NanoPhotoBioSciencesVolume **** (2014), Article ID ******, 5 pagesdoi:

Review Article

Artificial neural networks and their application in biological and agricultural researchesIzabela A. Samborska1, Vladimir Alexandrov2, Leszek Sieczko3, Bożena Kornatowska4, Vasilij Goltsev2, and Hazem M. Kalaji1,*1 Department of Plant Physiology, Warsaw University of Life Sciences SGGW, 02-776 Warsaw, Poland2 Department of Biophysics and Radiobiology, Faculty of Biology, St. Kliment Ohridski

University of Sofia, 8 Dr. Tzankov Blvd., 1164 Sofia, Bulgaria;3 Department of Experimental Statistics and Bioinformatics, Warsaw University of Life Sciences SGGW, 02-776 Warsaw, Poland

4 Institute of Environmental Protection-NRI, Department of Nature and Landscape Conservation

Received ****** 2014; Accepted *****

Academic Editor: *****

Copyright © 2014 ****.

Keywordsartificial neural networks, synaptic weights, ANN in biology, ANN in agriculture, data analysis, artificial nervous system

AbstractIn the present paper we show that data analysis using artificial neural networks (ANNs) has been increasingly applied worldwide in a range of scientific fields, including biological and agricultural research. Based on ANN, the analysis of results can be obtained in a relatively short time, even when considering lots of data. The method has become an attractive alternative for accepted statistical methods, and provides mean results fitting well the pattern of variable and hard to foretell phenomena in biological and agricultural systems.

* Corresponding authors: Dr. Hab. Hazem M. Kalaji, Phone: +48 664943484, Email: hazem@kalaji.pl

1. IntroductionArtificial neural networks (ANN) are the systems of handling data, the benefits of which

have been more and more recognized in various fields of technology and science. Thanks to their ability to tackle complex calculation issues they are progressively applied to solving practical problems. The neural networks can be applicable in a magnitude of science and knowledge domains. ANN’s main advantage is the fact that task solving is done by putting forward input signals stimulating network capability to learn and recognize patterns. This way complicated algorithms or rule-based programming are not always necessary to find right answers. ANN’s performance and its mode of computing information reflect the activity of the central nervous system that seems to be never-failing with its superlative processes of transmitting information.

The aim of constructing ANNs was to create artificial intelligence inspired by work of human brain, even though the latter has not yet been fully understood. On the other hand, one has to bear in mind that each individual neuron of the nervous system is a very important part of transmitting information. Thousands of small and independent neurons can act together and this allows analyzing and simultaneous solving a wide variety of complex tasks. No machine could be able to do it in such a reliable way. Computers are most capable to perform advanced calculations and they do this much faster and more efficiently than any human being, nevertheless, analyzing and learning on mistakes can be made by man’s brain only. ANNs are based on the idea of adjoining computer’s and man’s brain abilities. The main asset of neural networks is the ability of their neurons to take part in an analysis when working simultaneously but independently from each other. In other words, the neurons function as those in the brain and this provides for a possibility to construct a system based on technology such as computers equipped in a variety of programs to solve complex tasks.

Ever since, human beings have observed the universe and contemplated natural phenomena. Unknown processes have been tried to be understood, however even contemporary science has not been able to endow with unequivocal explanation of the processes happening in nature and living organisms. From the time of first research, knowledge and technology have considerably progressed, however this is not enough to come back with all the questions to answer by the humankind. Human beings constitute the inseparable and inherent element of nature. Consequently, contemporary research concentrates more and more on biological models, and the latter are worth improving and developing towards further application. An example of such research is the work on information systems and methods of analyzing and reprocessing information (Kosiński

2007). In the process of creation of such systems natural world is still a superlative paradigm as for example man’s brain and nervous system are able to reprocess information in a parallel way using thousands or millions of diminutive components for performing subsequent operations, and this allows tackling very complex issues. The systems created by nature are capable to achieve tasks through attaining, verifying and testing various modes of accomplishing a designated goal. Besides, natural systems are capable to eliminate damaged elements without disrupting operation of the whole system. Therefore, the brain of man indicates incredible flexibility as well as ability to adapt to given conditions – even extremely difficult, and to handle or eliminate useless components. Its supplementary assets are connecting and associating capabilities.

