How To Predict Cyanotoxins From A Model Using Machine Learning And Support Vector Regression

Transcription

1 Environmental Research 122 (2013) 1 10 Contents lists available at SciVerse ScienceDirect Environmental Research journal homepage: Hybrid modelling based on support vector regression with genetic algorithms in forecasting the cyanotoxins presence in the Trasona reservoir (Northern Spain) P.J. García Nieto a,n, J.R. Alonso Fernández b, F.J. de Cos Juez c,f.sánchez Lasheras d,c.díaz Muñiz b a Department of Mathematics, Faculty of Sciences, University of Oviedo, Oviedo, Spain b Cantabrian Basin Authority, Ministry of Agriculture, Food and Environment, Oviedo, Spain c Mining Exploitation and Prospecting Department, University of Oviedo, Oviedo, Spain d Department of Construction and Manufacturing Engineering, University of Oviedo, Gijón, Spain article info Article history: Received 21 May 2012 Received in revised form 29 October 2012 Accepted 2 January 2013 Available online 29 January 2013 Keywords: Statistical machine learning techniques Cyanobacteria Cyanotoxins Genetic algorithms (GAs) Support vector regression (SVR) abstract Cyanotoxins, a kind of poisonous substances produced by cyanobacteria, are responsible for health risks in drinking and recreational waters. As a result, anticipate its presence is a matter of importance to prevent risks. The aim of this study is to use a hybrid approach based on support vector regression (SVR) in combination with genetic algorithms (GAs), known as a genetic algorithm support vector regression (GA SVR) model, in forecasting the cyanotoxins presence in the Trasona reservoir (Northern Spain). The GA-SVR approach is aimed at highly nonlinear biological problems with sharp peaks and the tests carried out proved its high performance. Some physical chemical parameters have been considered along with the biological ones. The results obtained are two-fold. In the first place, the significance of each biological and physical chemical variable on the cyanotoxins presence in the reservoir is determined with success. Finally, a predictive model able to forecast the possible presence of cyanotoxins in a short term was obtained. & 2013 Elsevier Inc. All rights reserved. 1. Introduction Cyanobacteria are photosynthetic prokaryotes lacking the typical membrane-bound organelles Z such as nuclei and choloroplasts found in true algae. Consequently they are now classified as bacteria and known most correctly as cyanobacteria although the term blue green algae is still used frequently. Cyanobacteria can be found in almost every conceivable environment: in oceans, lakes and rivers as well as on land. Even they flourish in Artic and Antarctic lakes (Quesada et al., 2006; Reynolds, 2006), hotsprings and wastewater treatments plants. Under favourable conditions, certain cyanobacteria can dominate the phytoplankton within a water body and form nuisance blooms. Cyanobacteria have come to the attention of public health workers because many freshwater and brackish species can produce a range of potent toxins called cyanotoxins (Spoof et al., 2006; Reynolds, 2006), and in freshwater ecosystems are the most common cause of eutrophication. The blooms are not always green (Smith et al., 2008; Huisman et al., 2010). They can be blue, and even some cyanobacteria species are coloured brownish-red. Furthermore, the water can become malodorous when the cyanobacteria in the bloom die. n Corresponding author. Fax: þ address: [email protected] (P.J. García Nieto). Therefore, cyanotoxins are an important environmental problem in reservoirs (Vasconcelos, 2006; Stewart et al., 2006). Water is never perfectly clean and polluted water is also a continuing threat to human health and welfare (Dasí et al., 1998; de Hoyos et al., 2004). The toxins include neurotoxins, hepatotoxins, cytotoxins, and endotoxins (Dixit et al., 2005; Willame et al., 2005; Seckbach, 2007; David et al., 2009; Peschek et al., 2011). Most reported incidents of poisoning by microalgal toxins have occurred in freshwater environments, and they are becoming more common and widespread (Negro et al., 2000). Cyanotoxins are often implicated in what are commonly called red tides or harmful algal blooms (HABs) (Fogg et al., 1973). Lakes and oceans contain many single-celled organisms called phytoplankton. Under certain conditions, particularly when nutrient concentrations are high, these organisms reproduce exponentially. The resulting dense swarm of phytoplankton is called an algal bloom. These can cover hundreds of square kilometres and can be easily seen in satellite images. Individual phytoplankton rarely live more than a few days, but blooms can last weeks (de Hoyos et al., 2004). On the one hand, a genetic algorithm (GA) is a search heuristic that mimics the process of natural evolution (Goldberg, 1989; Davis, 1991; Sivanandam and Deepa, 2010). In this study, this heuristic is used to carry out a dimensional reduction by identifying patterns in the experimental data set. This technique permits the selection of six main variables from a total number of 24 predicting /$ - see front matter & 2013 Elsevier Inc. All rights reserved.

