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Ecological Modelling 279 (2014) 100–113

Contents lists available at ScienceDirect

Ecological Modelling

j ourna l h omepa ge: www.elsev ier .com/ locate /eco lmodel

orestMAS – A single tree based secondary succession modelmploying Ellenberg indicator values

imon Kolmanic a,∗, Nikola Guida, Jurij Diacib

University of Maribor, Faculty of Electrical Engineering and Computer Science, Smetanova 17, SI-2000 Maribor, SloveniaUniversity of Ljubljana, Biotechnical Faculty, Jamnikarjeva 101, SI-1000 Ljubljana, Slovenia

r t i c l e i n f o

rticle history:eceived 23 October 2013eceived in revised form 13 February 2014ccepted 18 February 2014vailable online 12 March 2014

eywords:bandoned agricultural landecondary successionllenberg indicator valuescological neighbourhoodpecies compositionndividual-based model

a b s t r a c t

Over recent decades farmland abandonment has affected large areas of the landscape. To better predictthe changes associated with this process, we developed a secondary succession model based on Ellenbergindicator values describing the ecological niche of a tree along environmental gradients. These values arecompared with local ecological factors dependent on terrain conditions. The terrain is represented by aDigital Terrain Model, where the local conditions are represented by a light availability model, climatedata, soil properties, and a combination of a water flow model and average annual rainfall data. Eachtree in our model is associated with its immediate circular ecological neighbourhood and is treatedindividually from the seedling stage through to its decay. Each year, tree heights, actual vigour, andneighbourhood radii were calculated. When two radii intersected, the vigour of both trees was compared.The weaker of the two became dominated, leading to stress-related mortality. When a tree reached theadult stage, it produced seeds that established new seedlings that competed for light and nutrition. Tostart the simulation, the initial amount of seed was planted on bare ground. It was possible to monitor

the succession phases either visually or statistically. 3D tree models were used to visualize a tree at anyage, generating realistic landscape images useful for demonstrating long-term changes in the culturallandscape to non-experts. The results were compared with those from previous field studies in variousareas of Slovenia. Apart from predicting landscape changes after farmland abandonment, the model canbe used for forecasting the regeneration process after clearcutting or natural disasters.

© 2014 Elsevier B.V. All rights reserved.

. Introduction

In the late 1940s, entire villages were abandoned in Slovenia.he affected regions became economically unimportant and haveemained so. In recent decades a similar process has been occur-ing in Slovenia and in the Balkans. It is occurring at a much slowerate and for different reasons, but with similar consequences. Farm-and with higher production costs is being abandoned and is slowlyeing colonized by forest. Since this process is gradual, people areostly unaware of it. To prevent the stagnation of the affected

egions, there is a need for appropriate tools, firstly to point out theecessity for new policies by highlighting the long-term changes

n the cultural landscape, and secondly to support the decisionaking process. One possibility to better understand the processould be the use of forest growth simulators, gap models, or

∗ Corresponding author. Tel.: +386 2 220 7475; fax: +386 2 220 7272.E-mail addresses: simon.kolmanic@uni-mb.si, simon.kolmanic@gmail.com

S. Kolmanic).

ttp://dx.doi.org/10.1016/j.ecolmodel.2014.02.016304-3800/© 2014 Elsevier B.V. All rights reserved.

similar tools. Thorough overviews of these simulators are givenin Liu and Ashton (1995), Bugmann (2001), and Pretzsch et al.(2008). Although these simulators are very impressive, they werecreated to support decisions aligned with forest management andare mainly focused on the annual biomass and volume increment ofexisting stands. Growth models are based on the long-term mea-surements of increments in tree diameters and heights taken atpredefined time intervals, usually every five years. The oldest mea-surements used in the SILVA growth model (Pretzsch et al., 2002),for example, even date all the way back to 1870. Because thesemeasurements were used to predict timber production in particu-lar stands, only economically important tree species, such as Piceaabies (L.) H. Karst., Abies alba Mill., Pinus sylvestris L., Fagus syl-vatica L., and Quercus petraea (Mattuschka) Liebl., were included.Other trees of little economic value, but of high ecological impor-tance, such as Betula pendula Roth, Salix caprea L., Carpinus betulus

L., and Alnus glutinosa (L.) Gaertn., were left out. From a compu-tational point of view, forest gap models such as JABOWA (Botkinet al., 1972), ForClim (Bugmann, 1996), and many others (Bugmann,2001) are very interesting since the forest is abstracted as a

l Modelling 279 (2014) 100–113 101

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Table 1Scale for the Ellenberg soil acidity (reaction) indicator (ER).

Value pH range Meaning

1 ≤4.4 Extremely acidic2 4.5–5.0 Very strongly acidic3 5.1–5.5 Strongly acidic4 5.6–6.0 Moderately acidic5 6.1–6.5 Slightly acidic6 6.6–7.3 Neutral7 7.4–7.8 Slightly alkaline8 7.9–8.4 Moderately alkaline

S. Kolmanic et al. / Ecologica

omposite of many small patches of land mostly without any inter-ction among them. These models are therefore especially suitableor parallel computing on graphics processing units with the possi-ility of considerable speedups (Garland et al., 2008); however, an

mportant drawback in virtually all of them is that the early stagesf succession cannot be simulated because the height of trees muste 2 m or higher (Bugmann, 2001). Another approach is presented

n the work of Pueyo and Beguería (2007), who developed a Markovogistic model for predicting the rate of secondary succession. In the

odel, the land can be covered by crops, shrubs, or different typesf local forest according to its elevation, but detailed forest compo-ition and water and nutrient availability due to local topographicalonditions play only a secondary role. Another problem is that tran-ition probabilities in the model are obtained from observations ofediterranean mountainous areas that are quite specific and not

eneral enough for our purposes. An important problem in existingorest simulators is that their results are primarily aimed at forestryxperts and are thus difficult for the general public to understand. Inrder for the statistical results to achieve greater impact, the visual-zation of changes in the cultural landscape should be implementeds well.

We therefore developed ForestMAS, a new forest simulationodel for secondary succession in which all of the important

pecies are taken into consideration. Since obtaining reliable quan-itative data on autecology proved impossible for so many treesver a short time period, indicator values as proposed by Ellenbergt al. (1992) were used. The Ellenberg system has already beenonfirmed by several authors (e.g., Persson, 1981; van der Maarel,993; Diekmann and Dupré, 1997; Koerner et al., 1997; Diekmann,003) and has also been partially used in SILVA (Pretzsch et al.,002) and ForClim (Bugmann, 1996). The Ellenberg indicator valueEIV) for tree light demand was used in SILVA and ForClim, andn additional EIV for temperature was employed in ForClim. Inrder to fully describe plant needs, additional indicator valuessoil moisture, acidity, and nitrogen/nutrients requirements) werentroduced in ForestMAS.