Artificial neural networks attempt to take off the work of human brain, and there still are carried out investigations on improving and updating their complex structures. In spite of considerable development of several indirectly connected scientific fields as well as various research methods and techniques, ANNs mimic the work of man’s nervous system only partially. Thus, the help of multifaceted tools, such as relevant computer programs, algorithms and other mathematical tools is needed when ANNs are used for analyses. Often ANNs are mathematical models, which need employment of an appropriate software. There has been research carried out on various algorithms applied in the analyses performed by ANNs. This approach allows the processes of network learning and makes man’s work easier, especially when dealing with complex tasks where traditional statistical methods cannot be applied.

Data concerning plant tissues are habitually classified as continuous data (e.g. size, weight), and they are frequently analyzed with statistical methods such as ANOVA. However, only normally distributed or scattered data can be analyzed this way. In the case of as much complex data as those biological, there should be applied different methods of analysis. What’s more, in biological research, forecasting should be performed using a suitable method, and this is possible when ANNs are applied.

The study carried out by Gago (Gago et al. 2010) showed that ANN is an useful tool in modeling intricate and non-linear relationships contingent on data not visible from the first sight, and which are most possible to be rejected by the researcher. The authors showed that ANN gave good results in the field of biology, and especially in the case of plants. However, if the analysis is to be successful, the data has to be optimized towards taking into consideration many various factors, such e.g. those environmental or genetic. Thanks to ANN, variables can be independently introduced into the network and factor permutations can be foreseen. So as to run the analysis of this kind there has to be input of as much as

possible data on different factors. ANN is capable to reject unnecessary ones and select those most important for achieving sound results (Gago et al. 2010). Learning performed by the network runs automatically and it is based on the selection of appropriate values of weights. In the case of ANN, there are distinguished two major learning paradigms, each corresponding to a particular abstract learning task. These are: supervised learning (with the so called “teacher”) and unsupervised learning (without “teacher”). The first paradigm is used when there exists a possibility to verify the answers given by the network. In this case, for each input vector there has to be known the value of an output vector, in other words – an exact solution to a given task. The second learning paradigm is applied when task solution is not known. Somebody constructs artificial neural network when he study complex processes depend on many variables. The ANNs are used in almost all fields of science such as biology, ecology, physics, chemistry, agronomy, economy, medicine, mathematics and computers science. The aims of ANNs are to predicted complex process when there are some inputs (for example in agronomy these are soil quality, nutrients, and cropping year) end single output (crop yield) (Wieland and Mirschel 2008). Among various mathematical models, just ANN showed to be the most useful tool for the analysis of chlorophyll fluorescence signals. The method has proved to be very precise being able to obtain expected and true results at 95% level. Therefore, it seems that it will be further developed and improved in biological research (Tyystjärvi et al. 1999).

2. First ANN models

Each individual neuron in the nervous system is independent and essentially works alone. At the same time, it transmits information obtained from prior neurons to further ones. In the case of artificial neural networks, this means that a given neuron sums up input signals with appropriate weight values obtained from a prior neuron and creates a non-linear threshold function of the sum obtained, which is followed by sending a signal to other connected neurons. The rule functioning in ANN is based on zero-one system, i.e.: “all” or “nothing”. In preliminary neural models the output signal was determined as a binary number 0 or 1. The value 0 meant neural activation lower than neuron activity threshold, and the value 1 was attributed to neuron agitation higher than the threshold of neuron activity.

One of the first, most known and well described examples of artificial neuron networks is the Perceptron constructed and described by Rosenblatt in 1958 (Rosenblatt 1988). The

author explicated dynamic neuron systems based on the perceptron model of the nervous cell. In keeping with Rosenblatts’s theory, the function of neuron activation has two binary values, i.e. 0 or 1, and the neuron was described by the McCulloch-Pitts model (Osowski 2013.). The net design had many advantages, however its effects were not fully satisfying. The greatest benefit of the net was the fact that it acted appropriately even though one of its elements was damaged. In any case the perceptron was the first model of effectively functioning neural network. On the other hand, the net could not realize more complex tasks, and it indicated considerable susceptibility to various changes which were inextricable elements in the process of learning (Tadeusiewicz 1993) Marvin Minsky and Seymour Papert (1969) criticized the above model in their book (“Perceptrons: an introduction to computational geometry”), which resulted in dramatic cuts of financing further research of this kind (Osowski 2013.; Newell 1969). Thus, the latter were continued on much smaller scale, only in a few research centers.