2 2 P.J. García Nieto et al. / Environmental Research 122 (2013) 1 10 variables in this complex problem, with minimal loss of information. GAs belong to the larger class of evolutionary algorithms (EA) (Haupt and Haupt, 2004; Engelbrecht, 2007), using techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover. On the other hand, support vector regression (SVR) is a novel learning technique based on statistical learning theory and the structural risk minimization principle, which has been successfully used for nonlinear system modelling (Vapnik et al., 1997; Taboada et al., 2007; de Cos Juez et al., 2010; Sánchez Lasheras et al., 2010; Suárez Sánchez et al., 2011). The SVR parameters must be determined carefully in order to obtain the most efficient SVR model (Vapnik, 1998; Keerthi, 2002; Schölkopf and Smola, 2002; Shawe-Taylor and Cristianini, 2004). In other words, an inappropriate choice of the SVR hyperparameters will result in over-fitting or under-fitting, and different hyperparameter settings may also give place to significant differences in performance (Cristianini and Shawe-Taylor, 2000; Steinwart and Christmann, 2008). Therefore, the optimal selection of SVR hyperparameters is an important step in a SVR fit. The aim of this research work is to construct a hybrid GA SVR model to identify spatial cyanotoxins in waterways in the Trasona reservoir (Principality of Asturias, Northern Spain) (see Fig. 1). The GA-SVR technique is aimed at highly nonlinear biological problems with sharp peaks and the tests carried out in this research work proved its high performance. It is a non-parametric regression technique and can be seen as an extension of linear models that automatically models non-linearities and interactions as those analysed in this innovative research work successfully. The Trasona reservoir, which was initially destined to the industrial supply, is complemented at present with a recreational utilization as a high performance training centre of canoeing. It is an eutrophic ecosystem, which has been characterized for cyanobacteria outcrops in certain periods, which sometimes has produced variable concentrations of cyanotoxins, mainly mycrocistins. This innovative research work is structured as follows. In the first place, the necessary materials and methods are described to carry out this study. Next the obtained results are shown and discussed. Finally, the main conclusions drawn from the results are exposed. 2. Materials and methods 2.1. Experimental data set The data set used for the hybrid GA SVR model developed here were collected over 6 years (from 2006 to 2011) from lots of samples in Trasona reservoir and the total number of data processed was about 151 values. The supplementary site-specific experimental data set associated with this article can be found at the following online link: The information of the biological parameters is expressed in biovolume (cubic millimetres per liter) of phytoplankton species. Specifically, this reservoir was sampled several times a month from January 1, 2006 to December 31, 2011, following the sampling protocols for lakes and reservoirs of the Spanish Ministry of Agriculture, Food and Environment, which are consistent with the guidelines established by the European Union and international agencies dealing with these issues (Quesada et al., 2004). In practice, a single point of sampling is taken into account in the place of greater depth of the reservoir. The samples were taken with a Niskin hydrographic bottle at different depths in the euphotic zone (Dasí et al., 1998). The values of phytoplankton and concentrations of cyanotoxins, chlorophyll and other physicochemical parameters were determined from a sample composed of five homogeneous subsamples obtained with the hydrographic bottle at various equidistant depths in the euphotic zone (Quesada et al., 2004; Reynolds, 2006). In this research work, we have taken into account the two dominant species of the cyanobacteria community: Microcystis aeruginosa (see Fig. 2 left) and Woronichinia naegeliana (see Fig. 2 right). The main goal of this research work was to obtain the dependence relationship of cyanotoxins (output variable), expressed in micrograms per liter, as a function of the following two groups of input variables (Reynolds, 2006): a. Biological parameters M. aeruginosa (mm 3 /l) is a type of harmful blue-green algae which is also referred to as colonial cyanobacteria (see Fig. 2 left). W. naegeliana (mm 3 /l) is a kind of cyanobacteria present in waters of a lower trophic status (see Fig. 2 right). Other cyanobacteria (mm 3 /l): All cyanobacteria excluding the two previous ones. Examples of these species may include some potentially toxic species such as Microcystis flos-aquae, Microcystis novacekii, Anabaena flos-aquae and Anabaena crassa. Diatoms (mm 3 /l) are a major group of algae, and are one of the most common types of phytoplankton. Chrysophytes (mm 3 /l) are small flagellates that are a yellowish brown colour. They can also be found singly or in a colony. Chlorophytes (mm 3 /l) refer to a highly paraphyletic group of all green algae within the green plants group. Other phytoplankton species (mm 3 /l): They represent the rest of the phytoplankton species excluding the previous ones. Chlorophyll concentration (mg/l): Chlorophyll is an extremely important biomolecule, critical in photosynthesis, which allows plants to obtain energy from light. b. Physical chemical parameters Fig. 1. (a) Aerial photograph of the city of Avilés (Northern Spain) (2) and the Trasona reservoir (1); and (b) an aerial photograph of the Trasona reservoir in great detail. Water temperature (1C): This is a measurement of the intensity (not amount) of heat stored in a volume of water. Temperature affects the solubility of many chemical compounds and can therefore influence the effect of pollutants on aquatic life. Ambient temperature (1C): Simply means that the temperature of the Trasona reservoir s surroundings that affects water temperature.

