the application of multivariate analytical techniques to the study of marine benthic assemblages....

7/29/2019 The Application of Multivariate Analytical Techniques to the Study of Marine Benthic Assemblages. Xjenza 3:2 (199

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Review ArticleThe Application of M ultivariate Analytical Techniques to the Study ofMarine Benthic Assemblages:A Review with Special Reference to the M altese Islands.Rene M. Micallef and Patrick J. SchembriDepartment o f Biology, University of Malta, Msida MS D 06, MaltaSummary. In recent years there have been numerous studies made on the marine benthic assemblages of Maltesecoastal w aters , either as elements of the seasca pe, or in order to gain an understanding of the nature of theseassem blages and of the factors which structure them , or to assess the potential of such assem blages as ind icators ofenvironmental cha nge , principally that due to anthropogenic activities. The massive data sets generated by such studiescan realistically only be analysed objectively using an array of sophisticated statistical techniques that it has only beenpossible to app ly now tha t powerful computers are readily available.Starting with the basics of data a nalysis, this paper reviews the statistical techniques currently used for the ana lysis ofbenthic assemb lages, particularly those that have been found suitable for the type and character of data from theMediterran ean. Em phasis is placed on multivariate techniques, since benthic data are usually highly mu ltivariate. Abrief review of the developm ent of these techniques and of their application to benthic ecological research is also given.The objective is to provide a guide to techniques and to the literature which local workers m ay find useful as a startingpoint when designing an experimen tal, data co llection, or analytical protocol.

Keywords: multivariate analysis, diversity, similarity, ordination, classification, benthos, biotic communities,Maltese Islands.

IntroductionThe study of the marine benthic assemblages of Maltesecoastal waters has developed along parallel lines as hasthe subject on a global scale, albeit with a considerabletime lag. Thus, the earliest studies were made bynaturalists who were primarily interested in cataloguingthe biota (for example: McAndrew, 1850; Mamo inCamana, 1867; Aradas and Benoit, 1870; Medlycott,1870; Benoit and Gulia, 1872; Gulia, 1873; Sommierand Caruana Gatto, 1915; Despott, 1919; Caruana Gattoand Despott, 1919a,b). At most, these works includedonly general indications of abundance and habitat. Whilefaunistic and floristic studies have continued to thepresent, starting in the mid-1960s, attention shifted to thestudy of the biology of individual species, mainlyaspects of physiology, biochemistry, behaviour andautecology (for a compilation of the earlier work, seeBannister, 1974; see also Lythgoe and Woods, 1966),with some workers attempting to relate the biology ofthe species they studied to synecology (for example,Bannister, 1970; Zammit, 1972; Schembri and Jaccarini,1978; Fenech, 1980).The study of marine benthic assemblages as biologicalentities was pioneered locally by the work of Crossettand Larkum (1966), Crossett et al. (1965), Larkum et al.(1967), and Drew (1969) on algal assemblages, .and ofBiggs and Wilkinson (1966), Wilkinson et al. (1967)and Richards (1983) on molluscan assemblages. In thelate 1980s, the marine benthic assemblages of theMaltese Islands started being systematically investigatedby two research groups based at the Department ofBiology of the University of Malta. Many of these

studies are as yet unpublished (for abstracts see Axiak1993, 1994, 1995, and Dandria 1996, 1997).This work has taken two directions: (1) the descriptionof assemblages as elements of the seascape - what maybe termed the 'geographical approach'; and (2) a morebiological approach in which the focus is communitystructure and function. The geographical approach hasbeen necessitated by the need to map and characterisethe marine environment in connection with theassessment of the environmental impact of coastaldevelopment projects and the identification anddesignation of marine protected areas (Anderson et al.,1992; Borg and Schembri, 1993; Mallia and Schembri,1995a; Schembri, 1995; Pirotta and Schembri, 1997a,b;Borg et al., 1997a,b).The primary objective of the biological study of localmarine assemblages is to gain an understanding of thenature of these assemblages and of the factors whichstructure them (see abstracts in Axiak 1993, 1994, 1995,and Dandria 1996, 1997; see also Borg and Schembri,1995a,b). A secondary, but important objective is to usebiotic assemblages as indicators of environmentalchange, principally that due to anthropogenic activities(Borg and Schembri, 1993, 1995c; Mallia and Schembri,1993, 1995b).As has happened elsewhere, the trend has been to movefrom purely descriptive work to quantitative studies. Forall but a few impoverished benthic assemblageshowever, such studies generate massive data sets. Theready availability of powerful computers has permitted


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10 Micallef R . and Schembri P.

the application of a wide array of sophisticated statistical between the spec ies, using their pattern of distributiontechniques to the analysis of such data sets, allowing among the samples.greater objectivity and more reliable conclusions to bedrawn. However, the statistical analysis of ecological Data in the sample-species matrix can be theoreticallydata can be a double-edged sword - a powerful tool plotted as a multi-dim ensional graph. In Q-M odeprovided that the appropriate metho d is chosen and that analysis, for two specie s, a two-dim ensional graph isits strengths and limitations are un derstood, but obtained, with each axis representing one species. Ifotherwise likely to lead to quite erroneous conclusions Species A is represented on the x-axis, and Species B on(James and McCulloch, 1990 ). This is perhaps even the y-axis, Samp le 1, which contains 2 individuals ofmore so in the local situation, where numerical ecology Species A and 5 individuals of Species B, would be theis a fledg ling field. point (2,5) on the said graph (Fig.1). In R-M odeanalysis, the samples are the axes and the species are theStarting with the basics of data analysis, this paper points.reviews the statistical techniquescurrently used for the analysis ofbenthic assemblages, withparticular emp hasis on those thathave been found suitable for thetype and character of data fromthe Mediterranean. It alsoprovides a brief review of the V) 6development of these .-,techniques, and of their $application to benthic ecological 4research in the Mediterranean. It ais not our intention to review theentire field, nor the underlyingstatistical theory - - th i s hasalready been done by far betterqualified workers than ourselves(for example, Williams, 1971; 0 1 2 3 4 5 6 7Afifi and Azen, 1979; Field etal., 1982; Gauch, 1982; Ludwig Species Aan d 1988' Burd et Figure 1. The multidimensionality of data sets in community ecology.1990; Everitt and Dunn, 1991;James and McCulloch, 1990; Clarke and W arwick,1994). What we attempt to do here is to provide a guideto techniques and to the literature which local workersmay find useful as a starting point when designing anexperim ental, data collection, o r analytical protocol.1. The Data M atrixQ-Mode an d R-Mode ana lys isCommunity ecology data is usually based on an analysisof the species present in the given samples, including ameasure of abundance. The standard method ofpresenting these data is in the form of a sample-speciesmatrix (Table 1).

Since plots beyond the third dimension cannot bevisualised (although they can be calculated), and sincecases of data with less than four samples or species areseldom encountered in practice, statistical m ethods mustbe invoked to summarise the data to a two- or three-dimensional representation. Besides summarisation,which must be relatively objective and produceeffectively presentable results, 'pattern analysis'techniques should also help ecologists to investigate thestructure in their data (Gauch, 1982). Such asummarisation entails discarding some of theinformation (dimensionality) present in the sarnple-species matrix.Statistical analysis procee ds from this table and can be Th e simplest technique s reduce the dimen sionality of theperformed in two modes, Q-Mode (Normal) and R - data to a minimum - a single variable for each species o rMode (Inverse). Q-M ode analysis seeks to determine sample - hence losing a considerable amount ofrelationships between samples, based on a comparison of information. Such techniques are known as univariatethe distribution of species within each sample. R-mode techniques. More complex methods (distributional andanalysis, on the other hand, focuses o n relationships multivariate techniques) take more of the dimensionalityTable 1 . Sample-species matrix