A key part of ForestMAS is the visualization of landscape changesuring secondary succession. There are a number of algorithmsvailable for this purpose in the literature, e.g., Weber and Penn1995), Prusinkiewicz and Lindenmayer (1996), and Pałubicki et al.2009). Plant visualization algorithms generally involve a largeumber of parameter values and are computationally demanding.orestMAS makes use of the faster Holton model (Holton, 1994),hich works equally well for both deciduous and coniferous trees

nd can generate high precision tree geometric models at any treege. We used the Holton model to generate a series of tree imagest different ages, which served as textures that were mapped onhree intersecting planes and thus gave the impression of a 3D treet any camera angle. This is acceptable since the trees are part ofhe landscape images and with the use of textures we obtain theame quality of tree images in much less time.

With the ability to produce realistic landscape images, Forest-AS enables the observation of any long-term landscape changes.

f the area is small enough (<10 ha), these changes can be seen in aeal time animation, but for larger areas only static images can beenerated.

. Materials and methods

.1. Ellenberg indicator values

Reliable data describing plant requirements are necessary foreveloping a consistent secondary succession model. Reliable long-erm measurements exist for economically important tree species,ut these make up only a small number of the species that are

9 ≥8.5 Strongly alkalinex (10) Indifferent

important for secondary succession. Such measurements do notexist for pioneer species that are extremely important for sec-ondary succession but have little or no economic value, suchas Betula pendula and Salix caprea (Connell and Slatyer, 1997;Kimmins, 2004). One solution to this problem lies in the CentralEuropean plant classification system proposed by Ellenberg et al.(1992). Ellenberg indicator values (EIVs) provide simple ordinalclasses where plants are ranked according to their requirements forsoil acidity, nutrients, soil humidity, continentality, temperature,soil salt content, and light. The indicators for land plants contain val-ues on a 10-point scale, where the last point, denoted by the valuex, indicates that the given indicator has no influence. Each plantin the Ellenberg classification is thus described by a set of sevennumbers expressing the average plant requirements along sevenfundamental gradients. In order to employ EIVs in ForestMAS, thefollowing steps were necessary:

(1) Substituting the mostly descriptive EIV boundaries with solidvalues – this step was necessary in order to adapt the discrete EIVsto interpretable and measurable values for site quality. The indi-cator for light, the most often used EIV, classified plants on a scalebetween light demanding and shade tolerant. Therefore, the maincriterion was the obstruction of sunlight. The sites that receiveddirect sunlight all day were given the maximum value based onwhich the scale is adapted. In the case of soil acidity, a differentapproach was used. Table 1 shows an example of the quantitativeborders for the soil acidity EIV proposed by the Natural ResourceConservation Service of the US Department of Agriculture (SoilSurvey Division Staff, 1993).

The temperature EIV in the Ellenberg classification system is asubstitution for the annual sum of degree-days used in JABOWA(Botkin et al., 1972) and algorithms used in the majority of latergap models to define the effect of temperature on tree growth.It is strongly correlated with the terrain elevation and, with theexception of the last two points (8 and 9), is bound to altitudi-nal vegetation zones. The last two points on the EIV temperaturescale designate very hot climate typical for sub-Mediterranean andMediterranean areas. The highest average annual temperatures inSlovenia exceed 12 ◦C in only a few coastal regions, and are mostlybetween 10 and 12 ◦C, which has also been the case in the last 10years for all lower areas of the country. Therefore, in ForestMASthe temperature borders depend entirely on the terrain elevationwith point 1 in areas with elevation higher than 1650 m and point9 in areas lower than 200 m. In order to apply the nutrient EIV, wetook into account the work of Hawkes et al. (1997), who used Ellen-berg EIVs for acidity, moisture, and nutrients to assess soil quality inBritish forests. They measured the total amount of elements impor-tant for plant growth (N, K, Ca, C, Mg, and P) and showed thatthe quantities of total N, C, and P were not important for sepa-rating sites with different EIV for nutrients, which was consistent

with the previous work of Khanna and Ulrich (1984), who notedthat the N status of plantation soils was usually assessed by therate of mineralization. Instead, they proposed a combination of the

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inimum amount of N and soil pH. According to these findings,he proper combination of particular elements is necessary for theseful employment of EIV for nutrients. We therefore used a soil

ndicator named Ground index, which is a combination of soil tex-ure, the rate of soil evolution, and bedrock. It describes the soiluitability for agricultural use and ranges from 7 to 100, whichakes it easy to adapt to the Ellenberg 9-point scale. In order to

efine the quantitative border values for the water EIV, the aver-ge annual rainfall for study sites in Slovenia from 1971 to 2000as used, where again the maximum value was applied to adapt

he scale. The EIV for salinity was not used since coastal plants wereot included in the simulation. Since most of the climate properties

mportant for tree survival were already accounted for by the mois-ure, light availability, and temperature EIVs, the continentality EIVas also omitted.

(2) Map site quantity values across the study area based on GISnalysis of a Digital Terrain Model (DTM) – the study area in Forest-AS was represented by a DTM with a 10 m × 10 m resolution. To

ssess light availability, a light model was combined with the DTM.o estimate soil moisture, average annual precipitation, the DTM,nd water holding capacity values were used. For parameters suchs light availability and soil moisture, it was necessary to calculatehe values with special models, while the temperature depends onhe DTM elevation points and therefore does not need any furtherttention. For the calculation of soil moisture values, a water flowodel was combined with the average rainfall quantity over the

tudy area and the water holding capacity value. Soil acidity andutrient availability values were estimated from appropriate digitaloil maps (Vrscaj et al., 2005).

(3) Determine the terrain quantity values for every pixel on bareround in the study area and normalize values in step 1 and 2 tonterval [0,1]. For the normalization of moisture, soil acidity, nutri-nts, and temperature, the highest numbers in the database aresed, while for the normalization of light availability, the maximumalue calculated on the site is used.

(4) At each cycle correct the light availability for individual treesn account of higher neighbours. This change then directly affectshe height of the tree.

A detailed description of steps 2 and 4 can be found in Sections.2 and 2.3.1, respectively.

.2. Calculation of terrain properties

To calculate plant growth potential, we compared plant require-ents with the conditions on site. The areas in our study are

epresented by a digital terrain model (DTM) in which data on soilcidity, nutrient availability, and temperature are mapped to pointsf the terrain grid. It was necessary to calculate soil moisture anderrain sunniness since the data available from the Slovenian Envi-onment Agency measured at a grid resolution of 1 km × 1 km areoo sparse.

