Ecological Applications, 21(4), 2011, pp. 1352–1364 Ó 2011 by the Ecological Society of America
Selecting statistical models and variable combinations for optimal classification using otolith microchemistry LE´NY MERCIER,1,6 AUDREY M. DARNAUDE,1 OLIVIER BRUGUIER,2 RITA P. VASCONCELOS,3 HENRIQUE N. CABRAL,3 MARIA J. COSTA,3 MONICA LARA,4 DAVID L. JONES,5 AND DAVID MOUILLOT1 1
Ecosyste`mes Lagunaires, UMR 5119, CNRS, IFREMER, IRD, Universite´ Montpellier 2, CC93, Place Euge`ne Bataillon, 34095 Montpellier Cedex 5, France 2 Ge´osciences Montpellier, UMR 5243, Universite´ Montpellier 2, CC 60, Place Euge`ne Bataillon, 34095 Montpellier Cedex 5, France 3 Centro de Oceanografia, Faculdade de Ciˆencias da Universidade de Lisboa, Campo Grande, 1749-016 Lisbon, Portugal 4 Department of Natural Science, St. Petersburg College, Clearwater Campus, Clearwater, Florida 33759 USA 5 College of Marine Science, University of South Florida, St. Petersburg, Florida 33701 USA
Abstract. Reliable assessment of fish origin is of critical importance for exploited species, since nursery areas must be identified and protected to maintain recruitment to the adult stock. During the last two decades, otolith chemical signatures (or ‘‘fingerprints’’) have been increasingly used as tools to discriminate between coastal habitats. However, correct assessment of fish origin from otolith fingerprints depends on various environmental and methodological parameters, including the choice of the statistical method used to assign fish to unknown origin. Among the available methods of classification, Linear Discriminant Analysis (LDA) is the most frequently used, although it assumes data are multivariate normal with homogeneous within-group dispersions, conditions that are not always met by otolith chemical data, even after transformation. Other less constrained classification methods are available, but there is a current lack of comparative analysis in applications to otolith microchemistry. Here, we assessed stock identification accuracy for four classification methods (LDA, Quadratic Discriminant Analysis [QDA], Random Forests [RF], and Artificial Neural Networks [ANN]), through the use of three distinct data sets. In each case, all possible combinations of chemical elements were examined to identify the elements to be used for optimal accuracy in fish assignment to their actual origin. Our study shows that accuracy differs according to the model and the number of elements considered. Best combinations did not include all the elements measured, and it was not possible to define an ad hoc multielement combination for accurate site discrimination. Among all the models tested, RF and ANN performed best, especially for complex data sets (e.g., with numerous fish species and/or chemical elements involved). However, for these data, RF was less time-consuming and more interpretable than ANN, and far more efficient and less demanding in terms of assumptions than LDA or QDA. Therefore, when LDA and QDA assumptions cannot be reached, the use of machine learning methods, such as RF, should be preferred for stock assessment and nursery identification based on otolith microchemistry, especially when data set include multispecific otolith signatures and/or many chemical elements. Key words: Artificial Neural Networks; classification method; fish origin; habitat discrimination; induced coupled plasma-mass spectrometer (SB ICP-MS); Linear Discriminant Analysis; nursery habitats; otolith microchemistry; Quadratic Discriminant Analysis; Random Forest; trace elements.
INTRODUCTION Discrimination of natal sources, juvenile nursery grounds, and migration paths is a key issue in fishery management and population ecology. Potential fish habitats are highly diverse, especially in coastal zones (lagoons, estuaries, rocky reefs, sandy beaches, and so on) and are of primary interest for conservation and resource sustainability issues. As anthropogenic pressure on the littoral zone intensifies, coastal ecosystems Manuscript received 14 October 2009; revised 11 August 2010; accepted 19 August; final version received 28 September 2010. Corresponding Editor: J. W. White. 6 E-mail:
[email protected]
experience increasing pollution, eutrophication, and habitat degradation (e.g., Nixon 1995, Kemp et al. 2005), resulting in habitat loss and population fragmentation (Levin et al. 2001). In this context, understanding and measuring connectivity between coastal habitats available for young and adult fish is essential to define marine protected areas, quotas for recreational and commercial fisheries, and critical nursery habitats (Gillanders et al. 2003). Several recent technological advances allow the assessment of the movement of marine fish in their natural environment. Among them, otolith microchemistry has emerged as an efficient tool to identify migration paths and fish nursery habitats (Campana et
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al. 1994). Otoliths (fish ear stones) grow throughout the lifetime of teleost fish, and incorporate the environmental history of individuals through their structure and chemistry, acting as natural tags (Campana 1999). Unlike bones, the material incorporated into otoliths is not reabsorbed and growth is continuous (Panfili et al. 2002). Calcium carbonate is laid down on a protein matrix in the otolith, while incorporation of other elements is regulated by various processes. Elements under weak internal controls (trace elements and some minor ones, including Sr, Mn and Ba) are the most valuable in assessing fish location because they vary according to both ambient and physiological conditions (Panfili et al. 2002). Until recently, only a few of these elements (Sr, Mg, Mn, and Ba) were routinely measured in otoliths. However, with technological improvements, otolith chemical data sets have expanded toward more complete sets of elements, including trace metals and rare earth elements (Arslan and Paulson 2003). New approaches consider otolith elemental compositions to be fingerprints for the water masses inhabited by fish (Dorval et al. 2007), thereby allowing retrospective identification of their nursery origin (Thorrold et al. 1998b), stocks (Campana et al. 1999), and migration patterns (Babaluk et al. 1997, Fodrie and Herzka 2008). Successful assignment of fish to their habitats runs up against methodological and theoretical issues. Otolith microchemistry depends on the way elements are incorporated in the otoliths (Walther and Thorrold 2006). Otolith fingerprints must correlate with water chemistry (Bath et al. 2000). But one of the major issues for the successful assignment of fish using fingerprint data sets, and one that is often overlooked, is the choice of the statistical method for habitat discrimination and the conditions for its application. Since 1990, several classification methods have been applied to otolith chemical data sets (Edmonds et al. 1991, Gillanders and Kingsford 2000), but very few studies have attempted to compare their efficiencies (Thorrold et al. 1998a) and no consensus has emerged yet on the most appropriate method to discriminate water masses. Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) are still predominantly used, although they fail to model the complex and nonlinear relationships observed in such large multivariate data sets (Tan et al. 2006). When using otolith fingerprints to discriminate water masses, data transformations are needed to satisfy the requirements of the method, but are not always successful and may lead to spurious requirements (Wilson 2007), and those requirements may not be fulfilled after such transformations. Indeed, a brief review of randomly chosen papers among the vast literature dealing with otolith fingerprints analyzed with parametric methods (56 studies, from Kalish 1991 to Fontes et al. 2009) indicated that normality is a major breakpoint: 35% of the papers did not clearly address this issue, only 5% of the papers had