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The Application of Multivariate Analytical Techniquesinto account. Data sets in community ecology aremultivariate (multidimensional), hence theoretically bestanalysed by multivariate methods, and the discussion ofsuch analyses will constitute the bulk of this paper.However, we shall begin by taking a brief look atunivariate techniques.2. U niva r i a t e a na ly t ic a l m e thodsThere are two main approaches to univariate dataanalysis. One reduces the data for a sample to an index(a 'diversi ty index' , for example, Shannon-Wiener 's ,Simpson's, and many more; see below) and, using'traditional' statistics (analysis of variance, the chi-squared test, and others), compares the indices. Theother approach is to select an indicator species andperform these same tests on its abundance in differentsamples.2.1 Diversity and similarity measures2.1.1 Alpha, beta, and gamma diversityA typical mo dem 'textbook' definition of alpha, beta, andgamma diversities would be as follows (Lincoln et al.,1998):a-div ersity: T he diversity or richness of a species withina particular habitat, commun ity, local areaor individual sample.0-diversity: T he richness of a species in a specifiedgeographical reg ion; the rate and extent ofchange in species along a g radient f rom onehabitat to others.y-diversity: Th e richness of a species across a range ofhabitats within a geographical area orin widely separated areas.Diversity, however, is one of those concepts in ecologythat have proven to be very elusive to mathematicaldefinition. Robert H. Whittaker introduced the idea ofdifferent level s of diversity in the 19 60s and this

continued to develop through the years, with muchactive participation on his part (Colinvaux, 1993). Theoriginal idea sparked from the dichotomi between'within habitat diversity' and 'between habitat diversity'which Whittaker called alpha and beta diversity,respectively. Extending the conc ept, we get, on on e side,point diversity, that is, diversity found in very smallsamples, and on the other side, gamma diversity, that is,diversity between whole regions. The inherent problemwith such a classification is the subjectivity of scale, thatis, what one understands by 'small samp le', 'habitat ' , and'region'.In 1972. Whittaker redefined beta diversity as "ameasure of the rate and extent of change in speciesalong a gradient, from one habitat to others"(Southwood, 1978). Mathematically, Whittaker firstexpressed his second version of 0-diversity as the ratioof a-diversity to y-diversity, and eventually refined thisto consider it equal to the mean similarity among sites.Th e most significant point to note, however, is that 0 -diversity is a vector qua ntity (ignoring Whittaker's initialand forgotten definition) while a - and y-diversities arescalar, although both kinds are very elusive toquantification.As all natural ecosystems exhibit some degree ofdominance, whereby a few species are much moreabundant than the rest, it is clear that a goodquantification of a - or y-diversity must inclu de, besidesnumber of species (species r ichne ss) , some m easure ofevenness, that is, the relative proportions of individualscontributed by each species (for mathematicalapproaches to the phenomenon of dominance see Cassie,1962; Whittaker , 1965; McNaughton and W olf , 1970;Tokesh i, 1990). A habitat with 10 0 individuals and 1 0distinct species is considered to be more diverse if eachspecies contributes 10 individuals than if on e species

Station

contributed 91 of the individualspresent. The weight one gives toeach of these two ingredients(richness and evenness) is asubjective issue, and the amountof recipes available, moreofficially termed diversityindices, is immense. AsSouthwood (1978) puts it, "thereis no universal 'best-buy',although there are richopportunities for inappropriateusages", and one must select anindex according to the purposeof one's research. A typicalindex is the Shannon diversityindex1 (see Fig. 2).2.1.2 Similarityldistance measuresGiven this situation, it isvirtually impossible there canever be a universally acceptedabsolute measure of diversity,Figure 2. Univariate measures: Shannon-Wiener diversity with standard error bars for a and much of the current effortlocal benthic data set (see Micallef, 1997 and Appendix B) . TX (diamonds) = Ta 'Xbiex site; ZP (circles)= Zonqor Point site; M P (triangles) = Mignuna Point site. ' More properly known as the Shannon-For each site, the stations are arranged on the x-axis in order of increasing Wiener index, it is incorr-distance from the shore. Note that the three sites have different patterns of ~ ~diversity change with de pth, reflecting the level of pollution at each site. p.651.


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12 Micallef R . and Schembri P .goes into the field of P-diversity, that is, relativemeasures of the change in diversity from habitat tohabitat. Here too there are numerous indices,representing similarity (or distance, its inverse) betweenhabitats. However, from mathematical examination andpractical use, a handful of measures have proven to bevery robust, and are becoming established as standardsin all fields of ecology; notable amongst these is theBray-Curtis coefficient (see Faith et a[., 1987).It is significant to note at this point that similarity (ordistance) measures, although considered as measures ofP-diversity, can actually distinguish clearly between twohabitats with the same species richness and dominancepattern, but with different species composition. Thisbroadens their scope beyond studies of anthropogeniceffects on ecosystems, wherein changes of diversity withpollution levels are well defined, to the study of howcommunity composition varies along more subtleenvironmental gradients. The idea of comparativemeasures also lends itself to better mathematicaltreatment, hence, comparing N habitats, or in practice,samples, we do not end up with 10 values of absolutediversity, but, taking the similarity (or distance) betweeneach and every habitat or sample, we obtain N ( N - 1 ) / 2values (assuming the measure taken between habitats/samples j an d k is the sam e as that between k and j). Thismeans that each habitat or sample contributes to N -1 ofthe variables, and s o the data for each habitat or sample,which is multivariate in nature, is not tied up into onevariable, as in the former case. Analysis of this type ofdata, although m ore comp utationally demanding, is thusdesirable, as it contains more information than for theunivariate case, and is not over-sum mxise d on the onset.2.2.3 Diversity indices an d indicator speciesAs we have seen, diversity is difficult to quantify, andthe choice of a suitable diversity index can be quitedemanding. On the other hand, selecting an indicator

Species rank

species is also problematic. In typical ecological datasets, a few dominant species are present to some extentin most, if not all, of the samples. It is clear that thesespecies are ubiquitous, and variations in theirabundances tend to reflect the cl u m ~ e d istribution ofindividuals characteristic of most ecological systems,rather than consistent patterns in biological or physicalparameters (e.g. pollution gradients). o n the othkr han d,many rare species will be present i n very few of thesamples, hence their occurrence is so sporadic thatanalysis based on these species tends to be too noisy toprovide any insight into interesting patterns andrelationships, especially if standard parametric modellingis used (see below). The significance of all this is thatindicator species are hard, if not impossible, to decideupon a priori. That is to say, one cannot easily select agood indicator species before one sees the data set to beanalysed. And here is the point: selecting an indicatorspecies after having examined the data set, that is, aposteriori, is statistically unacceptable. This is becausethe selection is based on the idea that this s~ecies sbetter than others according to some criterion chosen bythe analyst, and this introduces bias in the rest of theanalysis.2.2.4 Standard parametric m odellingStatistical testing can be broadly classified into two maintypes: parametric tests, which assume that the datafollow some particular distribution (e.g. normal,binomial, linear); and no n- pa ra m et ri c tests, that makeno such assumptions. Parametric tests are usually morerobust and powerful than non-parametric ones, but areuseless if the actual distribution of the data departssignificantly from that assumed . To reme dy th is, the datamay be modelled, the distribution determined, and thenmathematically transformed to fit the distributionassumed by the test (usually the normal distribution).However, this procedure is n i t very practical, and givenits poor performance with actual ecological data, it isdiscouraged by many workers in& the field (e.g. Clarke andWarwick, 1994)+A' XBlEX- * - Z O N Q O R P O I N T

- - .- A - - - M I GN U N A P OI N T

2.2 Dist r ibu t iona l methodsSeveral distributional methods ofanalysis have been proposed,however, although more robustthan univariate methods, they areusually less powerful thanmultivariate analytical methodsas they still largely ignore themultivariate nature of the data.These methods will not betreated in detail, given that thefocus of this review is mainly onmultivariate methods, however,K-Dominance Curves and plotsof Abundance-Biomass Compar-ison (ABC plots) will be brieflydiscussed because of theirincreasing use in studies ofbenthic assemblages, partic-

Figure 3. K-dominance plot for the algal taxocene from a local benthic study (see Micalle f, ularly those concerned with1997 and Appendix B). Note that Ta' Xbiex, the most polluted site, had the lowest pollution.diversity.


