limnology and oceanography: methods · rumohr for providing the soft-bottom data and mathieu cusson...

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Introduction

Species richness is the simplest and most commonly acceptedmeasure of biodiversity (Whittaker 1972; Magurran 1988; Gaston

1996) and is crucial for testing ecological models, such as the sat-uration of local communities colonized from regional speciespools (Cornell 1999). Ecological limitation (i.e., saturation) meansthat with increasing number of available species in the regionalpool or with invasion events, local richness does not increasebeyond an intrinsically determined maximum (Srivastava 1999).Thus, if only regional richness is driving local richness, a positivelinear relationship is often predicted (Cornell and Lawton 1992;Srivastava 1999). Conversely, while concerns have been expressed(Loreau 2000; Hillebrand and Blenckner 2002; Ricklefs 2004), ithas been widely accepted that if local assemblages are saturatedwith species due to ecological interactions and niche overlap, anasymptotic relationship is expected (Cornell and Lawton 1992;Cornell and Karlson 1997; Srivastava 1999).

Several studies that seek to explain and/or test the relation-ship between local and regional diversity have assessed the

Estimation of regional richness in marine benthic communities:quantifying the errorJoão Canning-Clode1,2*, Nelson Valdivia3, Markus Molis3, Jeremy C. Thomason4, and Martin Wahl11Leibniz Institute of Marine Sciences at the University of Kiel, Duesternbrooker Weg 20, D-24105 Kiel, Germany2University of Madeira, Centre of Macaronesian Studies, Marine Biology Station of Funchal, 9000-107 Funchal, Madeira Island,Portugal3Biologische Anstalt Helgoland, Section Seaweed Biology, Foundation Alfred-Wegener-Institute for Polar and Marine Research,marine station, Kurpromenade 201, D-27498 Helgoland4School of Biology, Newcastle University, Newcastle Upon Tyne, United Kingdom, NE1 7RU

AbstractSpecies richness is the most widely used measure of biodiversity. It is considered crucial for testing numerous eco-

logical theories. While local species richness is easily determined by sampling, the quantification of regional rich-ness relies on more or less complete species inventories, expert estimation, or mathematical extrapolation from anumber of replicated local samplings. However the accuracy of such extrapolations is rarely known. In this study,we compare the common estimators MM (Michaelis-Menten), Chao1, Chao2, ACE (Abundance-based CoverageEstimator), and the first and second order Jackknifes against the asymptote of the species accumulation curve, whichwe use as an estimate of true regional richness. Subsequently, we quantified the role of sample size, i.e., number ofreplicates, for precision, accuracy, and bias of the estimation. These replicates were sub-sets of three large data setsof benthic assemblages from the NE Atlantic: (i) soft-bottom sediment communities in the Western Baltic (n = 70);(ii) hard-bottom communities from emergent rock on the Island of Helgoland, North Sea (n = 52), and (iii) hard-bottom assemblages grown on artificial substrata in Madeira Island, Portugal (n = 56). For all community types, Jack2showed a better performance in terms of bias and accuracy while MM exhibited the highest precision. However, invirtually all cases and across all sampling efforts, the estimators underestimated the regional species richness, regard-less of habitat type, or selected estimator. Generally, the amount of underestimation decreased with sampling effort.A logarithmic function was applied to quantify the bias caused by low replication using the best estimator, Jack2.The bias was more obvious in the soft-bottom environment, followed by the natural hard-bottom and the artificialhard-bottom habitats, respectively. If a weaker estimator in terms of performance is chosen for this quantification,more replicates are required to obtain a reliable estimation of regional richness.