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normality of their entire data set (e.g., Chittaro et al. 2006), and the remaining studies transformed their data. After transformation, 30% of the papers acknowledged non-normality of the data (e.g., Gillanders et al. 2001, de Vries et al. 2005, Elsdon and Gillanders 2005). Yet very few authors have tried to use alternative techniques (Gutierrez-Estrada et al. 2008), although machine learning classification methods, like Random Forest (RF) or Artificial Neural Networks (ANN) might greatly improve pattern recognition, as they already have in medical and other ecological studies (Perdiguero-Alonso et al. 2008, Care et al. 2009, Oppel et al. 2009). Comparison between classical and machine learning-oriented techniques would then be a great help for practitioners working with otolith fingerprints. Another neglected issue is the optimum number and the nature of the chemical elements to be included in the analysis. Among the numerous studies using otolith fingerprints as a tool for discrimination of fish origin (e.g., Thresher 1999, Gillanders et al. 2003, Brazner et al. 2004, Fodrie and Herzka 2008), very few reported the link between discrimination accuracy and the list of chemical elements analyzed. Some of them focused on a single element, examining how its signature explained a part of the accuracy power (Hamer et al. 2006, Lamson et al. 2006), and many questions are left unanswered. For example, are all chemical elements useful to assign otolith fingerprints to water masses? Does a combination with many elements perform better than combinations with few elements? The answers to these questions are far from trivial, since the measurement of elements with concentrations near detection limits may have more noise than signal in the discrimination. In this context, we decided to use three distinct otolith data sets, gathered from different fish species and coastal habitats, to evaluate for the first time the influence of (1) the classification method used for discrimination and (2) the list of chemical elements measured on the accuracy of fish origin identification using otolith fingerprints. This should provide valuable methodological advances and allow the optimization of results of numerous future otolith microchemistry and connectivity studies. MATERIALS
AND
METHODS
The otolith fingerprint data sets used were derived from the otolith chemical signatures of various fish species collected in the main fish nursery sites or habitats of three separate coastal areas (Fig. 1). French lagoon and U.S. coastal nurseries data sets are based on monospecific otolith signatures, but the Portuguese estuaries data set includes multi-specific signatures, which allows the investigation of the influence of the number of fish species included in the analysis for habitat discrimination. Data sets French lagoons.—Otolith fingerprints for this data set were obtained from 164 juveniles of Gilthead seabream
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FIG. 1. Location of the sampling areas for fish otoliths in (A) French lagoons, (B) Portuguese estuaries, and (C) U.S. coastal nurseries. In each case, sampling sites retained for this study are indicated in gray. The figure is adapted from Vasconcelos et al. (2007) and Lara et al. (2008).
(Sparus aurata L. 1758) caught in six coastal lagoons spread along the French coast of the Gulf of Lions (northwest Mediterranean Sea; Fig. 1A). Biological features of S. aurata, sampling design, otoliths preparation, and details of the solution-based induced coupled
plasma-mass spectrometer (SB ICP-MS) settings can be found in Appendix A. Otolith concentrations were successfully measured for 18 elements plus Ca. Elements with aberrant measures (negative measures, calibration errors) were removed,
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and concentrations below limits of detection (LOD) were set to 0. Elements for which .25% of the measures were below LOD were not included in the study (for technical considerations and biases in LOD treatment, see Panfili et al. 2002). Therefore, the final data set for this area corresponded to the otolith composition (11 chemical elements) for 164 juveniles caught in six distinct coastal lagoons. Portuguese estuaries.—This data set was derived from the otolith signatures obtained by Vasconcelos et al. (2007) using 210 juveniles from five species (Solea solea, Solea senegalensis, Platichthys flesus, Diplodus vulgaris, and Dicentrarchus labrax) caught in eight estuaries (Douro, Ria de Aveiro, Mondego, Tejo, Sado, Mira, Ria Formosa, and Guadiana) recognized as major fish nurseries (sensu lato) along the coast of Portugal (northeast Atlantic Ocean; Fig. 1B).The original study looked for a chemical signature allowing the identification of nursery origin for each species using LDA with jacknife cross-validation. All details regarding fish sampling, otolith preparation, and analyses using SBICPMS can be found in Vasconcelos et al. (2007). In the present study we used the data set obtained for the five species as a whole to test the ability of the different classification methods to decipher fish origin based on multi-specific otolith fingerprints. As in the original study, two elements (Cd and Ni ) were removed before analysis because the precision in measurement was poor. Because QDA application to this data set required the number of individuals in each location to be greater than the number of chemical elements used for habitat discrimination, only five out of the eight locations originally sampled were retained. Therefore, the final data set for this area corresponds to the otolith compositions (10 chemical elements) obtained for 154 juveniles of five species caught in five distinct estuaries. U.S. coastal nurseries.—This data set was derived from the otolith fingerprints data obtained by Lara et al. (2008) using 432 juvenile specimens of grey snapper (Lutjanus griseus) caught within a variety of coastal nursery habitats (mangroves and seagrass meadows around mangrove islands or in embayments) from southeastern Florida (USA, Gulf of Mexico, Fig. 1C). In the original study, sampling areas were grouped into six zones (Biscayne Bay, East Florida Bay, West Florida Bay, Florida Keys, Dry Tortugas, and Ten Thousand Islands). The classification of sites was ad hoc because there was no water chemistry available to guide site grouping. QDA with leave-one-out cross-validation was used to differentiate Florida Bay from the other zones. All details regarding fish sampling and otolith preparation and analysis using SB-ICPMS can be found in Lara et al. (2008). To match the levels of detection criterion used with the two other data sets, 18 chemical elements were retained out of the 32 measured in Lara et al. (2008). Because QDA application requires the number of individuals in each location to be greater than the
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number of chemical elements used for habitat discrimination, the Dry Tortugas group was not included in the present study. Therefore, the final data set for this area corresponds to the otolith compositions (18 chemical elements) obtained for 419 juveniles caught in five distinct coastal nurseries. Classification methods In this study, we compared accuracy in habitat discrimination in two basic statistical methods (Linear Discriminant Analysis [LDA] and the Quadratic Discriminant Analysis [QDA]) and two machine learning methods (Random Forest [RF] and Artificial Neural Networks [ANN]). They were chosen for their easy implementation and parametrization. LDA, also called Linear Discriminant Function Analysis (LDFA), its derivatives, such as Canonical Discriminant Analysis (CDA), and QDA are currently the most commonly used methods for classifying otolith fingerprints (e.g., Gillanders and Kingsford 2000, Brown 2006, Hobbs et al. 2007).Their purpose is to predict the membership of individuals to predefined classes (here, nursery habitats) by building discriminant axes that are linear or quadratic combinations of chemical elements maximizing the standard deviation between groups while minimizing it within groups (Fisher 1936). Multivariate normality and homoscedasticity of the data are assumed for this method. When the homoscedasticity is removed, the discriminant function becomes quadratic, resulting in QDA (Seber 1984). These requirements have to be achieved before using LDA and QDA, and data transformations must often be carried out to reach or to come close to these requirements. Potential drawbacks to these methods include weak performance when groups are strongly nested and a tendency towards overfitting (Dixon and Brereton 2009). Random Forest (RF) has not previously been used for discrimination among fish habitats based on otolith fingerprints. However, this method is used in medical and ecological studies (Biau et al. 2008, Care et al. 2009, Oppel et al. 2009) and was successfully applied to discriminate fish populations using parasites as biological tags (Perdiguero-Alonso et al. 2008). While other machine learning methods are available, we chose RF because of its easy usage and its ability not to act as a black box. Classification with RF is based on classification trees (Breiman 2001). A classification tree follows rules to recursively split the data set into binary groups. With RF, many trees are built. Each tree is built from a random subset of the data using bootstrap resampling with replacement of individuals (i.e., the ‘‘in-bag’’ individuals). The individuals not used for building a specific tree (i.e., the ‘‘out of bag’’ individuals) are then used to measure the prediction ability of that tree. For a given tree, at each node, a random subset of predictors are searched to find one that maximizes the within-
