radial increments underincreasing levels of the Ledava River (maxL 8–10, minL 4–7,minL 8–10) and decreasing duration of the sun radiation(t-sun 4–7, t-sun 8–10). The left side of the graph representsvery dry and sunny years, whereas wet and cloudy yearsare presented on the right. Three curves present modeledradial increments at three different levels of late white frost

or further decreased levels of the Ledava River (and conse-

in the spring (d-wf 4–7): minimum, average and maximumobserved number of days with white frost.

3. Results

Regression correlation coefficients showed that minimumLedava River levels were the most important attribute affect-ing radial growth in this ecosystem (minL; Table 1). Otherselected attributes (Table 1) were maximum and averageLedava River levels (maxL, averL), duration of sun radiationand number of days with white frost in the spring (d-wf).Black alder radial growth seemed to be relatively indifferent totemperature fluctuations, precipitation (prec), potential evap-otranspiration (ETo) and to the drought stress index (prec-ETo)within the observed range of values.

The overview of the 12 selected CIPER models with the low-est RRMSE is presented in Table 2. The experiment jnj3 2m waschosen for further work according to the complexity, reliabilityand reasonableness. It proved the lowest mistake, low equa-tion degree (Table 2) and the most reliable behavior. Attributesthat proved to be the most important in this model are age,minimum Ledava River levels in the first (from April to July;minL 4–7) and in the second part of the growing season (fromAugust to October; minL 8–10), maximum Ledava River levelsin the second part of the growing season (maxL 8–10), duration

of sun radiation in the first (t-sun 4–7) and in the second partof the growing season (t-sun 8–10), number of days with latefrost in the spring (from April to July; d-wf 4–7). The resulting

2 1 5 ( 2 0 0 8 ) 180–189

model in a form of polynomial equation was

radial increment(mm) = + − 0.0511025526922 × minL 8 − 10

+ − 0.0291795197998 × maxL 8 − 10+ − 0.017479975134 × t-sun 4 − 7+0.0346935385853 × t-sun 8 − 10+ − 1.950606536E − 05 × t-sun 8 − 102+ − 2.01014710248 × d-wf 4 − 7+9.35586778387E − 05 × minL 4 − 7

×t-sun 4 − 7+ − 0.000179339939732 × minL 4 − 7

×t-sun 8 − 10+6.45688563611E − 05 × minL 8 − 10

×t-sun 8 − 10+3.06551434164E − 05 × maxL 8 − 10

×t-sun 4 − 7+0.00282485442386 × t-sun 4 − 7 × d-wf 4−7+ − 0.00141078675225 × t-sun 8 − 10

×d-wf 4 − 7+7.91071710872

(1)

Our analysis showed that the precision of individualcoefficients does not importantly affect the outcome. Confi-dence intervals were calculated for every coefficient. Thosecalculations show that there is 95% confidence that withfour scientific digits we are preserving the stability of themodel.

The comparison of modeled and measured values is pre-sented in Fig. 1. The graph on changes of modeled incrementsunder increased levels of the Ledava River and decreasedduration of sun radiation are shown in Fig. 2. Fig. 3 presentssensitivity analyses.

The correlation coefficient between modeled radial incre-ments and the average measured increments of eight trees is0.877. This agreement is higher than it is predicted in CIPERbecause CIPER operates with the data on radial increments ofindividual trees, not on their average values.

In the absence of white frost (r-incr. mind-wf 4–7 in Fig. 2)the optimal conditions for the radial growth are at a bit belowthan average level of the Ledava River and at a bit above thanaverage duration of sun radiation (Fig. 2). In both wetter anddrier conditions (higher or lower levels of the Ledava River)the increments decrease. Especially pronounced decrease isobserved in humid and cloudy years. Frequent late frosts sig-nificantly affect radial increments as well. However, years withnumerous days of frost were rare in the period under study.

Overview of the results reveals that the model predicts thelowest radial increments under the following combinations ofenvironmental conditions:

• Low Ledava River levels in the first part of the growing sea-son, high Ledava River levels through the second part ofthe growing season, high sun radiation through the wholegrowing season, and more number of days with late whitefrost in the spring.

• High Ledava River and low sun radiation duration through-out the growing season, higher number of days with whitefrost.