*Corresponding author: E-mail: [email protected]

AcknowledgmentsWe appreciate the assistance of the late J. S. Gray and Robert Clarke in

the initial development of these ideas. We would like to thank HeyeRumohr for providing the soft-bottom data and Mathieu Cusson for hissuggestions and critical review in this manuscript. We further thank InkaBartsch and Manfred Kaufmann for providing additional species inventoriesfor the natural and artificial hard-bottom habitats, respectively. The manu-script was significantly improved by the suggestions of three anonymousreferees. J. Canning-Clode was supported by a Fellowship from theGerman Academic Exchange Service (DAAD) and J.C. Thomason by theRoyal Society.

Limnol. Oceanogr.: Methods 6, 2008, 580–590© 2008, by the American Society of Limnology and Oceanography, Inc.

LIMNOLOGYand

OCEANOGRAPHY: METHODS

Canning-Clode et al. Estimating regional species richness

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regional species pool based on published species lists and byconsulting taxonomic experts (e.g., Hugueny and Paugy 1995;Lawes et al. 2000; Witman et al. 2004; Harrison et al. 2006).However, complete inventories of the fauna and flora of aregion are exceptionally hard to obtain and will probablyremain unavailable for most regions for the next few centuries(Petersen and Meier 2003; Hortal et al. 2006). This problem ismore delicate in the marine environment where there is a largephyletic diversity in certain groups and limited informationabout others, e.g., Porifera (Foggo et al. 2003). Moreover, it isdifficult to appreciate to what degree such inventories are com-plete or incomplete (Soberon and Llorente 1993), and compar-isons between published species lists are frequently unreliabledue to different sampling methods, terminology, or data han-dling systems (Dennis and Ruggiero 1996). In addition, whensaturation in certain assemblages is to be investigated, thespecies capable to recruit into this habitat type (the relevantrichness) are only a subset of the entire regional richness.

To deal with these difficulties, a number of estimation tech-niques have been developed to extrapolate from the known tothe unknown, i.e., from a reasonable number of properlyinventoried samples to the true number of relevant species ina certain area (Colwell and Coddington 1994). These tech-niques can be grouped into three classes: (i) parametric mod-els, (ii) non-parametric estimators, and (iii) extrapolations ofSAC (species accumulation curves) (Magurran 2004). Whenspecies fit a log normal distribution, i.e., a case of a paramet-ric model to estimate species richness, it is possible to estimatethe theoretical number of species in the community byextrapolating the shape of the curve. Most of the parametricmethods are, however, reported to perform improperly andhave not been used in recent years (Melo and Froehlich 2001).

In contrast, the non-parametric estimators have been sug-gested to perform better than SAC and parametric methods(Baltanas 1992; Colwell and Coddington 1994; Walther andMorand 1998; Walther and Martin 2001; Hortal et al. 2006).These non-parametric estimators were originally developed toestimate population size based on capture-recapture data andadapted to extrapolate total species richness (Williams et al.2002). With this technique, species richness is estimated fromthe prevalence of rare species in each sample but does notextrapolate beyond the last sample to an asymptote. In itsplace, these models predict richness, including species notfound in the sample, from the proportional abundances ofspecies within the total sample (Soberon and Llorente 1993).Several evaluations on the performance of different estimatorshave been carried out (see review from Walther and Moore2005). In most cases, the estimators Chao1 (Chao 1984),Chao2 (Chao 1984, 1987; Colwell 2005), first order Jackknife(Jack1 - Burnham and Overton 1979; Heltshe and Forrester1983), and second order Jackknife (Jack2 - Smith and Van Belle1984) perform better in terms of bias, precision, and accuracythan other estimators (Walther and Moore 2005). In a recentstudy, Hortal et al. (2006) compared 15 species richness estimators

using arthropod abundances data and concluded that Chao1and ACE (Abundance-based Coverage Estimator, Chao andLee 1992; Chazdon et al. 1998; Chao et al. 2000) have shownthe best performance among all estimators. For the marinesystem, Foggo et al. (2003) performed an evaluation on theperformance of six estimators using simulations. They con-cluded that the estimator’s performance was affected by sam-pling effort, and no particular estimator performed best in allcases. Nevertheless, Foggo et al. (2003) suggested Chao1 as themost appropriate choice for a limited number of samples,acknowledging that its performance may vary significantly incases of larger spatial scales and species richness. In these cir-cumstances, the frequency of rare species could deteriorate theperformance of Chao1 (Foggo et al. 2003). This was later con-firmed by Ugland and Gray (2004) in benthic assemblages ofthe Norwegian continental shelf where Chao1 provided alarge underestimation of true richness.

