CHANGES OF DOMINANT TREE SPECIES AREAS OVER THE PAST CENTURY IN LITHUANIA: A MATHEMATICAL APPROACH

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1 FORESTRY AND WOOD PROCESSING Iveta Varnagirytė-Kabašinskienė 1,2, Audrius Kabašinskas 3,4 1 Lithuanian Research Centre for Agriculture and Forestry 2 Aleksandras Stulginskis University, Lithuania 3 Kaunas University of Technology, Lithuania 4 Kaunas College, Lithuania i.varnagiryte@mi.lt; audrius.kabasinskas@ktu.lt Abstract The changes of areas of eight tree species in Lithuania during the past century were analysed. Aiming to apply the different approaches in forest studies, the Exponential smoothing method for forecasting the changes of the tree areas for the 25 years was used. The data dating from was analyzed as a time series. The descending trend was identified for Scots pine (Pinus sylvestris L.) and European ash (Fraxinus excelsior L.) and increasing trend for Norway spruce (Picea abies (L.) H. Karst.), common oak (Quercus robur L.), birch species (Betula pubescens Ehrh. and Betula pendula Roth), black alder (Alnus glutinosa (L.) Gaertn.), European aspen (Populus tremula L.) and grey alder (Alnus incana (L.) Moench). The Exponential Trend with Multiplicative Seasonality (ET-MS) model was fitted for almost all investigated tree species with exception of European ash. For the latter species, the Damped Trend with Multiplicative Seasonality (DT-MS) model was chosen. Mean absolute percentage error of the model in all cases did not exceed 2%. Key words: tree species, areas, statistical analysis, mathematical forecast. Introduction Recently the changes of tree distribution, abundance and habitat boundaries have often been associated with the warming of the climate. Such forecasts can be found even for Lithuanian tree species (Lekevičius et al., 2011; Ozolinčius, ; Ozolinčius et al., 2014). According to the vegetation zones range projections, Lithuanian territory will still remain in the mixed forest zone over the next century (Gonzalez et al., 2010). As composition of the dominated tree species will not significantly change in the near future, we used other approach for the forecast of tree species areas ignoring the climate factor. There are eight most dominated tree species in Lithuanian forests. These include both coniferous forest tree species, i.e. Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies (L.) H. Karst.), and deciduous species, i.e. common oak (Quercus robur L.), European ash (Fraxinus excelsior L.), birch species (Betula pubescens Ehrh. and Betula pendula Roth), black alder (Alnus glutinosa (L.) Gaertn.), European aspen (Populus tremula L.) and grey alder (Alnus incana (L.) Moench). The stands of the mentioned tree species occupy almost 99% of all Lithuanian forests (Lietuvos miškų ūkio statistika, 2011). The data of various tree composition in Lithuanian is available from to and are given as irregulary observed time series. There are various methods to forecast time series behaviour: different smoothing methods (moving average, exponential smoothing etc.), ARMA ARCH and their modifications (ARIMA, SARIMA, VAR, VARMAX etc.), simulation of stochastic processes, neural networks (Zhang and Qi, 2005), etc. A vector autoregression (VAR) method is used when we can identify some endogenous and exogenous variables, which influences time series behaviour, i.e. abiotic (climate change, temperature, precipitation etc) and biotic (insect, fungi damages) factors. The simplest, from the mentioned above, is a smoothing method. The exponential smoothing and its modifications are mostly used for the forecasting time series. This simple method is based on the idea that the last data observed is more important than that from far history (Brown, 1956; Holt, 1957). Most of modifications are focusing on the fact if a trend, seasonality/periodicity and some irregular fluctuations are observed. Scientific literature is rich with applications of this method in different areas: economics/management (Bermúdez et al., 2008), transportation (Grubb et al., 2001), operational research (Taylor, 2003). However, we did not succeed in finding any published material where the Exponential smoothing method was used in the forest research. In this paper we use models with a damped trend and multiplicative seasonality (DT-MS), and the exponential trend with multiplicative seasonality (ET-MS). Damped trend models are used for time series which exhibit a descending trend in some forecast horizon (Hyndman et al., 2008). Exponential trend models better fit series which are more likely increasing in a long time horizon (Hyndman et al., 2008). The multiplicative seasonality/periodicity is used in cases if time series exhibits the seasonal/ periodical behaviour with a different amplitude (Gardner, 1985; Chatfield et al., ). 35