To calculate the terrain moisture, we assumed that the annualainfall volume is uniformly distributed and falls perpendicularly tohe xy plane. Therefore, all DTM squares initially receive the samemount of rain. To estimate the correct amount of soil moisture, theoil type must also be taken into consideration. For this purposee employed a digital map of the soil water holding capacity of

gricultural land in Slovenia (Vrscaj et al., 2005), which is mappedo the DTM of the study area. If the terrain is steep and the waterolding capacity is low, most of the water runs off and the soil drains

aster. The runoff amount for each (i, j)-th square is determined byts slope factor si, j, calculated by the following formula:

i,j = 1 − �ni,j;z (1)

where �ni,j;z is the z coordinate of the unit normal vector of (i,)-th square. The initial amount of water mi,j received by the this

elling 279 (2014) 100–113

square is obtained from the average annual rainfall quantity on thesite. If the square is above a predefined water level, which can bedetermined from the z coordinate of its centre point c(i, j), a certainamount of water runs off to its lower neighbouring squares. Thiswater is distributed equally to all the lower neighbours. Each ofthem additionally receives �mi,j water, which is calculated by thefollowing equation:

�mi,j = �si,jmi,j

n(2)

where n (0 ≤ n ≤ 4) is the number of lower neighbours of the (i,j)-th square and � is the coefficient of the water holding capacityof the square. The process of the water flow calculation is startedfrom the highest squares and continues towards the lowest ones.Because this calculation can lead to excessive differences in soilmoisture between neighbouring squares, an average filter is usedto distribute soil moisture more evenly in the neighbourhood:

mi,j = mi−1,j + mi+1,j + mi,j + mi,j+1 + mi,j+1

5(3)

To calculate the light availability attribute, we adopted the solarradiation model proposed by Zaksek et al. (2005). The authors pro-posed a quasiglobal radiation model where the energy receivedis dependent on the solar incidence angle, soil topography, andweather. The earth’s surface, in our case represented by a DTM at a10 × 10 m resolution, is based on a square grid. For each DTM squarewe calculated the energy received from the sun. We ignored theinfluence of weather conditions since they change on a larger scalethan our simulation area. Moreover, the density of meteorologicalstations in Slovenia is too low to be of use in our model. However,climate data from meteorological stations, such as cloudiness, caneasily be included in the model if needed. The Zaksek model wastherefore simplified and consequently made much faster. To cal-culate the amount of sunlight received by the (i, j)-th square, weagain use its centre point ci,j. The amount of energy at ci,j is propor-tional to the sun’s incidence angle ˛t between the square normalni,j and the vector lt in the direction of the sun. Since the sun’s posi-tion constantly changes, the vector lt is a function of time and thesun’s declination. Because our model is limited to relatively smallareas, the sun’s declination can be fixed and its position pt can becalculated in discrete time samples with the next equation:

pt =

⎧⎪⎨⎪⎩

p0 + t(pn − p0)n

, t = 0, 1, . . ., n

pn + t(p2n − pn)2n

, t = n + 1, . . ., 2n

(4)

where p0 and p2n are the sunrise and sunset positions, respectively,pn is the midday position of the sun, and 2n is the number of sam-ples during the day. At the equinox for example, when the day andnight are of equal length, n must be greater than five to get a sampleat least at each hour during the daytime. When the sun’s positionpt at any given time is known, the vector lt between points ci,j andpt can also be determined (Fig. 1 a).

The light availability on the (i, j)-th square is calculated with thehelp of the angle ˛t between the square normal ni,j and the vectorlt, which is calculated by the following formula:

cos ˛t = ni,j It (5)

The angle ˛t is also used for determining whether the DTM

square is shaded or not, which is very important. If ˛t is positive andsmaller than �/2, then the square is exposed to direct sunlight. Oth-erwise the square is shaded and receives only a predefined amountof diffuse light (Fig. 1b).

S. Kolmanic et al. / Ecological Modelling 279 (2014) 100–113 103

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ig. 1. Light availability calculation: (a) Sun positional samples needed for the calcquares to direct sunlight. The approaches are explained in text.

The light availability li,j(t) on a given square at time t is thusetermined by the following equation:

i,j(t) ={

�(t) cos ˛t, 0 ≤ ˛t ≤ �/2,

lambient, otherwise(6)

here �(t) is a weighting function, which amplifies the light duringhe hours closer to noon, defined by the following equation:

(t) =

⎧⎪⎨⎪⎩

1 + t

nt = 0, 1, . . ., n

2 − (t − n)n

t = n + 1, . . ., 2n

(7)

The final light availability on the (i,j)-th square is the amount ofolar energy received during the entire day and thus calculated byhe next sum:

i,j =2n∑

t=0

li,j(t) (8)

Although our light availability model is much faster than that ofaksek, it is still too complex to be used for hourly based light avail-bility calculation. To solve that, we again used a similar approacho that of Zaksek and his colleagues. They calculated the quasiglobaladiation energy at ten-day intervals, where the energy was deter-ined for the mean day on an hourly basis and was then multiplied

y ten. The annual quasiglobal radiation energy was finally cal-ulated with the sum of the energy over all decades. Despite thisimplification, the energy calculation process remained slow. Bytudying their results, we observed that a good approximation ofight availability from March to September, which represents therowing season for all trees in our model, can be achieved withhe light availability values at the Northward equinox and North-rn solstice, calculated on an hourly basis. In order to get the lightvailability for the entire season, the first value is multiplied by twond then added to the second one multiplied by five. After the lightvailability was calculated on the entire DTM, we used a value of 0.2or the ambient light setting. The light availability was normalizedccording to the highest calculated value, representing the lightvailability on the square most exposed to direct sunlight duringhe day.

All site quality values are between 0 and 1 and can be visualizedy quadrangles of different colour with corresponding sizes from

to the whole area of the DTM square (Fig. 6). The site quality

uadrangles are therefore dense if the values are high but sparsetherwise. For example, we can observe the tops of hills in Fig. 6b,hich receive more light than the hillsides, or the soil pH in Fig. 6c,hich is mostly neutral or slightly acidic.

n of light availability on the (i,j)-th square. (b) Determination of exposure of DTM

2.3. Tree competition model

Trees compete for light, water, and nutrients. The most success-ful ones prevail and form a stable population. In order to modelthis competition, we applied the idea of ecological neighbourhoods,defined as the region in which a tree is active or has some influenceduring an appropriate period of time (Wright, 1943, 1946; Addicottet al., 1987). Since a tree is a static entity, its ecological neighbour-hood can be represented by a circle. As a tree grows, the radiusof its ecological neighbourhood increases and so does the area ofits influence. This approach is widely used in population dynam-ics models (Gates and Westcott, 1978; Pacala and Silander, 1985;Czárán, 1998; Berger and Hildenbrandt, 2000; Berger et al., 2008).Trees can grow if their basic requirements, as described by EIVs, aremet.

The balance among the site conditions and tree require-ments (EIV) determines a numerical value called growth potential,which directly influences how fast a tree grows in the model.We also calculate actual vigour, which is the growth potentialreduced in proportion to the tallest tree. Taller trees shade smallerneighbouring trees. Growth potential is also reduced in proportionto the oldest trees, which is important mainly for trees in early lifestages. In the simulation there is often the case of a large number ofyoung trees competing with a much older one. If the height differ-ence between the young trees and the old tree is large enough,the majority of young trees eventually die. With a reduction ofactual vigour in proportion to the older tree, the mortality of youngtrees is slightly increased, which speeds up the simulation consid-erably. The actual vigour, Eq. (13), is important when the ecologicalneighbourhoods intersect. In this case the vigour of both trees iscompared, and the tree with less vigour becomes dominated. If atree is dominated, there is a high probability that it will die.