Finally, the third category of assessing inventory complete-ness is through the extrapolation of SAC. In such curves, thecumulative number of species is plotted against a cumulativemeasure of sampling effort, e.g., the number of individualsobserved, samples or traps (Moreno and Halffter 2000; Gotelliand Colwell 2001). The species richness can then be estimatedby fitting an equation to the curve and estimating its asymp-tote. While many functions have been proposed for this task(see Tjørve 2003 for a review in possible model candidates),the negative exponential function, the Clench equation, theWeibull function, and the Morgan-Mercer-Flodin(MMF)model have been frequently used (Soberon and Llorente 1993;Colwell and Coddington 1994; Flather 1996; Lambshead andBoucher 2003; Jimenez-Valverde et al. 2006; Mundo-Ocampoet al. 2007). In theory, the asymptote’s location represents the“true richness”, i.e., the total number of species that would beobserved with a hypothetical infinite sampling effort (Soberonand Llorente 1993; Colwell and Coddington 1994; O’hara2005; Jimenez-Valverde et al. 2006). The quality of the fittingof the equation to the curve and, thus, the reliability of theplateau should relate directly to the number of replicates.

The current study addresses the estimation of regional richnessusing a novel approach. First, we extrapolate to the asymptote of theSAC for three data sets, each with a large number of replicates andfrom three different types of marine benthic communities. Second,using the asymptote’s location as a reference for “true” regional rich-ness, we then compare precision, bias, and accuracy of the regionalrichness produced by six different estimators - Michaelis-Menten(MM), ACE, Chao1, Chao2, Jack1, and Jack2. Finally, we quantifythe estimation error as a function of sampling effort.

Materials and proceduresFor this study, we explored three sets of benthic communi-

ties: (i) soft-bottom: In Kiel Bay, Western Baltic, (54°38.3′ N,10°39.6′ E) 70 replicates of macrofaunal samples were collectedto investigate the performance of species richness estimationtechniques. The 70 samples were collected from the same site


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in the early autumn of 1995 at the Station “Millionenviertel14” using a 1000 cm2 van Veen grab at a depth of 24 m (cov-ering a total of 7 m2 of sea bed). Samples were preserved in 4%formaldehyde and later identified to species level (Rumohr1999; Rumohr et al. 2001). (ii) In spring 2006, in HelgolandIsland, North Sea (54°11.4′ N, 07° 55.2′ E) one of us (NV) sam-pled sessile hard-bottom communities and identified them tospecies level in 52 replicate quadrates of 400 cm2 in intertidalrocky abrasion platforms. The study site “Nordostwatt” coversapproximately 450 m2 and is located in the northeast part ofthe island and was extensively studied and inventoried byJanke (1986). Janke (1986) described horizontal belts in theintertidal as the Enteromorpha, Mytilus, Fucus serratus, and Lam-inaria zones. The data we use in this report are from 7 sub-habi-tats distributed in the F. serratus habitat. (iii) In early summer2004, young hard-bottom communities were collected byimmersing 56 replicate polyvinylchloride (PVC) panels (225cm2) for 5 mo at Madeira Island, Portugal, NE Atlantic (32°38.7′N, 16° 53.2′ W). The panels were distributed in 12 PVC rings(60 cm dia, 25 cm height) hung from a buoy at approximately0.5 m depth. Minimum distance between rings was 5 m. Theoriginal study focused on the influence of disturbance andnutrient enrichment in hard-bottom assemblages (Canning-Clode et al. 2008). For the purpose of this analysis, only sessilespecies on untreated control panels were taken into considera-tion. Hereafter, these datasets are referred to as soft-bottom,natural hard-bottom, and artificial hard-bottom, respectively.

