Internat. Rev. Hydrobiol.
95
2010
4–5
330–342
DOI: 10.1002/iroh.201011205 ,1
IBRAIM FANTIN-CRUZ* , OLAVO PEDROLLO1, CLÁUDIA COSTA BONECKER2, DAVID DA MOTTA-MARQUES1 and SIMONI LOVERDE-OLIVEIRA3 1
Instituto de Pesquisas Hidráulicas – Universidade Federal do Rio Grande do Sul, 91501-970, Porto Alegre, RS, Brasil; e-mail:
[email protected] 2 Núcleo de Pesquisas em Limnologia, Ictiologia e Aqüicultura – Universidade Estadual de Maringá, 87020-900, Maringá, PR, Brasil 3 Instituto de Ciências Exatas e Naturais – Universidade Federal de Mato Grosso, 78735-901, Rondonópolis, MT, Brasil
Research Paper Zooplankton Density Prediction in a Flood Lake (Pantanal – Brazil) Using Artificial Neural Networks key words: zooplankton dynamics, real time predictive, back-propagation, water quality, shallow lakes, floodplain
Abstract Ecologic relationships are usually non-linear and highly complex. For this reason, artificial neural networks (ANN) were selected to model zooplankton density groups in the Coqueiro lake in the northern Pantanal of Brazil. The input layer used 11 limnological variables with 13 neurons in the hidden layer; the output layer consisted of three zooplankton groups. Samples were collected monthly between April 2002 and May 2003, at three different points of the lake, two of which were used for training the ANNs and the other for validation. The ANN model performed well at predicting the density of zooplankton groups (coefficients of determination r2 were 0.88, 0.50 and 0.82 for rotifers, cladocerans and copepods, respectively). The comparison between models, and the ANN techniques used, demonstrated that zooplankton densities, observed one month previously, did not influence current densities, which were determined by limnological conditions in the lake. It was also shown that the processes that relate zooplankton to their environment remained stable during the study, while a model sensitivity analysis showed that the density dynamics of zooplankton groups in the Coqueiro lake were strongly influenced by availability of food (phytoplankton and detritus) and by variations in water-level. It can be concluded from the study that ANNs are a powerful tool both for predicting zooplankton densities and for understanding their relationships with the environment.
1. Introduction Lakes subject to regular flooding exhibit high functional complexity because of large seasonal changes that result from droughts and floods. This variability causes changes in habitat spatial structure, requiring the biota to adapt to changes in the physical and chemical environments (JUNK et al., 1989). Because of the spatial and temporal complexity of ecological processes occurring in such lakes, ecosystem analysis and prediction by means of linear empirical models is of limited
* Corresponding author
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value. Such models commonly reduce the data and simplify relationships between variables in a way that frequently leads to the loss of valuable information and to distortions of ecological truth, by failing to take into account the true complexity of non-linear relationships. From the biological viewpoint, patterns of species existence and abundance of species usually show non-linear complexities in their relations with the habitat spatial heterogeneity and interactions with other species. For these reasons, artificial neural networks (ANNs) can be an attractive alternative as a tool for analyzing and modeling ecological data, since they can take account of specific factors such as non-linearity, adaptation and generalization (SCHLEITER et al., 1999). Most applications of ANNs in ecology have been concerned with formulating predictive models, and with pattern recognition. In aquatic ecology, ANNs have been used extensively for predicting algal growth (RECKNAGEL et al., 1997; OLDEN, 2000; JEONG et al., 2001) and for studies of the relations between environmental variables and macro-invertebrates (HOANG et al., 2001), aquatic insects (WAGNER et al., 2000) and fish (MASTRORILLO et al., 1997; REYJOL et al., 2001; OLDEN and JACKSON, 2002a). In the case of zooplankton, which is the focus of the present study, the use of ANNs for predictive modeling is still at an early stage; an important application was reported by RECKNAGEL et al. (1998) who developed predictive models of zooplankton community dynamics in Lake Kasimigaura (Japan). More commonly, the zooplankton is used only as an input variable in ANNs models predicting algal abundance (RECKNAGEL et al., 1997; OLDEN, 2000; JEONG et al., 2001). However, construction of a model of zooplankton behaviour is particularly important because of their enormous ecological relevance. Zooplankton occupy an intermediary position in the food chain and play a part in many ecological processes, such as energy flow and nutrient cycling (PINTO-COELHO, 1998) and also act directly on “bottom-up” and “top-down” mechanisms, thereby promoting changes in the environmental trophic structure (CARPENTER et al., 1985). With these points in mind, the objectives of the present study were: 1) to determine how well ANNs predicts densities of zooplankton groups (Rotifera, Cladocera and Copepoda), using eleven environmental variables as predictors; 2) to determine the contribution of each environmental variable for prediction; 3) to explore whether knowledge of densities estimated at an earlier sampling date (30 days previously) gives better estimates of present densities; 4) to explore the stability of processes relating zooplankton to environmental variables. To achieve these objectives, a data-base was used from a periodically-flooded lake in the northern Pantanal of Brazil.
