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CHAPTER 13SPECIES DIVERSITY MEASURES(Version 5, 23 January 2014)Page13.1 BACKGROUND PROBLEMS . 53213.2 CONCEPTS OF SPECIES DIVERSITY . 53313.2.1 Species Richness . 53413.2.2 Heterogeneity. 53413.2.3 Evenness . 53513.3 SPECIES RICHNESS MEASURES. 53513.3.1 Rarefaction Method . 53513.3.2 Jackknife Estimate . 54713.3.3 Bootstrap Procedure . 55113.3.4 Species Area Curve Estimates . 55313.4 HETEROGENEITY MEASURES . 55413.4.1 Logarithmic Series . 55513.4.2 Lognormal Distribution . 56413.4.3 Simpson's Index . 57613.4.4 Shannon-Wiener Function . 57812.4.5 Brillouin’s Index. 58313.5 EVENNESS MEASURES . 58413.5.1 Simpson’s Measure of Evenness . 58513.5.2 Camargo’s Index of Evenness. 58613.5.3 Smith and Wilson’s Index of Evenness . 58613.5.4 Modified Nee Index of Evenness . 58713.6 BETA-DIVERSITY MEASUREMENTS . 58813.7 RECOMMENDATIONS . 59013.8 SUMMARY . 591SELECTED REFERENCES . 592QUESTIONS AND PROBLEMS . 593

Chapter 13Page 532A biological community has an attribute which we can call species diversity, andmany different ways have been suggested for measuring this concept. Recentinterest in conservation biology has generated a strong focus on how to measurebiodiversity in plant and animal communities. Different authors have used differentindices to measure species diversity and the whole subject area has becomeconfused with poor terminology and an array of possible measures. Chiarucci (2012)and Magurran and McGill (2011) have reviewed the problem. The problem atpresent is that we have a diversity of measures for communities but they do notalways perform well (Xu et al. 2012). In this chapter we explore the measures thatare available for estimating the diversity of a biological community, and focus onwhich measures are best to use for conservation assessment.It is important to note that biodiversity has a broader meaning than speciesdiversity because it includes both genetic diversity and ecosystem diversity.Nevertheless species diversity is a large part of the focus of biodiversity at the localand regional scale, and we will concentrate here on how to measure speciesdiversity. The principles can be applied to any unit of ecological organization.13.1 BACKGROUND PROBLEMSThere are a whole series of background assumptions that one must make in order tomeasure species diversity for a community. Ecologists tend to ignore most of thesedifficulties but this is untenable if we are to achieve a coherent theory of diversity.The first assumption is that the subject matter is well defined. Measurement ofdiversity first of all requires a clear taxonomic classification of the subject matter. Inmost cases ecologists worry about species diversity but there is no reason whygeneric diversity or subspecific diversity could not be analyzed as well. Within theclassification system, all the individuals assigned to a particular class are assumedto be identical. This can cause problems. For example, males may be smaller in sizethan females – should they be grouped together or kept as two groups? Shouldlarval stages count the same as an adult stage? This sort of variation is usuallyignored in species diversity studies.

Chapter 13Page 533Most measures of diversity assume that the classes (species) are all equallydifferent. There seems to be no easy away around this limitation. In an ecologicalsense sibling species may be very similar functionally while more distantly relatedspecies may play other functional roles. Measures of diversity can address thesekinds of functional differences among species only if species are grouped intofunctional groups (Boulangeat et al. 2012) or trophic nodes (De Visser et al. 2011).Diversity measures require an estimate of species importance in thecommunity. The simple choices are numbers, biomass, cover, or productivity. Thedecision in part will depend on the question being asked, and as in all questionsabout methods in ecology you should begin by asking yourself what the problem isand what hypotheses you are trying to test. Numbers are used by animal ecologistsin many cases as a measure of species importance, plant ecologists may usebiomass or cover, and limnologists may use productivity.A related question is how much of the community should we include in oursampling. We must define precisely the collection of species we are trying todescribe. Most authors pick one segment bird species diversity or tree speciesdiversity and in doing so ignore soil nematode diversity and bacterial diversity.Rarely do diversity measures cross trophic levels and only rarely are they applied towhole communities. Colwell (1979) argues convincingly that ecologists shouldconcentrate their analyses on parts of the community that are functionallyinteracting, the guilds of Root (1973). These guilds often cross trophic levels andinclude taxonomically unrelated species in them. The choice of what to include in a"community" is critical to achieving ecological understanding, yet there are no rulesavailable to help you make this decision. The functionally interacting networks canbe determined only by detailed natural history studies of the species in a community(Baskerville et al. 2011).13.2 CONCEPTS OF SPECIES DIVERSITYEarly naturalists very quickly observed that tropical areas contained more species ofplants and animals than did temperate areas. To describe and compare differentcommunities, ecologists broke the idea of diversity down into three components –