Predicting the asymptote of the SAC—Species accumulationcurves (SAC) were used (PRIMER 6, Clarke and Gorley 2006) tocalculate the total number of species observed (“Sobs Curve”) atmaximum sample size. Here, we used 52 replicates as maximumsampling size for all habitats because this was the maximumreplicate number found in all habitat samples. Replicates werepermuted randomly 999 times. The analytical form of the meanvalue of the accumulation curve over all permutations wasgiven by the UGE Index (Ugland et al. 2003). Ugland et al.(2003) developed a total species curve (T-S curve) from SACobtained from single subareas. This curve can then be extrapo-lated to estimate the probable total number of species in a givenarea (Ugland et al. 2003). They showed for the Norwegian con-tinental shelf that the conventional SAC gave a large underesti-mation compared with the T-S curve. To estimate the asymptoteof the SAC (which we treat as ‘true’ regional richness in thisanalysis) for all habitats, the nonlinear Morgan-Mercer-Flodin(MMF) growth model (Morgan et al. 1975) was chosen. TheMMF model was selected by the curve fitting software CurveEx-pert (Hyams 2005) because of its superior fit regarding coeffi-cient of correlation (r ) and standard error of the estimate (SE )in all three data sets. The MMF model takes the form:

y = (ab + cxd) / (b + xd)

where y is species richness, and x represents the number of repli-cates. The parameters a, b, c, and d have the following interpre-tation: a is the calculated ordinate intercept of the replicates-

species richness curve; c represents the maximum species rich-ness. i.e., asymptote of the curve, as the number of replicates (x)approaches infinity; b and d are model parameters that describethe shape of the curve between the two extremes (Morgan et al.1975). This model was previously used in two studies that per-formed a regional estimation of deep sea and littoral nematodes(Lambshead and Boucher 2003; Mundo-Ocampo et al. 2007). Inthose studies, estimates were obtained by extrapolation from aSAC based on number of individuals, rather than number ofsamples based on the UGE index as we do here.

Species richness estimations using variable replicate numbers—We employed the frequently used software ‘EstimateS’ (version7.5, Colwell 2005) to investigate the effect of sample size(number of sampling units representing the replicates of ‘localrichness’) in estimating regional richness. This program com-putes sample-based rarefaction curves for a variety of speciesrichness estimators, presenting the mean number of randomsample re-orderings. Rarefaction and SAC were computed tentimes (using 10 randomly drawn sub-sets of replicates fromthe entire data-set) for the replication levels 2, 4, 8, 16, 32, and52 for each habitat. Because there were 70, 52, and 56 avail-able replicates for the soft-bottom, natural hard-bottom, andartificial hard-bottom data sets, respectively, there was ahigher chance of samples overlap when selecting the 32 and52 samples sets. The rarefaction curve was based on 100 ran-domizations of the number of replicates sampled. We focusedour investigation on five non-parametric estimators as well ason the asymptotic Michaelis-Menten (MM) richness estimator(Raaijmakers 1987) (Table 1). These six estimators were previ-ously used in several evaluations and were reported to performwell (Walther and Moore 2005, see their table 3). Rosenzweiget al. (2003) theoretically differentiated these two varieties ofestimators. Non-parametric estimators intend to overcomesample-size insufficiencies and to report the number of speciespresent in sampled habitats. They operate only on the resultsobtained from a subset of the total data set and do not repre-sent an extrapolation. In contrast, MM extrapolates speciesnumber to the asymptote of the SAC (Rosenzweig et al. 2003).‘EstimateS’ calculates the MM estimator in two ways: (i) foreach of the 100 randomizations, which is then averaged(MMRuns), or (ii) the mean accumulation curve is calculatedby averaging over 100 accumulation curves derived from 100runs (MMMeans). We used the latter because of its less erraticestimation (Colwell 2005; Walther and Moore 2005).