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The Application of Multivariate Analytical Techniques 13

ABUNDANCE

BIOMASS

10

Species rankFigure 4. Abundance-biomass (ABC) curves for the molluscan taxocene from a samplecollec ted using a hand-net (60 strokes covering an area of ca.20m2) from aPosidionia oceanica meadow a t a depth of 16m off the White Tower headland,Malta. (Hassan Howege, unpublished). This plot is typical of a non-polluted, non-disturbed system.In k-dominance curves, each sample is represented by aplot, and comparison of sample-sites involves comparisonof these plots. The species within the sample are rankedaccording to dominance (the highest in abundance orbiomass first), and placed on the x-axis, which has alogarithmic scale. On the y-axis, the cumulative percentageabundance is plotted (Fig. 3). The purpose of such curves,as stated by Clarke (19 90) is:"to extract information o n the dominance pattern within asample, without reducing that information to a singlesummary statistic, such a s a diversity index."In a set of k-dominance curves one expects the curves withlowest diversity to reside on top of others with higherdiversity. Thus in samples with low diversity, one usuallyfinds a few species with very high abundances - these arehence the lowest in abundance rank and cause the first fewy-values in the c urve to be very high. Mo re diverse sampleswould have less dominance and hence lower initial y-values, so that the plot is less elevated than for less diversesamples. The span of the cu rve in the x-dimension indicatesthe total number of species (species richness), that is, thesecond component of diversity.A numb er of mod ification s may be introduced to render theplots clearer for the purposes of inspection. One may opt tocompare dominance separately from number of species byre-scaling the x-axis from 1-100 (relative species rank),hence obtaining Lorenz Curves. Another option is to

transform the y-axis for sets ofsamples wherein the curvesapproach a cumulative frequencyof 100% for most of their length.Clarke (1990) proposes the useof the logistic transformation:yie= log [(I + y,) l( lOl- yi)]

Some researchers have alsoproposed the use of partialdominance curves wherebyearlier values cannot affect laterpositions on the curve (seeClarke, 1990 for details).In ABC plots, the principle isextended such that tw o attributesare considered on the y-axis -cumulative percentage biomassand cumulative percentageabundance, and tw o curves result(Fig.4). Warwick (1986) hypo-thesises that in non-disturbedcircumstances, the biomasscurve rests over the abundancecurve, but as pollution (andhence disturbance) increases, therelative positions are expected toshift so that the abunda nce curveresides above the biomass curve.Several recent studies .(e.g.Reizopoulou et al., 1996) havefound this technique quite robust-for use in marine ecology. A

very clear account of the use of ABC plots is given inClarke and Warwick (1994).Distributional methods can sometimes prove to be veryuseful, especially in the analysis of disturbedenvironments. For example, on the 10th April 1991, anoil spill (from the carrier 'Agip Abruzzo') occurred in theLigurian Sea, and Danovaro et al. (1995) set out toinvestigate its effects using univariate, distributional andmultivariate methods. Shannon-Wiener diversity, Hill 'sevenness and some other measures were used in theunivariate analysis, and k-dominance curves were alsoplotted. Grou p average clustering, the AN OS IM test, andNMDS (both using Bray-Curtis similarities derived from4th root transformed data - see below) constituted themultivariate techniques em ployed in this study. The dataon nematodes, identified to genus level, gave veryinterpretable results in the multivariate analysis, but thek-dominance curves gave a clearer picture.3. The multivariate nature of ecological data sets3.1Features of nudtivariate data setsWe have already stated that data sets in ecology aremultivariate in nature, and as Clarke and Warwick(1994) emphasise, highly so. This is because everysample is described by several species abundances, eachof which is considered as a different variable, and,inversely, each species is described by its abundances inseveral sam ples.


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14 Micallef R. and Schembri P."The need for multivariate ana lysis arises whenevermore than one characteristic is measured on a numberof individuals, and relationships among thecharacteristic s make it necessa ry for them to be studiedsimultaneously" (Krzano wski 1972, as cited in Gauch1982).Therefore, the fact that each sample in a typicalcommunity study is described by the abundances ofseveral spec ies, several enviro nmen tal factors, andseveral relationships and associations between thesevariables, clearly explains why ecological data sets arehighly multivariate. Like all other multivariate data sets,they exhibit the followin g four characteristics.

I . RelationshipsSeveral relationships are usually present inecological data: those between samples, whichare elucidated by Q-mode analysis; thosebetween species, which are the objective of R-mode analysis; and combinations of both,investigated by special analytical techniques.Different samples may be taken from differentareas or from the same area at different times.Relationships of species distributions withenvironmental factors are extremelyimportant; if these are known, they revealmuch about community structure,khile on theother hand, knowledge of the latter can helpdetect changes in the former, effectivelymaking community structure a bio-indicator.2. NoiseCommunity data is usually very noisy, that is,many secondary patterns are present thatobscure the more important and interestingunderlying structure. Gauch (1982) gives onedefinition of noise in this context:"Noise is variation in a species' abundancescoord:-zted markedly less with variation inothc species' abundan ces than the larger co-ordinations observed."Such a definition renders the distinctionbetween noise and significant relationships (orco-ordinatio ns) rather subje ctive, but then, thisdepends very much on what one intends tostudy. Causes of noise include localdisturbances, environmental heterogeneity atscales smaller than that of the sample area,and chance occurrence and establishment ofspecies. The goal of analysis is to summarisethe data in such a way as to eliminate noiseand yet retain all the interesting data structure.3.RedundancyRedundancy may be considered as the

opposite of noise. Normally, one is lookingfor recurrent patterns in the data, and the moreclearly these are brought out, the more evidentdoes noise (elements of the data that do not fitthe pattern) become, and hence the easier it isto remove. The elucidation of patterns isenhanced by the presence of redundant data.A definition of redundancy states that it"involves co-ordinate d species' responses andsimilar samples" (Gauch, 1982). In otherwords, samples that are similar to the onesalready present (such as replicates) do notprovide any extra information, they areredundant. Species can also be redundant iftheir abundances reflect directly theabundances of other species (e.g. theirpredators), hence the term 'co-ordinatedspecies' responses' .From the above, it should be clear thatredundancy in the data is desirable forstatistical analysis as it enhances the patternsbeing sought and distinguishes betweeninteresting relationships and noise, such thatthe noise can be excluded. However, aftermaking use of the redundancy in the raw datafor this purpose, the techniques themselvesmust remove it in the summarisation theyproduce. This is because redundancy leftwithin the results of analysis increases thebulk of the data but adds nothing to what isalready revealed. For a good discussion aboutredundancy and techniques for quantifying itin ecological communities, see Clarke andWarwick (1998).4 . Outliers"A n outlier is a sample of peculiar speciescomposition that has low similarity to allother species" (Gauch, 1982)This concept can be extended to species(species outliers) and to groups of samples/species. When a data matrix is composed oftwo or more blocks that differ considerablyfrom each other (a situation known asdisjunction), one block, usually the smallerone , can be considered as an outlier.In the final result, however, statistical outliersare also present: a samplelspecies may seemdifferent from the others simply because ofgaps in sampling and loss of dimensionalityduring analysis (for example, the typical set ofpoints not falling perfectly on the theoreticalregression line in any scientific experiment).An ideal analytical method is expected to


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The Application of Multivariate Analytical Tec h~riq ues 15

produce few statistical outliers.Techniques however must also be evaluatedon their method of dealing with communityoutliers. In community data these are mainlydue to disturbance and environmentalheterogeneity. Some statistical techniquesgive considerable importance to outliers,treating them as representing very longgradients, and hence compressing the rest ofthe data into a very tiny space. This makes itvery difficult, if not impossible, to noticemore significant relationships. The solutionhere is to remove the outliers and re-analysethe data. The most obvious of outliers is anempty sample (all entries are zeros); beforeanalysis using multivariate techniques, allsuch samples must be removed.