In the following paragraphs we present effects of increased

quently groundwater levels; Fig. 3A), increased or decreasedduration of sun radiation (Fig. 3B), combinations of decreasedLedava River levels and increased duration of sun radiation

e c o l o g i c a l m o d e l l i n g 2 1 5 ( 2 0 0 8 ) 180–189 185

Fig. 3 – Sensitivity analyses: modeled radial increments under measured attribute values and after individual attribute orattribute combinations were increased or decreased for 25%. Increased and decreased were (A) all Ledava River levels:minimum levels between April and July (minL 4–7) and between August and October (minL 8–10), maximum levels betweenAugust and October (maxL 8–10); (B) duration of sun radiation (h) between April and July (t-sun 4–7) and between Augustand October (t-sun 8–10); (C) all Ledava River levels (minL 4–7, minL 8–10 and maxL 8–10) and opposite change in all sunradiation periods (t-sun 4–7, t-sun 8–10); (D) all minimum River levels (minL 4–7, minL 8–10) and opposite change inmaximum River levels and sun radiation periods (maxL 8–10, t-sun 4–7, t-sun 8–10); (E) number of days with white frostbetween April and July (d-wf 4–7).

186 e c o l o g i c a l m o d e l l i n g 2 1 5 ( 2 0 0 8 ) 180–189

(Con

Fig. 3 –

(drier and sunnier years) and vice versa (wetter and cloudieryears) (Fig. 3C), combinations of decreased minimum Riverlevels and increased maximum River levels and duration ofsun radiation (drier and sunnier years with higher ground-water level fluctuations) and vice versa (wetter and cloudieryears with lower groundwater level fluctuations) (Fig. 3D), andeffects of increased or decreased abundance of late whitefrosts in the spring (Fig. 3E).

Changes of increments under changed levels of the LedavaRiver (Fig. 3A) indicate that increments more or less linearlydecrease as the River levels increase. The response is weakin sunny years with plenty of precipitation, and stronger insunny and dry years.

The effect of sun radiation (Fig. 3B) is dependent on thevalue of the other attributes. Generally an increase in theduration of sun radiation in otherwise sunny years causes adecrease in radial increments. On the other hand the samechange causes an increase in radial increments in cloudyand/or wet years. Both increase and decrease of sun radiationresult in increased oscillations of radial increments.

The effect of simultaneous change of the Ledava River lev-els (minL 4–7, minL 8–10, maxL 8–10; e.g. we increased them)and inverse change in the duration of sun radiation (t-sun 4–7,t-sun 8–10; e.g. we decreased them; Fig. 3C) is importantlyaffected by the appearance of white frosts and high LedavaRiver levels (maxL 8–10). High River levels cause a decrease inthe modeled increments and they diminish the importance ofsun radiation levels. White frosts cause a decrease of modeledincrements in the majority of cases.

Very important is also the effect of maximum LedavaRiver levels (maxL 8–10; Fig. 3D). Increased maxL 8–10 levelscause an increase in radial increments in drier and cloudierconditions. Increased maxL 8–10 levels have the same effectunder conditions of reduced Ledava River levels and increasedduration of sun radiation. Moreover, the study showed thatincrease in maxL 8–10 further increases differences in radialincrements between wet and dry years. On the contrarya decrease in this attribute functions like a buffer and itdecreases differences in radial increments between dry andwet years.

Except in very dry and sunny years an increase in the num-ber of days with white frost (d-wf 4–7) causes a decrease ofradial increments (Fig. 3E). In agreement with our expectationsa decrease in the d-wf 4–7 stimulates radial increments.

tinued ).

4. Discussion

The selection of the best model remains an important ques-tion in machine-learning tasks. In our work the reliability(RRMSE) and the reasonableness of the model under chang-ing values of individual attribute or attribute combinationswere used as the most important indicator of the appropriate-ness of the model. Besides this, simple models were preferred(Table 2).

In comparison to the other models under examinationthe selected one shows much higher predicting power onradial increments under study (Fig. 1) and much higher agree-ment with knowledge-based expectations. The behavior of themodel can be explained through physiological processes. Theonly response, which cannot be regarded as wholly suitable,was the reaction on frequent late white frosts in the spring.

4.1. Age

The absence of the attribute age in the selected model couldbe explained by the maturity of the stand. For mature treeswe expected slow and approximately linear negative trend ofradial increments in time, as it was confirmed by statisticalanalyses (Table 1). On the other hand the model suggests thata decrease of radial increments appeared due to the trend ofincreased duration of sun radiation in the past decade.

The description of changes in the radial growth in timewould be needed to enable completely dynamic modeling.To reliably distinguish effects of age we would need thedata on radial increments in some younger trees from thecorresponding stand or we would need longer series of hydro-meteorological and management data.

4.2. The Ledava River level and duration of sunradiation

The model predicts an important increase in oscillations ofradial increments as soon as meteorological or hydrologicalconditions importantly moves from the observed conditions.