Estimator performance evaluation—Following Walther andMoore (2005), we calculated three different quality indicatorsthat are commonly used to describe the performance of thechosen estimators: bias, precision, and accuracy. Bias quanti-fies the mean difference between an estimated richness andthe true species richness. For measuring bias, we used thescaled mean error:

Bias = (Ej – A),

where A is the asymptote of the SAC, Ej is the estimated

11An j

n

=∑


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species richness for the jth replicate, and n is the number of

replicates. Positive and negative bias indicates overestimationand underestimation, respectively.

Precision measures the variability of estimates amongrepeated estimation runs for a given sample. For measuring pre-cision, we used the complement of the coefficient of variation,the latter being the ratio of deviation (SD) and mean ( ):

Precision = 1 – (SD / )

Accuracy measures the closeness of an estimated value tothe true richness (Brose and Martinez 2004). It is often mea-sured using the mean squared error, combining bias, and pre-cision (Hellmann and Fowler 1999). Here we applied thescaled mean square error according to the formula:

Accuracy = 1 – ( (Ej – A)2),

where A is the asymptote of the SAC, Ej is the estimated speciesrichness for the j th sample, and n is the number of replicates.

Quantifying the relation between estimation error and number ofreplicates—The relative estimation error of the six estimatorswas expressed using the following formula:

y = (E/A) 100,

where y is the estimation error (in percent), E represents theestimated species richness given by an elected estimator, andA is the asymptote of the SAC in a given habitat. The estima-tion error was then plotted against the number of replicatesusing a logarithmic model. This model takes the form:

y = a + b ln(x)

where y represents the underestimation of a given estimator

when compared with the asymptote of the SAC of a givenhabitat, x is the number of replicates, and a and b are modelparameters. Here too, the model was selected by the curve fit-ting software CurveExpert based on a high value of r and lowestimate SE.

AssessmentPredicting the location of the asymptote—In all three habitats,

species richness increased as a function of sampling effort(Fig. 1). The total number of species observed in maximumsample size, i.e., 52 replicates, was 55 species in the soft-bottomhabitat, 43 species for the natural hard-bottom assemblages,and 32 species for the artificial hard-bottom habitat (Fig. 1).

The MMF model was chosen to extrapolate and predict thelocation of the asymptote. This model described the data ofthe SAC for the three habitats very well, with r ≈ 1 for allcurves (Table 2). Nevertheless, the model performed less wellfor the natural hard-bottom assemblages as indicated by agreater standard error of the estimate. The asymptote ofspecies richness (parameter c) was located at 103 species forsoft-bottom, 65 for natural hard-bottom, and 38 for the artifi-cial hard-bottom habitat (Table 2).

Estimator’s performance—In general, Jack2 performed better(with respect to bias and accuracy) at all replicate levels (lowsampling effort: < 8 replicates; intermediate sampling effort: 8-16 replicates; high sampling effort: > 16 replicates) in the threehabitats (Fig. 2). The estimator MM also had a satisfactory per-formance at low replication for all habitats, but with increas-ing sampling effort, its performance in terms of bias and accu-racy improved less steeply as for the other estimators. In mostcases, at low and intermediate sampling effort, Chao1, Chao2,and ACE performed worse. Bias decreased with rising sampling

12 1A n j

n

=∑

E_

E_

Table 1. Summary of the species richness estimators used for this analysis

Richness estimators Type Description References

ACE NP*Abundance-based coverage estimator. It is a modification of the Chao & Lee (1992) estima-

tors based on the ratio between rare (less than 10) and common species.