Considering the first point (relationships), it is preferableto work with a matrix (in Q-mode analysis) of thesimilarity of each sample with every other sample (e.g.multivariate analysis), than with a list in which eachsample is reduced to a single index value (univariateanalysis). Clearly, multivariate analytical methods aremore suited than univarate techniques to exploremultivariate data sets.The second point determines which techniques succeedand which fail in giving a representation of the dataacceptably close to reality. Statistical techniquesassuming a random distribution of species betweensamples (Q-mode analysis) usually are not suitable, sincein biological communities, the distribution of individualsis often clumped (see Burd et al., 1990). The clumpingdiffers from one community to another, so techniquesthat make no assumptions about the pattem ofdistribution of the data are preferable. Basic statistics donot offer sufficiently powerful methods of this kind,hence more specialised techniques have been 'borrowed'from a wide range of disciplines and introduced into thefield of community ecology. While some of thesetechniques can be extremely powerful if well applied.others can give totally misleading and insignificantresults. The point here is that one must select verycarefully which technique to use. Employing animproper statistical analytical technique may renderuseless years spent collecting data, as the resultsobtained will probably be incorrect or at least very poor.3.2 Treatm ent of data matric es prior to ntultivariateanalysis: the intplications of standardisation andtransforrrzation, and trunc ation of rare spe cies.One of the major problems with the use of univariatemeasures and the analysis of the indices they produce(see below) using parametric statistical techniques (e.g.ANOVA - analysis of variance2). is that such techniquesassume normality while actual community data tend tohave a skewed distribution. Appropriate trat~sformatiotlshelp to reduced the skewness and increase the symmetry2S ee Underw ood (1997) for a thorough account on the use of ANOVAin ecological expe riments.

so that these techniques can be applied. Since theemphasis of this review is on multivariate methods, weshall limit 6urselves to referring the reader to Clarke andWarwick (1994), Downing (1979) and Burd et al.(1990), who provide concise yet very clear introductionsto the subject.When applying non-parametric statistics, such asClassification and NMDS @Ion-metric MultidimensionalScaling), transformation of data sets is useful for a verydifferent reason - to weight the contributions of commonand rare species. A typical data set in marine benthiccommunity work would contain a few dominant (veryabundant) species, a good number of moderatelyabundant species, and some very rare species. The firsttwo categories are usually the most relevant, since therecorded abundance of the very rare species often doesnot reflect reality3.To avoid the useless bulk4 and the noise that very rarespecies confer to data sets, many workers recommendtheir removal. This operation, which we shall hereafterrefer to as 'trutzcation' must, however, be carefullyperformed. Field et al. (1982) recommend that allspecies that never constitute more than p% of the totalabundance (or biomass) of any sample be removed.where p is arbitrarily chosen such that a suitable numberof species are left (typically 50 to 60 species). It is veryimportant not to be 'overzealous' in truncation - formetric ordination techniques (e.g. Principal ComponentsAnalysis), which are very prone to noise caused by thepresence of rare species, it is essential, but NMDSrequires very little truncation, if any.Removing the rare species leaves the very common andmoderately common species. Often, the difference inabundance between these two groups of species isconsiderably large. Since many similarity measuresplace greatest emphasis on the most abundant taxa, themoderately common species, that may be as informativeas the very abundant species (or more), are givensecondary importance. Transformation seeks to addressthis issue, by decreasing the differences in abundanceand hence increasing the importance of moderatelyabundant species in the calculation of similarities5.

Very rare species cannot be acceptably sampled using the normal sizeof samples usually collected in most benthic work their capture istherefore very dependent on chance. In other words, if one individualof species A is recorded in a O.lm x O.lm quadrat, this does notnecessarily mean that A has an abundance of 100/m2 - in fact, this ismost probably incorrect. Similarity, a zero abundance in the quadratsample does not mean that the species is absent in the area. Sometimes,species are also found in unusual places (for example, in the case ofmacrofauna within harbours where fis he m~ en ort catches obtainedfrom deep water and dump the unwanted material at their berth). Rarerecords (e.g. a single specimen in a whole data set), besides beingobviously useless for analysis. add to the bulk of the data set andincrease the nolse.Additional data that is redund ant, that is, it adds to the size of the datamatrix (increasing analysis time immensely) but only serves toeniphasise a pattem that is evident even from a very small part of thedata set.Transfonilations must be used with care. In a recent stud Olsgard etal. (1997) have shown that under certain circumstances, $r examp le,when organisms are only identified to taxonomic levels higher than

species, the results of the analysis are greatly influenced by thetransfomlation used and the effects of transfomlation beconle strongeras taxonomic level increases; moreover, taxonomic resolution andtransfomlation affect the results of analyses in different and unrelatedways.


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16 Micallef R. and Schembri P.Th e most w idely used transform ations fall in the class ofpower transformation where, for an abundance y, thetransformed abundance y* is given by

for example:h = 0.5 for square root transformation, andh = 0.25 for 4t h oot (double square root) transformation.

Logari thmic transformations can be considered as par tof this family, since O, - l ) / h becomes equal to log, y ash a . Hence, since 'h, tends to zero in suchtransformations, they are more severe than dou ble squareroot transformations. On e cannot, however, use log y assuch, as when y = 0 this tends to negative infinity (andzero values abound in community ecology data sets),rendering the calculation of similarity indicesimpossible. Instead, log O, + I ) is used since this giveszero when y = 0. Strictly speaking, this transformationdoes not fall within the power class of transformations.From a review of recent scientific literature on thesubject (see below), it appears that some workers opt touse double square root transformation, while others uselog O,+ 1 ) . Clark e and Warwick (19 94) claim that:"there are rarely any practical differences betweencluster and ordination results performed following F.25or log ( I + y) transformations; they are effectivelyequivalent in focusing attention on patterns within thewhole co mm unity, mixing contributions from bothcommon and rare species."Th e only problem with logarithmic transfo m~ ation s theaddition of a constant (1) to the abundance value. Theresults would tend to differ if data is standardised toabundance per square metre or abundance per 10m2,with the effect of the constant being less felt in the lattercase. Double square root transformation is thereforebetter recommended, as it does not suffer from thisproblem.The most extreme method of transformation is thereduction of abundances to presence-absence data (thatis, all non-zero values are converted to 1). This shiftsimportance decidedly to the moderately abundant andrare species, since, for most assemblages, theseconstitute a larger portion of the data set than thedominant species.The choice of which transformation to use is abiological, rather than a statistical question, and dependson the objective of the study. If the main interest ischanges in the abundance of the most dominant species,a weak transformation (square root) is desirable. If thefocus of attention are the moderately-abundant species,then a mo re severe transformation (4'h root or log)should be applied. Alternatively, if the object of thestudy are the rare species, then presence-absencetransformation may be the most suita ble, possibly withvery little or no truncation (although this protocol isseverely prone to noise, as discussed above). The choicewh ethe r to tr an sfo rm o r not is not merely a biologicalone, however. Some amount of transformation isstatistically necessary in most cases. For instance, abiomass NMDS may be completely distorted by a