3 P.J. García Nieto et al. / Environmental Research 122 (2013) Fig. 2. The most abundant cyanobacteria species in the Trasona reservoir: Microcystis aeruginosa (left) and Woronichinia naegeliana (right). Secchi disk depth (m): The depth at which the pattern on the Secchi disk (a circular disk with alternating black and white quadrants, mounted on a pole or line) is no longer visible from the surface when it is lowered down in the water. It is a measure of water transparency, directly related to phytoplankton growth and eutrophication processes. Turbidity (NTU): This is a measurement of the suspended particulate matter in a water body which interferes with the passage of a beam of light through the water. Materials that contribute to turbidity are silt, clay, organic material, or micro-organisms. High levels of turbidity increase the total available surface area of solids in suspension upon which bacteria can grow. High turbidity reduces light penetration; therefore, it impairs photosynthesis of submerged vegetation and algae. Total phosphorus (mg P/l): This is a measure of both inorganic and organic forms of phosphorus. Phosphorus can be present as dissolved or particulate matter. It is an essential plant nutrient and is often the most limiting nutrient to plant growth in freshwater. It is rarely found in significant concentrations in surface waters. Phosphates concentration (mg PO 4 3 /l): This is a measure of the inorganic oxidized form of soluble phosphorus. This form of phosphorus is the most readily available for uptake during photosynthesis. High concentrations of orthophosphate generally occur in conjunction with algal blooms. Often a limiting nutrient in ecological environments. Its availability may govern the growth rate of the aquatic organisms. High phosphate levels gives place to eutrophication processes that increases cyanobacterial biomass with the subsequent cyanotoxins production. Total nitrogen concentration (mg N/l): This is a measure of that portion of nitrogen that is organically bound. Organic nitrogen includes all organic compounds such as proteins, polypeptides, amino acids, and urea. Essential to Earth s life. Nitrate concentration (mg NO 3 /l): This is the measurement of the most oxidized and stable form of nitrogen in a water body. Nitrate is the principle form of combined nitrogen found in natural waters. It results from the complete oxidation of nitrogen compounds. Excessive amounts of nitrogen may result in phytoplankton or macrophyte proliferations. Nitrite concentration (mg NO 2 /l): This is a measure of a form of nitrogen that occurs as an intermediate in the nitrogen cycle. It is an unstable form that is either rapidly oxidized to nitrate (nitrification) or reduced to nitrogen gas (de-nitrification). This form of nitrogen can also be used as a source of nutrients for plants. Nitrite is toxic to aquatic life at relatively low concentrations. Ammonium ion concentration (mg/l): This is a measure of the most reduced inorganic form of nitrogen in water. Excess ammonia contributes to eutrophication of water bodies. This results in prolific algal growths that have deleterious impacts on other aquatic life, drinking water supplies, and recreation. Ammonia at high concentrations is toxic to aquatic life. It can be easily oxidized to nitrate in oxidizing environments. Dissolved oxygen concentration (mg O 2 /l): This is a measure of the amount of oxygen dissolved in water. The dissolved oxygen concentration is subject to diurnal and seasonal fluctuations that are due, in part, to variations in temperature and photosynthetic activity. Dissolved oxygen is essential to the respiratory metabolism of most aquatic organisms. It affects the solubility and availability of nutrients, and therefore the productivity of aquatic ecosystems. Conductivity (ms/cm): This is the measurement of the ability of water to conduct an electric current, that is to say, the greater the content of ions in the water, the more current the water can carry. Ions are dissolved metals and other dissolved materials. Conductivity may be used to estimate the total ion concentration of the water, and is often used as an alternative measure of dissolved solids. Alkalinity (mg CaCO 3 /l): This is the measurement of the water s ability to neutralize acids. It usually indicates the presence of carbonate, bicarbonates, or hydroxides. Alkalinity results are expressed in terms of an equivalent amount of calcium carbonate. Waters that have high alkalinity values are considered undesirable because of excessive hardness and high concentrations of sodium salts. Water with low alkalinity have little capacity to buffer acidic inputs and are susceptible to acidification (low ph). Calcium concentration (mg/l) is essential for living organisms, in particular in cell physiology. The hardness of water is generally due to the presence of calcium and magnesium in the water. Harder water has the effect of reducing the toxicity of some metals (i.e., copper, lead, zinc, etc.). ph: Measures the acidity or basicity of an aqueous solution. Is the measurement of the hydrogen-ion concentration in the water. High ph values tend to facilitate the solubilization of ammonia, heavy metals and salts. The precipitation of carbonate salts (marl) is encouraged when ph levels are high. Low ph levels tend to increase carbon dioxide and carbonic acid concentrations. Lethal effects of ph on aquatic life occur below ph 4.5 and above ph 9.5. At the same time we have an information that it is quantitative on the abundance of phytoplankton species. They are measured in number of cells per mililiter. Fig. 3(a) shows the evolution of chlorophyll concentration and cyanobacteria cell number per millilitre in the Trasona reservoir from January of 2006 to December of Higher levels of both variables are observed at certain periods of the years 2006, 2007 and 2008, which are significantly greater than the values obtained in the years 2009, 2010 and The peaks in Fig. 3(a) correspond to the cyanobacteria blooms: summer and fall of those years. However, there are no cyanobacteria blooms in years 2009, 2010 and Fig. 3(b) shows the evolution of cyanotoxins concentration and cyanobacteria cell number per millilitre in the Trasona reservoir from January of 2006 to December of Similarly, the peaks in Fig. 3(b) correspond to the cyanobacteria blooms and large concentrations of cyanotoxins. Fig. 4 shows a photograph of the Trasona reservoir with a dense bloom of cyanobacteria in Specifically, cyanobacteria cell number per millilitre was less than 50,000 and cyanotoxins concentration was always zero in 2009, 2010 and In this sense, Fig. 5 shows a photograph of the Trasona reservoir in summer of 2009 without a bloom of cyanobacteria. In fact, the Trasona reservoir is an eutrophic ecosystem (Pérez-Martínez and Sánchez-Castillo, 2004; Álvarez Cobelas and Arauzo, 2006) which has been characterized for the presence of cyanobacteria. These last ones sometimes have produced variable concentrations of cyanotoxins, mainly microcystins (Chorus and Bartram, 1999; Quesada et al., 2004). Once the problem has been identified, civil works have been carried out in order to diminish the nutrients contributions to the reservoir. The guideline values for safe recreational water quality raises alert level 2 (World Health Organization, 1998) with values greater than 100,000 cells per millilitre and a microcystin concentration greater than 20.0 mg/l (see Fig. 3(a) and (b)). The inventories of cells were taken through an inverted microscope on settled samples. The cyanotoxins have been analysed by means of the high-performance liquid chromatography (HPLC) technique (American Public Health Association, 1998). The Trasona reservoir is located near the industrial city of Avilés (Asturias, Northern Spain). Practically chained to the Trasona reservoir, it is possible to observe a wetland created artificially in order to shelter one changeable aquatic avifauna. This lagoon is able to store approximately 50,000 m 3 of water and the almost constant level of the water sheet of this lagoon allows the building of nests of different species of birds Genetic algorithms Mathematical modelling has always been an integral part of behavioural ecology from its inception (Ruxton and Beauchamp, 2008). Mathematical modelling provides an opportunity to formulate hypotheses about ecological behaviour in a rigorous way

4 4 P.J. García Nieto et al. / Environmental Research 122 (2013) 1 10 Fig. 3. (a) Evolution of chlorophyll concentration and cyanobacteria cell number per millilitre as a function of time in the Trasona reservoir from January of 2006 to December of 2011; and (b) evolution of cyanotoxins concentration and cyanobacteria cell number per millilitre as a function of time in the Trasona reservoir from January of 2006 to December of 2011.