Chapter 13Page 534alpha, beta, and gamma diversity. Alpha (α) diversity is local diversity, the diversityof a forest stand, a grassland, or a stream. At the other extreme is gamma (γ)diversity, the total regional diversity of a large area that contains severalcommunities, such as the eastern deciduous forests of the USA or the streams thatdrain into the Missouri River. Beta (β) diversity is a measure of how differentcommunity samples are in an area or along a gradient like from the headwaters of astream to its mouth, or from the bottom of a mountain to the top. Beta diversity linksalpha and gamma diversity, or local and regional diversity (Whittaker 1972). Themethods of estimating alpha and gamma diversity are fairly straightforward, but themeasurement of beta-diversity has been controversial (Ellison 2010).We will proceed first to discuss methods that can be used to estimate alpha orgamma diversity, and discuss beta-diversity later in this chapter. As ecological ideasabout diversity matured and ideas of quantitative measurement were introduced, itbecame clear that the idea of species diversity contains two quite distinct concepts.13.2.1 Species RichnessThis is the oldest and the simplest concept of species diversity - the number ofspecies in the community or the region. McIntosh (1967) coined the name speciesrichness to describe this concept. The basic measurement problem is that it is oftennot possible to enumerate all of the species in a natural community or region,particularly if one is dealing with insect communities or tropical plant assemblages. .13.2.2 HeterogeneityIf a community has 10 equally abundant species, should it have the same diversityas another community with 10 species, one of which comprises 99% of the totalindividuals? No, answered Simpson (1949) who proposed a second concept ofdiversity which combines two separate ideas, species richness and evenness. In aforest with 10 equally abundant tree species, two trees picked at random are likely tobe different species. But in a forest with 10 species, one of which is dominant andcontains 99% of all the individuals, two trees picked at random are unlikely to bedifferent species. Figure 12.1 illustrates this concept.

Chapter 13Page 535The term heterogeneity was first applied to this concept by Good (1953) and formany ecologists this concept is synonymous with diversity (Hurlbert 1971). Thepopularity of the heterogeneity concept in ecology is partly because it is relativelyeasily measured.13.2.3 EvennessSince heterogeneity contains two separate ideas species richness and evenness it was only natural to try to measure the evenness component separately. Lloyd andGhelardi (1964) were the first to suggest this concept. For many decades fieldecologists had known that most communities of plants and animals contain a fewdominant species and many species that are relatively uncommon. Evennessmeasures attempt to quantify this unequal representation against a hypotheticalcommunity in which all species are equally common. Figure 13.1 illustrates this idea.13.3 SPECIES RICHNESS MEASURESSome communities are simple enough to permit a complete count of thenumber of species present, and this is the oldest and simplest measure of speciesrichness. Complete counts can often be done on bird communities in small habitatblocks, mammal communities, and often for temperate and polar communities ofhigher plants, reptiles, amphibians and fish. But it is often impossible to enumerateevery species in communities of insects, intertidal invertebrates, soil invertebrates,or tropical plants, fish, or amphibians. How can we measure species richness whenwe only have a sample of the community's total richness? Three approaches havebeen used in an attempt to solve this sampling problem.13.3.1 Rarefaction MethodSpecies accumulation curves are a convenient way of expressing the principlethat as you sample more and more in a community, you accumulate more and morespecies. Figure 13.2 illustrates this for small lizards sampled in Western Australia.There are two directions one can go with a species accumulation curve. If you can fita statistical curve to the data, you can estimate the number of species you wouldprobably have found with a smaller sample size. Thus if you have collected 1650lizards and you wish to compare species richness with another set of samples of1000 lizards, you can use rarefaction to achieve an estimated number of species