2. Material and Methods 2.1. Study Area The Coqueiro lake is located in the northern part of the Pantanal, near the town of Nossa Senhora do Livramento in the State of Mato Grosso, and lies in the Cuiabá watershed. It is linked to the River Paraguai, the main river in the Pantanal (Fig. 1). Altitude in the region varies between 100 and 130 m; the topography is low-lying and flat with a hydraulic gradient less than 15 cm/km. Regional climate is classified as Aw by Köppen: hot and humid, with summer rain and winter drought. Rainfall varies between 800 and 1400 mm/year, 80% of which occur between November and March. Mean annual temperature ranges between maxima of 29 to 32 °C and minima between 17 to 20 °C. The flood regime is unimodal and varies both spatially and temporally. The plain starts to become flooded when the rains begin in December, with most precipitation and most extensive flooding in February/March. Flooding causes seasonal changes to the morphometric characteristics of the lake, as described in Figure 1.
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Figure 1.
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Location of the Coqueiro lake showing the sampling points and lake morphometric characteristics during high and low water levels (From: LOVERDE-OLIVEIRA et al., 2007).
2.2 Choice of Input Variables Zooplankton are very sensitive to changes in environmental conditions (LEGENDRE and DEMMERS, 1984), and for this reason predictor variables were selected which integrated a set of factors related to zooplankton habitat in the Pantanal flood-plain and its contributing areas (ESPINDOLA et al., 1996; AZEVEDO and BONECKER, 2003; FANTIN-CRUZ et al., in press). In addition, the variables chosen also characterized each phase of the alternating stable states found in the Coqueiro lake, bearing in mind that it is one of a rather small number in tropical environments that are known to alternate annually between stable states (LOVERDE-OLIVEIRA et al., 2009). The authors cited showed that zooplankton are directly affected by water depth, chlorophyll a, dissolved oxygen and water temperature, since these variables describe the dilution effect from flooding, the availability of food and oxygen, as well as affecting metabolic rate and, consequently, reproduction of the zooplankton. Variables which indirectly affect zooplankton densities are water transparency and turbidity, which characterize the two phases of the alternating stable states; electrical conductivity, pH and alkalinity, which are measures of production and decomposition processes; and total nitrogen and total phosphorus, which characterize the system nutritional status.