5 P.J. García Nieto et al. / Environmental Research 122 (2013) Fig. 4. Dense bloom of cyanobacteria on the Trasona reservoir in covering the entire range of possible solutions (the search space). Occasionally, the solutions may be seeded in areas where optimal solutions are likely to be found. Evaluation: An evaluation function is applied in order to know the goodness of each of the solutions of the population. Stop criterion: The GA will stop when the optimum solution is found or after a certain number of iterations/generations. If the stop criterion is not accomplished then a new iterative loop is carried out. Selection: During each successive generation, a proportion of the existing population is selected to breed a new generation. Individual solutions are selected through a fitness-based process, where fitter solutions (as measured by a fitness function) are typically more likely to be selected. Certain selection methods rate the fitness of each solution and preferentially select the best solutions. Other methods rate only a random sample of the population, as this process may be very time-consuming. The fitness function, f, maps a chromosome representation into a scalar value so that G represents the data type of the elements of an n x-dimensional chromosome (Haupt and Haupt, 2004; Engelbrecht, 2007; Ordóñez Galán et al., 2011): f : G nx -R ð1þ Fig. 5. A photograph of the Trasona reservoir in summer of 2009 without a bloom of cyanobacteria. and the solutions that emerge illuminate the relationships between variables thought to be important in driving behaviour. The complexity of models inevitably increases, as relationships among independent variables are refined. While the predictions of more complex models are often subtler, the practical task of solving the equations of the model to find solutions becomes more difficult. This arises for two reasons. First, finding analytic solutions to complex models is challenging and often, remarkably even for relatively simple equations, beyond current capacity (Vrugt and Robinson, 2007; Ruxton and Beauchamp, 2008). Second, tractable solutions are often beyond the abilities of mathematically challenged researchers who are not always very familiar with mathematical techniques. This is especially the case in an empirically strong field like cyanobacterial ecology (Hense and Burchard, 2010; Wang et al., 2010). Heuristic search algorithms provide a mean to locate solutions in less tractable models.these algorithms involve the use of computer programs that search from the solution systematically in a predefined search space. Genetic algorithms (GAs), one particular class of search algorithms, have been used widely in fields as varied as biology, chemistry and economics (Goldberg, 1989; Davis, 1991; Haupt and Haupt, 2004; Sivanandam and Deepa, 2010). The genetic algorithms (GAs) are based upon Darwin s Theory of Evolution (Goldberg, 1989; Davis, 1991; Haupt and Haupt, 2004; Sivanandam and Deepa, 2010). The genetic algorithms are modelled on a relatively simple interpretation of the evolutionary process. However, it has proven to be a reliable and powerful optimization technique in a wide variety of applications. Holland in 1975 was the first to propose the use of genetic algorithms for problem-solving (Holland, 1975; Goldberg, 1989; Davis, 1991). The GA uses the current population of strings to create a new population whereby the strings in the new generation are on average better than those in the current population. The selection depends on their fitness value. The selection process determines which string in the current will be used to create the next generation. The crossover process determines the actual form of the string in the next generation (Engelbrecht, 2007; Ordóñez Galán et al., 2011). Weak individuals are discarded and only the strongest survive. In this way, how do they work? Initialization: Initially many individual solutions are randomly generated to form an initial population. The population size depends on the nature of the problem, but typically contains hundreds or even thousands of possible solutions. Traditionally, the population is generated randomly, Crossover: In genetic algorithms, crossover is a genetic operator used to vary the programming of a chromosome or chromosomes from one generation to the next. It is analogous to reproduction and biological crossover, upon which genetic algorithms are based. Crossover operators can be divided into three main categories based on the arity (i.e. the number of parents used) of the operator. This gives rise to three main classes of crossover operators (Engelbrecht, 2007; Ordóñez Galán et al., 2011): (1) asexual, where an offspring is generated from one parent; (2) sexual, where two parents are used to produce one or two offspring (the operator employed in the present research) and (3) multi-recombination, where more than two parents are used to produce one or more offspring. Mutation: A genetic operator, used to maintain genetic diversity from one generation of a population of algorithm chromosomes to the next. It is analogous to biological mutation. Mutation is used in support of crossover to ensure that the full range of allele is accessible for each gene. Mutation is applied at a certain probability, p m, to each gene of the offspring, ~x i ðtþ, to produce the mutated offspring x i ðtþ. The mutation probability, also referred to as the mutation rate, is usually a small value, p m A½0,1Š, to ensure that good solutions are not distorted too much. Given that each gene is mutated at probability p m, the probability that an individual will be mutated, taking into account that the individual contains n x genes, is given by (Haupt and Haupt, 2004; Ordóñez Galán et al., 2011) nx Prob ð~x i ðtþ is mutatedþ¼1 1 p m ð2þ Replacement: The least-fit population is replaced with new individuals Support vector machines for regression SVMs are a set of related supervised learning methods used for classification and regression that can universal approximate any multivariate function to any level of accuracy (Cortes and Vapnik, 