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Regression-Based Modeling of Environmental Factors Affecting 412 Chiang Mai J. Sci. 2011; 38(3) Chiang Mai J. Sci. 2011; 38(3) : 412-429 http://it.science.cmu.ac.th/ejournal/ Contributed Paper Regression-based Modeling of Environmental Factors Affecting Macrobenthic Fauna in Middle Songkhla Lake, Thailand Uraiwan Sampantarak*[a], Noodchanath Kongchouy**[b], and Saowapa Angsupanich [c] [a] Pattani Inland Fisheries Research and Development Center, Department of Fisheries, Pattani 94160, Thailand. [b] Department of Mathematics, Faculty of Science, Prince of Songkla University, Songkhla 90112, Thailand. [c] Department of Aquatic Science, Faculty of Natural Resources, Prince of Songkla University, Songkhla 90112, Thailand. Author for correspondence; e-mail: *[email protected], **[email protected] Received: 23 March 2010 Accepted: 21 June 2011 ABSTRACT The main objective of this study was to consider multivariate multiple regression (MMR) as an alternative to canonical correspondence analysis (CCA) for examining associations between macrobenthic fauna assemblage densities and environmental characteristics. The data used for this comparison comprise macrobenthic fauna densities and water quality parameters including sediment characteristics obtained from nine sampling sites in Middle Songkhla Lake at bimonthly intervals from April 1998 to February 1999. The outcome variables were the densities of twenty four macrobenthic fauna families with greater than 35% occurrence, log- transformed to remove skewness. Factor analysis was used to defi ne fi ve predictors including three composite variables based on salinity, physical sediment characteristics, and physico- chemical properties of water and sediment, together with total suspended solids and dissolved oxygen as single variables. The results show that MMR can be used as an additional or alternative method and has some advantages over the CCA method. Keywords: macrobenthic fauna, multivariate multiple regression model, factor analysis, canonical correspondence analysis. 1. INTRODUCTION Macrobenthic fauna are recognized them are unable to avoid adverse conditions as sensitive indicators of environmental brought about by natural stresses or human disturbance [1-3] partly because of the limits impacts. Moreover, their relative longevity, to their mobility. They can be very mobile but with many species having life cycles over only at a scale of mm or cm; pollution acts at two years, allows them to integrate responses a scale of 100s of metres or more. Many of to environmental processes over extended Chiang Mai J. Sci. 2011; 38(3) 413 time periods [4]. In addition, the observed method for assessing relationships between distribution of macrobenthic fauna may be species abundance and their environmental useful in diagnostic studies and environmental predictors, for the simple reason that it is monitoring [5]. It is desirable to fi nd a useful the natural extension of ordinary regression predictive model for assemblages to identify analysis involving a single outcome to any factors infl uencing their absence or presence, number of mutually correlated outcomes such and abundance, and which can be used in as species abundances. It is thus of interest management of environments. to compare this method with its biologically Clarke and Warwick [6] outlined the preferred counterpart using common sets of basic methods commonly used by biological biological data relating taxonomic abundances scientists for preliminary analysis of their data. to environmental determinants. For this For comparative studies to assess associations comparison we used data from a study between taxa abundance and environmental involving macrobenthic fauna abundances predictors, canonical correspondence analysis and various water and sediment characteristics [7] is used extensively in the biological collected at specifi ed locations in an estuarine literature [8]. Some important studies using lake over a period of one year, reported by this method include those reported by Angsupanich et al. [22]. Rakocinski et al. [9], Hawkins et al. [10], Joy and Death [11], Guerra-García et al. 2. MATERIALS AND METHODS [12], Hajisamae and Chou [13], Morrisey et al. [14], Ysebaert et al. [15], Quintino et al. 2.1 Materials [16], Anderson [17], Glockzin and Zettler Data on macrobenthic fauna abundances [18]. This non-parametric method gives and various water and sediment characteristics graphical displays in biplots but does not were collected bimonthly from April 1998 to provide numerical measures of strengths of February 1999 at nine specifi c locations in the associations and their standard errors. Such Middle Songkhla Lake in Southern Thailand measures are provided by regression models, (Figure 1). For more details on the study area provided data are