2.3. Data Collection Water samples were collected monthly between April 2002 and May 2003 below the surface, at three different sampling sites within the lake (see Fig. 1). Samples were analyzed for the following
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parameters by means of portable equipment: water temperature and electrical conductivity (MC-126Mettler Toledo), pH (MP 120-Mettler Toledo) and dissolved oxygen (MO 128-Mettler Toledo). Total alkalinity was estimated by potentiometric titration (GOLTERMAN et al., 1978; MACKERETH et al., 1978). Water depth and clarity were measured using a Secchi disc with 0.3 m of diameter and turbidity was determined with a turbidimeter PHACH 2100. Total nitrogen and phosphorus were determined by spectrophotometry (GOLTERMAN et al., 1978; MACKERETH et al., 1978). Chlorophyll-a was extracted with ethanol and analyzed according to NUSCH and PALME (1975). To obtain the zooplankton samples, 100 liters of water (per sample) were filtered using a plankton net (68 μm) with suction pump, and preserved in paraformaldehyde 4%. In the laboratory, rotifers, cladocerans and copepods were determined in subsamples of 1 mL in a Sedgwick-Rafter chamber. A minimum of 250 individuals per sample were counted, where densities were low, the total sample volume was counted.
2.4. Artificial Neural Networks An artificial neural network (ANN) is a computational model analogous to the way in which biological neurons function. Research into ANNs has led to the development of various types of neural networks, the choice of which depends on the nature of the problem to be solved. The most widely-used ANNs for mapping variables from an input to an output space are multiple input-output, feed-forward neural networks, trained using a back-propagation algorithm. These consist of processing layers with each layer having several neurons, which are the nonlinear elements. Data are received by the neurons in the first layer (the input layer) and produce output signals which in turn stimulate neurons in the next layer, until the final layer (the output layer) is reached; the intermediate layers are termed hidden layers. The general ANN structure is shown in Figure 2, with the neurons, and their activation functions, represented by circles at the nodes, and with lines connecting nodes in different layers representing the flow of information. Each neuron computes an output, based on the weighted sum of all its inputs, according to its activation function, and each line has associated one weight, which is estimated during a training phase. The most widely-used training method for a multi-layer network is the method of error back-propagation (RUMELHART et al., 1986). The weights of each neuron are updated by using what is termed the “delta rule”, separately for each neuron: wk + 1 = wk – η∇ (E(wk)) , where η is the magnitude of the learning step, taken with a negative sign; w are the neuron synaptic weights, and E is the quadratic error of the network output. The inputs to each neuron are the outputs from the preceding layer, and its errors, when the neuron is not an output neuron, are found from the product of the weights in the following layer with the derivative of the activation function, and with the errors of that layer. This algorithm may be used either in batch mode, or in sequential mode. In batch mode, all input/ target training pairs are supplied to the algorithm, resulting in a set of trained weights for that cycle. This is repeated many times, until a satisfactory improvement is achieved. In sequential mode, each training pair is submitted sequentially, one at a time, resulting in weights that are improved continuously. Batch mode is the quickest and easiest to program, and is therefore the most widely used. However, the
Figure 2: Example of neural network architecture.
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sequential mode is useful in circumstances where the objective is to control a system, or to reproduce time-varying dynamical processes. Typically, for an ANN to be trained, both a training and a test set of data are required, with input/ output pairs taken from real data. The former is used to train the network, and the latter, here termed the validation sample, is used to assess the performance of the network after training. A training set must be sufficiently representative of conditions likely to be encountered during subsequent use of the model. In sequential mode, training continues during the application phase, but a preliminary training is necessary, which may be in batch mode. When training a neural network, it is possible for over-fit to occur. If the model has more nodes or layers than is necessary for the particular application, weights are then influenced by random variations in input and output variables, and unsatisfactory results are found when the fitted network is applied to new data not used for training. Initial values for the synaptic weights in the neural network were chosen at random, so that distinct paths were always traced out on the errors surface at each new initiation, thus ending up at different local minima. It is desirable that training be repeated many times, with the best results being selected. This considerably reduces the probability that the search ends up at a local minimum a long way from the global minimum. In addition, since the best fit is identified from the test-sample responses, the possibility of overfitting is reduced but, if overfitting does occur, the degree of overfit is smaller.