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group homogeneity when used as a criterion for node splitting. Each new group is then split again in a recursive manner. In the case of RF, the recursive process stops when further splitting results in no additional gain in homogeneity. Thus, two levels of randomization occur in the RF process: one in the initial selection of individuals (fish signatures) for the building of each tree, and one in the selection of the variables (chemical elements) used for group splitting at each node. RF builds a collection of classification trees (500 in our case, i.e., a forest) from which a consensus is established: ‘‘In-bag’’ individuals are run down each tree to obtain a single prediction of origin. Predictions across trees comprising a forest are combined according to ‘‘majority rules’’ to obtain a final prediction of the forest. RF requires no distributional assumption of the data set, and there is no overfitting (Breiman 2001). One possible drawback to the method of RF is that it acts as a black box: Multiple trees providing potentially different predictions are used to construct a forest, but final predictions of the forest are determined by vote; there is no ‘‘final’’ tree to examine or visualize. Nevertheless, it is possible to obtain the contribution of each predictor within each ‘‘successful’’ vote and assess its contribution toward classification using the Gini index (Cutler et al. 2007). Here, we chose not to use the internal prediction error generated using the ‘‘out-ofbag’’ individuals, but instead relied on a cross-validation procedure to have a common way to evaluate prediction accuracy between all the methods. Artificial Neural Networks (ANN) are commonly used in classification problems (Tan et al. 2006, Gutierrez-Estrada et al. 2008), but have rarely been used for discrimination using otolith fingerprints (Thorrold et al. 1998a). This method is based on machine learning algorithms inspired by neuronal learning processes. Input neurons project to hidden layers of neurons that are themselves connected to output neurons. Neurons are seen as simple operators where inputs are transformed into an output using a simple function (linear, logarithmic, et cetera). Connections between neurons are labile, and the training phase is an iterative process where connections are sought to maximize matching to observed outputs. This trained neural network is then used for prediction of output variables from input data set (Ripley 1993). Feed-forward neural networks with a single hidden layer were used. To assess the optimum number of hidden neurons, neural networks were trained using the best combinations of chemical elements obtained for each precedent technique (i.e., LDA, QDA, and RF). For each combination, 30 networks were built with 1 to 30 hidden neurons. Efficiency and calculation time varied greatly according to number of neurons and number of elements included in the analysis. The best compromise between minimizing computation time and maximizing efficiency was found using 25 neurons, and
this number was used for all subsequent analyses with ANN. Classification accuracy All data were expressed as molar ratios to Ca. For each chemical element, mean and standard deviation were calculated. For practical convenience, all ratios were standardized before analysis to give the same weight to all elements. This standardization changes the contribution of elements to the discrimination functions obtained from LDA and QDA, but not the prediction of the methods for a given combination of elements, which is the only aspect retained by our methodology. In order to identify the best classification method(s) and the optimal list(s) of elements for the identification of fish origin in the three examples studied, prediction accuracy (i.e., the percentage of correct assignment of the fish to their actual habitat) was assessed for each statistical method and each possible combinations of 1 to N chemical elements. Accuracy does not take into account all of the aspects of discrimination. However, it is very intuitive, and proved to give, for our examples, the same results for method comparisons than more complex indexes, like the True Skill Statistics (Allouche et al. 2006; Appendix B). For each data set, the total number of combinations is given by N X N k¼1
k
¼ 2N 1
with k being the number of elements included in the combination, and N the total number of elements measured (11, 10, and 18 in the French lagoons, the Portuguese estuaries, and the U.S. coastal nurseries, respectively). As a result, 262 143 different combinations of elements were tested for the U.S. coastal areas data set, against 2047 and 1023 only for the French lagoons and the Portuguese estuaries data sets, respectively. For each combination, 75% of the fish individuals (training data set) were randomly chosen to train the classifiers, and the 25% remaining (prediction data set) were used to measure the quality of prediction. This method of cross-validation was chosen to avoid circular reasoning when the same data are used to construct and evaluate the discrimination function (Kohavi 1995). To avoid sampling effect, the training subset was resampled 15 times. For each method, we thus measured prediction accuracies over 15 replicates, calculated a mean accuracy for each combination, and provided the corresponding confidence interval at 95%. We then identified best and worst combinations of elements for each method, data set, and combination size (number of elements), with the exception of ANN for the U.S. coastal nurseries data set, since calculation time would have been prohibitive. Although time consuming, this exhaustive procedure presents the advantage of being equally applicable to all methods and to compare prediction efficiency between all elements combinations, which is not the case of
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FIG. 2. Accuracy in assigning fish origins by otolith microchemistry obtained according to element combination size (combinations with 1, 2, ..., N elements) for Random Forest (RF; in red), Artificial Neural Networks (ANN; in orange), Linear Discriminant Analysis (LDA; in blue), and Quadratic Discriminant Analysis (QDA; in green) in the three data sets tested: (A) French lagoons, (B) Portuguese estuaries, and (C) U.S. coastal nurseries. In each case, the shaded area depicts the difference between maximum and minimum accuracies for a given method, and calculated mean accuracy is shown by the bold colored line.
common variables selection procedures. Hence, for each of the statistical methods tested, procedures exist for selecting variables (elements) to maximize prediction efficiency. To further investigate the added value of our method in the identification of the best element combinations, accuracies were also calculated for two common variables selection procedures: a stepwise
forward variable selection procedure using the Wilks’ lambda criterion based on successive MANOVA for LDA and QDA (Mardia et al. 1979) and a stepwise procedure using the Gini Index for RF (Breiman 2001). All statistical analyses were carried out using R software (R Development Core Team 2008). More specifically, the packages FactoMineR, class, gtools,
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TABLE 1. Maximal accuracy (95% CI in parentheses) in assigning fish origins for each otolith data set obtained with each method. French lagoons Method LDA QDA ANN RF
Maximal accuracy (%) 89 88 87 92
Portuguese estuaries
No. elements
(0.6) (0.6) (0.8) (0.4)
8 8 5 9
Maximal accuracy (%) 55 61 67 75
(0.9) (1.0) (1.1) (0.7)
American Florida Bay
No. elements
Maximal accuracy (%)
No. elements
9 7 4 8
70 (1.6) 74 (2.0) 81 (2.7)
14 13 12
Notes: Abbreviations are: LDA, Linear Discriminant Analysis; QDA, Quadratic Discriminant Analysis; ANN, Artificial Neural Networks; and RF, Random Forest. Ellipses indicate that no data are possible.