Chapter 13Page 536that would be seen at a lower sampling rate. The second use is to extrapolate thespecies accumulation curve to an asymptote that will reveal the total number ofspecies in the community.8Community ANo. of speciesobserved765Community B4Species richness321(a)02086410No. of quadrats sampled0.4Community ARelative abundance0.20.00.4Community BHeterogeneity0.20.00.4Community C0.2(b) 0.00.2Relative abundanceEvenness higher(c)0.10.0EvennessEvenness lower0.20.10.01357Species9

Chapter 13Page 537Figure 13.1 Concepts of species diversity. (a) Species richness: community A has morespecies than community B and thus higher species richness. (b) Heterogeneity: communityA has the same number of species as community B but the relative abundances are moreeven, so by a heterogeneity measure A is more diverse than B. Community C has the sameabundance pattern as B but has more species, so it is more diverse than B. (c) Evenness:when all species have equal abundances in the community, evenness is maximal.Accumulated number of 0No. of individuals caughtFigure 13.2 Species accumulation curve for the small reptiles of the Great Victoria Desertof Western Australia from Thompson et al. (2003). There were 1650 individuals of 31species captured in pitfall traps. These curves illustrate the principle that the larger thesample size of individuals, the more species we expect to enumerate.The problem with this second objective is that if there are many species in thecommunity, species accumulation curves keep rising and there is much uncertaintyabout when they might level off at maximum species richness. Let us deal with thefirst objective.One problem that frequently arises in comparing community samples is thatthey are based on different samples sizes. The larger the sample, the greater theexpected number of species. If we observe one community with 125 species in acollection of 2200 individuals and a second community with 75 species in acollection of 750 individuals we do not know immediately which community hashigher species richness. One way to overcome this problem is to standardize all

Chapter 13Page 538samples from different communities to a common sample size of the same numberof individuals. Sanders (1968) proposed the rarefaction method for achieving thisgoal. Rarefaction is a statistical method for estimating the number of speciesexpected in a random sample of individuals taken from a collection. Rarefactionanswers this question: if the sample had consisted of n individuals (n N), whatnumber of species (s) would likely have been seen? Note that if the total sample hasS species and N individuals, the rarefied sample must always have n N and s S(see Figure 13.3).Sanders' (1968) original rarefaction algorithm was wrong, and it was correctedindependently by Hurlbert (1971) and Simberloff (1972) as follows:( )E Sˆ n N Ni n 1 N i 1 n s(13.1)where:( )E Sˆ n Expected number of species in a random sample of n individualsS Total number of species in the entire collectionNi Number of individuals in species iN Total number of individuals in collection Nin Value of sample size (number of individuals) chosenfor standardization (n N ) N Number of combinations of n individuals that can be chosen from n a set of N individuals N !/ n ! ( N n ) !The large-sample variance of this estimate was given by Heck et al. (1975) as:( )var Sˆ n sN i 1 n 1 N n s 1 s 2 i 1 j i 1 N Ni Ni n 1 N n N Ni N Ni n n N Ni NJ n N n (13.2)

Chapter 13Page 539where( ) Variance of the expected number of species in avar Sˆ nrandom sample of n individualsand all other terms are defined above.Expected number of species120100Diatoms in Box 880604020001000300020004000NNo. of individuals in sampleFigure 13.3 Rarefaction curve for the diatom community data from Patrick (1968). Therewere 4874 individuals in 112 species in this sample (“Box 8”). Original data in Table 13.1. Ifa sample of 2000 individuals were taken, we would expect to find only 94 species, forexample. This illustrates the general principle that the larger the sample size of individuals,the more species we expect to enumerate.TABLE 13.1 TWO SAMPLES OF A DIATOM COMMUNITY OF A SMALL CREEKIN PENNSYLVANIA IN 1965aNumber ofindividualsSpeciesBox 8Box 7Nitzxchia frustulum v. perminuta14461570Synedra parasitica v. subconstricta456Navicula cryptocephalaNumber ofindividualsSpeciesBox 8Box 7Melosira italica v. valida615455Navicula cryptoocephala v. veneta66450455Cymbella turgida58Cyclotella stelligera330295Fragilaria intermedia55Navicula minima318305Gomphonema augustatum v. obesa516