1995; Vapnik, 1998). SVMs were originally developed to solve classification problems (Taboada et al., 2007). They were later generalized to solve regression problems (Vapnik et al., 1997; de Cos Juez et al., 2010; Sánchez Lasheras et al., 2010; Suárez Sánchez et al., 2011) in a method called support vector regression (SVR). The model produced by support vector classification only depends on a subset of the training data, because the cost function for building the model ignores training points that lie beyond the margin. Analogously, the model produced by SVR only depends on a subset of the training data, because the cost function for building the model ignores any training data that are close (within a threshold e) to the model prediction. The basic idea of SVR is briefly described here. Rather than classify new unseen variables! ^x into one of two categories ^y ¼ 71, we want to predict a real-valued output for y 0. Hence, the training data is of the form f! x i,t i g, wherei ¼ 1,2,:::,L, yar,! x AR D (Steinwart and Christmann, 2008; Fletcher, 2009): y i ¼! w U! x i þb ð3þ The SVR uses a more sophisticated penalty function: a penalty is not imposed if the predicted value y i is less than a distance e away from the actual value t i, i.e., if 9t i y i 9oe. Referring to Fig. 6, the region bound by y i 7e 8i is called an e- insensitive tube. Another modification to the penalty function is that output variables outside the tube are allocated one of two slack variable penalties, depending on whether they lie above x þ or below x ð Þ the tube, where x þ 40, x 40 8i (Fletcher, 2009): t i ry i þeþx þ ð4þ t i Zy i e x ð5þ

6 6 P.J. García Nieto et al. / Environmental Research 122 (2013) 1 10 Table 1 Set of biological input variables used in this study. Biological input variables Microcystis aeruginosa (mm 3 /l) Woronichinia naegeliana (mm 3 /l) Other cyanobacteria (mm 3 /l) Diatoms (mm 3 /l) Chrysophytes (mm 3 /l) Chlorophytes (mm 3 /l) Other species of the phytoplankton (mm 3 /l) Microcystis aeruginosa Woronichinia naegeliana (synergistic interaction variable) (mm 6 /l 2 ) Chlorophyll concentration (mg/l) Name of the variable Microcystis_aeruginosa Woronichinia_naegeliana Other_species_Cyanobacteria Diatoms Chrysophytes Chlorophytes Other_phyto Microcys Worochinia Chlorophyll Fig. 6. Regression with e-insensitive tube. The SVM problem can be formulated as follows (Fletcher, 2009; Suárez Sánchez et al., 2011): 0 ( ) /w!,cð! 1 x iþsþb y i Zeþx þ 1 min! 2 :w! : 2 þc XL i ðx þ i þx i Þ y i ð/w!,cð! x iþsþbþzeþx B i A i ¼ 1,:::,L ð6þ w,b,n i ¼ 1 x þ i,x i Z0 where c : X-Z is a transformation of the input space into a new space Z, usually a larger dimension space, where we define an inner product by means of a positive definite function k (kernel trick) (Cristianini and Shawe-Taylor, 2000; Shawe- Taylor and Cristianini, 2004; Steinwart and Christmann, 2008): /cð x! Þ,cð x!0 ÞS ¼ X i c i ð x! Þc i ð x!0 Þ¼kð x!, x!0 Þ The above problem is quadratic with linear constraints, and so the Kuhn Tucker optimality conditions are necessary and sufficient. The solution, which can be obtained from the dual problem, is a linear combination of a subset of sample points denominated support vectors (s.v.) as follows (Steinwart and Christmann, 2008; Fletcher, 2009):! X w ¼ b i cð! x iþ)f w,b ð! x Þ¼ X b i /cð! x iþ,cð! x ÞSþb ¼ X b i kð! x i,! x Þþb ð8þ s:v: s:v: s:v: The reason that this kernel trick is useful is that there are many regression problems that cannot be linearly regressed in the space of the inputs x!, which might be in a higher dimensional feature space given a suitable mapping. Different kernel functions are described in the bibliography, for example: Radial basis function (RBF) (Shawe-Taylor and Cristianini, 2004; Fletcher, 2009): kð x! i, x! jþ¼e ð99 x! i x! j99 2 =2s 2 Þ Polynomial kernel (Shawe-Taylor and Cristianini, 2004; Fletcher, 2009): kð x! i, x! jþ¼ðx! iu x! j þaþ b where a and b are parameters defining the kernel s behaviour. To sum up, to use an SVM to solve a regression problem for data that is not linearly separable, we need to first choose a kernel and relevant parameters that can be expected to map the nonlinearly separable data into a feature space where it is linearly separable. 3. Analysis of results and discussion The biological and physical chemical input variables considered in this research work are shown in Tables 1 and 2, respectively (Whitton and Potts, 2000; Reynolds, 2006; Gault and Marler, 2009; Huisman et al., 2010). Note that one of the variables is equal to the product of the variable M. aeruginosa multiplied by the variable W. naegeliana due to the coexistence of these two species of cyanobacteria in order to reproduce their dynamics without intervention of external factor. This mathematical formulation adds a multiplicative additional term to take into account the interaction of both species according to a more realistic modelling in Biology (Allman and Rhodes, 2003; Barnes and Chu, 2010). Furthermore, the information of the biological parameters is expressed here in biovolume (cubic millimetres per liter) of phytoplankton species while cyanotoxins (output variable) and chlorophyll concentrations ð7þ ð9þ ð10þ Table 2 Set of physical chemical input variables used in this study. Physical chemical input variables Water temperature (1C) Ambient temperature (1C) Secchi disk depth (m) Turbidity (NTU) Total phosphorus (mg P/l) Phosphates concentration (mg PO 3 4 /l) Total nitrogen concentration (mg N/l) Nitrate concentration (mg NO 3 /l) Nitrite concentration (mg NO 2 /l) Ammonium concentration (mg/l) Dissolved oxygen concentration (mg O 2 /l) Conductivity (ms/cm) Alkalinity (mg CaCO 3 /l) Calcium concentration (mg/l) ph values Name of the variable Water_temperature Ambient_temperature Secchi_disk_depth Turbidity Total_phosphorus Phosphates_concentration Total_nitrogen_concentration Nitrate_concentration Nitrite_concentration Ammonium_concentration Dissolved_oxygen_concentration Conductivity Alkalinity Calcium_concentration ph_ values in micrograms per liter. Therefore, the total number of predicting