When a tree reaches the adult stage, it starts to produce seeds.Greene and Johnson (1994) suggested that total seed crop mass isdirectly proportional to some measure of plant vegetative size andthe individual mass of the seed depending on the tree species. Thenumber of seeds produced varies greatly. While the mean annualnumber of seeds produced by Betula pendula is greater than 20,000,the number of seeds produced by Quercus varies greatly, from lessthan 200 in normal years (Downs and McQuilkin, 1944) to morethan 3000 in mast years (Gurnell, 1993). Although there are largenumber of studies and models of seed production, we could not useany of them because we do not estimate above ground vegetativebiomass in our model, which is crucial for these other models. In

order to solve this problem, we empirically determined the max-imum number of seeds a tree of a given species can produce. Thenumber of seeds an individual tree produces thus depends on itsheight and the given maximum seed number for the particular

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pecies. Each seed is then individually planted and starts to com-ete with other plants.

.3.1. Tree growth modelThe current tree height hi depends on the current tree age and

he maximum tree height that the particular species can reach. Tostimate hi in regard to age is a complex problem (Hunt, 1982;soularisa and Wallaceb, 2002; Hunt et al., 2002) and is generallyefined by a growth function that depends on the tree species andite conditions (Mayer, 1977), see Fig. 2a. The influence of the sites so important that the shapes of growth curves for the same treepecies can be completely incongruous depending on whether theite conditions are good or poor. This complexity is also reflectedn the growth submodels in all gap models from JABOWA (Botkint al., 1972), the earliest model, to more recent ones such as ForClimBugmann, 1996). In ForClim the maximum growth equation pro-osed by Moore (1989) is used. In this equation many parametersre included that are difficult to evaluate for every area of interestor secondary succession (Fig. 2b). Upon closer inspection we canee that the shapes of the growth curves for different tree speciesre similar. We therefore set out to construct a general growth curve

¯ (a) that would cover the entire life cycle of a tree. Variable a is theormalized tree age. In its general form the maximum height theree can reach and the maximum age are normalized, but they areeplaced by characteristic values for a given tree species (in certainrowth conditions). When constructing h(a), we used the work ofurger (1926), who covered all of the most important Europeanree species over 24 years of research. We also combined theseata with studies of the relationship between tree age and heightor Picea abies stands in the Mezaklja region (Pisek, 2002). The func-ion h(a) in Fig. 2c has been adjusted to return the expected heightf trees of any age on excellent growing sites. In order to obtainhe height h(ai, pi,s) of the i-th tree at point pi of age ai of species s,

easured in metres, the following equation is used:

(ai, pi, s) = hmax(S)ıh(ai, pi, s)h(ai) (9)

here hmax(s) is the maximum height a tree of species s can reachn metres and ıh(ai, pi, s) is the height damping factor accountingor poor growth conditions and site elevation, which is determinedy:

h(ai.pi, s) ={

�(pi)∏

x∈{L,T,F,R,N}P(Ex(s), pi) > 0.015

0.9�(pi), elsewhere(10)

�(pi) is a linear function between 1 (800 m above sea level) and.2 (1800 m) since trees within the same species closer to the tim-erline do not grow as tall as those at lower altitudes. The function(Ex(s),pi) is defined by Eq. (12) and gives the plant a survival prob-bility for a given EIV x (L – light, T – temperature, F – moisture, R –oil pH, and N – nutrients). Additionally, in Fig. 2a it can be seen thathe growth curves within the same species differ greatly depend-ng on the quality of the growing site. We defined the growing sites poor if the survival probability P(Ex(s),pi) is lower than 0.015,hich indicates a large difference between the plant requirements

nd site conditions in at least one EIV. In this case the tree heights further reduced by 10%. Thus, with Eq. (9) the growth curve forny species in the model at any given site can be derived (Fig. 2d).

.3.2. Growth potential and actual vigour calculationParameters such as the growth potential and actual vigour are

alculated for each tree over a one-year cycle. The growth potentials a tree’s ability to survive without being influenced by the sur-

ounding vegetation, and is mostly dependent on site conditions.lthough site conditions and competition are the most important

actors for tree survival, they are not the only ones. There are a num-er of random events that can cause tree death, including insects,

elling 279 (2014) 100–113

diseases, wounds, decay, and herbivores. It is impossible to includeall of these factors in the model individually because there are toomany parameters that have to be taken into account, and someof these events are even unpredictable. In order to include thesefactors in the model, we considered the fact that the impact of neg-ative events is greater on younger tees than on older ones. Mortalitydue to strong competition is also higher in younger trees. Mortalitydecreases for mature trees and rises again when the tree is olderdue a decrease in vitality. The growth potential of a tree thereforedepends on its growth site position, species, and age. The growthpotential w(ai,pi,s) of the i-th tree at point pi of age ai of species scan be calculated by the next equation:

w(a, pi, s) =2∏

x∈{L,T,F,R,N}P(Ex(s), pi) + P(ai, s)

3(11)

where P(Ex(s),pi) measures the differences between the plantrequirements and the terrain properties at point pi for the EIV x (L –light, T – temperature, F – moisture, R – soil pH, and N – nutrients).Meanwhile, P(ai, s) is the survival probability based on the tree’sage.

The function P(Ex(s),pi) can be determined by the following for-mula:

P(Ex(s), pi) ={

1 − |Tx(pi) − Ex(s)|, 0 < Ex(s) < 1

1, Ex(s) = 1(12)

where Ex(s) is the normalized EIV (Ex(s) = Ex(s)/10) and Tx(pi) isthe terrain property at point pi for the given EIV x.

The current tree age ai has a value between 0 and 1 where 0is the seed stage and 1 is the maximal age, which varies greatlyfrom species to species (Fitschen, 1994; Brus and Robic, 2002; Brus,2004). The general probability function based on age was modelledwith the assumption that all trees are initially weak and vulnerableeven if the site conditions are perfect. Over time plants becomestronger and more resilient. Therefore, the probability of survivalgradually increases until it reaches a maximum, which occurs at40% of the plant’s expected lifespan. At 80% of the expected lifespan,the probability of survival begins to drop until it again reaches itsminimum (Fig. 3a).

The individual probability function based on the age of a tree ofa given species is obtained by multiplying the abscissa of the gen-eral probability by the maximal life expectance of the tree species,which results in distinct shapes of the probability curves for differ-ent species (Fig. 3b).

Tree age and tree height influence actual vigour, which is a keyfeature for the tree competition model. The actual vigour v(ai, pi,s) of the i-th tree at age ai and height hi growing at position pi isdetermined by the next equation:

v(aipi, s) = �(s)(ai, pi, s)w(ai, pi, s) (13)

where �(s) is the damping factor according to the maximum agethe tree can reach and (ai, pj, s) is the damping factor based on thecurrent tree height.

The factor �(s) can be calculated by the following equation:

�(S) = tmax(S)maxj∈{1,...,S}(tmax(j))

(14)

where tmax(s) is the maximum age a tree of a given species scan achieve in years and S is the number of tree species withinthe model. As can be seen in Eq. (14), the damping factor �slightly prefers longer-lived species over shorter-lived ones since

the former have greater competitive capabilities (McArthur andWilson, 1967; Horvat Marolt, 1973).