chance capture of a very large-bodied species. Similarly,in an abundance data set, a small-bodied species (e.g.barnacle spat) can attain very large abundance valuesand render the presence of all other species insignificant.3.3A brief comparison of measures ofsimilarityldistanceThere are two main classes of similarity (or distance)coefficients, as has been hinted above. One groupconsiders only presence-absence (binary coefficients),while the second considers both presence-absence andrelative abundance (quantitative coefficients).An example of the first class is Jaccard's Coefficient.For two samples, j and k, this considers the number ofspecies common to both (the higher this number, thelarger the similarity) and balances this out with thenumber of species found only in j or in k (this reducesthe similarity). A scaling factor is introduced in thedenominator so that some independence of the actualnumber of species present is achieved and so that thecoefficient takes a value between 0 and 1 (or 0 and100%).The more popular binary measures areS ~ r e n s e n ' sCoeff icient (also known as the Dice orCzekanowski coeff icient) , McConnaughey'sCoeff icient and Ochiai ' s Index . The main problem withthese measures is that they implicitly perform apresence-absence transformation, which is usually toosevere and prone to errors due to the chance occurrenceof rare species, as discussed above.One of the biggest debates on the subject of similaritycoefficients is w hether to introduce joint absences o r not.If all but two of the samples in a data set contain acertain species, would those two samples be somewhatmore similar to each other than to the rest? In certainscientific disciplines, that consider other attributes ratherthan species, the answer may well be yes, but in ecology,where data sets abound with zero values, it makes nosense to consider joint absences. As Field et al. (1982)put it:"Taking account of joint absenc es has the effect ofsaying that estuarine and abyssal samples are similarbecause they both lack outer-shelf species."Table 2 lists the more popular coefficients whichconsider abundance. The idea of introducing abundancesin a similarity measure was first proposed by Bray andCurtis in 1957, who m odified the So rensen coefficient toobtain the measure now known as the Bray-Cur t i sCoeff icient (see Southwood, 1978) . Many havecriticised this measure, mainly becau se of the im portanceit gives to dominant species (it obviously does nottransform the data as do binary m easures), howev er, withappropriate transformation, many now recognise itsrobustness. In the same category as the Bray-Curtisdistance, one finds the C an b er ra Me tr ic , which is alsovery popular among ecolog ists. The re are two objectionsto the use of this measure. The first is that the scalingt e n in the denominator is placed within the summation ,the consequence of which is that rare species are giventoo much importance. Th e second objection is that whenno individuals of a species are present in on e sam ple butare present in the other sample, the index attains its111aximum alue (see Krebs, 1989).


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Tlte Application of Multivaridc Ar~aiylicalTeclirriques 17

Equation"

Canberra metric(Adkinsfom) .

~ucl idia -n istance

DistanceRelative . anh hat tat(Absolute) Distance

Chord Distance

T a b l ~ -2 . The more popular quanrirarive uoefficicnrs (rliiir is. those considering abundances) for comparing w osamples j and k.(a) Symbols: i = ro w (species) no.; n = number of species prcsznr in o n e o r both of die sarnples (species richness of jand k wh en pcoled together); y ,1 = abundance (o r b i on~ a ss )in the given row and colunm of the dam rnarrix.(b) Refercnccs 1 = Krebs (1989); 2 = Clarke and W:~rwick (1994); 3 = Ludwig and Rcynolds (1988); 4 = Brower eral. (1990); 5 = Faith er 01. (1987) .

A second category of quantitative coefficients is theAbsolu te Euclidian family of measures. h e simplest ofwhich is the Ma nh al ta n (Absolute. Ciry-Block) distancelhat provides the link with the previous category (Bray-Curtis and Canberra). Actually, the Bray-Curtis and theCanberra measures are forms of the Manhallan metric.with different standardisations (scaling terms in thedenominator). as can be observed in Table 2. Thequestion of standardisation comes back in EuclidianDistance. which also ranges from zero ro infinity and somay cause some problems in metric ordinations andclassification if il attams very large values6 (see Clarkeand Warwick, 1994). The formula recalls Pythagoras'theorern for the determination of the hypotenuse of aaiangle. Geometrically. it is the 'as the crow flies'distance between two points, while the Manhattandistance (sum o f the shorler sides of the miangle) is h eabsolute distance between two points. hence thealternative name, 'Absolute" (see Fig. I ) .6This is especially so m data scts w i h sevcr;~l ero cntrics. as is ~ypicalin coninlunlly eCo!ogr.

Euclidian g roup d is~ an ce s can be relativised(standardised, scaled) using m ore form al mathematicsh a n in the Canberra or Bray-Curtis renderings of theMarhattan metric. In this group. known as the RelativeEuclidian family. we f ind the Relat iv e Euc lidian (range0 + 2) . Re la t ive Manhat tan ( range 0 + 2) and theChord dis tance ( range 0 + 2) (see Ludwig andReynolds. 1988). The se last lwo m easures have beenfound quite robus1 by F a i h er al. (198 7) using simulateddata.The K ulczynski measure. although no1 very popular. wasalso found to be. among the most robust measuresavailable by Faith er al. (1987). who recommend its use(together with the Bray-Curtis measure and RelativeManhattan). We have also found it to be slightly superiorto the Bray-Curtis measure in the analysis of simulated

' f 011c imagines 3 city with slrcas Idid oul in a regular grid (~iiaybcVallerw. or as the nmic suggests. Mmhman m Nsw York). it is rhcshonrrsl distance one has ro walk lo go iron1 oric place lo another alongh e streets. hcncc the a lterr~arive drrle 'City 131ozk'.


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18 ~MicallefR. and Schembri P.

Satnple 1Sample 2Sample 3Sm1ple 4

Sample 3

S imi l a r i~y 13 Similarity 213 I --Similarity 114 I Sin~ilar i ty 14 S i n d x i t y 314I I --Table 3. Triangular Inatr lr of sinularities t'or a d ; ~ t i ~e[ consisting ul't'oursar~~ple!.

Samples 2+4 Sample 3

Sinlilarity 1 /(2+4)Similar ity 113 Sh i1; ~ri ty 2+4)/3

Table 4. Reduced triangular marrix for h e data in Tablc 3.

F i y r e 5. Dendrogram showing hierarchical classificauon of samples from a local bendicsmdy (see Micallel, 1997 and Appcndix B) based on the similarity of h e algaltaxocen e aggregared to genus levcl. Note that samples labelled C (Mignuna Point)arc separated from prac~ically ll the other samplcs at a similarity level of ca.6%.while those labelled A (Ta' Xbiex) and B (Zonqor Point) are separated at asimilarity lcve l of ca.15%.

data modelled on local marinebenthic assemblages (MicalIef.1997).4. Class i f icat ion an dordina t ion4.1 Clossificution techniquesClassification, or clusteranalysis, involves organisationof the units being analysed intogroups, according to a similarity(or distance) measure calculatedbetween the units. The result istypically presented as a dendro-gratn, a plot that appears ratherlike a family tree or anorganisation chart (Fig. 5 ) . Sucha plot assumes hierarchicalclassification, how ever, reticulateclustering is also possible,whereby the unils overlap like anet. Hierarchical m ethods are byfar the most common, beingeasier to visualise andunderstand (Krebs. 1989).Usually. in community ecology,one takes the similaritiesbetween each pair of samples orspecies to construct a triangularsimilarity muirir (Table 3).As can be seen, the similaritiesalong the top left to boltom rightdiagonal, for instance thatbetween Sample 1 and Sample1, are left out, being obviously100%, and only the mangularsection benealh this diagonal isfilled, as the triangle on theorher side is a m irror ima ge (i.e.Similarity 211 equals Similariiy112).k t us suppose thar the highestsimilarity in Table 3 is thatbetween samples 2 and 4(Similarity 214). One can groupsamples 2 an d 4 together, andproduce a second rnacrix (Table4 )Similarity 1/(2+4) can bederived by several ways. Onemay, for instance, take theaver age between Similarity 112and Similarity 114. a techniqueknown as g r o u p a v e r a g elinkage. Alternatively, one maytake the higher of rhe values(single l inkage) or the lower(comple te l inkage) . Theprocedure we have followed isagglomerative in nature, as i tproceeds with the units beingbrought together at ever lower


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Th e Application of Multivariate Armlytical T echniques 19levels of similarity until a matrix containing only onevalue results. Another way to combine similarities is toassume that all units form part of a group, and then tobreak that group down into subgroups, a techniquetermed divisive classification. Theoretically, divisivemethods are considered superior to agglomerative ones,because in the latter, anomalies at very low levels arefairly common, and since these are locked up in thestructure as it forms, the bad combinations cascade. Inother words, due to the limitations of the similaritymeasures, if two similarity values (such as Similarity 213and Similarity 214 in Table 3) are very close, twodifferent indices may not differentiate between the two(for example, Morisita's Index could consider Similarity214 as higher than Similarity 213, but Jaccard'scoefficient may provide values the other way round).Obviously, there is only one correct natural ranking(although none of the techniques available may be ableto reproduce it faithfully for all values and in everyanalysis) and a discrepancy may cause the wholeclustering pattern to be disrupted, since the actualsimilarities are forgotten as grouping proceeds. Divisivemethods should also be less com putationally demanding,as one is usually interested in the higher-level groups,and a sma ll num ber of operations are needed to divide agroup into a few major~subgroups.However, althoughthis argument makes much sense, divisive methods arenevertheless more computationally demanding since agood method must introduce enough sophistication todeal with the next point (monothetic/polythetic strategies- see below). Due to this problem, divisive methods havenot, as yet, gained much ground in marine ecology,where very large data sets are com monplace. In plantecology, however, divisive clustering using techniquessuch as TWINSPAN have been used extensively.The easiest divisive strategy to conceive is monothetic.