Until the eighties of the last century, scientific discussions on neural networks were not carried out, and only rapid development of Very-Large-Scale Integration (VLSI) technologies instigated new-fangled interest in the methods of information processing, including neural networks (Osowski 2013.). The work by Hopefield (1982) on ANNs was the milestone in development of research in this field, ever since conducted in an increasing number of designated scientific centers. Hopefield’s works contributed significantly to substantial enhancement of granting scientific projects on ANNs, which not only resulted in establishing novel network types, but also added to the progress on practical implementation of this method. At the same time, quick progress of information and computer systems resulted in creation of innovative solutions and greater possibilities of exploring, learning and testing ANNs.

Research on artificial neural networks has been yet conducted, and nowadays this has become a more and more popular domain of knowledge being willingly used in various scientific fields.

3. Application of artificial neural networksNeural network model was constructed based on surveillance of the nervous system and

readiness to imitate its operations. So far, among all human organs the nervous system has been the least understood, and maybe this is the reason why it has been so eagerly studied. The cerebral cortex covering both cerebral hemispheres plays significant cognitive and intellectual functions. It consists of and 1010 nerve cells and 1012 glial cells. It is believed that the number of the connections between cells is app. 1015 (Tadeusiewicz 1993).

Artificial neural networks were invented based on the model of the human brain. Similarly to the brain which consists of a huge number of neurons, ANN possesses lots of elements with the aim to process and transmit information to the next element. In the same way as in the nervous system, ANN’s elements are called neurons. The neurons are associated in the structures, the so called networks, by linkages called weights. Beneficial is the fact that during the learning process weight values can be freely changed or else modified. The mode of linking neurons in the net as well as their distribution and incidence determine network type and the mode of its action (Fig.1).

Figure 1: Design of a simple Artificial Neural Network with i input variables and k neurons in its output layer (modified after Aji et al., 2013)

In Fig 1 a simple model of artificial neuron called Perceptron is shown. The sets x1,…xi

represent input signals (for example leaf water content, nutrients, soil quality and other agricultural factors), the wki are synaptic weights, vk is a linear combiner output, φ(.) is an activation function, yk is an output, bk is a bias, uk is net input and this is the sum of all inputs multiple by all synaptic weights. Each individual constituent of the network takes signals from the other one placed in a preceding layer. The connection between the inputs is characterized by the weight coefficient wki and bias bk (Svozil et al. 1997) The signals are multiplied by the so called weighting factors, i.e. synaptic weights, and next they are summed up.

(1)Then the output is:

(2)

The next step is the change stimulated by the transfer function (depending on the goal of net’s operation), and the output signal generated is further transmitted to neurons in

1  jk

i

kjj

w xu

k k ky u b

subsequent layer. In order to achieve a solution to any task there are needed input and output signals of a given network, and the latter constitute the answers to the questions asked (input signals).

In the practice often are used multilayer artificial neural networks, because single layer neural networks cannot solve complex problems. Nowadays, the large majority of constructed and applied neural networks possess at least three layers. There always has to exist input layer and output one, and in between there are middle layers, the so called: hidden (Tadeusiewicz 1993). The neurons can be linked together in many different ways, for example using feedback loops (a signal obtained from the cells in the output layer is transmitted back to the input layer) or else by establishing links within the same layer (analogously to brain operation) (Fig. 2).

Figure 2: Wiring diagram of m input variables with neurons in the hidden layer and k output layer neurons

At the stage of net projecting, the most important are assignation and selection of an appropriate spatial arrangement of the network under construction, i.e. the number of its layers and the number of neurons in each of them. This is a very important step, since too few layers or neurons can cause obtaining mistaken results, whereas overstatement forwards can lead to biased fitting tested data (Lasoń et al. 2001).