The damping factor (ai, pi, s) prefers older trees to youngerones, which provides additional stability to the model, and is

S. Kolmanic et al. / Ecological Modelling 279 (2014) 100–113 105

F ing sit( th cu

c

et

2

Topa

ig. 2. (a) Annual increment curves of different tree species and on different growMoore, 1989). (c) General growth curve used in ForestMAS and (d) Individual grow

alculated by the next equation:

(ai, pi, s) = (ıh(ai, pi, s)h(ai) + h(ai, pi, s)/maxk∈{1,...,S}(hmax(k)))2

(15)

Taller tree species are thus preferred over shorter ones or shrubsven at a young age. But even with both damping factors �(s) and(ai, pi, s) in place at a young age, it was still possible for youngerrees to supplant older ones due to better site conditions.

.3.3. Tree competition and the self-thinning modelCompetition among trees is a dominant cause of tree mortality.

hrough competition the forest structure changes such that mostf the initial species vanish and the remaining ones form stableopulations. As a consequence of these changes, the biodiversitylso varies. All of this can be achieved in the model by a relatively

es (Mayer, 1977). (b) Example of maximum growth functions used in gap modelsrves derived from the general growth curve on a good growing site.

simple mechanism. The competition process is based on ecologicalneighbourhoods of trees represented by circles. This solution hasalready been successfully used (e.g., Green, 1997; Deussen et al.,1998; Green et al., 2006). Similar to that described in Deussen,the ecological neighbourhood radius in our model grows propor-tionally to tree height. If the ecological neighbourhoods of twoneighbouring trees intersect, the vigour of both trees is comparedand the less vigorous one becomes dominated. The dominated treestops growing and can die according to an estimated probability.The probability of tree death is a random number between 0 and1 − v(ai, pi, s). But since the calculation is repeated during the nextsimulation year, all dominated trees will die eventually. This leadsto self-thinning, which is a natural process whereby the number

of trees per unit area decreases as the average tree size increases.This process can be described by the equation proposed by Yodaet al. (1963), which is also known as the self-thinning law, or the3/2 law, to describe the inverse relationship between plant biomass

106 S. Kolmanic et al. / Ecological Modelling 279 (2014) 100–113

and (

aonwclteoaf

r

wutcPL

odtoApptta2tbwtttttbcod

Fig. 3. (a) Universal tree survival probability according to age

nd density. In our model the self-thinning law defines the growthf an ecological neighbourhood radius, but the Yoda equation can-ot be used directly since we lack data on plant biomass. Instead,e used the research of White and Harper (1970), which showed a

orrelation between plant size and the number of plants in a popu-ation, and of Norberg (1988), who showed that the ratio betweenree height and the ecological neighbourhood, which he called anxclusive ground area, remained constant throughout stand devel-pment. The neighbourhood radius ri for a tree of species s, age ai,nd height h(ai, pi, s) can therefore be estimated with the followingormula:

i = sh(ai, pi, s) (16)

here s is a constant depending on the species (Table 2). The val-es of the constant s approximate the width and development ofhe rooting system of trees and were obtained experimentally byomparing the simulation results with observations from Mozirskaozganija (Puncer, 1962; Kranjc, 1981; Diaci, 1996; Mutec, 1994;ekse, 2007).

As the simulation starts within the area of interest, the seedsf the tree species growing in the neighbourhood are uniformlyistributed. To obtain the initial seed distribution we use data onhe growing stock and its composition by groups of tree species,btained by Slovenia forest service and issued by the Ministry ofgriculture and the environment of Slovenia. Since there are noioneer species included in the growing stock, we add 20% seeds ofioneer species to the growing stock distribution with equal quan-ities of seed in the first iteration. The community distributions inhe years of local maxima of the Simpson biodiversity index at 3nd 19 years and the community distribution of the forest after00 years are used to calculate the mortality rates for the includedree species, which are then used to generate the input seed distri-ution for the next simulation run. The seed number for a speciesith the highest mortality rates are decreased while at the same

ime the seeds of other species are equally increased equally by theotal of the same value. The final seed distribution is obtained afteren simulation runs. Seeding with the obtained seed distribution ishen repeated at each simulation cycle until the vegetation reacheshe predefined coverage of 40%. Seed is subsequently produced only

y the new vegetation. At each cycle a new neighbourhood radius isalculated, and if two ecological neighbourhoods intersect, the treef lower vigour becomes dominated. The dominated tree eventuallyies and gives way to new trees (Fig. 4).

b) Derived tree survival probability for selected tree species.

In Fig. 4 we can see the result of competition between Picea abies,Betula pendula, Pinus sylvestris, Salix caprea, Populus tremula L., Larixdecidua L., Juniperus communis L., Laburnum alpinum J.Presl, Corylusavellana L., and Berberis vulgaris L. over a 20-year period (5, 10, and20). Each tree is represented by its ecological neighbourhood, whichcorresponds to the tree height. Each colour represents a particularspecies. Over the first 10 years (Fig. 4a and b) the main specieswere Populus tremula and Salix caprea, but after 20 years, they arereplaced by Picea abies, which is also a dominant species in thearea. We can clearly see that the population size of one species onlyincreases as a result of decreases other species, which can occurvery quickly and may even lead to their extinction.

It can be observed that the self-thinning model corresponds tostress-related mortality in gap models. Although competition is themost important cause of tree death, it is not the only one. In eachyear there is a 0.1% chance that a tree will die due to unpredictedevents, which corresponds to the background mortality found ingap models.

2.3.4. Tree reproduction modelReproduction enables forest to spread across the landscape. In

our model all trees are treated as monoecious and capable of pro-ducing seed.

Although the trees in our model are treated individually, thisapproach could not be applied to seeds because they are toonumerous. In addition, most annually produced seeds are eaten bypredators, stay dormant as a part of the seed pool in the ground(Hibbs and Fischer, 1979; Templeton and Levin, 1979; Beatty,1991), or just fail to germinate and decay. Therefore, rather thanaccount for the entire seed production, we generate relatively smallnumbers of seedlings, which then compete with older trees. Thus,the number of individuals within the model remains manageableand we do not have to take the seed pool in the ground into consid-eration, simplifying the reproduction model greatly. The numberof the new seedlings gi for a tree i of age ai and species s growingat pi is calculated for each tree that is not dominated individuallywith the following equation:

gi = �(s)ıh(ai, pi, s)h(ai) (17)

where �(s) is the maximum number of seedlings a tree ofspecies s can produce. As can be seen from Eq. (17), the number ofnew seedlings depends on tree height, which corresponds to treebiomass and the given species.

S. Kolmanic et al. / Ecological Modelling 279 (2014) 100–113 107

Table 2Tree species used in the afforestation model.