transformed to reduce and data collection see Angsupanich et al. skewness. [22]. The macrobenthic fauna samples were Although exceptions exist, such collected using a Tamura’s grab (0.05 m2), as studies by Liang et al. [19] exploring sieved consecutively through the screens and relationships between benthic fauna and water fi xed in 10% Rose Bengal-formalin for later quality variables using structural equation identifi cation. modeling (SEM) and by Warton and Hudson The densities of macrobenthic fauna [20] for tests of multivariate abundance were recorded as the number of individuals data using multivariate analysis of variance per square meter (ind m-2) for each species. (MANOVA), multivariate multiple regression A total of 161 taxa of macrobenthic fauna (MMR) analysis is not commonly used in were found and classifi ed into 81 families. In the biological literature for analyzing species many cases the species could not be identifi ed abundance patterns, possibly because of exactly, so the outcomes were classifi ed by skewness in data sets (see, for example, family instead of species. With nine locations Warton [21]). However, with an appropriate and six bimonthly data study periods, we data transformation to remove skewness, this defi ned the occurrence for a specifi ed family method would appear to be an ideal statistical as the proportion of these 54 occasions on 414 Chiang Mai J. Sci. 2011; 38(3) which at least one organism was found. For salinity (Sal), water pH (wpH), dissolved the purposes of our comparison study, we oxygen (DO), total suspended solids (TSS), selected the 24 families with greater than 35% with sediment pH (spH), total nitrogen occurrence, thus covering 93.2% of the total content (TN), organic carbon content (OC), macrobenthic fauna assemblages. and grain size (percentages of sand, silt, and Environmental variables comprised water clay). These data were measured with three depth (wDep), water temperature (wTemp), replications on each occasion. Figure 1. Songkhla Lake and sampling sites (labeled 1-9). Chiang Mai J. Sci. 2011; 38(3) 415 2.2 METHODS To satisfy statistical assumptions, promax rotation in preference to varimax, the response variable was defined as which requires the rotation to be orthogonal log(1cudensity), with the multiplier c chosen [26, 27]. to best approximate normality of error distributions. The predictors comprised 2.2.2 Multivariate Multiple Regression environmental components derived from a Multivariate multiple regression (MMR) factor analysis together with unique variables is used to evaluate the effects of multiple not accommodated by the factor model. predictor variables on multiple response The methods compared were canonical variables. The model [25] may be defi ned in correspondence analysis (CCA) using matrix form as CANOCO Version 4.5 [23] and multivariate multiple regression (MMR) using R Version 8 n u p & nuq % qu p ( nu p (1) 2.10.0 [24]. In this formulation Y(nup) is an observed 2.2.1 Factor Analysis matrix of p response variables on each X Factor analysis was performed on the of n occasions, (n u q) is the matrix of q environmental variables with the aim of predictors (including a vector of 1s) in substantially reducing correlations between columns and n occasions in rows, B them that could mask their associations with (q u p) contains the regression coefficients E the outcome variables (see, for example, (including the intercept terms), and (n u p) is Chapter 9 of Mardia et al. [25]). Each factor a matrix of unobserved random errors with identifies correlated groups of variables. mean zero and common covariance matrix Ideally each group (which should contain at . Ordinary (univariate) multiple regression least two variables to contribute to the factor arises as the special case when p 1. If (k) analysis) contains variables having small q1 environmental predictors fi (k 1, correlations with variables in other groups. 2,…, q 1) are available, the prediction model To achieve this goal, any variable uncorrelated for outcome j on occasion i may be expressed with all other variables is omitted from as the factor analysis. Each factor comprises q1 k k weighted linear combinations of the variables yij P j ¦E j f i (2) and these factors are rotated to maximize the k 1 weights of variables within the factor group The model fi t may be assessed by plotting and minimize the weights of variables outside the residuals against normal quantiles [28], the group. The resulting weights are called and also by using the set of r-squared values “loadings”. Variables omitted from the factor for the response variables to see how much analysis due to low correlation with all other of the variation in each is accounted for by variables (high “uniqueness”) are treated as the model. separate predictors, so predictors
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