The next essential step in ANN constructing is the process of network learning. There exist a few methods for the training process of ANNs and they depend on the type of the neural networks. The artificial neural networks with one and many hidden layers are formed the group of feed forward networks. The other type of ANN is the self-organized map of Kohonen (Kohonen 1982).

Few algorithms exist for the training of the feed forward networks. The aims of algorithms are to find the set of weights that minimizes the error between expected output y’ and the actual output y. The algorithm, which is often used, is called backpropagation algorithm or also called the Levenberg Marquardt algorithm. This method for training of

ANNs is a combination of the steepest descent method (Rumelhart et al. 1986) and the Gauss–Newton method (Osborne 1992). It is important to choose such synaptic weights, which will generate expected results as input signals. Testing is a crucial undertaking before selecting a specific net. This means preparing the so called sets of certain inputs together with the results which should be obtained. At the beginning, the synaptic weights are chosen randomly, however sometimes there can be applied algorithmic methods of selection (Lasoń et al. 2001). Such potential network is subject to many examinations and tests so as to check how many errors she makes. Testing is finished when an anticipated level of correct results is achieved. This decreases the risk of making wrong decision during the selection process of the right net.

In the process of the training, the adaptation of weights can lead to so called overtraining problem. In this case, the network can reproduce the training data quite well but when new data is introduced to the network the error is large. There exist some strategies to solve this problem. The one strategy is the network should start with a ‘‘simple’’ structure with one or two hidden layers and go over stepwise to more complicated structures. In many works have been shown that values of the weight affect the network and overtraining arises. This problem is avoided by regularization (MacKay 2003).

The subsequent phase of network construction is testing data sets, which were formerly used in the process of network learning. Concluding on effectiveness of the net tested depends on passing this stage. If the results at this stage are unsatisfactory, it is worth to start the process of learning over again.

Certain conditions have to be ensured to have ANN functioning as well as there has to be known its structure and an appropriate model has to be selected to meet our needs. Thus, in order to construct an appropriate model there have to be solved the following issues:

finding the type of task representation in the manner allowing to understand the result obtained with the use of ANN; this means that input stage of the net will help to determine a solution to an output task;

knowing and establishing values for all initial components of ANN; determining suitable energy function, the minimum of which will reflect an optimal

solution to an output task; setting up the weights of connections between the structures and knowing the

number of exterior agitations; knowing diversity of ANN components’ dynamics so as to not allow decreasing

energy function value.

The self-organized maps (SOM) are used when inputs are known, but output is unknown. This ANN was developed from Finnish scientist Teuvo Kohonen in 1987. This network is organizes as a two or three-dimensional grid and its goal is to convert high dimensional input signal into a low dimensional discrete output signal (Tiwari and Misra 2011). The every units of the map j are connected to each unit i in the input layer. The sets of input units are expressed as a column vector xi. The values of connection weights wij(t) are initially small. We must remember that weight is a function of time. Once the weights are initialized, three important processes are started for forming of SOM – competition, cooperation and synaptic adaptation (Kohonen 1982). The competition is a process, which leads to determination of neuron-winner. We shall determine the neuron-winner through minimization of the difference between input data xi and the weight wij(t). The neuron which respond maximally to input vector and which has a minimum distance to the weight vector is a neuron-winner ki.

(3)

This neuron and its neighboring neurons form topological neighborhood. The center of this cluster is the neuron-winner. The neuron-winner and other neurons from topological neighborhood are adapted to reduce a distance between weight vector and input vector:

(4)

In the equation (4) hj(t) is so called neighborhood function and it is equal to one when it relate to neuron-winner, and it is zero when it relate to remaining neurons. The η(t) is learning-rate parameter (Chon 2011). Initially the η(t) has a value η0. After that, the values are reduced and they approximate to zero. The corrective process (4) increases the productivity of the SOM. Since 1990 the SOM has been used for many biological researches (Ferrán and Ferrara 1992) such as molecular biology, ecology, genetics and so on, because these networks are very powerful and flexible.

argmin ( )j i iji

k x w t

( 1) ( ) ( )( ) ( )ij ij i ij jw t w t t k w h t

Figure 3: Schematic diagram of Self-Organized Map

Artificial neural networks are employed for solving theoretical and practical problems, which need solutions based on time consuming and complex calculations. The speed of information processing and obtaining the results with the use of neural networks provides for good possibilities of solving even very work and time consuming tasks.