2.5. Models and Their Application The basic architecture of the ANN used here was a network with a single intermediate (hidden) layer of nodes with sigmoid bipolar activation function. A linear activation function was used for the output layer (Fig. 3). Two ANN models were explored for the purpose of predicting densities of zooplankton groups. The first model, denoted by RNL, used only the 11 limnological variables for predicting the three groups (rotifers, cladocerans and copepods) as shown in Figure 4a. After training, two alternative forms of this model were explored: RNL · 1 with fixed synaptic weights (Wi,1 = Wi,j = Wi,n), and RNL · 2 in sequential mode, with successive adaptation of synaptic weights to new validation sequences (Wi,1 ≠ Wi,j ≠ Wi,n).
Figure 3. Architecture of the ANN used for predicting zooplankton groups density in the Coqueiro lake (Northern Pantanal-Brazil).
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Figure 4. a) ANN model with only limnological variables (RNL); b) ANN model with both limnological variables and earlier state variables (RNLS), used for predicting zooplankton group densities in the Coqueiro lake, northern Pantanal, Brazil.
The second model, RNLS, used not only the 11 limnological variables as input, but also variables derived from earlier zooplankton group densities. These variables were obtained from earlier observations of the system and were submitted to the ANN model in chronological sequence, as in Figure 4b. As with the first model, two alternatives of RNLS were explored after training it: RNLS · 1 in which synaptic weights were fixed (Wi,1 = Wi,j = Wi,n), and RNLS · 2 in sequential mode, with successive adaptation of synaptic weights to new validation sequences (Wi,1 ≠ Wi,j ≠ Wi,n). The comparison between the models RNL and RNLS gives a measure of how far the densities of zooplankton groups observed in one sampling period influence the densities observed in the following sampling period, whilst the comparison between the two alternatives of each model (alternative 1, fixed mode, and alternative 2, adaptive mode) enables any changes to be detected in the processes that govern the relationships between zooplankton and their environment, and whether changes in processes lead to different responses for the same values of input variables. In addition, better performance in the adaptive mode could indicate whether there is an initial loss of generality from over-fitting in batch mode, which is recovered when the model is used in adaptive mode. To evaluate the relative usefulness of each limnological input variable for predicting densities of zooplankton groups, a sensitivity analysis of the ANN model was used based on the algorithm of GARSON (1991). This method partitions the synaptic weights between the intermediate and output layers into components associated with each entry node so that the resulting weight associated with each input reflects its importance. Further details, with an example of application, are given in GOH (1995). The sensitivity analysis was applied to the model judged most efficient for the purpose of predicting zooplankton group densities; to evaluate the predictive ability of each model, a coefficient of determination (r2) was calculated together with the mean squared error (MSE). The models were trained with information from samples collected at points E1 and E3 (28 samples); samples from collection point E2 were used for validation (14 samples). No specific criterion was used to identify the training and validation samples, since it was assumed at the outset that processes linking the environment to zooplanktonic groups are spatially constant, as demonstrated by LOVERDEOLIVEIRA et al. (2009) in studies of the same lake. The required total number of neurons at the hidden layer was determined by comparing performance of models with from 2 to 25 neurons in this layer. The best performance was obtained with 13 neurons and the maximum number of iterations was 50 000. As a means of dealing with the problem of random variability in initial conditions, each model had a preliminary training each with 20 initializations, with the best result determined from the validation series. Input and output variables were scaled to the range –1 to 1. Although neural networks can deal
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with data differing by orders of magnitude, scaling results in more reliant predictions (OLDEN and JACKSON, 2002b). Also, the output variables were converted to logarithms so that small values could be more easily visualized.
3. Results 3.1. Limnological Description of the Coqueiro Lake Since it becomes flooded, the Coqueiro lake shows two well-defined hydrological periods determined by the existence or otherwise of a connection between the lake and the main river channel. In the season when water levels are high, the lake is linked to the River Cuiabá (as in April and May 2002; and from January to May 2003). This occurs when the River Cuiabá reaches the 3.00 meter-level (Fig. 5a). When water levels are low, the lake becomes isolated (as from June to December 2002; Fig. 5a). Environmental variables monitored on this study varied according to the depth of the lake, except for water temperature, which remained stable (Fig. 5b). Water was found to be slightly acid, with pH values closer to neutral during the high water season (Fig. 5c). In the
Figure 5. Variation in time of mean limnological conditions in the Coqueiro lake, sampled at points E1, E2 and E3 between March 2002 and May 2003.