Increased oscillations of the Ledava River levels (increaseddifferences between the first and the second parts of the grow-ing season or between maximum and minimum levels) resultin decreased radial increments and increased oscillations of

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adial increments, both changes indicating higher stress andecreased stability of ecosystem function.

Levanic and Kotar (1996) found that radial increments wereteadily decreasing since 1965 in the majority of the researchlots in the neighboring black alder stands in Crni Log. Only onne plot they observed a slight improvement of radial growth

n the past decade of the studied period. It is possible that treesn this plot, as well as the trees in this research, were ableo slowly adapt to the new conditions and to take advantagef them. Unfortunately we do not have the data on morpho-

ogical and physiological changes of root system and in thehizosphere within this period.

Trees that are growing on sites with permanently highroundwater are known to develop shallow roots (Eschenbach,995; Brus, 2005; Keeland and Sharitz, 1997). The roots of alder,n the other hand, are reported to have the ability to break wellelow the water table (Whyte and Sisam, 1949, cit. in McVean,956, 1953). This could be able to explain the trade-off betweenhe expectations and the modeling results in dryness.

Keeland and Sharitz (1997) note that temporary flooding ofhree flood-tolerant conifer species caused root deterioration,hereas trees on permanently flooded locations developedater roots which were adapted to inundation. They explain

hat long-lasting flooding results in a more stable soil envi-onment and adapted root system. Trees growing in suchonditions do not have to invest a lot of energy into a root sys-em reconstruction and they show improved biomass growthIremonger and Kelly, 1988; Keeland and Sharitz, 1997). This isn agreement with the assertions of Levanic and Kotar (1996)hat high groundwater fluctuations represent the major threato these stands.

The importance of groundwater levels and groundwaterscillations is stressed also in the results of this study. Bothigh water levels in otherwise dry seasons and absence ofooding (low maxL 8–10) in wet years have positive effectsn radial increments. High oscillations of groundwater levelave negative effect on radial growth. Increase in maximumroundwater levels could be beneficial only when seriousrought takes place. More detailed physiological study woulde needed for more accurate conclusions.

Changes in the Ledava River levels and duration of sunadiation have the opposite effect on modeled radial incre-

ents in dry years compared to wet and sunny years (Fig. 3Cnd D). Increase in sunniness in otherwise wet years resultn increased radial increments, whereas the same changeauses a decrease in modeled increments in dry years (yearsith low levels of the Ledava River). Besides, these fluctua-

ions of the Ledava River level cause much higher changes ofadial increments in cloudy years compared to years with highun radiation. The model suggests that trees easily sustainigh groundwater level in years with high rate of photosyn-hesis. High photosynthesis could promote the transport ofxygen into the roots (Iremonger and Kelly, 1988; Grosse andchroder, 1986; Schroder, 1989; Dilly et al., 2000). At the sameime higher photosynthesis enables higher transport of assim-lates to the nodules and consequently higher rate of nitrogen

xation (Wheeler, 1971; Gordon and Wheeler, 1978; Dawsonnd Godon, 1979; Pizelle, 1984; Dilly et al., 2000).

Previous conviction was (Nemesszeghy, 1986; Levanic, 1993;olenko, 2004; personal communication) that a moderate

5 ( 2 0 0 8 ) 180–189 187

decrease in groundwater table was the major reason for adecrease in the vitality of these stands and consequently adecrease in radial increments. On the contrary our results sug-gest that a decrease in radial increments due to the droughtstress appears only when both very low groundwater table andhigh intensity of sun radiation takes place. Cloudy and rainyyears, on the other hand, are declared to much more impor-tantly restrict radial increments. This could be explained bythe oxygen stress (Iremonger and Kelly, 1988; Keeland andSharitz, 1997) and a simultaneous decrease in the nitrogen fix-ation process (McVean, 1953; Iremonger and Kelly, 1988) underhigh groundwater levels. These results suggest that the standhas developed deep roots and that it is this way adapted tothe local conditions. Consequently it is not endangered dueto lowered groundwater table. However, care must be takennot to generalize these findings to all stands in the area. It isknown (Nemesszeghy, 1986) that only some tenths of centime-ters higher altitude of a growing site can significantly affectgrowth conditions and significantly change reactions of blackalder radial increments on the groundwater level fluctuations.

The decrease of radial increments under high Ledava Riverlevels (and consequently high groundwater levels) is in con-trary with the knowledge about the high degree of adaptationsof this tree species to high groundwater levels. In opposition tothe results we expected a decline of radial increments underlow groundwater table (Levanic, 1993).