Artificial neural networks can perform various functions, of which most popular are: approximation, classification of formulas, prediction, compression, interpolation and association. A model of a typical network is presented in Fig. 2. Most of the time, ANN acts in keeping with non-linear function y= f (x), where y is realized vector function of different variables and x – a universal approximate.

If ANN is used with the aim to recognize patterns or classification, then net learning is based on recording various pattern features, distribution of main components of the pattern, elements of Fourier’s transformation, and etc. It is important to find the elements distinguishing the patterns, since based on them the decision will be made on assigning data to a specific class.

In the case when we intend ANN to foresee or determine potential answers of the system, when based on the values obtained in the past, information on variable x is indispensable at the time before the prediction x(m-1), x(m-2),…, x(m-N). In the situation as such, the net constructed makes a decision on the value to be estimated when testing a sequence at the current moment m.

4. Neural networks in agricultural and biological sciencesIn the agricultural systems, such e.g. plant environments, which are characteristic of

sudden and quick changes of conditions, the selection of an appropriate net is not easy. Such environments indicate non-linearity of variables in time and are affected by many unknown factors. Therefore, it is difficult to assess complex relationships between input and output in the system founded on analytical methods. Recently, the intelligent control system based on artificial intelligence (AI) has become one of the most advanced technologies in system, learning (Hashimoto.Y 1997).

There are many methods currently used in agricultural and biological sciences. However, sometimes it appears that they are not sufficient enough for analyses and estimates based on scores of the results obtained. Thus, using ANNs has become more and more popular in the abovementioned domains of science. Thanks to ANN application it is possible to assess whether the factors investigated are correlated, as it was examined in the study on relationships of soil erosion and precipitation carried out by Kim and Gilley (2008). The results of simulations performed by these authors with the use of models derived from ANNs indicated that the amount of soil erosion was positively correlated with the amount of precipitation and run-off. Additionally, it was found that water erosion was a result of detaching soil particles by raindrops. In general, transport of soil particles by flowing water can cause a considerable loss of water quality. At the same time, it was concluded that ANN could generate the models which reflected non-linearity in plants’ nutrient environment resultant of soil erosion set off attributable to water excess. The latter can also lead to uncontrolled nutrient leaching (Kim and Gilley 2008). Neural Works Professional II/PLUS (NeuralWorks, Carnegie, Pennsylvania) Version 5.22 software was used in the abovementioned research for the construction of a multi-layer net. The package allows elaboration of own model through providing selected net parameters and system control.

The multi-layer perceptron (MLP) has been acknowledged as the architecture of artificial neural networks which can be trained by the algorithm of backward propagation of errors (BP) (Kim and Gilley 2008). ANNs can be applied in studies on decreasing herbicide rates, and thereby on negative effects on environment. Research on optimizing herbicide rates gave more defined results with the use of multi-layer perceptron BP trained, vector quantization and various methods based on self-organizing maps (SOM) (Moshou et al. 2001b). Aji et al. (2013) applied ANN in their study concerning palm oil. There are many diseases which can attack palms, which results in a substantial decrease in oil production. Detection of any pathogen at early development stages is hardly possible, thus the authors conducted their study by means of specific technology designated for disease early

diagnosis and classification as well as adjustment of right treatment. It was proposed to train ANN in image processing, and as a result 3 threatening palm diseases could be diagnosed. The complex linearity method was designed so as to cut down the duration of time needed for disease recognition. The method allowed using mobile devices in investigations. It was based on visual analyses performed by means of image processing in specially designed spatial system in ANN. This way 87.75% of diseases were identified in palm leaves following the classification model in the learning process. The optimal number of ANN’s layers selected by the authors was 6 (Aji et al. 2013).