We have been assuming during this discussion thatclustering is based on similarity measures. Taking twohypothetical sam ples, 1 and 2, a rudim entary sim ilaritymeasure can be constructed by considering the numberof species found in both. out of the total number ofspecies. This is a presence-absence measure, as it doesnot take relative abundances into account. We can, ofcourse, consider abundances, to achieve measures suchas the Bray-Curtis similarity. On the other hand, we maynot work with similarity measures at all, but take theabundance of a single species, or, in general, anyparticular variable, and use it to compare the units(samples). W e have thus constructed a univariate versionof cluster analysis, better known as a monotheticclassification. In divisive strategies, the easiest way todivide a group is to find a single attribute found in someof the members but not in others, and separate the unitson this basis. This is monothetic divisive clustering, andit suffers from the severe limitations we met in otherunivariate techniques. Dividing groups by taking severalcriteria into account at once is also possible, but requiressophisticated algorithms demanding m uch co mputationalpower, and that are more difficult to understand(Williams, 1971), hence turning the analysis into ablack-box. Because of this, many ecologists have steeredclear of divisive techniques, and for the purposes of thepresent review, it would not make much sense to delvefurther into this abandoned area of statistical ecology.The clustering method of choice for the analysis ofbenthic assemblages is polythetic hierarchicalagglomerative @HA) classification.A final point about linkage needs to be made. Single andcomplete linkage are theoretically attractive since theyare non-metric. If, instead of the original triangularsimilarity matrix, one alters the matrix so that the actualvalues are replaced by similarity rank. an identicaldendrogram would be obtained.

Simil-arity

100%

Simil-arity

A B C D E

SamplesA B C D E F

Samples

-This is an advantage over group-average clustering. However.sin& linkage has tendency toform chains of linked samples,with each successive stage in theagglomerative process simplyadding another sample to anever growing group (Fig. 6A).while complete linkage has theopposite effect - it producesmany small clusters at an earlystage (Fig. 6B).In practice, most workers prefergroup-average linkage (seeliterature review below) as it hasbeen found. from experience. toachieve an acceptable balancebetween these two extremes.Classification of simulated datasets modelled on local marinebenthic assemblages hasc o n f i m ~ e dhis to be hue also forlocal situations (Micallef. 1997).

Figure 6. Typical results obtained using (A) single linkage, and (B) complete hkage, in Several researchers have foundpolythetic hierarchical agglomerative classification of five samples. that group-average hierarchical


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20 Micallef R . and Schembri P .

agglomerative clustering is efficient in the detection ofchanges in the structure of benthic assemblages along apollution gradient, particularly when combined withother methods as recommended by Clarke and Warwick(1994). For example, Simboura et a/ . (1995) appliedABC curves and this clustering strategy after-transforming the original data matrix using loglo, and tcomparing the samples using the Bray-Curtis similaritymeasure. Univariate measures (Shannon-Wiener'sdiversity, Pielou's evenness) were also used. Thetechniques confirmed one another and provided a clearpicture of the situation. Reizopoulou et al. (1996)compared macrozoobenthic assemblages in threeMediterranean lagoons (Tsopeli in the Ionian Sea, Vivariin the Aegean Sea, and Goro in the northern Adriatic)having different levels of disturbance. Comparisons ofdiversity (Shannon-Weiner's index), ABC plots andgroup-average cluster analysis (of loglo transformeddata, using the Bray-Curtis similarity measure) wereperformed. The latter two methods separated the threelagoons, and the dredged site at Goro was clearlydistinguished from the other sites that were not asdisturbed.4.2 Ordination techniquesOrdination seeks to depict a multidimensional data set asa low-dimensional plot in which similar entities areplaced close together and dissimilar ones far apart. Thevariety of techniques available is immense, and here weshall only consider the major ordination-strategies ofrelevance to community ecology.One group of ordination techniques, that has becomeknown as geometric projection methods (Kenkel andOrlbci, 1986), was very popular among ecologists in the1960s and 70s, possibly since these methods weredeveloped by plant ecologists rather than by researchersin other disciplines. The original, and most popular,technique was proposed by J. R. Bray and J. T. Curtis ina 1957 paper published in Ecological Monographsentitled "An ordination of the upland forest communitiesof southern Wisconsin". This technique is formallyknown as Polar Ordination, however, i t is often termedBray-Curtis or Wisconsin Ordination, for obviousreasons. Although the technique is now out of favourwith ecologists, this seminal paper has had a greatinfluence:

It introduced the Bray-Curtis similarity measure(see Krebs, 1989), now very popular among ecologistsdue to its proven robustness (Faith et al., 1987; Clarkeand Warwick, 1994). This was also the first similaritymeasure to consider relative abundance.

It gave rise to a whole range of ordination methodsthat had the effect of promoting ordination techniques inecology, where they were scarcely known.

It also stimulated research in the distribution ofspecies along environmental gradients (see Whittaker,1975), that eventually gave rise to the development ofdirect gradient analysis (see below).Polar Ordination involves selecting two samples to serveas poles at two extremes of an environmental gradient

(typically the samples which the distance measureconsiders most dissimilar), and placing these samples attwo ends of a line, at a distance given by thedissimilarity measure multiplied by a factor x (to convertthe measure to actual distance on the plot paper orscreen). The distance measure between each of the othersamples and the two poles is calculated, multiplied by x,and geometrically speaking, placed at the intersection(on one side of the line) between two circles centred atthe poles and with a radius equal to distance from therespective pole multiplied by x, Obviously, this is inpractice achieved algebraically with a computerprogram.The major flaw in Polar Ordination is the selection of thepoles. The greatest distance is usually that between twosamples of which at least one is an outlier (see Gauch,1982). Choice of the poles is therefore subjective, andmust be done a priori (as has been discussed above),hence, very evident gradients are needed (Kenkel andOrlbci, 1986).A second group of ordination methods are termed metricordination methods, indicating that the actual value ofthe distance measure between any two samples is used inthe analysis and is somewhat conserved even in the finalplot (Minchin, 1987). On the other hand, in the thirdgroup, non-metric techniques, only the rank order ofthe distances between the samples is used.The oldest and best-known metric method is PrincipalComponents Analysis (PCA) and involves the reductionof dimensionality by maximisation of variance along afew main axes. In other words - taking the two-dimensional case - it works by extrapolating points on atwo-dimensional graph, normally onto the line of best fit.Doing this in the multidimensional case produces theprincipal component (axis 1) such that when all thepoints are extrapolated onto this line, the greatestdistance (least clumping, maximum variance) betweenthe points is achieved (Fig. 7). The second axis must beperpendicular to the first, and, given this criterion, mustachieve maximum variance. In the three-dimensionalcase, the third axis is defined by virtue of the first twoand the criterion that i t must be perpendicular to both,but in n dimensions, there are n-1 axes that can beproduced independently ( n - 1 degrees of freedom). Usinga statistic, one obtains the variance (information)explained by each component, and for an acceptabletwo-dimensional plot (axis 1 vs. axis 2) a considerableamount of the variance (typically >70%) in the data mustbe given by these two components.The concept of 'line of best fit' is derived from theapplication of sum of squares and cross-products (SSCP)techniques, which assume linearity of the data. Formally,this type of analysis is termed eigenanalysis. PCA worksdirectly on the original data matrix, having an in-builtdistance measure (the Euclidian distance). One PCAvariant, PCoA (Principal Co-ordinates Analysis) workson triangular distance matrices (hence allowing muchmore flexibility*) - this is also termed metric

In other words, i t does not use Euclidian distances (and hence doesnot suffer the problems relative to this class of measures discu ssed inthe last p n f section 3.3)


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The Application of Multivariate Analytical Techn iques 21

multidimensional scaling. PCA, and PCoA areconceptually simple and computationallystraightforward, however, they have the followinglimitations:The amount of distortion introduced at eachreduction in dimensionality builds up and cannot beremoved down the chain - hence, their distance-preserving properties are poor.