klaR, MASS, mda, and randomForest were used. All the additional scripts created for comparisons of classification methods and variable selection are available online.7 RESULTS Classification accuracy Assignment accuracy varied with elements used for classification across all methods and data sets examined (Fig. 2). However, the following patterns were observed. For all methods and data sets, minimal and mean classification accuracies increased progressively with the number of elements from 15% to 35%, respectively, for combinations with only one or two elements from 54% to 91%, respectively, when using the entire suite of elements. However, maximum accuracies peaked before the whole set of elements was used. They reached a maximum for an intermediate number of elements (4–14), depending on the method and the data set (Table 1). Depending on the classification method, with our procedure, maximum accuracies ranged between 89% and 92%, 55% and 75%, and 70% and 81% for the French lagoons, the Portuguese estuaries, and the U.S. coastal nurseries data sets, respectively, the maximum being always reached when using RF. With the variables selection methods, accuracies ranged between 85% and 87%, 39% and 68%, 67% and 77% for the French lagoons, the Portuguese estuaries, and the U.S. coastal nurseries data sets, respectively (Table 2). For all the methods examined, RF displayed the greatest sensitivity to the number of elements used for prediction. Irrespective of the data set, mean and minimum accuracies with this method showed the most consistent increase with the number of elements (Fig. 2). The inflexion point for maximum accuracy was always reached using fewer elements with ANN (with 4–5 elements vs. 7–9 elements for the other methods), but with lower maximal accuracies (67–88%) than for RF (75–92%) (Table 1). Overall, for combinations of more than three elements, RF consistently outperformed the other methods. LDA, QDA, and ANN displayed less consistent results, with performances 7
hhttp://www.ecolag.univ-montp2.fr/i
varying by data set (Fig. 2). Compared to the other methods, LDA showed good accuracies for the French lagoons and the U.S. coastal nurseries data sets, but exhibited the worst accuracy for the Portuguese estuaries data set. Differences in maximum accuracy for this method were as high as 34% between data sets (Table 1). ANN was not tested on the U.S. coastal nurseries data set, but performed better for the French lagoons than for the Portuguese estuaries data set (Fig. 2), with a difference in maximum accuracy of 20% between the two data sets (Table 1). QDA showed the worst accuracies for both the French lagoons and the U.S. coastal nurseries data sets. Differences in maximum accuracy for this method were up to 27% between data sets (Table 1). Optimal element combinations Those element combinations displaying greatest accuracies varied with classification method used and the data set analyzed (Table 3). Regardless of the method used for prediction, three elements (Li, Na, Mn) were selected for the Portuguese estuaries data set, eight elements (Li, Mg, P, Sc, Mn, Fe, Rb, Nd) for the U.S. coastal nurseries data set, and five elements (B, Ba, Li, Rb, Y) for the French lagoons data set. Li was present in all optimal combinations of predictors, regardless of the method and the data set (Table 4). Nevertheless, the other elements in the best combinations differed from one data set to the other, and according to the method. Irrespective of the method, habitat discrimination was maximized when also including Mn for the Portuguese estuaries data set, Mn and Mg for the U.S. coastal nurseries data set, and Y and B for the French lagoons data set. Recurring elements leading to best accuracies were Li, Mn, and Sr for LDA; Li and Sr for QDA; Li for ANN; and Ba, Li, and Mn for RF (Table 3). DISCUSSION These results stress the importance of both classification method and element list selection when using otolith fingerprints to identify fish origin. Results accuracy in each case will depend on the method performance, the characteristics of the otolith data set, and the list of elements included in the analysis.
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TABLE 2. Accuracy for combinations obtained by variable selection procedures for each prediction method. Stepwise selection with Wilks’ k
Selection by Gini index decrease
Accuracy (%)
Accuracy (%)
Data set
Element combination
LDA
QDA
Element combination
RF
French lagoons Portuguese estuaries U.S. coastal nurseries
Li B Mg Mn Rb Sr Y Ba Li Na Mg K Mn Zn Sr Pb Li Na Mg P Sc Mn Fe Rb Sr Y Ba La Nd Tm
87 (7.0) 39 (16.0) 67 (3.0)
85 (5.0) 50 (17.1) 72 (4.9)
Li B Mn Rb Sr Y Ba Li Na Mg Mn Zn Sr Pb Li Na Mg P Sc Mn Fe Cu Rb Sr Y Cd Ba La Nd
87 (3.9) 68 (8.2) 77 (5.6)
Note: Prediction method abbreviations are: LDA, Linear Discriminant Analysis; QDA, Quadratic Discriminant Analysis; and RF, Random Forest.
Choice of the discrimination method Multielement otolith fingerprint data have been widely analyzed with LDA or QDA, despite difficulties to get the underlying assumptions of these methods (e.g., Elsdon et al. 2008). Few studies have employed more than one discrimination method (Thorrold et al. 1998a). The present study is the first attempt to compare the discrimination accuracy of several methods for the analysis of otolith fingerprints. We obtained large differences in accuracy between the four discrimination methods examined. One could argue that the performance of RF over LDA and QDA was due to the violation of assumptions required by the latter two methods. Indeed, more complex data are more likely to violate the assumptions of multinormality required for LDA and QDA methods. None of the data sets examined in this study conformed to this assumption. The French lagoons data showed the lowest deviation from multinormality (see Appendix C for values of normality and multinormality within each group). Thus, it was foreseeable that the ability of LDA and QDA to discriminate habitats would be higher for the French lagoons data set. Nevertheless, RF and ANN achieved high accuracy too, and RF outperformed these two methods even for the French lagoons data. The
deviation from multinormality cannot fully explain the low accuracies obtained for the Portuguese estuaries data. LDA is known to be less effective with non-normal data, and QDA can be strongly influenced by noninformative elements (Tan et al. 2006, Dixon and Brereton 2009). In our case, LDA performed well for the French lagoons data set, but displayed the lowest accuracies for the Portuguese data set; whereas QDA yielded the lowest accuracies for the French lagoons and U.S. coastal nurseries data sets. Moreover, the deviation from multinormality is similar among the Portuguese estuaries and the U.S. coastal nurseries data, while the corresponding differences in maximal accuracies are much greater. Thus, beyond the violation of assumptions, LDA and QDA failed to accurately predict the origins of fish in the Portuguese data set because these methods do not model nonlinear (or non-quadratic) relationships, such as threshold effects, or complex interactions among predictor variables. ANN achieved high accuracy for French lagoons and Portuguese estuaries data sets with smaller combinations of elements relative to other methods. It has been previously shown that ANN was more accurate than LDA in classifying fish with unknown origin (Thorrold et al. 1998a). In the present study, accuracy of ANN was
TABLE 3. Combinations allowing the best accuracy in origin assignment. Data set and method
Combination elements
French lagoons LDA QDA ANN RF
Li Li Li Li
B B B B
Portuguese estuaries LDA QDA ANN RF
Li Li Li Li
Na Na Na Na
U.S. coastal nurseries LDA QDA ANN RF
Li Li Li
Na Na
Mn Mg Mg
Mn
Mg Mg
K K
Mg Mg Mg
P P P
Rb Rb Rb Rb
Sr Sr
Mn Mn Mn Mn
Cu
Sc Sc
Y Y Y Y
Sb
Ba Ba Ba Ba
Zn Zn
Sr Sr
Ba
Cu
Zn
Sr
Ba
Mn Mn Mn
Fe
Cu
Rb Rb Rb
Fe
Sb
Cu
Pb Pb Pb Pb Pb Sr Sr
Y Y
Cd
Ba
La La
Nd Nd Nd
Tm Tm
Notes: Abbreviations are: LDA, Linear Discriminant Analysis; QDA, Quadratic Discriminant Analysis; ANN, Artificial Neural Networks; and RF, Random Forest. Italicized elements are those present in all best combinations for a given data set. Ellipses indicate that no data are possible.