Xiaoli Li and Yong He (2008) applied ANN in their study on tea leaves. The observations were conducted in 3 different tea gardens, and altogether 293 tea varieties were investigated. The aim of the study was discrimination of tea leaves based on visible and near-infrared reflectance (Vis /NIR) spectra. Good accuracy of classification was obtained and discrimination of low quality tea leaves with the use of ANN was 77.3% for all three tea gardens observed. The authors constructed appropriate models recognizing tea leaves’ defects based on specific records. ANN’s training was performed by means of BP, which allowed the net processing exemplary patterns as well as estimating probability that the object studied fitted data introduced during the process of net training. According to the authors, Vis/NIR signals showed a good potential for discrimination of tea leaves with low quality. Even though the readings could be disturbed by the factors such wind or sunlight angle, ANN processing appeared to be a good method for differentiation of tea leaves.

Water uptake by plant roots is an important process in the hydrological cycle. It is not only crucial for plant growth, but also plays an indispensable role in determining microorganism communities as well as in shaping soil physical and biochemical properties. Root capability to extract water from soil depends on both soil and plant properties. Qiao et al. (2010) analyzed water uptake in soil environment bearing in mind that water absorption by roots is reliant on density and humidity of soil around growing roots. Determination of volume, conformation and distribution of roots in soil poses a lot of difficulties for scientists since non-invasive methods for explicit description of the whole plant root system have not been yet elaborated. Thus, the authors proposed an alternative method (still tested) based on ANN analyses of data on plant water uptake. Data used for analyses in the input layer of ANN were: soil moisture, electric conductance of the soil solution, stem height and diameter, potential evaporation and air humidity and temperature. Output data concerned water uptake by plant roots at different soil depths. The absorption rate was estimated based on direct measurements of mass balance, evaluation of soil moisture following Darcy's law and assessment of water content in soil derived from calculation of capillary potential at 100 cm depth. The analysis performed with the use ANN was non-invasive, time efficient and

indicated the same results as those obtained by means of other methods. Therefore, successful model realization offered alternate and practical means for estimating water absorption by plant roots in the soil solution (Qiao et al. 2010).

For two decades, some plant researchers have used fluorescence kinetic curves for ANNs (Zaimov 1992; Tyystjärvi et al. 1999; Moshou et al. 2001b). These curves are used for input or output data in ANNs according to aim of investigation. The antenna complexes characteristics are highly variable and specific for varies groups of plant species. Kirova et al. (1992) have found that structural and functional characteristics of the photosynthetic machinery contains enough information about the taxonomic classification of the studied plants.

Photosynthetic apparatus is the main structural and functional element of the plant cell. Its reaction centers are highly conservative with low species-specific characteristics.

Water deficit is one of the most important environmental factors limiting sustainable yields and needs a reliable tool for its quantification. Research in this field encompasses registration of the photo-induced signal of prompt fluorescence (PF) and that of delayed fluorescence (DF) as well as modulated fluorescence and reflectance at 820 nm to analyze the changes in photosynthetic machinery performance in bean leaves first as fresh and then drought gradually. Taking into account the intensity of water deficit, there can be assessed various changes in essential plant processes, such as e.g. photosynthesis. Using data on PF, DF and MR there was constructed ANN which was capable to recognize a relative water in a series of “unknown” samples with a correlation between calculated and gravimetrically determined water content values of about R2 ≈ 0.98 (Goltsev et al. 2012).

Several researchers confirm that application of ANN is unfailing in the determination of a relative amount of water in collected plant leaves. The method can also be applied to determine plant stress. ANN has a future in detecting plant stress and disturbances in the functioning of assimilation apparatus (Frick et al. 1998; Salazar et al. 2009).

Zaidi et al. (1999) used ANN with BP so as to evaluate lettuce in terms of its growth. The authors designed ANN consisting of 5 to 8 processing units (input, output and hidden layers). There was used clinorotation at a range from 0 to 25 rotations/min at rotation range between 0 and 5. Average width and height of plants after transplanting were used for decision making on the selection of plants for further investigations. Fifty eight training data sets were tested until 22 124 of interactive data were obtained. The results obtained based on as many analyses made the authors conclude that ANN was an appropriate method for

evaluations of plant growth under simulated conditions (Zaidi et al. 1999; Prasad and Dutta Gupta 2008).

