## 2.1. Artificial neural networks

Artificial neural networks are models that imitate the working mechanism of the nerve cells in the human brain, in a mathematical structure. The basic structure of artificial neural networks is made up of artificial nerve cells, called neurons. To form an artificial neural network, neurons need to work together. Neurons are also given names such as nodes, units, or processing elements. In an artificial neural network, the structure formed by neurons coming together in the same line is called a layer. Layers are also basic parts of artificial neural networks. There are three types of layers in an artificial neural network, which are the input layer, the intermediate (hidden) layer, and the output layer. The layers are also in contact with each other.

Neurons in the input layer are responsible for reception the input data transmitted to the model. However, they do not proceed with the input data. Instead, they only transmit the input data to the hidden layers. The hidden layers are responsible for building the model. Finally, the output layers are obliged to transmit the output values, obtained in the model, to the required environments. While an artificial neural network has only one input and one output layer, the number of hidden layers may be more than one. Any neuron in the hidden layer proceeds with the information it receives from the input layer and transmits it to the neurons in the next layer. However, in some types of artificial neural networks called feedback networks, this transmission is in the form of transmitting to the previous layer or to the input layer. The first step in the working mechanism of a neuron is the reception of the inputs and weights from the outer world or from the other neurons. These inputs and weights may be provided by sample data or by the outputs of other neurons. After the reception of inputs and weights, the neuron expresses this information as an additive model called the net function. The output of the neuron is formed by a function called the activation function whose input is the net function. The general expression of a net function is given in Eq. (1).

$$a=\sum {w}_{i}{x}_{i}$$

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where \({x}_{i}\) denotes the input values and \({w}_{i}\) denotes the corresponding weights. There are many different types of activation functions. For example, sigmoid function is a popularly used activation function whose structure is given by Eq. (2).

$$F\left(a\right)=\frac{1}{1-{e}^{a}}$$

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where \(a\) is the value resulted from the net function in Eq. (1). The result produced by the activation function is the output of the neuron. Although neurons may have input values more than one, they have just one output value. Figure 1 briefly displays the working mechanism of a neuron.

An artificial neural network needs to be trained to produce accurate and consistent results. The training process is to make the network gain the ability of producing the correct outputs by calculating the necessary coefficients with the help of the input values in the sample data set.

Artificial neural network models have some advantages over the classical models. One of this advantaged is that they store the information over the entire network and a few pieces of information loss do not prevent the model from working. Additionally, they can produce outputs without getting affected by errors or corruptions in the data drastically. Moreover, the model can be trained with the help of other examples and previous studies, as the network is also capable of learning from similar networks. Artificial neural networks can work together to complement each other. Thus, they can perform multiple tasks at the same time. Another advantage of the artificial neural networks is that they can solve complex and nonlinear problems more successfully than the conventional approaches. They also do not require any assumptions or prerequisites in terms of data and model structure. Artificial neural networks are also able to learn from data and make decisions. Unlike the other classical models requiring fixed variance, they are still able to model the data when the assumption of fixed variance does not hold.

However, there are also some disadvantages of the artificial neural networks such as their performances are heavily dependent on the hardware level of the computer used. Additionally, there are not definite rules to follow to build a model except for a few thumbnail rules. Thus, building an appropriate model may depend on personal experiences and trials. As causality is not considered when building a model, they may produce unexpected results. Moreover, there is a necessity of converting all the input values into numerical data, which can be difficult sometimes for some kinds of variables. During the learning phase, it is not possible to observe how artificial neural networks operate. Thus, it is not possible to explain the reason behind the output values. Finally, it cannot be guaranteed that the estimated artificial neural network is the optimum one.