Species tmax(s) hmax(s) s �(s) Ellenberg indicator values

[years] [m] EL ET EM ER EN

Fagus sylvatica L. 400 40 0.143 30 3 5 5 x xUlmus glabra Huds 500 40 0.133 30 4 5 6 7 7Acer pseudoplatanus L. 500 40 0.143 30 4 x 6 x 7Ulmus laevis Pallas 500 35 0.167 30 4 6 8 7 7Betula pendula 100 27 0.100 30 7 x x x xQuercus robur L. 500 40 0.182 25 7 6 x x xQuercus petraea (Matt.) Liebl. 700 40 0.185 25 6 6 5 x xQuercus pubescens Willd. 500 20 0.167 25 7 8 3 7 xCarpinus betulus 160 30 0.133 30 4 6 x x xOstrya carpinifolia Scop. 300 20 0.180 30 4 8 4 x 5Fraxinus ornus L. 100 20 0.180 30 5 8 3 8 3Alnus glutinosa 600 30 0.200 30 5 5 9 6 xAlnus incana (L.) Moench 500 20 0.179 30 6 4 7 8 xSalix alba L. 600 30 0.222 30 5 6 8 8 7Castanea sativa Mill. 1000 35 0.200 25 5 8 x 4 xSalix caprea 75 10 0.208 40 7 x 6 7 7Populus tremula 90 25 0.125 35 6 5 5 x xLaburnum alpinum 150 10 0.189 10 5 7 3 8 4Corylus avellana 60 8 0.200 15 6 5 x x 5Berberis vulgaris 20 5 0.200 10 7 x 4 8 3Rosa canina L. 15 5 0.200 15 8 5 4 x xJuniperus communis 2000 15 0.222 20 9 x 4 x 2Pinus nigra Arnold 500 40 0.185 30 7 7 3 9 2Pinus sylvestris 600 38 0.200 30 7 x x x xLarix decidua 400 40 0.154 30 8 x 4 x 3Abiens alba 500 50 0.178 30 3 5 x x x

9

sortstt0t

Picea abies 600 50 0.17

When the number of new seedlings is determined, their growthites must be established. As a starting point we used the workf Sagnard et al. (2007), whose model was developed based onesearch of seed dispersal in Fagus sylvatica and Abies alba. To reflecthe different seed propagation methods specific to different treepecies with different seed weights, the probability �(s) was addedo each of the tree species whether the new seedlings emerge near

he parent tree or not. For example, if �(s) corresponds to the value.8, 80% of seedlings emerge within a 50 m radius of their parentree according to the general planting distribution where 25% of

Fig. 4. Tree competition results after: (a) 5

33 5 3 x x x

these seedlings emerge within 5 m radius from the parent, 50%between 5 and 10 m and the remaining 25% between 10 and 50 mradius. The rest of the original seedlings amount can emerge any-where within 100 m from the parent tree (uniform distribution).The whole procedure is reflected in the distribution of cumulativedistances between seedlings and nearest adult tree, F(d), shown inFig. 5.

With a v(s) of 90% for Fagus sylvatica and 80% for Abies alba, weachieved a similar distribution of cumulative distances F(d) to thatfound in Sagnard et al. (2007). In Fig. 5 the cumulative distances for

years, (b) 10 years, and (c) 20 years.

108 S. Kolmanic et al. / Ecological Modelling 279 (2014) 100–113

Fig. 5. Distribution of cumulative distances among seedlings and adult trees. F(d)– general distribution, v(s) = 100%, the distributions for Fagus sylvatica, v(s) = 90%,Abies alba, v(s) = 80%, and Betula pendula, v(s) = 60%. v(s) = 60% defines that 60% ofseed will germinate within the radius of 50 m of their parent among which 25% willgerminate in the radius up to 5 m, 50% between 5 and 10 m, and 25% between 10a[o

Bbs

3

otfii(FengttTsastv

yKDtmt(wsgtb

alwuP

Table 3Observed tree species density in trees per hectare on permanent research plots inMozirska Pozganija.

Tree species Time [years]

31 38 56

Picea abies 6139 6296 3009Salix caprea 1670 1083 183Populus tremula 748 357 139Betula pendula 391 357 243Larix decidua 109 104 96Pinus sylvestris 30 26 13Juniperus communis 91 52 0Laburnum alpinum 78 70 26Corylus avellana 43 48 35Rosa canina 4 4 4Berberis vulgaris 4 4 4

nd 50 m radius. The remaining 40% of seed is equally distributed on the interval0,100] m. This is resulted in the function F(d), which is on the interval [0,100] greaterr equal to that of v(s).

etula pendula can also be seen with v(s) of 60%. The new seedlingsegin to compete with the rest of the vegetation during the nextimulation cycle.

. Results

To test our secondary succession model, we ran simulationsn several areas not larger than 900 ha due to computer limita-ions. In Slovenia abandoned farmland is typically surrounded byorest or at least forest is in close proximity. Therefore, the lands uniformly germinated by seeds corresponding to the surround-ng forest structure. Currently, we are able to use 27 tree speciesTable 2) for which data have been gathered from Burger (1926),itschen (1994), Brus and Robic (2002), Brus (2004), and Ellenbergt al. (1992), but because of the surrounding forest structure, it wasever necessary to apply all the species at the same time. The seedserminated uniformly during each simulation year until the vege-ation was too dense. The tests were divided into two parts. Firstly,he course of secondary succession was studied in different areas.he succession results were always consistent with processes pre-ented in Horn (1974), Connell and Slatyer (1997), Kimmins (2004),nd Cojzer and Brus (2010). In all cases a forest with a stable compo-ition and population developed. In the second part we evaluatedhe simulation results by comparing them with long-term obser-ations of secondary succession in different parts of Slovenia.

Among the most important of these observations were the 57-ear-long observation of the Mozirska Pozganija reserve in theamnik-Savinja Alps (Puncer, 1962; Kranjc, 1981; Mutec, 1994;iaci, 1996; Lekse, 2007), data from 30 years of research into

he spontaneous afforestation of abandoned hay meadows in theountains of Kriska gora and Breginjski Stol (Muzik, 2008), and

he 20-year-long observation of overgrowth in the Haloze regionCojzer and Brus, 2010). For the purposes of comparison, ForestMASas equipped with different statistics such as the forest compo-

ition and population structure overview, the community historyraph, the age and height distribution for selected tree species, andhe history of changes in the Simpson (1949) and Shannon (1948)iodiversity indices.

The Mozirska Pozganija area, covering 82 ha, was devastated by fire in 1950 that destroyed most of the vegetation and is by far the

argest connected area of observation. The only surviving species

ere Larix decidua and Pinus sylvestris. Parts of the region remainednmanaged and were later declared as a nature reserve. Mozirskaozganija is a part of the Mozirje Mountains and lies between

1100 and 1450 m above sea level. The total annual precipitationis 1233 mm and temperatures range between −4 ◦C and 23 ◦C. Thefirst research in Mozirska Pozganija was done in 1962 (Puncer,1962). In 1981, 23 permanent circular research plots with a radiusof 5.64 m were established in the reserve. Plots were placed in theshape of cross with 13 plots in one direction and 10 plots in other,thus covering 6.6 ha of land. Between 1981 and 2007 (Kranjc, 1981;Diaci, 1996; Lekse, 2007), all dendroflora on the research plots wascounted and examined (Table 3). The data from this long periodof spontaneous vegetation development proved very important forour work.