In other, ANNs were used for identification of plant viruses. The results obtained indicated that the method applied provided for a right and reliable tool, helpful in easing the analyses. Therefore, it was suggested to use ANN as an alternative for traditional methods used in verification of lots of data (Glezakos et al. 2010).

A trial on evaluation of the effects of environmental factors on banana leaves using ANN confirmed usefulness of this method. There have been conducted similar as well as totally different studies with the use of ANN in agricultural research (Bala et al. 2005; Diamantopoulou 2005; Movagharnejad and Nikzad 2007; Zhang et al. 2007). The majority of the latter concerned forecasting (Jiang et al. 2004 ; Uno et al. 2005; Savin et al. 2007). Jiang et al. (2004) described ANN model with backward propagation. The algorithms used during net training concerned forecasting winter wheat yield using spatial information. Uno et al. (2005) elaborated models for yield prediction in corn using statistical and ANN methods based on various data on plant vegetation. Greater accuracy was obtained with ANN model, which was better than one of the three typical experimental models. Savin et al. (2007) studied connective utilization of ANNs, fuzzy sets, fuzzy neural networks (FNNs) and granulated neural networks (GNNs). Soares et al. (2013) attempted to foresee cultivation efficiency of fields distributed throughout Russia. The abovementioned studies indicated ANN as the best means for analyses of this kind.

Application of artificial neural networks in agricultural and biological research has become more and more accepted, especially in research concerning the prediction of events (Hashimoto.Y 1997; Moshou et al. 2001a; Kim and Gilley 2008; Qiao et al. 2010; Šťastný et al. 2011) ANNs have been applied inter alia in sciences such as: medicine (Malmgren 2000; Lweesy et al. 2011; Akdemir et al. 2009 ; Feng et al. 2012), technical (António et al. 2008; Ahmadi 2011; Niaki and Hoseinzade 2013; Selvakumar et al. 2013), economics (Thinyane and Millin 2011; Landajo et al. 2012; Azizi 2013; Zanger 2013; Ashhab et al. 2014), chemistry (Sroczyński and Grzejdziak 2002; Fogelman et al. 2006; Ozkan et al. 2011; Harris and Darsey 2013; Fathy and Megahed 2012) and also in numerous other scientific fields (Trichakis et al. 2011; Guarini 2013; Citakoglu et al. 2014). This method has been constantly developing and gaining more and more worldwide recognition. In unison, constant progress of science, knowledge and technology makes even very complex mathematical analyses possible in a relatively short time. The latter is an unquestionable advantage of ANNs and causes that they can be applied in almost all scientific domains. A relatively short time for obtaining the results is an advantage of actual development of computer sciences and

technologies. The systems operating nowadays are often capable to process information thousands of times faster than those acting in the eighties or nineties of the 20th century, that is when rapid development of informatics occurred and computers entered households all over the world. Only 20-30 years before, all this would be impossible since that much effective computers equipped in that competent programs did not exist then. At the present time, computers possess incredibly better memory systems, which are characteristic of fast processing, and thus they are capable to process vast amounts of data in a short time. The abovementioned futures make joining together nature and rapidly developing technology most useful in the progress of research on ANNs. The latter in turn allows to reach the answers to numerous questions asked by global scientists of miscellaneous domains. Thanks to this progress humankind can get to the bottom of more and more secrets of the world around and unrivalled Mother Nature.

5. The future of ANN application Despite that, yet the application of ANN in the field of biological and agricultural

sciences is limited, it is highly expected that it will be one of the major research tools in those fields in the near future. The reason behind that is the big demand to understand and predict the behaviour of any system based on different physiological processes. The fast development of electronic devices and research equipment will allow more and more to have a huge number of data in a very short time, even in one second. Only ANN will be able to deal with such huge number of data to underline the trends and specific reactions and behaviours of individuals. It can be applied to predict abiotic and biotic stressors effects on living organism, this will allow to find practical solutions for plant production and avoid huge loss of money e.g. in the field of mineral fertilization.

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