Chao and Lee 1992; Chazdon

et al. 1998; Chao et al. 2000

Chao1 NP*Abundance-based estimator based on the number of rare species in a sample, i.e., represent-

ed by less than 3 individuals.Chao 1984

Chao2 NP*

Incidence-based estimator. Takes into account the distribution of species amongst samples,

i.e., the number of species that occur in only 1 sample (‘rare species’) and the number of

species that occur in exactly 2 samples.

Chao 1984, 1987

Jack1 NP* First-order Jackknife. Is based on the species occurring only in a single sample.Burnham and Overton 1979;

Heltshe and Forrester 1983

Jack2 NP*Second-order Jackknife. Is based on the species occurring in only 1 sample as well as in the

number that occur in exactly 2 samples.Smith and Van Belle 1984

MMMean P†Michaelis-Menten Mean richness estimator. Computes the mean accumulation curve. Is calcu-

lated by averaging over all accumulation curves derived from the selected runs.Raaijmakers 1987

*NP, non-parametric estimator†P, parametric estimator


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effort and was consistently negative (i.e., underestimation) forall estimators in the soft-bottom and natural hard-bottomhabitats (Fig. 2A-B). In the artificial hard-bottom habitat, too,all six estimators underestimated the asymptote of the SACwith the single exception that at replicate level 52, Jack2 pro-duced the only overestimation ever observed (Fig. 2C). Gener-ally, the underestimation was more pronounced for the soft-bottom communities.

Accuracy improved steadily with increasing replication,with a similar slope in all community types, but generally moresmooth in the soft-bottom communities (Fig. 2D-F). Jack2 wasthe most accurate estimator in all habitats when replicationexceeded 2. At low and intermediate sampling effort, MM wasas accurate as Jack2 for the natural and artificial hard-bottomhabitats (Fig. 2E – F). In contrast, MM was the least accurateestimator for the soft-bottom community (Fig. 2D) and at highsampling effort for the other two habitats.

Precision of the estimation increased rapidly in the first 10replicates and more slowly after that (Fig. 2G-I). This patternwas similar in all communities, probably because it is a statisti-cal property (i.e., it approximates to the standard deviation).Nevertheless, in the natural hard-bottom assemblages, Jack2showed a high imprecision at intermediate sampling effort due

to a large variability of species richness within replicates (Fig.2H). In this habitat both of the Chao estimators showed weakprecision at low sampling effort. Precision was 1 at maximumsampling effort for the natural hard-bottom habitat as therewas only one possible combination of the 52 replicates (Fig.2H). MM showed high precision in almost all levels of replica-tion and all community types. While the shapes of all curvesare comparable for the 3 community types, for a similar qual-ity of estimation fewer replicates are required for the artificialhard-bottom community than for the soft-bottom community.

In summary, Jack2 seems to be the most appropriate choiceat all levels of sampling effort for all habitats. MM constitutesan alternative solution at low sampling effort for the naturaland artificial hard-bottom habitats.

For all community types and all estimators, the relativeestimation error and its error decreased with increasing repli-cation (Fig. 3). It should be noted, however, that the decreasein error, especially at replication levels 32 and 52, might be anartifact caused by the statistically increased probability of re-sampling of the same replicates.

In the soft-bottom data-set, underestimation was neverlower than 35%, even at maximum sampling size (Fig. 3A). Inthe natural hard-bottom communities, it was always largerthan 20% (Fig. 3B).The underestimation was lowest for theartificial hard-bottom habitat (Fig. 3C). At low sampling effort,which probably is the most common case in ecological stud-ies, MM and Jack2 yield a substantially better estimation ofregional richness than the other four estimators for all assem-blages. At maximum sampling size for the artificial hard-bot-tom habitat, average estimation error was below 20% for MM,ACE, Jack1, Chao1, and Chao2, while Jack2 overestimated theasymptote of the SAC (Fig. 3C).