The results obtained by the selected model are in agree-ment with the findings of Levanic (1993) who did not findany evidence that drought would cause a decrease in radialincrements in these stands. He also found that radial incre-ments were often low in wet years. He concluded that blackalder could grow on these sites as long as it has access togroundwater. A decrease in growth of black alder trees andseedlings grown in inundated soil was also confirmed inthe experiments of Kaelke and Dawson (2003) and McVean(1953).

4.3. Thinning

Thinning measures usually cause a subsequent increase inthe growth of the remaining trees as they gain advantageof additional resources. Only in the first year after thinninga smaller reduction of growth can take place due to higherinvestments into the root system and into the canopy as wellas due to disturbances of the soil system. In our case CIPERdid not include management-related attributes in any of thegenerated equations. Three possible explanations exist forthe low importance of thinning in our stand. The first is thatadult trees, in contrast to young stands, do not respond inten-sively on changed conditions in the canopy (Levanic, 1993).The second possibility is that trees were not removed in theclose neighborhood of the trees under study during the thin-ning measures. The third possible reason is a relatively lownumber of thinning measures performed in the period understudy.

growth and depressed height growth of young red alder trees.A slight increase of radial increments after thinning was alsoobserved in the study of Berntsen (1961, 1962; cit. in Hibbs etal., 1989) in 21- and 11-year-old stands.

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188 e c o l o g i c a l m o d e l l

4.4. White frost

According to the model frequent white frosts stimulate radialincrements at low Ledava River levels and high sun radia-tion intensities, whereas increments rapidly fall toward zeroat higher River levels and lower sun radiation intensities. Theinsufficient number of years with frequent late white frostswas the most probable reason for the inexplicable behavior ofthe model under high number of late white frosts.

The model suggests that white frost is important, but itcannot be destroyable for this tree species.

4.5. Temperature

Low importance of temperatures for the radial growth ofblack alder trees in this area was found also in the researchof Levanic (1993), whereas Horacek et al. (2003) found thatmean daily temperatures, precipitation and soil water sup-ply were important for the radial increments of a floodplainforest. Temperature fluctuations also importantly affectedradial growth of moist forests in Lithuania (Kairiukstis andStravinskiene, 1987).

Overall radial increments were importantly affected byenvironmental conditions in August, September and October.This seemed quite unusual as the majority of radial growthof trees usually takes place until July (Keeland and Sharitz,1997; Lebaube et al., 2000; Costa et al., 2003) and it decreasessharply afterwards. However, in black alder trees or seedlingssome growth can take place even as late as in September orNovember (Eschenbach, 1995; Kaelke and Dawson, 2003; Costaet al., 2003). Growth in the second part of the growing seasoncan be pronounced in trees with diffuse porous wood and withcontinuous growth. Their radial growth follows the budburstand black alder is known to sprout new leaves as late as inSeptember (Eschenbach, 1995).

5. Conclusion

The applied machine learning algorithm has proved its advan-tages and usefulness in ecological modeling. The examinationof the selected growth model implies some new findings aboutthe responses of black alder on dynamic changes of environ-mental attributes. It was showed that the combination of theLedava River level (and consequently groundwater level) andthe duration of sun radiation have the major influence on thedynamics of radial increments on the selected study site. Adecrease in annual radial increments due to the drought stressappeared only in years with the lowest groundwater levelsand the highest sun radiation intensities. The groundwaterlevel was especially important in years with high durationof sun radiation, whereas sun radiation was more importantin years with high groundwater levels. There was no indi-cation that a decrease in groundwater table alone could bea reason for tree decline on this site in the present time.However, trees must undergo several important adaptations

of root system to survive in changed conditions. In a sud-den decrease of groundwater these trees most probably wouldnot have enough time for appropriate adaptations. On thecontrary, trees adapted to lower groundwater levels are neg-

2 1 5 ( 2 0 0 8 ) 180–189

atively affected by high groundwater level. This can explainhigh decrease in radial increments in very humid and cloudyyears.

The results indicate that high oscillations of groundwa-ter result in increased oscillations of radial increments. Highoscillations in water conditions represent a stress to thesestands and they demand high-energy investments for mor-phological and physiological modifications of the root system.We infer that high fluctuations of groundwater level are moststressful for these stands.

The appearance of late white frost at the time of leafunfolding can importantly affect radial increments, but it isnot likely to cause a decline in black alder trees.

Acknowledgements

We would like to express our gratefulness to the personnel ofthe Slovenia Forest Service, Regional Unit Murska Sobota, tothe Slovenian Forestry Institute in Ljubljana and to the Depart-ment of Knowledge Technologies at the Jozef Stefan Institutein Ljubljana. Moreover, we would like to thank the Environ-mental Agency of Slovenia for providing meteorological data.

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