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TABLE 4. List of the five most common elements in the best combinations for each method. Element ranking, French lagoons Method LDA QDA ANN RF
1 Y Y Y Y
(11) (11) (11) (11)
2 Li Li Li Li
(10) (10) (10) (10)
3 B B B B
(8) (8) (9) (9)
Element ranking, Portuguese estuaries
4
5
1
2
3
4
5
Ba (7) Sr (8) Rb (7) Ba (8)
Rb (7) Ba (7) Ba (6) Mn (6)
Sr (10) Li (8) Mn (9) Li (9)
Mn (8) Mn (8) Na (9) Na (9)
Li (7) Sr (8) Li (7) Mn (8)
K (6) Na (7) Zn (6) Mg (7)
Mg (6) Zn (7) Pb (5) K (6)
Notes: Abbreviations are: LDA, Linear Discriminant Analysis; QDA, Quadratic Discriminant Analysis; ANN, Artificial Neural Networks; and RF, Random Forest. The number in parentheses next to each chemical element indicates the number of occurrences in the best combinations. French lagoons had 11 best combinations, Portuguese estuaries had 10 best combinations, and U.S. coastal nurseries had 18 best combinations. Ellipses indicate that no data are possible.
high, irrespective of the data set, and offers the best compromise between accuracy and the number of elements required for prediction. Despite its efficiency, computation time is prohibitive (it could not be achieved on the U.S. coastal nurseries data set; Table 5), limiting its application to smaller data sets when screening all possible subsets of elements. RF yielded the best performance, in terms of absolute maximum and mean accuracy as already shown in other medicine and ecology studies (Biau et al. 2008, Perdiguero-Alonso et al. 2008, Sun et al. 2008, Dixon and Brereton 2009). The Portuguese estuaries data set is an archetypal case showing that RF can cope with highly heterogeneous data. Accuracy reached 75%, indicating that the use of RF in discrimination method paves the way to multispecies nursery identification. This key milestone has already been evoked but barely reached in past studies (Reis-Santos et al. 2008). Such a strategy would allow the inference of a global chemical signature of a space from various species and potentially offer a robust way to identify the origin of a single fish from a vast corpus of various species chemical signatures. Our example demonstrated the high potential offered by RF in site discrimination based on otolith fingerprints (Biau et al. 2008, Elith et al. 2008). Differences between data sets Assessing the reasons for variation in discrimination accuracy between otolith fingerprint data sets faces many problems. Best site discriminations were minimal for the Portuguese estuaries data set, maximal for the French lagoons data set, and intermediate for the U.S. coastal nursery data set, irrespective of the discrimination method used. This suggests that the scale of observation, the nature of fish studied, and the type of habitat largely determine discrimination accuracy, irrespective of the method. Scale of study differs according to the fish species considered and the types of habitats it colonizes (Chittaro et al. 2006), whereas discrimination ability depends on the contrasts among sampling locations (Rooker et al. 2007, Clarke et al. 2009). For the French lagoons data, where accuracies were the highest (from 89% to 92%), fish habitats consisted of isolated lagoons with a wide range of salinities (ranging from 15 to 36) and different anthropogenic loads
(Accornero et al. 2008, Ifremer 2008). The noticeable variations in water chemical composition between the French lagoons facilitated their discrimination, and explains the greater accuracies obtained for these data whatever the method used. The U.S. coastal nurseries data set was derived mainly from open coastal habitats, suggesting a common marine influence for each nursery. Some studies have already highlighted the difficulty in differentiating fish origins within a homogeneous area (Thorrold et al. 1997, Gillanders and Kingsford 2003). The proximity between some nursery areas (e.g., west and east Florida Bay) reinforces this hypothesis and may explain the intermediate level of best accuracies for U.S. coastal fish. The Portuguese estuaries data set, which showed the lowest accuracies for all methods, was the only one derived from multi-specific otolith signatures. The five fish species used to generate the data set differ by their behavior and ecology (Vasconcelos et al. 2007a) and may incorporate chemical elements into their otoliths differently, which may potentially decrease the habitat predictability due to a confounding species effect. Classical classification methods (i.e., LDA or QDA) fail when dealing with more than two species (Reis-Santos et al. 2008). Actually, only RF reached an acceptable accuracy of 75%. The results confirm that data sets with monospecific chemical fingerprints taken from separate sites with markedly contrasting water chemistries are easier to analyze. Increasing the number of species or defining sites from a geographic continuum decrease accuracy power irrespective of the discrimination method. Best otolith element combinations Depending on the technology used and the species studied, previous studies utilizing otolith fingerprints showed two opposite strategies with regards to the number and the list of elements used for classification, either using a few major and easily detectable otolith elements (such as Sr, Mn, Ba, Na, and Pb) for site discrimination (e.g., Gillanders and Kingsford 2000), or, as new ICPMS allowed it, increasing the list of chemical elements measured expecting that it will produce a more discriminating signal (e.g., Chittaro et al. 2006). Both methods gave acceptable results, but no comparison was ever made to assess the optimal strategy. The chemical
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TABLE 4. Extended. Element ranking, U.S. coastal nurseries 1
2
3
4
5
5
Rb (18) Mg (16) Mn (16)
Li (16) Li (15) Sc (16)
Ba (14) Sr (14) Li (15)
Mn (14) Rb (14) Mg (13)
Mg (13) Mn (13) Cd (12)
P (13) La (12)
composition of otoliths is under both environmental and physiological controls (Fowler et al. 1995, Chang et al. 2004, Walther and Thorrold 2006, Arai et al. 2007). Physiological factors induce species-specific incorporation of elements, whereas environmental influence tends to create common patterns between species (Reis-Santos et al. 2008). Nevertheless, it is very difficult to test interactive effects of both these endogenous and exogenous parameters. Thus, it remains elusive to predict a set of chemical elements to measure for habitat discrimination, regardless of the species and the study area. Strategies of variable selection are known to be biased. Stepwise procedures are dependant of the order variables are introduced to the model both in forward addition and backward elimination procedures. The stepwise selection procedures adopted provide good global results, but are consistently inferior to optimal combinations (Tables 1 and 2). For the Portuguese data set, the combination retained by variable selection gave low accuracy (39%), highlighting the biases of such procedures with complex data. Lithium (Li ) was the only element selected by all discrimination methods and for all data sets. Li is an alkali element and its affinity to otolith aragonite has been previously reported (Halden and Friedrich 2008). Its relevance to discrimination of coastal habitats might result from these characteristics. Li concentrations in the water, and subsequently in the otolith, might reflect the geology around certain fish habitats with important freshwater inputs (Friedrich and Halden 2008), through the weathering of Li from particular rocks near the coast. All other useful chemical elements differed from one location to the other, irrespective of the classification method, probably following environmental differences among the sites discriminated. For the Portuguese estuaries data set, manganese (Mn) and sodium (Na) were retained irrespective of the method, probably because of the strong differences in anthropogenic influences (Mn) and salinity (Na) existing between the estuaries studied (Vasconcelos et al. 2007). For the U.S. coastal nurseries, six elements (Li, Mg, Mn, Nd, P, and Rb) were retained. Out of these, four (Li, Mn, P, Rb) had already been identified as particularly useful for site discrimination in the original study, where inter-sites differences in their concentration were explained by differences in sediment composition (Lara et al. 2008). For the French lagoons data set, five elements (B, Ba, Li, Rb, Y) were retained as relevant. B and Ba are