variables used was 24 in this study. It is important to select a model that best fits the experimental data. In this research work, the fitted hybrid GA SVM model has a coefficient of determination R 2 equal to 0.95 and a correlation coefficient equal to These results indicate an important goodness of fit, that is to say, a good agreement is obtained between our model and the observed data. In attempting to model real-world problems or concepts using computational methods, the selection of an appropriate representation is of considerable importance (Vapnik, 1998; de Cos Juez et al., 2009). The selection of features can have a considerable impact on the effectiveness of the overall resulting regression algorithm: the hybrid GA SVM model. The main purpose of feature selection is to reduce the number of features used in regression while maintaining an acceptable accuracy. This matter is carried out using an appropriate genetic algorithm in the first step of the analysis. To fix ideas, a genetic algorithm (GA) is typically defined by following types of parameters (Haupt and Haupt, 2004; Engelbrecht, 2007; Sivanandam and Deepa, 2010; Ordóñez Galán et al., 2011): size of the population, number of generations, mutation probability, if clones are allowed or not, criterion to judge the quality of subsets and cardinality of the subset. In this research work, the basic GA parameters and their values are shown in Table 3. According to the results shown in Table 4, the 24 original variables of this nonlinear complex problem are reduced to six main variables with minimal loss of information. In this sense, the most significant variable in cyanotoxins prediction (output variable) is W. naegeliana. The second significant variable is the product of the concentration of M. aeruginosa by the concentration of W. naegeliana (Microcys Worochinia), the third is water

7 P.J. García Nieto et al. / Environmental Research 122 (2013) Table 3 Training basic parameters and their values for the genetic algorithm. Parameters Table 4 Evaluation of the importance of the variables that form the model: best variablesubset selected. Order of relevance Variable Value Size of the population 150 Number of generations 100 Mutation probability 1% Clones allowed No Criterion (indicates which criterion is to be used in judging the quality of the subsets) Standard coefficient of determination R 2 Cardinality of the subset that is wanted 6 1 Woronichinia_naegeliana 2 Microcystis_aeruginosaWoronichinia_naegeliana 3 Water_temperature 4 Turbidity 5 Total_phosphorus 6 Alkalinity temperature, the fourth is turbidity, the fifth is total phosphorus and finally the sixth is alkalinity. The 24 variables are reduced to six variables with minimal loss of information and they are sufficient to predict the blooms of cyanobacteria with production of cyanotoxins in the Trasona reservoir. The cyanobacteria community in this reservoir is mainly composed by M. aeruginosa and W. naegeliana. If W. naegeliana increase significantly its presence, this will be a clear warning that we may be near a bloom of cyanobacteria with risk of cyanotoxins. If we add a significant increase in the presence of M. aeruginosa, the two cyanobacteria species (M. aeruginosa and W. naegeliana) produce a result greater than the sum of their individual effects. Thus, the cyanotoxins production seems to be increased in a nonlinear way by the combined presence of both species. The physical chemical parameters (water temperature, turbidity, total phosphorus and alkalinity) are also important in the cyanotoxins forecasting since cyanobacterial composition of the reservoir depends on them. These last four variables are directly related to most of the physical chemical parameters considered in this study so that it is a logical result the variables reduction carried out. Thus, water temperature is a consequence of ambient temperature. They are directly related if no thermal discharge takes place. Obviously, water temperature is the most influential parameter in the cyanobacterial growth, and this variable is kept after the mathematical process as a main variable. Dissolved oxygen is also related to the water temperature since as water temperature increases, dissolved oxygen decreases. This same behaviour is observed for turbidity and Secchi disk depth: the higher turbidity, the lower Secchi disk depth. Total phosphorus is another of the selected variables while phosphates not. However, phosphates were implicitly considered since the total phosphorus includes all kind of phosphorus compounds. The remaining parameters removed such as the conductivity and nitrogen compounds (total nitrogen, nitrates, nitrites and ammonium) have very little influence on cyanobacterial growth. Indeed, it is well known that cyanobacteria are able to fix nitrogen from the atmosphere so that it is not a limiting nutrient as the phosphorus. At the same time, 15 reservoirs were studied from 2006 to 2011 to fulfil their levels of eutrophication (Ortiz-Casas and Peña Martínez, 1984). These reservoirs are located in the Cantabrian basin (Northern Spain). Twelve of these reservoirs have less than 1% of the cyanobacterial biovolume with respect to the overall biovolume of the samples. Only two of them, the San Andrés reservoir and the La Barca reservoir, have more than 30% of the cyanobacterial biovolume with respect to the overall biovolume of phytoplankton. Therefore, these two reservoirs are similar to the Trasona reservoir. However, the Trasona reservoir is singular, because the cyanobacterial biovolume in case of blooms of cyanobacteria was equal to 100% with respect to the overall biovolume of the samples (Sabater and Nolla, 1991). The cyanobacteria community of the San Andrés reservoir is mainly composed by M. aeruginosa (75%) and W. naegeliana (18%). The values of W. naegeliana and high values of the synergistic variable (Microcys Woronichinia_) warn of a high risk of cyanotoxins. The water temperature (its high values indicate a shallow reservoir), the turbidity (high values of an eutrophicated reservoir, ratified by the high values