They give too much weight to the actual value ofthe distance coefficient - hence, they are extremelysensitive to outliers that in practice compress most of therelevant sample (or species) points to a tiny area at thecentre of the plot, making interpretation impossibleunless the outliers are removed aposteriori.They assume independence (orthogonality) offactors (components), which must therefore beperpendicular to one another. This adds to the rigidityand care must be exercised in interpretation asmathematically independent factors need not represent

independent patterns in nature (James and McCulloch,1990).They assume linearity, that is, that distribution of

the proportions is approximately normal. To someextent, this requirement may be satisfied by proper

transformation of the original data set (e.g. logarithmictransformation).PCA is very rigid in defining similarity (does notapply for PCoA).

Another PCA variant is known as Factor Analysis. Thisdoes not require orthogonality (independence) of factors,and seeks the maximal correlation among the variables,rather than maximum variance.Correspondence Analysis (CA, also known asReciprocal Averaging) is the basis of another family ofmetric techniques, based on an older and quite subjectivemethod known as weighted averages ordination (WA).In the latter, species (for example) are given weights(quite subjectively), and the matrix is transformed tomultiply each cell by the respective species weight. Asample score in the ordination results from the averagingof the transformed entries for each species within thatsample. Hence, one obtains sample scores from speciesscores (the weights). It is of course also possible to dothe reverse analysis, that is, to obtain species scoresstarting from sample scores.Correspondence analysis starts by arbitrary assignmentof species scores (weights) and thence calculates samplescores (or vice versa). The second iteration works out

Principal component 1Figure 7 Two-dimensional PCA ordination of the abundance of decapod crustaceans

(double square root transformed) in 17 suction sanlples collected from a localPosidonia oceanica meadow. Samples were collected from 6m (A), 1 m (B), 16111(C) and 7-1111 (D). The numeral indicates the collection period: 1 - August 1993, 7-- December 1993.3 - April 1994. PC1 (x-axis) and PC2 (y-axis) together accountfor 78% of the total sample variability. Note segregation of the shallow water

species scores from the samplescores calculated in the firstiteration, and so on, until thescores stabilise. The scores thusconverge to a unique solutionafter a number of iterations,which solution is not influencedby the initial (arbitrary) choiceof scores (hence removing thesubjectivity in WA). Although atfirst sight this seems to havevery little to do with PCA, it isnonetheless another form ofeigenanalysis (see James andMcCulloch. 1990). The finalscores are actually the first axis,comparable to PCA's principalcomponent. The second axis ofCA (and further components, ifrequired), is obtained in a similariteration procedure, but thelinear effects of the first axis arefactored out (see Palmer, 1993).The method suffers from what isknown as the arch effect(curvilinear distortion, horseshoeeffect: Clarke and Warwick,1994: Minchin, 1987: Palmer,1993: James and McCulloch,1990; Gauch 1982). To add yetanother metaphor to an alreadyample list. an ordinationsuffering from this effect

samples (6m and l lm ) f& the deeper water samples (16111 and 21n1). (Data re-analysed from Borg and Schembri, 1998). L

appears as a 'rainbow' of sample(or species) points, with the~ o i n t swell s e~a rat ed long one


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22 Micallef R. and Schembri P.

axis and very poorly distanced along the perpendicularaxis. PCA and PCoA also suffer considerably from thisphenomenon. Hence, a variant of CA has been proposed,known as Detrended Correspondence Analysis (DCAor DECORANA), that essentially splits the CAordination space into segments, and stretches or shrinksthe scale in each segment accordingly to remove the archeffect. Although this appears to be too manipulative tosome, it is done with considerable objectivity. However,some arbitrary decisions are in-built in the algorithm andhidden from the user - thus it "[erects] a communicationbarrier between the data analyst and ecologist" (Clarkeand Warwick, 1994) as the algorithm is conceptuallycomplex.The third class of ordination methods that we shalldiscuss is that of non-metric methods. The best knowntechnique is NMDS (Non-Metric MultidimensionalScaling) which, as has been stated above, uses rank orderof the values in the triangular similarity (or distance)matrix. The sample points are typically spread outrandomly in a three-dimensional space, and theirpositions optimised (to reflect the distance rank order,either locally or globally - see Minchin, 1987) by amathematical algorithm until a minimum value of stressis reached (Fig. 8) . The data are similarly reduced from

3- to 2-dimensions (see Clarke and Warwick, 1994). Theprocedure has a tendency to find local stress minima andget locked inside these 'small holes' without finding the'big crater', using the analogy of a ball thrown on roughground. To rninimise the possibility of not finding theminimum stress configuration, the procedure must berepeated several times (with different starting positions)from which the final configuration with the minimumstress value is adopted. (More details on the NMDSalgorithm are in Appendix A.)Another form of ordination known as GaussianOrdination (Gauch and Chase, 1974; Gauch et al.,1974) seeks to maximise the least-squares fit of theabundance of each species in a sample to a Gaussiancurve, hence obtaining sample points (from a first-guessarrangement) by "iterative fitting that chang es theordination values to produce optimal Ga ussia n it for allthe species together" (Gauch et al., 1974). After severalevaluations of the technique by a number of workers,Gauch himself dismissed it due to its computationalcomplexity (Gauch 1982) while Minchin (1987) foundthe method to be highly sensitive to quantitative noise.The technique is now out of favour with most ecologistsand is hardly mentioned in the literature.

Figure 8 NMDS plot for the molluscan taxocene from a local Cymodocea nodosa meadow,based on abundance, after truncation at the 3% level, double square roottransformation and using the Kulczynski similarity measure. Stress = 0.12. Theradius of the circles is proportional to the Cymodocea shoot density. Note theclear separation into two groups: an upper one consisting of samples collectedfrom 4m where shoot density was high, and a lower group collected from 8mwhere shoot density was low. (Data re-analysed from Howege and Schembri,1997).

A mathematical treatment ofmost of the above techniques canbe found in Afifi and Azen(1979) and in Everitt and Dunn(1991), amongst others.5. Other statistical methodsHereunder we discuss someother statistical techniquespertinent to the analysis ofcommunity ecology data.1. Direct Gradient Analysisembraces a set of techniques thatdisplay the distribution oforganisms along gradients ofimportant environmental factors.One way this is done is to fit astatistical distribution (typicallythe normal or log-normal curve)to each species within samplestaken along an environmentalgradient. This form of directgradient analysis can be used toconstruct models on whichsimulations can be based. A vervinteresting technique, (Detren-ded)CanonicalCorrespondenceAnalysis, is a canonicalAnalysis variant involving tR,?fusion of species-sample datawith environmental data toproduce a separate ordinationmethod (see ter Braak, 1986;Palmer, 1993; ter Braak andVerdonschot, 1995; Thiolouse etal., 1995).2. Ordinations can be compared