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known to reflect marine influence and vary with salinity (Campana 1999). This explains their relevance since the coastal lagoons studied display different levels of connection with the sea. As alkali elements, Li and Rb may reflect the differences in the geology between the different catchment areas (Friedrich and Halden 2008). Yttrium is less trivial because its concentration may also reflect the pollution levels of the lagoons (Neal 2007). It is surprising that the major elements were not found to be more discriminating. Sr, for example, is retained by QDA and LDA only, indicating that major chemical elements are not always the most useful and that their efficiency for habitat discrimination might be biased by the method used for classification. This clearly confirms that no consensus set of elements can be used for effective coastal sites discrimination at all times. Moreover, irrespective of the method used, best maximum accuracies were obtained for an intermediate number of elements, indicating that some elements provide more noise than signal for nursery discrimination and also reflect the features of their statistical distributions. This contradicts conventional wisdom that more elements always result in better accuracies (Arslan and Secor 2008). In order to optimize discrimination accuracy, selection of an optimal subset of chemical elements is therefore essential. However, stepwise variable selection procedures are often biased (Rencher and Larson 1980). It is therefore recommended that one quantify the concentration of as many chemical elements as comprehensive as possible, and then select a subset of the most informative ones, using an iterative method such as we describe. As performance of a given method depends on the type of data analyzed and elements used, we provide the R code allowing practitioners to compare the four methods tested and to select chemical elements from the whole data set. As promising ways and future improvements, the resulting list could be used to run more sophisticated classification methods, such as clustering and Markov Chain Monte Carlo procedures (MCMC; White et al. 2008). Our study demonstrates that the choice of both the list of chemical elements to be measured in the otoliths and the method used for discrimination are important for an optimal assignment of fish origin based on otolith fingerprints. Random Forest (RF) provides better results, regardless of the three data sets tested, has fewer statistical requirements for its application than classical TABLE 5. Indicative calculation time (in hours) for each data set and each discrimination method. Data set
LDA
QDA
ANN
RF
French lagoons Portuguese estuaries U.S. coastal nurseries
26 6 70
34 8 90
96 50
60 15 240
Notes: Abbreviations are: LDA, Linear Discriminant Analysis; QDA, Quadratic Discriminant Analysis; ANN, Artificial Neural Networks; and RF, Random Forest. Ellipses indicate that no data are possible.
LE´NY MERCIER ET AL.
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techniques like LDA or QDA, and is faster to run than ANN. Hence, as technical improvements allow the increase in the size of the data sets with more elements and more individuals analyzed, the probable deviation from multinormality will force the transformation of the data to use LDA and QDA. Current literature rarely focuses on these requirement issues: About a third of published papers do not clearly state if requirements are fulfilled. However, statistical-methods sections of papers need to address this concern transparently and completely before parametric tests are used. If transformations do not lead to multinormality, machine learning methods, such as RF, may be a valuable alternative. Here, RF performance allows accurate habitat discrimination based on multispecies otolith data sets. The chemical elements classically used for discrimination are not retained, while some unusual elements provide useful signal. Therefore, we suggest a first step, such as that applied in the present study, consisting of the selection of chemical elements based on the comparison of all chemical elements combinations. Overall, these results highlight an important area of consideration and should motivate future research. ACKNOWLEDGMENTS This research project was funded by the French National Research Agency (ANR) through the young-scientist research program LAGUNEX (07-JCJC-0135). The authors thank local fishermen for their assistance with fish sampling and Awa Ndiaye for help with otolith preparation. LITERATURE CITED Accornero, A., R. Gnerre, and L. Manfra. 2008. Sediment concentrations of trace metals in the Berre Lagoon (France): an assessment of contamination. Archives of Environmental Contamination and Toxicology 54:372–385. Allouche, O., A. Tsoar, and R. Kadmon. 2006. Assessing the accuracy of species distribution models: prevalence, kappa and the true skill statistic (TSS). Journal of Applied Ecology 43:1223–1232. Arai, T., M. Ohji, and T. Hirata. 2007. Trace metal deposition in teleost fish otolith as an environmental indicator. Water, Air, and Soil Pollution 179:255–263. Arslan, Z., and A. J. Paulson. 2003. Solid phase extraction for analysis of biogenic carbonates by electrothermal vaporization inductively coupled plasma mass spectrometry (ETVICP-MS): an investigation of rare earth element signatures in otolith microchemistry. Analytica Chimica Acta 476:1–13. Arslan, Z., and D. Secor. 2008. High resolution micromill sampling for analysis of fish otoliths by ICP-MS: effects of sampling and specimen preparation on trace element fingerprints. Marine Environmental Research 66:364–371. Babaluk, J., N. Halden, J. Reist, A. Kristofferson, J. Campbell, and W. Teesdale. 1997. Evidence for non-anadromous behaviour of Arctic Charr (Salvelinus alpinus) from Lake Hazen, Ellesmere Island, Northwest Territories, Canada, based on scanning proton microprobe analysis of otolith strontium distribution. Arctic 50:224–233. Bath, G. E., S. R. Thorrold, C. M. Jones, S. E. Campana, J. W. McLaren, and J. W. H. Lam. 2000. Strontium and barium uptake in aragonitic otoliths of marine fish. Geochimica et Cosmochimica Acta 64:1705–1714. Biau, G., L. Devroye, and G. Lugosi. 2008. Consistency of random forests and other averaging classifiers. Journal of Machine Learning Research 9:2015–2033.