Only specimens greater than 30 cm were measured. Because thefirst measurement was done after 31 years, we did not have cleardata on the first stage of succession when the area was overgrownby shrubs and pioneer species, but we did have a long-term viewof the process of pioneer species replacement by Picea abies, thedominant species in the area. The early stages of secondary suc-cession could therefore be observed only by simulation. To confirmthe simulation results, we compared them with those measured inTable 3. We tested our model in two areas with different sizes. Thesmaller one, S1, was placed in the centre of the research plots’ cross,to get the highest possible cover density in the research plots. Thearea covered 1 ha and completely included 10 plots. The larger area,S2, included all 23 research plots and covered the entire 6.6 ha ofland. The simulation results of the larger area are available in thesupplementary material.

The area of Mozirska Pozganija, together with calculated mois-ture, can be seen in Fig. 6a. The calculated light availability isdisplayed in Fig. 6b, and the mapped pH and nitrogen availabilityare shown in Fig. 6c and d, respectively.

The simulation results are presented in Table 4. They fitted wellwith the observations in the field. The root mean square error was117.9, 194.8, and 198.5 after 31, 38, and 56 years of succession,respectively.

A minor deviation from the expected can also be observedin year 56 when the population decline of Picea abies was notlarge enough. This deviation is even larger on simulation area S2.Notwithstanding the size of the simulation area or the averagenumber of seeds distributed at the start of the simulation, wealways obtained the expected proportions amongst the populationsizes although the population sizes may have varied. In all casesthe pioneer forest was replaced by climax forest with a stable pop-ulation. The structure of the resulting forest was similar during allsimulation runs.

Another interesting aspect of the model evaluation was the dif-ference in the observed and simulated tree mortality when the

proportions of trees between two successive measurements werecompared (in Fig. 7, for example, we used measurements at years

S. Kolmanic et al. / Ecological Modelling 279 (2014) 100–113 109

F lculatec .

3c

9udsitch

TS

ig. 6. Landscape encompassing Mozirska Pozganija with site quality values: (a) caalculated light availability, (c) mapped soil pH, and (d) nutrition availability values

8 and 56), where quite a significant difference can be seen in thease of Larix decidua.

Based on the observation of Mozirska Pozganija, there were still6 trees of that species after 56 years of succession, while in the sim-lation this number was only 4.3. This result is expected since Larixecidua is a sun-loving tree; its light EIV of 8 was the highest in theimulation. When the surrounding area was occupied by Picea abies,t perished. The observed difference can be explained by the fact

hat the simulation was run from the bare ground, which does notorrespond to the real starting conditions since some Larix deciduaad survived the initial fire and therefore had a greater competitive

able 4imulation results – the average value and standard deviation of trees per hectare over 1

Tree species 31 years 38 years 5

E(X) �x E(X) �x E

Picea abies 6041.5 93.8 6194.4 142.6 3Salix caprea 1333.3 82.0 453.5 67.7

Populus tremula 856.1 71.2 298.2 69.7

Betula pendula 502.7 68.8 395.2 49.7

Larix decidua 169.0 20.2 48.9 9.3

Pinus sylvestris 47.8 12.4 33.0 13.1

Juniperus communis 76.5 8.6 63.4 8.1

Laburnum alpinum 70.3 15.4 22.9 7.1

Corylus avellana 83.7 14.1 26.3 7.7

Rosa canina 3.4 1.6 0.0 0.0

Berberis vulgaris 6.5 2.5 0.8 1.3

d moisture where darker area represent the area of Mozirska Pozganija reseve, (b)

advantage than in the simulation. In Fig. 7 it can also be seen thatthe mortality of Picea abies and Salix caprea is lower than that inreality. Therefore, the mortality of other species is slightly higher,but these differences have a minor effect on the forest composition(Fig. 8). In year 38 after secondary succession began we can observethe first deviation in the population of Salix caprea, which is lowerthan that observed, and as a result the proportion of Picea abieswas higher. The effect of the lower mortality rate of Picea abies can

again be observed in year 56. These results also indicate the needfor interaction among the vegetation and site, which is currentlylacking.

0 runs of secondary succession in Mozirska Pozganija on simulation area S1.

6 years 100 years 200 years

(X) �x E(X) �x E(X) �x

646.1 130.4 3033.6 131.8 2372.1 194.6198.2 71.3 33.3 19.0 0.0 0.0

31.9 15.9 0.1 0.3 0.0 0.0169.2 43.0 103.4 25.7 33.8 33.9

4.3 6.8 0.0 0.0 0.0 0.03.9 4.6 0.3 0.7 0.0 0.0

13.5 3.1 2.5 2.1 0.1 0.30.9 1.0 0.0 0.0 0.0 0.01.8 2.3 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.0

110 S. Kolmanic et al. / Ecological Modelling 279 (2014) 100–113

0%10%20%30%40%50%60%70%80%90%

100%

Observed

Simula�on

fwtttwScAatosmbyr

w(

sato

oca

Fig. 7. Observed and simulated mortality in Mozirska Pozganija.

To verify the output of our model for early stages of spontaneousorest expansion, we compared the simulation results with theork of Cojzer and Brus (2010). Their study covered much shorter

ime periods of secondary succession but provided an insight intohe early development phases. Changes in biodiversity during thatime were also compared. Again, the simulation results fitted wellith respect to tree composition as well as to changes in the

impson and Shannon biodiversity indices. As tree species beganolonizing abandoned farmland, species richness increased rapidly.ccording to the research of Cojzer, the first local maximum waschieved six years after the farmland had been abandoned and washen followed by a drop in biodiversity. The final local maximumf species richness occurred after 16 years. Our simulation resultshowed similar behaviour. In Mozirska Pozganija the first localaximum was achieved in year 3 since the land was completely

arren at the simulation start. The second maximum occurred inear 19 and was followed by a steady decline until only one speciesemained (Fig. 9).

These results regarding forest dynamics were also in accordanceith studies of Auclair and Goff (1971), Whittaker (1972), Finegan

1984), and Bazzaz (1975, 1996).In order to increase public understanding of secondary succes-

ion and its consequences for abandoned farmland, statistical toolsre not enough. People need to see the changes in the landscapehey know. Landscape visualization is therefore an important partf ForestMAS.

In Fig. 10 the simulation results of secondary succession in partf Mozirska Pozganija can be seen. In order to show all stages of suc-ession, we start with bare ground and show afforestation resultsfter 5, 10, 31, 100, and 200 years.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Obs. Sim . Obs . Sim . Obs . 31 years 38 years 56 yea

Fig. 8. Observed and predicted forest composition dur

Fig. 9. Changes of Shannon biodiversity index H′ during the afforestation process inMozirska Pozganija. As Cojzer and Brus (2010) observed the first two local maximaare characteristic for the early stages of secondary succession.

The visualization, however, requires additional computerresources. This is also the reason for the lack of tall grasses andherbs, which would give a more realistic look to the landscape atthe beginning of secondary succession. In order to conserve com-puter resources, we used a technique from older computer gameswhere the image of the tree was used as the texture on two or threeintersecting planes to give the impression of 3D trees. In our casethe required tree images were generated by the Holton tree model.Thus, the landscape visualization is fast and can be done in real timefor small simulation areas, but can take up to a few minutes forareas larger than 30 ha. Nevertheless, the benefit of fostering pub-lic understanding of the consequences of unmanaged secondarysuccession makes visualization worth the additional time.