## 2.2. Multilayer perceptron model

A multilayer perceptron model can be defined as an artificial neural network, which is based on the perceptron model. The perceptron model is simply a single layer artificial neural network. Perceptron itself can also be defined as a type of neuron, where the net function includes the sum of weighted data and a bias value. During the introduction period of artificial neural networks, it was seen that the perceptron model was insufficient in solving nonlinear problems. Thus, Rumelhart et al. (1986) proposed the multilayer perceptron model by adding a new layer of neurons called the hidden layer, which exists between the input layer and the output layer, to the perceptron model. Artificial neural networks having more than two layers are also called deep neural networks. Thus, the multilayers perceptron models are also deep neural network or deep learning models. An example of multilayer perceptron model is demonstrated in Fig. 2.

Multilayer perceptron model is a supervised learning model. The model is trained by a sample input and output data set so that the network learns to produce outputs that are close to the real output values existing in the data set. The difference between the observed data and the estimated data is called error (\(\epsilon\)). During the training process, the model adjusts the parameters, or the weights and biases, to reduce the error, so that to produce the most accurate outputs. The most important property of the multilayer perceptron model is the backpropagation process, which means recursively adjusting the weights to minimize the difference between the observed and estimated values. During the backpropagation process, the total loss is propagated back into the network to calculate the amount of loss for which each neuron is responsible. Meanwhile, the weights are re-adjusted to minimize the loss and the process continues until the amount of error is stabilized. The error can be measured in various ways such as the mean absolute error (MAE), the root mean squared error (RMSE), the relative absolute error (RAE), and the root relative squared error (RRSE). MAE can be defined as the mean of the absolute values of the error terms. Calculation of MAE is given as follows.

$$MAE=\frac{1}{n}\sum _{i=1}^{n}\left|{\epsilon }_{i}\right|$$

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where \(n\) is the data size and \({\epsilon }_{i}\) are the error terms. RMSE is the square root of the mean value of the squared error terms, which can be calculated as follows.

$$RMSE=\sqrt{\frac{1}{n}\sum _{i=1}^{n}{\epsilon }_{i}^{2}}$$

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RAE and RRSE values, however, can be calculated by the following equations.

$$RAE=\frac{\sum _{i=1}^{n}\left|\widehat{x}-x\right|}{\sum _{i=1}^{n}\left|\stackrel{-}{x}-x\right|}$$

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$$RRSE=\sqrt{\frac{\sum _{i=1}^{n}{\left(\widehat{x}-x\right)}^{2}}{\sum _{i=1}^{n}{\left(\stackrel{-}{x}-x\right)}^{2}}}$$

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where \(x\) is the observed data, \(\widehat{x}\) is the estimated data and \(\stackrel{-}{x}\) is the mean value of \(x\).

The correlation coefficient (\(\rho )\) indicates the direction and the degree of the linear relation between the actual data instances and the estimated instances produced by the constructed model. Calculation of the correlation coefficient is as follows.

$$\rho =\frac{\sum _{i=1}^{n}\left[x-E\left(x\right)\right]\left[\right(\widehat{x}-E\left(\widehat{x}\right)]}{\sqrt{{\sum _{i=1}^{n}\left[x-E\left(x\right)\right]}^{2}\sqrt{{\sum _{i=1}^{n}\left[\right(\widehat{x}-E\left(\widehat{x}\right)]}^{2}}}}$$

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where \(x\) is the observed data and \(\widehat{x}\) is the estimated data given by the model. \(E\left(x\right) and E\left(\widehat{x}\right)\) are the expected values of \(x\) and \(\widehat{x}\), respectively. The correlation coefficient \(\rho\) is a value between − 1 and 1. A \(\rho\) value close to 1 indicates a strong positive linear relationship between the observed and estimated data instances while a \(\rho\) value close to -1 is an evidence of a strong negative linear relationship. If the \(\rho\) is 0, there is no relationship between \(x\) and \(\widehat{x}\).

When building artificial neural networks, there are not definite rules to decide about the number of layers, and the number of neurons existing in each layer. These values are highly dependent on personal experiences and trials. However, during the model selection phase, the models with higher correlation coefficients and lower error measures are preferred.