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Figure 6. Variation in time of mean relative abundance in the zooplankton community of the Coqueiro lake, sampled at points E1, E2 and E3 between March 2002 and May 2003.
low water season, dissolved oxygen, chlorophyll a, phosphorus and total nitrogen concentrations are generally high, Secchi depth is reduced and turbidity is high (Fig. 5d, e and f). In the high-water season, on the other hand, water is more clear and electric conductance and alkalinity are higher; nutrient concentrations and turbidity are lower (Fig. 5b, c, d and f). Zooplankton structure also showed temporal changes (Fig. 6). On average, rotifers were the major component in all the periods studied, and cladocerans and copepods were more plentiful during the high-water season (Fig. 6). 3.2. Evaluation of the ANN Predictive Model of Zooplankton Dynamics The RNL model, using only limnological input variables, performed better than the model RNLS which included both limnological variables and earlier estimates of state variables, independently of zooplankton group and fitting mode (Table 1). Thus it is concluded that density of zooplankton groups observed one month previously did not influence the ability of the ANN model to predict densities in the current month. In addition, the two fitting modes (1, with fixed synaptic weights; and 2, with adaptive synaptic weights) showed no difference in predictions made for the three groups, in either of the two models. An exception was the model RNL for rotifers, where the adaptive mode performed slightly better, as shown by a larger coefficient of determination (Table 1). Similarly, relationships found between zooplankton groups and limnological variables during the training stage were maintained during validation, since the changes that occurred in the synaptic weights did not appreciably affect the results. To predict the dynamics of zooplankton groups, the ANN model with limnological variables and fixed synaptic weights (RNL · 1) was therefore selected because of its better predictive performance (Table 1), and because it was easier to use, and required less time to train it, than the model RNL · 2. In terms of the coefficient of variation r2, the model RNL · 1 was better at predicting rotifers and copepods than cladocerans (Table 1). However the model over-estimated the density of rotifers, mainly in the prediction of local minima, whereas for cladocerans the tendency was to under-estimate densities, but with good prediction of local
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Table 1. Performance of neural network models used to predict densities of zooplankton groups in the Coqueiro lake (r2, coefficient of determination; MSE, mean squared error). Legend: RNL = ANN with only limnological variables as input; RNLS = ANN with both limnological variables and estimates of earlier state variables; 1 = fixed synaptic weights; 2 = adaptive synaptic weights. Models
Training Rotifers r
RNL 1 RNL 2 RNLS 1 RNLS 2
Figure 7.
2
0.90 0.90 0.87 0.88
Cladocerans 2
MSE
r
2.18 2.02 1.25 1.21
0.54 0.54 0.35 0.35
Validation Copepods 2
MSE
r
3.27 3.16 5.61 5.59
0.83 0.83 0.79 0.79
Rotifers 2
MSE
r
0.46 0.47 0.81 0.80
0.88 0.89 0.86 0.86
Cladocerans 2
Copepods
MSE
r
MSE
r2
MSE
2.30 2.13 1.33 1.31
0.50 0.50 0.34 0.34
3.82 3.74 5.69 5.69
0.82 0.82 0.78 0.78
0.50 0.51 0.86 0.86
Dynamics of densities of zooplankton groups in the Coqueiro lake, observed at site E2, and as predicted by ANNs between March 2002 and May 2003.