2 The aim of the study was to analyse and forecast the changes of forest tree species in Lithuania and to create the most suitable mathematical models. Materials and Methods The study area was the teritorry of Lithuania located in the Northern Europe and covering an area of 65,200 km 2. To assess the individual tree species distribution and forest species composition trends in Lithuania during the last century, data from literature and Forest statistics of various editions since 1932 were analyzed: Lithuanian Statistical Yearbook (Lietuvos statistikos metraštis, 1932; 1939); Forest management of Lithuanian SSR (Lietuvos TSR Miškų ūkis, 1971); Production operating indicators of Forest enterprises (Miškų įmonių gamybinės veiklos rodikliai, ; 1981; 1990); Forestry production operating indicators (Miškų ūkio įmonių 1990 m. ir m. suvestiniai gamybinės veiklos rodikliai, 1991) and the Forest statistics (Miškų statistika NMI, 2002) for the recent decades, i.e. the data from 1998 to. Field research methodology was described in detail in fieldwork instructions (Kuliešis ir kt., 2005). For the forecast of the tree species areas and the changes of forest species composition during the next 25 years, regardless of the climate parameters, we used the Exponential smoothing with the multiplicative seasonality/periodicity (length of the seasonal cycle p=12 years) (Table 1). Hereα specifies the constant (non-seasonal, nontrend) smoothing; δ specifies the seasonal smoothing (applicable only to analyses that include a seasonal component); φ specifies trend smoothing (applicable to damped trend models); γ specifies trend smoothing (applicable to linear and exponential trend models, Model characteristics Table 1 General equation of the model Damped Trend, Multiplicative Seasonality Model (DT-MS) Exponential Trend, Multiplicative Seasonality Model (ET-MS) Initial values of the model,, Smoothed value of the series at time t here m 2 is the mean for the second seasonal cycle, m 1 is the mean for the first seasonal cycle, p is the length of the seasonal cycle,,, here k is the number of complete seasonal cycles, m k is the mean for the last seasonal cycle, m 1 is the mean for the first seasonal cycle, p is the length of the seasonal cycle. Trend component at time t Smoothed seasonal factor at time t Forecast function 36

3 and for damped trend models without seasonality); S 0 is a smoothed value of the series at initial time; T 0 is an initial trend component, ε t = Y t X ˆ t is a residual. The length of the seasonal cycle p=12 years was selected automatically (naïve method, see the discussion section for details). All model parameters are estimated by the least squares method using EXCEL and the STATISTICA software package. For the data analysis we used standard mathematical-statistical methods. Results and Discussion To clarify the changes of Lithuanian forest tree species composition in the recent decades, we analyzed the data from the year. We found significant changes in the forest species composition over the past 90 years in Lithuania (Table 2). According to the raw data (the data sampled in decades were shown in Table 2), we identified the tree species with a descending trend for Scots pine and European ash and an increasing trend for other species. For each species, depending on the specifics of the trend, we estimated (using the least squares method) parameters of the Damped Trend, Multiplicative Seasonality Model (DT-MS) and Exponential Trend, Multiplicative Seasonality Model (ET-MS) (Table 3). The best model was selected automatically by STATISTICA software by comparing SSE and MAPE errors of different models. The results given in Table 3 showed that if δ was zero (Scots pine, black alder and European ash), a constant unchanging seasonal component was used to generate the one-step-ahead forecasts. If the δ parameter was equal to 1 (Norway spruce, common oak, silver birch and European aspen), then the seasonal component was modified maximally at every step by the respective forecast error times some function depending on α. In most cases, when seasonality was present in the time series, the optimum δ parameter was between 0 and 1 (grey alder). Mean absolute percentage error of the model in all cases did not exceed 2% (Table 3). Using the abovementioned parameters, we developed a mathematical forecast model for each tree species (see Table 1). For almost all investigated coniferous and deciduous tree species we fitted the model Exponential Trend, Multiplicative Seasonality (ET-MS). For European ash, according to the nature of changes and the mean absolute percentage error, the model Damped Trend, Multiplicative Seasonality (DT-MS) was chosen. Area of forest tree species in (%) Table 2 Forest type Assessment year Scots pine Norway spruce Silver birch black alder grey alder European ash common oak European aspen Model parameters Table 3 Forest type Model parameters model α δ φ γ T 0 S 0 Model error, MAPE (%) Scots pine ET-MS Norway spruce ET-MS common oak ET-MS European ash DT-MS Silver birch ET-MS black alder ET-MS European aspen ET-MS grey alder ET-MS

4 Scots pine During this period the areas of both growing coniferous tree species decreased in Lithuania, but still they are the dominant species in the forests (Table 2). In comparison with or 1932, the area of Norway spruce decreased about times, or from 35.4% to 20.8%. Not as much as Norway spruce, Scots pine also declined, especially over the last 50 years. By applying the exponential data smoothing method (the exponential smoothing with multiplicative seasonality/ periodicity), we conducted the forecast of Lithuanian forest tree species changes for the next 25 years, i.e. until Mathematical modelling showed that, in accordance with the 90-year trend of Scots pine and Norway spruce and under the current climatic conditions, the areas of coniferous tree species would continue to decrease but with a slower rate (Figure 1 and 2). The area of dominant deciduous tree species, except for European aspen, increased within a 90- Figure 1. The area of Scots pine stands during and forecast until 2037 (ET-MS model) Norway spruce Figure 2. The area of Norway pine stands during and forecast until 2037 (ET-MS model). year period in Lithuania. The area of aspen was only 3.8% in, while in the 1972 year it was 6 7% (Table 2). The most significant decline of the aspen area was recorded in Our forecasts for the nearest 20 years for this tree species were not very pessimistic. According to the Exponential Trend model, the area of aspen should not greatly decrease and stabilize at about % level. The comparison of all deciduous tree species revealed that mainly the area of Silver birch (R 2 = 0.85), and grey alder (R 2 = 0.84) has increased since. Birch covers the largest area among deciduous trees and its area consistently increased (Figure 3). Our forecast showed that a similar trend would be the same in the next 25 years, i.e. the area of birch stands would increase up to 24% in Lithuania (Figure 3). Meanwhile, the area of grey alder was quite different in various years (data not shown). For example, the increasing trend was observed up to 38