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using a technique called Procrustes Analysis (seeSchonemann and Caroll, 1970). Manually, this involvesstandardising the axis ranges (from 0 to 100) of twoordination plots, constructing the plots o n transparencies,and rotating the two until the best fit of one plot on theother is achieved. The root mean square average of thedistances between the observed and expected samplepoints gives a very robust statistic for evaluation of theordination method. Procrustes analysis is themathematical rendering of this plot-fitting algorithm.3. One type of non-parametric multivariate test fordifferences between groups of samples is ANOSIM(analysis of similarity, by analogy with ANOVA,analysis of variance), first described in Clarke and Green(1988). ANOSIM is used to test the hypothesis that anumber of samples in the data matrix constitute a group9.Starting from the triangular similarity matrix convertedto rank order similarities, one computes a test statisticcomparing the within-site differences (in the groupingsbeing tested) to the between-site differences, thenrecomputes the statistic under permutations of thesample labels to create a permutation distribution fromwhich the significance level of the first value can beestimated. The method can be extended to more complextwo-way grouping designs (see Clarke and Warwick,1994).4. In most studies on marine assemblages, the ultimateaim is usually to determine what is causing thecommunity structure to be the way it is. Abioticvariables for each sam ple, such as water temperature anddepth, suspended matter, sedim ent granulometry, organiccontent of the sediment, and the concentration ofchemical pollutants, are often determined in typicalstudies. The analysis of these parameters is lessdemanding on techniques than that of biotic variables --metric ordinations such as PCA, and distance measuressuch as Euclidian distance, which are not robust forspecies-samples m atrices, give acceptable results in suchcases, where zero values are rare.Linking environmental variables to ordinations can beperformed at several levels as described below, usingNM DS a s the ordination technique of choice.a. Sing le ab io t ic var iab le :If this is a discrete quantity (for examp le, mean sedimentparticle size or sea-grass s hoot density). one can give thedifferent values of this parameter different numbers orsymbols and plot these on the NMDS instead of thesample names (as has been done in Fig.8).b . Two or m o r e a b io t i c v a r i a b l e s(comparison of plots) :For two abiotic variables, a scatter diagram may beplotted. Otherwise an NMDS or PCA of the abioticvariables can be performed. The resulting scatterdiagram or ordination plot may be compared to the bioticordination using Procrustes analysis. The problem withg ~ eroup must be selected apriori: one should nor apply this test onclusters resulting from n~ ultiva riate nalysis (see Clarke and Wa wic k.1994)

this me thod , is that the. results depend on thedimensionality of the final plot.c. T wo o r m o r e a b io t i c v a ri a b l es(compar ison o f t r ian gu l ar matr ices) :One may rank the similarities in the triangular similaritymatrix for the biota, and in that for any two abioticvariables, and then compare the ranks of the biotic andabiotic triangular matrices using a weighted Spearman(or harmonic) rank correlation, a standard non-parametric statistical procedure. A statistic is obtainedthat takes values between -1 (ranks in completeopposition) and +1 (ranks identical). T he significance ofthis 'cam ot, however, be evaluated from statistical tables,since the similarities that are used for constructing theranks are not independent. However, one can create apermutation distribution similar to that for ANO SIM (forexample, the PRIMER suite of programs [Clarke andWarwick, 19941 includes one called RE LA TE) that canbuild such a distribution to test significance of thestatistic.The potential of this method extends much farther. Letus take, for example, the case where we have threeabiotic variables. A triangular similarity matrix of abioticvariables 1 and 2 (subset 1,2) is const ructed (usingEuclidian distancelo), ranked, and compared to theranked biotic triangular matrix to obtain a value of~ ( p ~ , ~ ) .his is repeated using abiotic variables 1 and 3,and again for variables 2 and 3, to construct the abiotictriangular similarity matrix" and determine p for eachca se (plV 3 nd ~ 2 , ~ ) .he combination of environmentalvariables giving the highest value of p should thereforeindicate the variables that are influencing the communitystructure most.ConclusionThe availability of a set of powerful statistical techniquesfor data analysis. we hope. will se rve as an inc ent ive formore studies on the benthic assemblages of the MalteseIslands. These techniques may also be applied to the re-analysis of exist ing-data-si ts, w h c h -ma y not haveyielded very useful results when analysed using moretraditional methods. The potential benefits of re-analysesof old data-sets have been amply demonstrated by. forexample, Papathanassiou and Zenetos (1993) who re-analysed the data of Zenetos and Papathanassiou (1989).Th is was a study of the recov&y of the benthicassemblages after the introduction of a tannery-effluenttreatment plant in the Gulf of Geras (Aegean Sea), whichreduced chemical pollution considerably. Th e re-analysise m p lo y ed u niva ri at e m e asur es ( ~ h a n n o n - ~ e in e r ' sdiversity index. Pielou's evenness), k-dominance curves.average-linkage herarchical agglomerative classl-fication. non-metric MDS and ANOSlM tests (the latterthree techniques being perfoimed 011 triangular similaritymatrices derived from log,,, transformed data, using theBray-Curtis similarity measure). The authors concludetheir 1993 report thus (Papathanassiou and Zenetus,1993):10As suggested by Clarke and Ain swo ~th 1993)." A PRIMER procedure called BIO-ENV calculates p fu r a l l p s s ib lecombinations of variables. Mole details are givm in Clarke andAinswonh (1993) and m CLrke and W aw ick (1994).


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24 MicaNef R. and Schembri P.

"The multivariate techniques and graphical descriptors(k-dominance curves) have detected the effects ofrecovery from pollution. Univariate methods, however,can only be applied with success in obvious cases ofmarked community disturbance and pollution impact .."Locally, Micallef (1997) re-analysed the data in Borg(1991), Mallia (1991) and Mallia (1993), again withfruitful results.However, given the wide array of methods available, andthe numerous formulations in which they can be applied,one has to find out which protocol works best in aparticular situation. Techniques that work well, say inthe Atlantic and North Sea, (for example the PRIMERprotocol) may not be so efficient in a different ecologicalsetting, such as the oligotrophic central Mediterranean.Zenetos et al. (1991) made use of M argal efs index12 ofdiversity to compare benthic communities in theCyclades Plateau (Aegean S ea) together with NMDS andgroup-average clustering on loglo transformed dataapplying the Bray-Curtis similarity measure. Theycompared ecological and palaeoecological data sets, andconcluded that care must be applied when drawingconclusions from limited data sets using these methods,since the expected separation into depth groups wasobserved when the analysis was performed on the totalliving fauna (329 taxonomic units) and the deadMollusca (211 taxonomic units), but it was not somarked when only the living Mollusca (41 taxonomicunits) were used.Recent work by the authors has sought to establish aprotocol of techniques best suited for local data sets(Micallef, 1997). Using standard parametric modelling,information was extracted from typical local data setsand used to create simulated data sets with thecharacteristics of local benthic communities. These weresampled using a known pattern, that NMDS and ClusterAnalysis were expected to reproduce. Using a variety ofsimulated communities, transformations, truncationmethods an d similarity indic es, we noted whichtechniques gave ordinations and classifications that bestreflected the original sampling pattem13 and henceestablished an optimum protocol of procedures.It was found that the removal of species that haveabun danc es of less than 3%14 in all sample s, such that adata set with not less than 30 species is obtained, helpsanalysis as it removes rare species (a considerable sourceof noise). Transformation of abundances to 4th oot wasfound to be necessary to decrease the differences in theeffects of rare and dominant species on similaritymeasures. Th e Kulczynski similarity measure was foundto be very robust, followed closely by the Bray-Curtissimilarity measure. Other results derived from this studywill be discussed in a future publication.AcknowledgementsThe data used to construct some of the illustrations thataccompany this work were collected by Joseph A. Borg,12A univariate measure'?Two-dimensional plots were compared by Procrustes Analysis.14Of the total abundance of al l species within a sample.

Adrian Mallia, and Dr Andrian Vaso, with the taxonomicassistance of Edwin Lanfranco, Constantine Mifsud andHassan M. Howege, and the technical assistance ofSarah Debono and Konrad Pirotta, as part of a projectdirected by Prof. Victor Axiak (Department of Biology,University of M alta) and partly fun ded by the EuropeanCommission under its MedSPA programme. We aregrateful to all these persons. Other data were provided byJoseph A. Borg, Hassan M. Howege and Adrian Mallia,whom we thank. We thank also Dr Richard Warwick(Plymouth Marine Laboratory, UK), Dr Michele Scardi(Stazione Zoologica 'Anton Doh m', Napoli, Italy) and DrTim T.J. Kenwards (Zeneca Agrochemicals, UK) forproviding valuable literature references. W e a re indebtedto Dr Martin Attrill (University of Plymouth) whorefereed this paper and offered many helpful suggestionsfor its improvement. This work was supported by aresearch grant from the University of Malta to PJS, forwhich we are grateful.

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the application of multivariate analytical techniques to the study of marine benthic assemblages....

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