Figure 8. Relative importance (as percentage contribution to the total) of limnological variables for predicting density of zooplankton groups in the Coqueiro lake in the northern Pantanal, Brazil. Legend: Chl = chlorophyll a; Turb = turbidity; Lev = water level; Tran = water transparency; Alk = alkalinity; Con = electrical conductivity; Nit = total nitrogen; Pho = total phosphorus; OD = dissolved oxygen; Tem = water temperature
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minima (Fig. 7a and b). Predictions of copepod densities were best overall, with good predictions throughout the series (Fig. 7c). Although the predictions at a point were subject to error, the model was capable of predicting the seasonal pattern in densities of zooplanktonic groups, with high densities in periods of low water and low densities in periods of high water (Fig. 7). The sensitivity analysis of the model RNL · 1 showed that the relative importance of network input variables varied from 1.81 to 19.18% (Fig. 8). This table shows that the most important driving variables of zooplankton group densities were chlorophyll a, turbidity and water depth.
4. Discussion Periodic flooding of the Pantanal is a consequence of overflow of the main rivers in the watershed, causing the formation of shallow lakes where depressions become filled; the lakes are connected, either directly or indirectly, with each other and with the main channel (FANTIN-CRUZ et al., 2008a). In the case of the Coqueiro lake, rising water level in the River Cuiabá is the main factor determining the connection between the lake and the river channel, together with the change in lake water from turbid to clear. This connection arises when the river level reaches 3.0 meters (Gauge site 66340000), thus determining the high and low water levels in this system. The relative abundance of zooplankton communities in the Coqueiro lake clearly reacts to changes in its habitat, such as alterations in limnological characteristics caused by this hydrological connection. During the high-water season (the period in which the lake is connected to the river channel) species with larger body-size prevail (cladocerans and copepods) whilst in the period when the lake remains isolated smaller organisms are more in evidence (rotifers). Studies of Pantanal lakes by ESPÍNDOLA et al. (1996) and FANTIN-CRUZ et al., (in press), also showed greater proportions of micro-crustaceans in seasons of high water-levels, when compared with low water-levels. The hypothesis suggested was that there would be a larger predation pressure on bigger organisms during the low water levels season due to the reduced habitat area, since the Coqueiro lake doubles its volume during high water season. In this region, predation by fishes has been reported as an important control on microcrustacean density (FANTIN-CRUZ et al., 2008b; PAIVA, 2010). From the comparison of the predictive capacity of the models RNL (using only limnological variables) and RNLS (using both limnological variables and estimates of earlier state variables), it was concluded that zooplankton density in one month did not influence density in the following month. That is, low zooplankton density in a given month is of little importance for prediction in the month that follows, because it is the limnological conditions during that month which will determine the densities of zooplankton groups. This is because of the short life-cycle of the organisms involved, whose populations and abundance are determined by environmental changes in the lake’s present state (LEGENDRE and DEMMERS, 1984). Although the use of the adaptive procedure (fitting synaptic weights at each time-step) gave no improvement in network performance, it allowed the possibility to be explored of changes in system function, together with the possible loss of generality by over-fitting. ANN models fitted in adaptive mode are likely to be especially useful where the processes involved are continually changing, since continual up-dating of synaptic weights should then lead to improved predictions. In the case of over-fitting, it is to be expected that the adaptive procedure will correct for the initial loss of generality over the course of application. It is therefore believed that for the period sampled, the functioning of the system stayed stable and that problems caused by over-fitting were avoided. This is supported by the results, since the goodness-of-fit statistics are very similar for both training and validation samples