Chapter 13Page 540N. secreta v. apiculata306206G. angustatum v. producta54Nitzschia palea270225G. ongiceps v. subclavata59N. frustulum162325Meridion circulare54Navicula luzonensis13278Melosira ambigua5--Nitzschia frustulum v. indica126180Nitzschia acicularis5--Melosira varians118140Synedra rumpens v. familiaris537Nitzschia amphibia9395Cyclotella meneghiniana48Achnanthes lanceolata75275Gyrosigma spencerii42Stephanodiscus hantzschii7459Fragilaria construens v. venter3--Navicula minima v. atomoides69245Gomphonema gracile310N. viridula6872Navicula cincta32Rhoicosphenia curvata v. minor61121N. gracilis fo. Minor3--Navicula minima v. atomoides5947Navicula decussis32N. pelliculsa5419N. pupula v. capitat310Melosira granulata v. angustissima5473N. symmetrica3--Navicula seminulum5236Nitzxchia dissipata v. media34N. gregaria4034N. tryblionella v. debilis31Nitzschia capitellata4016N. sigmoidea3--Achnanthes subhudsonis v. kraeuselii3951Anomoeoneis exilis2--A minutissima3561Caloneis hyalina22Nitzschia diserta3553Diatoma vulgare2--Amphora ovalis v. pediculus3353Eunotia pectinalis v. minor21Cymbella tumida2995Fragilaria leptostauron23Synedra parasitica2442Gomphonema constrictum2--Cymbella ventricosa2127G. intricatum v. pumila210Navicula paucivisitat2012Navicula hungarica v. capitat25Nitzschia kutzingiana1970N. protraccta23Gomphonema parvulum1866Synedra acus v. angustissima2--Rhoicosphenia curvata1822Bacillaria paradoxa1--Synedra ulna1836Cyclotella kutzingiana1--Surirella angustata1711Cymbella triangulum1--Synedra ulna v. danica1737Cocconeis sp.1--Navicula pupula1727Caloneis bacillum13Achnanthes biporoma1632Fragilaria bicapitat1--Stephanodiscus astraea v. minutula1621Frustulia vularis1--Navicula germainii1319Gomphonema carolinese11Denticula elegans124G. sp.1--Gomphonema sphaerophorum1140Navicula capitat v. hungarica11Synedra rumpens1113N. contenta f. biceps11S. vaucheriae1114N. cincta v. rostrata1--Cocconeis placentula v. euglypta105N. americana1--Navicula menisculus105Nitzschia hungarica1--

Chapter 13Page 541Nitzschia linearis1018N. sinuata v. tabularia1--Stephanoddiscus invisitatus1022N. confinis15Amphora ovalis916Synedra pulchella v. lacerata11Cymbella sinuata95Surirella ovata13Gyrosigma wormleyii95Achnanthes cleveii--2Nitzschia fonticola96Amphora submontana--1N. bacata97Caloneis silicula v. ventricosa--3Synedra rumpens v. meneghiniana917Eunotia lunaris--2Cyclotella meneghiniana small84E. tenella--1Nitzschia gracilis v. minor810Fragilaria pinnata--3N. frustulum v. subsalina710Gyrosigma scalproides--1N. subtilis716Gomphonema sparsistriata----Cymbella affinis63Meridion circulara v. constricta--3Cocconeis placetula v. lineata613Navicula tenera--3N. omissa--1N. ventralis--1N. mutica--1N. sp.--1N. mutica v. cohnii--1Nitzschia brevissima--1N. frequens--1aThe numbers of individuals settling on glass slides were counted. Data from Patrick(1968).Box 13.1 illustrates the calculation of the rarefaction method for some rodentdata. Because these calculations are so tedious, a computer program shouldnormally be used for the rarefaction method. Program DIVERSITY (Appendix 2 page000) can do these calculations. It contains a modified version of the program givenby Simberloff (1978). The program EstimateS developed by Robert Colwell(http://viceroy.eeb.uconn.edu/estimates/ ) calculates these estimates as well asmany others for species richness.Box 13.1 CALCULATION OF EXPECTED NUMBER OF SPECIES BY THERAREFACTION METHODA sample of Yukon rodents produced four species in a collection of 42individuals. The species abundances were 21, 16, 3, and 2 individuals. We wishto calculate the expected species richness for samples of 30 individuals.Expected Number of SpeciesFrom equation (13.1)