of the total phosphorus) and the alkalinity indicate the high risk of cyanotoxins along with the another set of physicochemical variables discussed above (Peretyatko et al., 2010). The cyanobacteria community of the La Barca reservoir is mainly composed by M. aeruginosa (57%) and W. naegeliana (25%). In a similar way, the values of W. naegeliana and the high values of the synergistic variable warn of a high risk of cyanotoxins. Water temperature (its high values are characteristic of a reservoir used to cool a coal power plant). This reservoir is eutrophicated (high values of the turbidity and total phosphorus). Furthermore, these values of turbidity are high because it is a shallow reservoir. The values of a eutrophicated reservoir are ratified by the high values of total phosphorus. Similarly, the physical chemical variables discussed above along with the alkalinity indicate the high risk of cyanotoxins presence (Peretyatko et al., 2010). As a consequence, W. naegeliana is the most important variable in the generation of cyanotoxins. Specifically, the cyanobacteria community of the Trasona reservoir is mainly composed by M. aeruginosa and W. naegeliana. It is well known that M. aeruginosa is potentially toxic. Up to now, there is only a partial evidence of toxicity of W. naegeliana (Willame et al., 2005). The majority of the samples which contained cyanotoxins were dominated by M. aeruginosa (47%), followed by W. naegeliana (38%). These data do not necessarily indicate that the dominant cyanobacteria is the largest producer of cyanotoxins (Willame et al., 2005). In order to take into account the intereraction between input variables M. aeruginosa and W. naegeliana, not considered in other works (Chorus and Bartram, 1999; Willame et al., 2005; Seckbach, 2007); it was necessary to add a new input variable equal to the product of the concentrations of the two above input variables in additioni to other variables empirically measured in the Trasona reservoir. The consideration of this interaction is known as synergy or synergistic behaviour. Therefore, the production of cyanotoxins from M. aeruginosa or from W. naegeliana increases due to the combined presence of both species: M. aeruginosa and W. naegeliana. The term synergy comes from the Greek word synergos, meaning working together (Corning, 2012). Among biologists, the use of the term synergy has been limited until recently mainly to certain especialized areas, such as the neurochemistry, cell biology and endocrinology. Moreover, most biologists recognize the subset of synergy known as emergent effects, as well as the synergies associated with coevolution. Synergistic response is a complicating factor in environmental modelling. Synergy has been advanced as a hypothesis on how complex systems operate. Environmental systems may react in a nonlinear way to perturbations, so that the outcome may be greater than the sum of the individual component alterations. Synergy is a room without walls in terms of which kinds of cooperative relationships are applicable and it is relevant at every level of living systems, from enzymes to ecosystems. The synergistic phenomenon has been

8 8 P.J. García Nieto et al. / Environmental Research 122 (2013) 1 10 observed in the two cyanobacteria species (M. aeruginosa and W. naegeliana) and it produces a result greater than the sum of their individual effects. Therefore, the cyanotoxins production is increased in a nonlinear way due to the combined presence of both species (Reynolds, 2006; Corning, 2012). On the one hand, water temperature affects the solubility of many chemical compounds and can therefore influence in the effect of pollutants on aquatic life. On one hand, the metabolic oxygen demand grows as water temperature increases, which in conjunction with reduced oxygen solubility, affects many species in a negative way (Arp and Yin, 1992; Blais et al., 1998). On the other hand, the synthesis of cyanotoxins is more frequent in warm waters than in cold waters. Temperature affects algal growth directly, but this growth is also concerned indirectly by the water temperature due to their influence on solubility of many chemical compounds. At the same time, ambient temperature affects the temperature of the Trasona reservoir s surroundings and thus it also concerns the water temperature and aquatic plants growth. Turbidity is a measurement of the suspended particulate matter in a water body and is usually produced by anthropogenic sources as forest harvesting, road building, agriculture, urban developments, sewage treatment plant effluents, mining and industrial effluents (France and Peters, 1995). High levels of turbidity increase the total available surface area of solids in suspension upon which bacteria can grow. High turbidity reduces light penetration (Nicholls et al., 2003) Therefore, it impairs photosynthesis of submerged vegetation and algae. In turn, the reduced plant growth may suppress fish productivity. The growth of phytoplanton contributes to turbidity. High levels of turbidity increase the total available surface area of solids in suspension upon which bacteria can grow. High turbidity reduces light penetration. Therefore, it impairs the photosynthesis of the submerged vegetation and algae. This situation favours the dominance of some cyanobacteria as M. aeruginosa (main productor of cyanotoxins), because of their ability to move up or down into the water column according to its need of light irradiance (Deng et al., 2007). Total phosphorus is an essential plant nutrient and is often the most limiting nutrient to plant growth in fresh water. Anthropogenic sources of total phosphorus are: sewage treatment plant effluent, agriculture, urban developments (particularly from detergents), and industrial effluents. Since phosphorus is generally the most limiting nutrient, its input to fresh water systems can cause extreme proliferation of algal growth. Inputs of phosphorus are the prime contributing factors to eutrophication in most fresh water systems (Smol et al., 1983; Likens, 1985; Prepas et al., 2001). Phosphorus can