4. Discussion

Secondary succession is an important process for forest dynam-ics over time. It is therefore not surprising that attempts havealready been made to describe the changes associated with it. Awide range of forest gap models exists. Most are used to predict

the impacts of global climate change on the long-term dynamics offorest structure, and some of these can also be used for the simula-tion of secondary succession. In order to use such models, a greatdeal of information about tree species and the simulation area is

Sim. Sim . Sim .

B. vulgaris

R. ca nina

C. avellana

L. alpinum

J. communis

P. sylvest ris

L. decidu a

B. pen dula

P. tremu la

S. ca prea

P. abi es

rs 100 year s 200 years

ing secondary succession in Mozirska Pozganija.

S. Kolmanic et al. / Ecological Modelling 279 (2014) 100–113 111

F (b) 5,(

ntssdtfiotacmtdcMmsTi

ig. 10. Secondary succession in Mozirska Pozganija in year (a) 0, abandoned land,f) 200, climax forest.

eeded. This information is difficult to acquire, but soil informa-ion systems have been established at the national and Europeancale. ForestMAS was therefore developed to combine the availableoil data with commonly accepted Ellenberg indicator values forescribing tree growth requirements. The most characteristic fea-ure of ForestMAS is its ability to treat each tree individually, whichrstly enables landscape visualization, and secondly provides thepportunity for future implementation of human intervention intohe secondary succession process. The single-tree based approachlso enables the implementation of tree mortality directly throughompetition, which is comparable to stress related mortality in gapodels. The background mortality in ForestMAS is achieved with

he help of the survival probability based on age and sudden treeeath, which can occur at each cycle and is age-independent. Byomparing the simulation data with the long-term observation inozirska Pozganija, it can be seen that the actual and simulated tree

ortality are very similar in the first 38 years of secondary succes-

ion. However, after 56 years some differences can be observed.his indicates that our model needs more refinement in simulat-ng interaction among vegetation and sites. The work of Dzwonko

regeneration stage, (c) 10, shrub stage, (d) 31, young forest, (e) 100, mature forest,

(2001), Gerten et al. (2004), and Hruska et al. (2012) could be a goodstarting point for this.

Similar to the data on soil and tree requirements in Forest-MAS, we also use only regularly collected and generally accessibleweather data in the form of long-term averages. As a consequence,there are insufficient data to implement bioclimatic filters such asthe prediction of the occurrence of frost events in spring or droughtevents in summer, which can be found in recent gap models andaffect tree mortality and forest composition. The mortality inducedby exogenous disturbances endangering whole stands, such asstorm damage (Lagergren et al., 2012), fire in FIRE-BGC (Keane et al.,1996), or bark beetles in PICUS (Lexer and Hönninger, 1998; Lexeret al., 2000), is currently not considered in ForestMAS.

The single tree based approach enables self-organizing foreststructure and thus simulates the response to natural catastrophesor clear-cutting. In addition, ForestMAS can be used to simulate

the response of young forest to tending for economically profitableand ecologically stable forest (Cojzer and Brus, 2010). However, themain drawback of this approach is the relatively small simulationarea compared to gap models. The complexity of the single tree

1 l Mod

bdcBanppgfrpmdsesbidsvssot

5

pibiacasftsiat

ssaamraadablanFae

bi

12 S. Kolmanic et al. / Ecologica

ased approach even with the use of multithreaded programmingoes not leave enough computing power to use more sophisti-ated algorithms such as those described in Cescatti (1997a,b) andrunner (1998) to calculate the light availability on the forest floort each cycle. In our model tree vitality is reduced in relation to tallereighbouring trees, which is similar but less accurate. Anotherroblem connected to the single-tree based approach and its com-lexity is the inability to simulate undergrowth such as herbs andrasses, which develop first on abandoned farmland or on clear-elled areas. These herbs can influence the regeneration and in someare cases significantly delay the entire process, as was observed inarts of the area of Breginjski Stol (Muzik, 2008). Currently, in ourodel the undergrowth is composed only of young trees, which

id not produce the same results as observed in Breginjski Stol. Toolve this problem, we could use the same approach as the gap mod-ls and present the undergrowth as a group, which influences theurvival probabilities of the seedlings within openings generatedy fallen trees. To implement this idea, however, additional stud-

es are necessary for determining the correct survival probabilityiminution factor for tree seedlings according to the undergrowthtructure. The lack of ground vegetation in the undergrowth is alsoisible in Table 4, where after 200 years the number of Norwaypruce is higher than expected according to the estimated growingtock in the surrounding areas due to an understory composed ofnly young trees. Nevertheless, since most of those trees die duringhe competition process, this is still acceptable.

. Conclusion

Farmland abandonment in high altitude regions due to higherroduction costs is not only a serious problem in Slovenia but also

n the whole Balkan region. As a consequence, there are substantialut slow changes in the affected regions ranging from the loss of

ncome and emigration of the working population to colonization ofgricultural land by forest. There exist a number of simulators thatan be successfully used to predict the landscape changes associ-ted with secondary succession, but their results are mostly of atatistical nature and oriented towards biomass increment. There-ore, these simulators have little impact on the general public andhe decision making process that could mitigate the negative con-equences of farmland abandonment. Another problem of equalmportance is that the quality input data for the simulators oftenssociated with long-term measurements is not available for arbi-rary areas of interest.

ForestMAS, a computer model of spontaneous forest expan-ion that occurs after farmland abandonment, was developed toolve these problems. Its main advantage is its use of generallyvailable terrain and plant data in the form of a GIS analysis of

DTM, soil maps, and EIVs for light, temperature, nutrients, soiloisture, and pH, which enables its use across Europe. The ter-

ain visualization engine is an important part of ForestMAS andllows landscape changes to be presented in the most understand-ble way possible through images of the changing landscape. Theevelopment of ForestMAS was inspired by Cojzer’s claim (Cojzernd Brus, 2010) that promoting young forest to an economically sta-le one can over the long term represent an alternative to income

oss due to abandoned agricultural production. Therefore, we usedn individual-based approach in order to test this claim by plan-ing different tending procedures in the future. As a consequence,orestMAS can also be used to predict the regeneration processfter clearcutting or natural disasters that destroy most of the veg-

tation on the affected areas.

ForestMAS was successfully tested in various areas in Slovenia,ut in order to achieve even better results, it would be useful to

nclude a sub model of interaction between the vegetation and

elling 279 (2014) 100–113

growing site as well as ground vegetation. Compared to gap mod-els ForestMAS covers relatively small areas. A future priority is toapply ForestMAS to larger areas by distributing the simulation loadto additional computers connected in a simulation network.

Acknowledgments

We would like to thank Mojca Dolinar and Mateja Nadbath fromthe Slovenian Environment Agency for average annual rainfall andsolar radiation data from 1971–2000 and Prof. Borut Vrscaj fromthe Agricultural Institute of Slovenia for soil fertility data.

Appendix A. Supplementary data

Supplementary data associated with this article can be found,in the online version, at http://dx.doi.org/10.1016/j.ecolmodel.2014.02.016.

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