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Brazner, J. C., S. E. Campana, and D. K. Tanner. 2004. Habitat fingerprints for Lake Superior coastal wetlands derived from elemental analysis of yellow perch otoliths. Transactions of the American Fisheries Society 133:692–704. Breiman, L. 2001. Random forests. Machine Learning 45:5–32. Brown, J. 2006. Using the chemical composition of otoliths to evaluate the nursery role of estuaries for English Sole Pleuronectes vetulus populations. Marine Ecology Progress Series 306:269–281. Campana, S. E. 1999. Chemistry and composition of fish otoliths: pathways, mechanisms and applications. Marine Ecology Progress Series 188:263–297. Campana, S. E., G. A. Chouinard, J. M. Hanson, and A. Frechet. 1999. Mixing and migration of overwintering Atlantic cod (Gadus morhua) stocks near the mouth of the Gulf of St. Lawrence. Canadian Journal of Fisheries and Aquatic Sciences 56:1873–1881. Campana, S. E., A. J. Fowler, and C. M. Jones. 1994. Otolith elemental fingerprinting for stock identification of Atlantic cod (Gadus morhua) using laser-ablation ICPMS. Canadian Journal of Fisheries and Aquatic Sciences 51:1942–1950. Care, M., J. Bradford, C. Needham, A. Bulpitt, and D. Westhead. 2009. Combining the interactome and deleterious SNP predictions to improve disease gene identification. Human Mutation 30:485–492. Chang, C., S. Lin, Y. Iizuka, and W. Tzeng. 2004. Relationship between Sr:Ca ratios in otoliths of grey mullet Mugil cephalus and ambient salinity: validation, mechanisms, and applications. Zoological Studies 43:74–85. Chittaro, P., P. Usseglio, B. Fryer, and P. Sale. 2006. Spatial variation in otolith chemistry of Lutjanus apodus at Turneffe atoll, Belize. Estuarine, Coastal and Shelf Science 67:673– 680. Clarke, L., B. Walther, S. Munch, S. Thorrold, and D. Conover. 2009. Chemical signatures in the otoliths of a coastal marine fish, Menidia menidia, from the northeastern United States: spatial and temporal differences. Marine Ecology Progress Series 384:261–271. Cutler, D. R., T. C. Edwards, K. H. Beard, A. Cutler, K. T. Hess, J. Gibson, and J. J. Lawler. 2007. Random forests for classification in ecology. Ecology 88:2783–2792. de Vries, M. C., B. M. Gillanders, and T. S. Elsdon. 2005. Facilitation of barium uptake into fish otoliths: influence of strontium concentration and salinity. Geochimica et Cosmochimica Acta 69:4061–4072. Dixon, S. J., and R. G. Brereton. 2009. Comparison of performance of five common classifiers represented as boundary methods: euclidean distance to centroids, linear discriminant analysis, quadratic discriminant analysis, learning vector quantization and support vector machines, as dependent on data structure. Chemometrics and Intelligent Laboratory Systems 95:1–17. Dorval, E., C. Jones, R. Hannigan, and J. van Montfrans. 2007. Relating otolith chemistry to surface water chemistry in a coastal plain estuary. Canadian Journal of Fisheries and Aquatic Sciences 64:411–424. Edmonds, J. S., N. Caputi, and M. Morita. 1991. Stock discrimination by trace-element analysis of otoliths of orange Roughy (Hoplostethus atlanticus), a deep-water marine teleost. Australian Journal of Marine and Freshwater Research 42:383–389. Elith, J., J. Leathwick, and T. Hastie. 2008. A working guide to boosted regression trees. Journal of Animal Ecology 77:802– 813. Elsdon, T. S., and B. M. Gillanders. 2005. Alternative lifehistory patterns of estuarine fish: barium in otoliths elucidates freshwater residency. Canadian Journal of Fisheries and Aquatic Sciences 62:1143–1152. Elsdon, T. S., B. K. Wells, S. E. Campana, B. M. Gillanders, C. M. Jones, K. E. Limburg, D. H. Secor, S. R. Thorrold,
June 2011
OTOLITH FINGERPRINTS AND RANDOM FOREST
and B. D. Walther. 2008. Otolith chemistry to describe movements and life-history parameters of fishes: hypotheses, assumptions, limitations and inferences. Oceanography and marine biology: an annual review 46:297–330. Fisher, R. A. 1936. The use of multiple measurements in taxonomic problems. Annals of Eugenics 7:179–188. Fodrie, F., and S. Herzka. 2008. Tracking juvenile fish movement and nursery contribution within and coastal embayments via otolith microchemistry. Marine Ecology Progress Series 361:253–265. Fontes, J., J. E. Caselle, M. S. Sheehy, R. S. Santos, and R. R. Warner. 2009. Natal signatures of juvenile Coris julis in the Azores: investigating connectivity scenarios in an oceanic archipelago. Marine Ecology Progress Series 387:51–59. Fowler, A. J., S. E. Campana, C. M. Jones, and S. R. Thorrold. 1995. Experimental assessment of the effect of temperature and salinity on elemental composition of otoliths using solution-based ICPMS. Canadian Journal of Fisheries and Aquatic Sciences 52:1421–1430. Friedrich, L., and N. Halden. 2008. Alkali element uptake in otoliths: a link between the environment and otolith microchemistry. Environmental Science and Technology 42:3514–3518. Gillanders, B., K. Able, J. Brown, D. Eggleston, and P. Sheridan. 2003. Evidence of connectivity between juvenile and adult habitats for mobile marine fauna: an important component of nurseries. Marine Ecology Progress Series 247:281–295. Gillanders, B. M., and M. J. Kingsford. 2000. Elemental fingerprints of otoliths of fish may distinguish estuarine ‘nursery’ habitats. Marine Ecology Progress Series 201:273– 286. Gillanders, B. M., and M. J. Kingsford. 2003. Spatial variation in elemental composition of otoliths of three species of fish (family Sparidae). Estuarine Coastal and Shelf Science 57:1049–1064. Gillanders, B. M., P. Sanchez-Jerez, J. Bayle-Sempere, and A. Ramos-Espla. 2001. Trace elements in otoliths of the twobanded bream from a coastal region in the south-west Mediterranean: are there differences among locations? Journal of Fish Biology 59:350–363. Gutierrez-Estrada, J., R. Vasconcelos, and M. Costa. 2008. Estimating fish community diversity from environmental features in the Tagus estuary (Portugal): multiple linear regression and artificial neural network approaches. Journal of Applied Ichthyology 24:150–162. Halden, N. M., and L. A. Friedrich. 2008. Trace-element distributions in fish otoliths: natural markers of life histories, environmental conditions and exposure to tailings effluence. Mineralogical Magazine 72:593–605. Hamer, P. A., G. P. Jenkins, and P. Coutin. 2006. Barium variation in Pagrus auratus (Sparidae) otoliths: a potential indicator of migration between an embayment and ocean waters in south-eastern Australia. Estuarine, Coastal and Shelf Science 68:686–702. Hobbs, J., W. Bennett, J. Burton, and M. Gras. 2007. Classification of larval and adult delta Smelt to nursery areas by use of trace elemental fingerprinting. Transactions of the American Fisheries Society 136:518–527. Ifremer [French Research Institute for Exploration of the Sea]. 2008. Re´seau de suivi lagunaire du languedoc-roussillon: bilan des re´sultats 2007. Report rsl-08/2008. Ifremer, Brest, France. Kalish, J. M. 1991. Determinants of otolith chemistry— seasonal variation in the composition of blood-plasma, endolymph and otoliths of bearded rock cod Pseudophycis barbatus. Marine Ecology Progress Series 74:137–159. Kemp, W., et al. 2005. Eutrophication of Chesapeake Bay: historical trends and ecological interactions. Marine Ecology Progress Series 303:1–29.