Chapter 13Page 542 E Sˆ n 1 i 1 ( )( )E Sˆ30s 42 21 42 16 42 3 30 30 30 1 1 1 42 42 42 30 30 30 42 2 30 1 42 30 21 42 30 42 30 N Ni n N n 21 30 042! 30! ( 42 30 )!(by definition)1.1058 1010 16 42 30 26 30 42 3 30 39! 30! ( 39 30 )!2.1192 108 2 42 30 40! 30! ( 40 30 )!8.4766 108( )E Sˆ300(by definition) 2.1192 108 8.4766 108 1 1 1 1 1.1058 1010 1.1058 1010 1 1 0.981 0.923 3.90 speciesThese calculations are for illustration only, since you would never use thismethod on such a small number of species.Large Sample Variance of the Expected Number of SpeciesFrom equation (13.2)

Chapter 13( )var Sˆ n( )var Sˆ30Page 543 sN i 1 n 1 N n s 1 s 2 i 1 j i 1 N Ni Ni n 1 N n N Ni N Ni n n N Ni NJ n N n 21 26 39 30 30 30 21 2639 1 1 1 42 42 42 30 30 30 30 30 30 40 42 21 42 16 40 1 30 2 42 21 16 30 30 30 30 42 42 30 30 42 21 42 3 30 30 42 21 3 30 42 30 42 21 42 2 1 30 30 42 21 3 42 303042 30 42 16 42 3 42 16 3 30 30 30 42 30 42 16 42 2 42 16 2 30 30 3042 30 42 3 42 2 30 30 42 3 2 30 42 30 Note that for this particular example almost all of the terms are zero.

Chapter 13Page 544( )(1.1058 10 ) Sˆ30var-10 0.0885 2.0785 108 7.8268 108 2 5.9499 106 ( ) ( )( Standard deviation of Sˆ30 )( )var Sˆ30 0.08850.297These tedious calculations can be done by Program DIVERSITY (seeAppendix 2, page 000) or by Program EstimateS from Colwell et al.(2012).There are important ecological restrictions on the use of the rarefactionmethod. Since rarefaction is not concerned with species names, the communities tobe compared by rarefaction should be taxonomically similar. As Simberloff (1979)points out, if community A has the larger sample primarily of butterflies andcommunity B has the smaller sample mostly of moths, no calculations are necessaryto tell you that the smaller sample is not a random sample of the larger set.Sampling methods must also be similar for two samples to be compared byrarefaction (Sanders 1968). For example, you should not compare insect light trapsamples with insect sweep net samples, since whole groups of species areamenable to capture in one technique but not available to the other. Most samplingtechniques are species-selective and it is important to standardize collectionmethods.The second objective is both more interesting and more difficult. If the speciesaccumulation curve does plateau, we should be able to determine the completespecies richness of the fauna or flora by extrapolating the rarefaction curve (Figure13.4). But the only way one can extrapolate beyond the limits of the samples is byassuming an underlying statistical distribution.The perils of attempting to extrapolate have been discussed by manyecologists. For example, Thompson et al. (2003) fitted 11 non-linear regressionmodels to lizard data from Western Australia and concluded that different regressionmodels fitted data from different sites and that extensive sampling was required toobtain even an approximate estimate of total species numbers in an area. Xu et al.

Chapter 13Page 545(2012) used 12 estimators of species richness for estimating the total flora of treesand shrubs in a tropical forest on Hainan Island, China. They knew from extensivework that the area contained 992 species of native trees and shrubs and sampled164 quadrats of 25 by 25 m.No. of speciesEstimated total number of speciesExtrapolated speciesaccumulation curveObserved samplesNo. of individuals sampledFigure 13.4 Hypothetical species accumulation curve and the fitted rarefaction curve toillustrate the problem of attempting to extrapolate from the sample to the total speciesrichness of the sampled community. Clearly as a larger and larger sample of individuals istaken, one ought to approach an asymptote. But extrapolation depends critically on theexact formulation of the fitted curve.They observed a total of 596 species, and the estimators of the total flora rangedfrom 664 species to 7620 species. These results stimulated Chiarucci (2012) to statethat no reliable method yet exists for estimating species richness in an area largerthan that actually sampled, a discouraging conclusion for species rich plantcommunities. For the present I suggest that rarefaction should not be used toextrapolate total species richness, although it remains most useful for interpolatingspecies richness of communities sampled at a lower rate than the observed data(Colwell et al. 2012).