be present as dissolved or particulate matter. It is an essential nutrient for plants and it is often the most limiting nutrient in the growth of the plants in fresh water. The phosphates concentration (mg PO 4 3 /l) is a measurement of the oxidized form of the soluble inorganic phosphorus. High concentrations of orthophosphate generally occur in conjunction with algal blooms. It is a limiting nutrient in ecological environments. Its availability may govern the growth rate of the aquatic organisms. High phosphate concentrations give place to eutrophication processes that increases cyanobacterial biomass with the subsequent cyanotoxins production. Alkalinity is the measurement of the water s ability to neutralize acids. It usually indicates the presence of carbonate, bicarbonates or hydroxides. Waters that have high alkalinity values are considered undesirable because of excessive hardness and high concentrations of sodium salts. Water with low alkalinity have little capacity to buffer acidic inputs and are susceptible to acidification (low ph). Acidic precipitation, mining and industrial effluents are anthropogenic sources that lower alkalinity (Noges, 1992; Keenan and Kimmins, 1993). Alkalinity is the measurement of the water s ability to neutralize acids. It usually indicates the presence of carbonates, bicarbonates, or hydroxides. However, carbonates and bicarbonates are part of the carbonate system with three soluble components in equilibrium: carbonate (CO 3 2 ), bicarbonate (HCO 3 ) and carbon dioxide (CO 2 ). When CO 2 concentration is increased both carbonate and bicarbonate concentrations are decreased (low alkalinity) because of the mentioned equilibrium. In these conditions, green algae (noncyanobacterial biomass) are favoured over cyanobacteria (Shapiro, 1984; Reynolds, 2006). Conversely, if the alkalinity is high, CO 2 -limiting conditions, cyanobacteria are predominant because they possess an environmental adaptation known as a CO 2 concentrating mechanism (Price, 2011). Alkalinity results are expressed in terms of an equivalent amount of the calcium carbonate. In the final step of this analysis, once selected the six main variables by using an appropriate GA, a regression model based on support vector machines (SVR model) was carried out with success in order to determine the cyanotoxins concentration in the Trasona reservoir. Cross validation was the standard technique used here for finding a suitable set of hyperparameters of the SVR model. The data set is randomly divided into l disjoint subsets of equal size, and each subset is used once as a validation set, whereas the other l 1 subsets are put together to form a training set. In the simplest case, the average accuracy of the l validation sets is used as an estimator for the accuracy of the method. The combination of the hyperparameters with the best performance is chosen (Schölkopf and Smola, 2002; Shawe-Taylor and Cristianini, 2004; Steinwart and Christmann, 2008). In this way, 10-fold cross-validation was used. Table 5 shows the optimal hyperparameters of the fitted SVM model. Cyanotoxin (µg/l) Table 5 Optimal hyperparameters of the fitted SVM model. Parameter Value SVM-type n-regression SVM-kernel Radial basis function g v 0.26 Number of support vectors Observation number Real values Predicted values Fig. 7. Comparison between the three blooms of cyanobacteria observed and predicted by the model on the Trasona reservoir from 2006 to 2011.

9 P.J. García Nieto et al. / Environmental Research 122 (2013) Finally, this research work was able to estimate the presence of cyanobacteria blooms from 2006 to 2011 in agreement to the actual cyanobacteria blooms observed with great accurateness and success (see Fig. 7). 4. Conclusions To summarize, cyanotoxins are a very common and serious problem for recreational reservoirs throughout the world. The commonly used diagnostic techniques, like limnological studies, require high costs for its implementation both from the material and human points of view. In this sense, there is an absolute necessity in developing alternative diagnostic techniques such as the hybrid GA SVR approach used in this innovative study. The main findings of this analysis can be summarized as follows: In the first place, the main purpose of this research work was to build a cyanotoxin diagnostic model by using a hybrid GA SVR approach in Trasona reservoir with the site-specific experimental data and this goal was achieved in this study successfully. We have used the biological input variables (phytoplankton species expressed in biovolume and the chlorophyll concentration) in combination with the most important physical chemical parameters. Secondly, a correlation coefficient equal to 0.98 was obtained when the hybrid GA SVR technique was applied to the experimental data set. The predicted results for the model have demonstrated to be consistent with the history of observed actual cyanobacteria blooms from 2006 to Thirdly, one of the main findings of this study was to set the order of significance of the variables involved in the prediction of the cyanotoxins presence. Specifically, W. naegeliana and the synergetic effect of the variable M. aeruginosa multiplied by W. naegeliana, are the two most influential variables in the cyanotoxins production. The third variable is water temperature, the fourth is turbidity, the fifth is total phosphorus and finally the sixth is alkalinity. Finally, the authors of this research work have confidence that the results obtained will be useful to tackle new future studies in other similar reservoirs and lakes by applying the same methodology developed here in predicting the presence of cyanotoxins. Acknowledgments Authors wish to acknowledge the computational support provided by the Departments of Mathematics, Construction and Mining Exploitation at University of Oviedo as well as pollutant data in the Trasona Reservoir of Avilés (Northern Spain) supplied by the Cantabrian Basin Authority (Ministry of Agriculture, Food and Environment of Spain). 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