5 . Later, from to 1990, the area of grey alder significantly decreased, while in the next 10-year period an obvious increase in this tree species was fixed again. Over the past decade, the area of grey alder stands remained relatively constant and was about %. The areas of European ash and common oak also increased quite significantly (R 2 = ) during the studied almost 100-year period but only the areas of oak stands expanded consistently. Our fitted model showed that the oak area is expected to increase by % until 2037 compared with and it should reach about 2.2%. While until the European ash was one of the healthiest tree species in Lithuania, and an obvious increase of ash area was still recorded until about, but in the recent years this species has become the most damaged species (Stakėnas et al., 2013). Onset of massive ash damages and mortality could be caused by both, unfavourable hydroclimatic conditions and by invasions of fungus Chalara fraxinea. Our mathematical forecast was quite pessimistic for this tree species, even regardless the disease progression. Under the present conditions and if the trend remains the same, we see the greatest area decrease over the next 25 years if all tree species in Lithuania are compared (Figure 4). A slight increase of black alder area was recorded in Lithuania during the past 90 years (Figure 5). Starting from 1932 until it has increased by about 1.3 times (Table 2). The first increase was recorded in 1950, later up to uneven changes were evident. The minimum area of black alder (5%) was found in and starting from this year up to now the increasing tendency still remains. Our forecast model shows that the area of black alder in the time period 2020 will be about %, while in it was 6.9%. 30 Silver birch Figure 3. The area of Birch stands during and forecast until 2037 (ET-MS model) European ash Figure 4. The area of European ash stands during and forecast until 2037 (DT-MS model). 39

6 8.0 Black alder Area % If compared black and grey alder, over the past 20 years the area of these two species was quite similar. The model estimates show that in the next years the area of grey alder will be by 1% less than black alder. We assumed that these analyses and forecasts could be important for the future forest management planning. From the scientific point of view, these results could be relevant aiming to reveal the reasons of forest tree species decline. However, we analysed and made the forecast for the actual published data (areas of the main tree species in Lithuania and their potential changes till ) and ignored the farming and reforestation specifics (policy) at various time periods. Many aspects could depend on the changes of forest subordination (a private, public or collective farm), the regulations and recovery (and/ or the forest management) rules, as well as natural factors (invasions of Ips typographus and various tree diseases, wind damages, etc.). We did not take into account the potential effects of climate change and the effects of related biotic and abiotic factors on individual tree species. According to the mentioned reasons, it is possible, for example, that the decline of Norway spruce areas could be faster. In such cases we could use other econometrical forecast methods, i.e. the vector autoregression (VAR) method or its modifications. The calibration of length of the seasonal cycle p also may improve the forecast. The Census I and Census II or their modifications are usually used for this purpose. Figure 5. The area of black alder stands during and forecast until 2037 (ET-MS model). Conclusions 1. The exponential trend with multiplicative seasonality (ET-MS) model was fitted for Scots pine, Norway spruce, common oak, Birch species, European aspen, black and grey alders, and the damped trend with multiplicative seasonality (DT- MS) model was chosen for European ash. Mean absolute percentage error of the model in all cases did not exceed 2%. 2. The study results showed that the areas of Scots pine and Norway spruce decreased in Lithuania over 90-year period and will continue to decrease in the next 25 years but at a slower rate. 3. The area of birch increased clearly and will continue to increase up to 24% in The area of oak expected to increase by % during the same period. The most pessimistic forecast was found for European ash (it will decrease to the level of 0.5%). 4. This forecast model could be further discussed and improved as the potential effects of climate change and other environmental factors were not included. Acknowledgements The paper presents research findings obtained through the long-term research program Sustainable forestry and global changes implemented by Lithuanian Research Centre for Agriculture and Forestry, Institute of Forestry. References 1. Bermúdez J.D., Segura J.V., Vercher E. (2008) SIOPRED: a prediction and optimisation integrated system for demand. TOP, 16 (2), pp Brown R.G. (1956) Exponential Smoothing for Predicting Demand. Arthur D. Little Inc., Cambridge, Massachusetts, USA, 15 p. 40

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