Chapter 13Page 546One assumption that rarefaction does make is that all individuals in thecommunity are randomly dispersed with respect to other individuals of their own orof different species. In practice most distributions are clumped (see Chapter 4) withina species and there may be positive or negative association between species. Fager(1972) used computer simulations to investigate what effect clumping would have onthe rarefaction estimates, and observed that the more clumped the populations are,the greater the overestimation of the number of species by the rarefaction method.The only way to reduce this bias in practice is to use large samples spread widelythroughout the community being analyzed.The variance of the expected number of species (equation 13.2) is appropriateonly with reference to the sample under consideration. If you wish to ask a relatedquestion: given a sample of N individuals from a community, how many specieswould you expect to find in a second, independent sample of n (n N) individuals?Smith and Grassle (1977) give the variance estimate appropriate for this moregeneral question, and have a computer program for generating these variances.Simberloff (1979) showed that the variance given in equation (13.2) providesestimates only slightly smaller than the Smith and Grassle (1977) estimator.Figure 13.3 illustrates a rarefaction curve for the diatom community data inTable 13.1. James and Rathbun (1981) provide additional examples from birdcommunities.TABLE 13.2 QUADRAT SAMPLING DATA SUMMARIZED IN A FORM NEEDEDFOR THE JACKKNIFE ESTIMATE OF SPECIES RICHNESSaQuadratSpeciesABCDEFRow 1

Chapter 13Page 5477001111481100114aOnly presence-absence data are required. Unique species are those whose row sumsare 1 (species 2 and 6 in this example). 0 absent; 1 present.13.3.2 Jackknife EstimateWhen quadrat sampling is used to sample the community, it is possible to use avariety of nonparametric approaches. They have been reviewed comprehensively byMagurran (2004) and I present only one here, the jackknife *, a non-parametricestimator of species richness. This estimate, called ‘Jackknife 1 by Magurran (2004),is based on the observed frequency of rare species in the community, and isobtained as follows (Heltshe and Forrester 1983a). Data from a series of randomquadrats are tabulated in the form shown in Table 13.2, recording only the presence(1) or absence (0) of the species in each quadrat. Tally the number of uniquespecies in the quadrats sampled. A unique species is defined as a species thatoccurs in one and only one quadrat. Unique species are spatially rare species andare not necessarily numerically rare, since they could be highly clumped. FromHeltshe and Forrester (1983a) the jackknife estimate of the number of species is: n 1 s k n ˆS (13.3)where:Sˆsnk Jackknife estimate of species richnessObserved total number of species present in n quadratsTotal number of quadrats sampledNumber of unique speciesThe variance of this jackknife estimate of species richness is given by:( ) var Sˆk2 n 1 s 2jf J n n j 1()where:*For a general discussion of jackknife estimates, see Chapter 16, page 000.(13.4)

Chapter 13( )var SˆPage 548 Variance of jackknife estimate of species richnessNumber of quadrats containing j unique species (j 1, 2, 3, . s )fJ k Number of unique speciesn Total number of quadrats sampledThis variance can be used to obtain confidence limits for the jackknife estimator:( )Sˆ tα var Sˆ(13.5)where:Sˆ Jackknife estimator of species richness (equation 12.3)tαStudent's t value for n 1 degrees of freedom for the appropriate value of αvar Sˆ Variance of Sˆ from equation (12.4)( )Box 13.2 gives an example of these calculations.Box 13.2 JACKKNIFE ESTIMATE OF SPECIES RICHNESS FROM QUADRATSAMPLESTen quadrats from the benthos of a coastal creek were analyzed for the abundance of 14species (Heltshe and Forrester, 1983a). For a sample taken from a subtidal marsh creek,Pettaquamscutt River, Rhode Island, April 1978.QuadratSpeciesStreblospio benedictiNereis succinesPolydora ligniS

alpha, beta, and gamma diversity. Alpha (α) diversity is local diversity, the diversity of a forest stand, a grassland, or a stream. At the other extreme is gamma (γ) diversity, the total regional diversity of a large area that contains several communities, such as the eastern deciduous forests

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