## 2.3. Study area

In Turkey, the owner and the manager of the state forests is General Directorate of Forestry (GDF), which is divided into regional directorates. In addition, Turkey is among the industrial wood producer countries in the world. Turkish Ministry of Development (MOD) reports that the annual wooden raw material consumption in Turkey is approximately 25.9 million m3. Moreover, 15.5 million m3 (60%) of wood is produced from the state forests by GDF, while 4.8 million m3 (19%) of the production belongs to the private forestry companies. It is declared that 15% (4 million m3) of the wood production comes from illegal harvesting from the state forests, while 6% (1.6 million m3) is obtained by importing (MOD, 2014). Figure 3 presents the annual industrial wood production quantities (m3) in Turkey between 2000 and 2022.

When Fig. 3 is examined, it is seen that the levels of the industrial wood production display a decreasing trend from 2000 to 2003. However, except for the slight decreases in 2009, 2013, and 2017, it is possible to say that the industrial wood production levels tend to increase every year.

Figure 4 shows the regional directorates in Turkey and the industrial wood production densities in these regions as of 2020 (GDF, 2020).

It can be seen in Fig. 4 that industrial wood production is denser in the western and the mid-western parts of Turkey. At the same time, it is clear that the areas where the most intensive production is carried out are generally the areas near the sea. Figure 5 presents the amounts of industrial wood (m3) produced in the regional directorates as of 2020.

Figure 5 suggests that the highest level of industrial wood production is observed in Kastamonu directorate, which significantly differs from the other directorates. The first four directorates Kastamonu, Bolu, Zonguldak, and Amasya having the highest production levels are all in the Black Sea region that forms the northern part of Turkey. Bursa and İzmir, which have the second highest production levels, exist in the western part of Turkey. The third highest production levels, however, are observed in the directorates Muğla, Adana, and Antalya, which are in the Mediterranean region forming the southern part of Turkey.

Figure 6 presents the kinds and the percentages of the industrial wood products produced from coniferous and non-coniferous wood in Turkey.

Figure 6 indicates that log that is produced from coniferous wood is the most popular product (42%). The second and third most popular products produced by using coniferous wood are fiber-chip wood (32%) and pulpwood (17%), respectively. When non-coniferous wood is considered, however, the most popular product appears to be fiber-chip wood (56%). The second and the third popular products produced by using non-coniferous wood are log (29%) and pulpwood (8%), respectively.

## 2.4. Data and variables

The data were collected from various resources. In the study, two reports of FAO were used to derive the data belonging to the variables (Koc et al., 2014; Özel et al., 2020). Additionally, a forestry sector report provided by The Union of Chambers and Commodity Exchanges of Turkey (UCCET) was also referred (UCCET, 2011). Additionally, two reports of GDF were also used (GDF, 2012; GDF, 2020). Moreover, a report about Turkish forestry published by Foresters' Association of Turkey (FOT) and the forestry statistics published by Ministry of Agriculture and Forestry (MAF) were referred to collect the data used in the study (FOT, 2019; MAF, 2019).

The data involve one dependent variable, which is the industrial wood production level, and four dependent variables, which are burned forest area, outbreaks of insects, outbreaks of diseases and severe weather events. The available data consist of 18 cases belonging to the years between 2000 and 2017. The variables, their units of measurement, and descriptions are provided in Table 1.

Table 1

The variables employed in the study

Variables | Descriptions |

Industrial wood production | The yearly level of industrial wood production (m3) |

Burned forest area | The yearly amount of burned forest areas (1000 ha) in forest fires |

Outbreaks of insects | The yearly amount of harmed forest areas (1000 ha) due to outbreaks of insects |

Outbreaks of diseases | The yearly amount of harmed forest areas (1000 ha) due to outbreaks of various diseases |

Severe weather events | The yearly amount of harmed forest areas (1000 ha) due to severe weather events |

Figure 7 presents the yearly amounts of harmed forest areas with respect to burned forest area, outbreaks of insects, outbreaks of diseases and severe weather events factors.