1363
Kohavi, R. 1995. The power of decision tables. Machine Learning 912:174–189. Lamson, H. M., J. C. Shiao, Y. Iizuka, W. N. Tzeng, and D. K. Cairns. 2006. Movement patterns of American eels (Anguilla rostrata) between salt- and freshwater in a coastal watershed, based on otolith microchemistry. Marine Biology 149:1567– 1576. Lara, M., D. Jones, Z. Chen, J. Lamkin, and C. Jones. 2008. Spatial variation of otolith elemental signatures among juvenile Gray Snapper (Lutjanus griseus) inhabiting southern Florida waters. Marine Biology 153:235–248. Levin, L., D. Boesch, A. Covich, C. Dahm, C. Erseus, K. Ewel, R. Kneib, A. Moldenke, M. Palmer, P. Snelgrove, D. Strayer, and J. Weslawski. 2001. The function of marine critical transition zones and the importance of sediment biodiversity. Ecosystems 4:430–451. Mardia, K. V., J. T. Kent, and J. M. Bibby. 1979. Multivariate analysis. Academic Press, New York, New York, USA. Neal, C. 2007. Rare earth element concentrations in dissolved and acid available particulate forms for eastern UK rivers. Hydrology and Earth System Sciences 11:313–327. Nixon, S. 1995. Coastal marine eutrophication: a definition, social causes, and future concerns. Ophelia 41:199–219. Oppel, S., A. Powell, and D. Dickson. 2009. Using an algorithmic model to reveal individually variable movement decisions in a wintering sea duck. Journal of Animal Ecology 78:524–531. Panfili, J., H. de Pontual, H. Troadec, and P. Wright. 2002. Manual of fish sclerochronology. Ifremer-IRD coedition, 2002. Ifremer, Brest, France. Perdiguero-Alonso, D., F. Montero, A. Kostadinova, J. Raga, and J. Barrett. 2008. Random forests, a novel approach for discrimination of fish populations using parasites as biological tags. International Journal for Parasitology 38:1425– 1434. R Development Core Team. 2008. R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Reis-Santos, P., R. Vasconcelos, M. Ruano, C. Latkoczy, D. Gunther, M. Costa, and H. Cabral. 2008. Interspecific variations of otolith chemistry in estuarine fish nurseries. Journal of Fish Biology 72:2595–2614. Rencher, A. C., and S. F. Larson. 1980. Bias in Wilks’ lambda in stepwise Discriminant Analysis. Technometrics 22:349– 356. Ripley, B. D. 1993. Statistical aspects of neural networks. Pages 40–123 in O. E. Barndorff-Nielsen, J. L. Jensen, and W. S. Kendall, editors. Networks and chaos: statistical and probabilistic aspects. Chapman and Hall/CRC Monographs on Statistics and Applied Probability, London, UK. Rooker, J., J. Bremer, B. Block, H. Dewar, G. De Metrio, A. Corriero, R. Kraus, E. Prince, E. Rodriguez-Marin, and D. Secor. 2007. Life history and stock structure of Atlantic Bluefin Tuna (Thunnus thynnus). Reviews in Fisheries Science 15:265–310. Seber, G. A. F. 1984. Multivariate observations. John Wiley and Sons, New York, New York, USA. Sun, X., Y. Li, X. Liu, J. Ding, Y. Wang, H. Shen, and Y. Chang. 2008. Classification of bioaccumulative and nonbioaccumulative chemicals using statistical learning approaches. Molecular Diversity 12:157–169. Tan, C. O., U. O¨zesmi, M. Beklioglu, E. Per, and B. Kurt. 2006. Predictive models in ecology: comparison of performances and assessment of applicability. Ecological Informatics 1:195–211. Thorrold, S. R., C. M. Jones, and S. E. Campana. 1997. Response of otolith microchemistry to environmental variations experienced by larval and juvenile Atlantic croaker (Micropogonias undulatus). Limnology and Oceanography 42:102–111.
1364
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Thorrold, S. R., C. M. Jones, S. E. Campana, J. W. McLaren, and J. W. H. Lam. 1998a. Trace element signatures in otoliths record natal river of juvenile American shad (Alosa sapidissima). Limnology and Oceanography 43:1826–1835. Thorrold, S., C. Jones, P. Swart, and T. Targett. 1998b. Accurate classification of juvenile weakfish Cynoscion regalis to estuarine nursery areas based on chemical signatures in otoliths. Marine Ecology Progress Series 173:253–265. Thresher, R. E. 1999. Elemental composition of otoliths as a stock delineator in fishes. Fisheries Research 43:165–204. Vasconcelos, R., P. Reis-Santos, S. Tanner, V. Fonseca, C. Latkoczy, D. Gunther, M. Costa, and H. Cabral. 2007. Discriminating estuarine nurseries for five fish species
Ecological Applications Vol. 21, No. 4
through otolith elemental fingerprints. Marine Ecology Progress Series 350:117–126. Walther, B. D., and S. R. Thorrold. 2006. Water, not food, contributes the majority of strontium and barium deposited in the otoliths of a marine fish. Marine Ecology Progress Series 311:125–130. White, J. W., J. D. Standish, S. R. Thorrold, and R. R. Warner. 2008. Markov Chain Monte Carlo methods for assigning larvae to natal sites using natural geochemical tags. Ecological Applications 18:1901–1913. Wilson, J. 2007. Priorities in statistics, the sensitive feet of elephants, and don’t transform data. Folia Geobotanica 42:161–167.
APPENDIX A Sampling design, otolith preparation, and analysis for the French lagoons data set (Ecological Archives A021-062-A1).
APPENDIX B True Skill Statistics for each optimal subset of elements (Ecological Archives A021-062-A2).
APPENDIX C Normality indexes for each data set (Ecological Archives A021-062-A3).
SUPPLEMENT R code for the algorithm used in this paper (Ecological Archives A021-062-S1).