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(Table 1). If there had been over-fitting, the lack of fit in the validation period would be much more evident than in the training period. Overall, the model gave good predictions of the seasonality in zooplankton group density (as shown by the acceptable values of coefficients of determination r2), showing that it adequately predicts relationships between input and output variables. However the errors in the estimated densities can be considered high for rotifers and cladocerans, when compared with those for copepods. These differences, as seen in the predictive capacity of the RNL model, show that the zooplanktonic groups respond differently to the predictor variables, which suggests that other variables not included in the model (such as predation by fishes) may be influencing group densities. Even so, the comparison of coefficients of determination found in the present work with those reported by FANTIN-CRUZ et al. (in press) for the same data-set suggests that the ANN model showed a 22% improvement over a linear model, thereby justifying its use. Having demonstrated that the ANN model was useful for predicting densities of zooplankton groups in a northern Pantanal lake subject to seasonal flooding, the sensitivity analysis provided information about relationships between zooplankton and environmental variables. This showed that chlorophyll-a has greatest effect on zooplankton density, so that food availability was the main regulating factor controlling community development. Despite the demonstrated importance of phytoplankton as a food source, zooplankton appear not to exert a negative effect on this community (LOVERDE-OLIVEIRA et al. 2009), suggesting that it is nutrients that are responsible for the control of phytoplankton, and hence indirect control of zooplankton. After chlorophyll-a, the sensitivity analysis showed that turbidity was the next most important environmental variable. It is believed that this is also related to food availability, although it would be most important for rotifers, the must abundant group. Many herbivorous rotifers, together with other genera classified as microphages by POURRIOT (1977), are closely related to the presence of detritus and its associated bacteria (OOMS-WILMS, 1997). This would explain the higher densities of rotifer populations found in periods of low water when the lake was isolated, and turbidity was greater. As shown by LOVERDE-OLIVEIRA et al. (2009), the alternation between clear and turbid states within the same seasonal cycle of the Coqueiro lake modifies habitat structure and, in consequence, the relationships between it and the different groups of aquatic organisms. According to theory, the ecology of a seasonally-flooded lake is determined mainly by its hydrological regime (JUNK et al., 1989). However, the sensitivity analysis showed that variation in water-level was only the third most important in determining density of zooplankton organisms. For zooplankton, the increase in water-level that result from flooding dilutes their densities and causes losses by transport to the flood-plain. Taking a systems view, flooding is a recognized macro-factor which modifies system functioning as a whole, and its effects on other variables must therefore be taken into account. Studies undertaken in the Pantanal suggests that variation in water-level is the main factor controlling zooplankton community structure on the time scale, with food availability and predation by fishes on the spatial scale (ESPINDOLA et al., 1996; FANTIN-CRUZ et al., 2008b; LOVERDE-OLIVEIRA et al., 2009; PAIVA, 2010; FANTIN-CRUZ et al., in press). In general, densities of zooplankton groups also changed with flooding season. Flood plain studies have identified the dilution effect of flooding in seasons of high water levels, and food availability in seasons of low water levels, for the reduction and increase, respectively, of zooplankton densities during flood seasons (ESPINDOLA et al., 1996; AOYAGUI and BONECKER, 2004; BONECKER et al., 2009; FANTIN-CRUZ et al., in press). The use of ANNs in ecology is restricted to cases where data are plentiful and where there is sufficient data to set aside for model validation (AGUILAR IBARRA et al., 2003). Despite this recommendation, even with a small data series available for network training (28 periods), the predictive ability of the models tested here may be considered satisfactory for predicting
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densities of zooplankton groups in independent samples describing current lake limnological status, suggesting further possible applications for ANNs.
5. Conclusions ANN modeling was shown to be appropriate and useful, both for prediction and for elucidating the seasonal dynamics of zooplankton groups, even with relatively short series of data. Because of their flexible architecture, the complexity and non-linearity in the functioning of a seasonally-flooded lake could be explored using ANN models, and it can be concluded that densities estimated in one sampling period did not significantly influence densities one month later, which were almost entirely a consequence of the limnological conditions in the intervening period. It can also be concluded that processes linking zooplankton to their environment remained stable over the period of analysis, since continual up-dating of synaptic weights in the ANN model gave no improvement in model performance. The sensitivity analysis demonstrated the potential of ANN models for testing hypotheses and for elucidating causal relationships between environmental variables and zooplankton dynamics. From these analyses, it can be concluded that the dynamics of zooplankton group densities in the Coqueiro lake in the northern Pantanal of Brazil were mainly determined by food availability (of phytoplankton and detritus) and by variation in water-level.
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