To investigate in more detail the estimation error in all habi-tats, we have selected a logarithmic model and the Jack2 esti-mator due to its best overall performance. The logarithmicmodel properly described the data for all habitats (Fig. 4; soft-bottom: r = 0.98, SE = 2.67; natural hard-bottom: r = 0.98, SE =3.39; artificial hard-bottom: r = 0.96, SE = 5.51). The estimationerror decreases with increasing replication. Based on this model,we quantified the bias caused by low replication for all habitats(Table 3). With each doubling of replication number the esti-mation error by Jack2 decreases in average by 6.6% for the soft-bottom habitat, 8.4% for the natural hard-bottom habitat, and8.5% for the artificial hard-bottom habitat (Fig. 4, Table 3).

Fig. 1. Species accumulation curves (SAC) for the three communitytypes. These curves were plotted using the UGE index calculated inPRIMER 6.0

Table 2. Coefficients of correlation (r ), standard error of the estimate (SE ), and parameter values of the MMF model used for theextrapolation of the asymptote of the SAC for all habitats

Parameters

Habitat a b c d r SESoft-bottom –8.12 3.41 102.67 0.38 0.999 0.074

Hard-bottom –63.05 0.63 65.48 0.27 0.999 0.205

Artificial hard-bottom –3.62 1.60 37.90 0.58 0.999 0.023


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Overall, we have demonstrated that Jack2 performed bestin all habitats. Using the logarithmic model, we predict thatone would need 1865 samples to reach the asymptote of theSAC in the soft-bottom habitat (Table 3). For the natural andartificial hard-bottom habitats, a considerably less samplingeffort would be required to reach the asymptote of the SAC.

DiscussionStudies that are searching for a clear understanding of the local

versus regional diversity pattern in the marine environment haveoften defined the number of species in a region by questioningexperts or consulting available species inventories (e.g., Witman etal. 2004; Harrison et al. 2006). In many poorly studied areas, how-ever, true regional species numbers are unknown. Therefore thestatistical estimation of regional richness, based on a limitednumber of replicates, constitutes an important alternative for the

marine realm. In the present study, we have evaluated the poten-tial and limitations of such an approach. For this purpose, weselected three data sets with a large number of replicates from dif-ferent temperate shallow water habitats. We compared the per-formance of six different estimators of regional richness against theasymptote of the species accumulation curve (SAC) using ran-domly selected replicates for a range of sample sizes.

The most conspicuous outcome of this analysis is that as ageneral rule the estimation of regional species richness basedon local assemblages underestimates the asymptote of theSAC, regardless of habitat type, number of replicates, orselected estimator. The only exception was when a single esti-mator, Jack2, using 52 replicates overestimated the asymptoteof the SAC in the artificial hard-bottom habitat. For all esti-mators, the amount of underestimation gradually decreasedwith increasing sample size.

Fig. 2. Bias (panels A-C), accuracy (D-F), and precision (G-I) of the selected estimators (MM, Chao1, ACE, Chao2, Jack1, and Jack2) for the three habi-tats using variable replicate numbers. *In panel H, precision was 1 at replicate level 52 as there was only one set of 52 replicates.


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The estimation error was greatest in the soft-bottom envi-ronment, followed by the natural hard-bottom and the artifi-cial hard-bottom habitats. Nevertheless, the similarity of theestimation error patterns between the three data sets is sur-prising in view of the (intentional) differences between theselected samples regarding community type, community age,diversity and method of sampling. For instance, the size of asingle sampling unit was 1000, 400, and 225 cm2, in the soft-bottom, natural, and artificial hard-bottom samples, respec-tively. Thus, at comparable species density, a single replicatefor the soft-bottom habitat possibly contained a larger pro-portion of the regional species pool than in the other samples.Also, the suspended PVC panels used for the Madeira data-setcan be considered island communities on patchy substrata,with diversity possibly constrained by habitat (panel) size,whereas the samples from the other two data sets were sub-areas from much larger contiguous habitats. Sample unit sizeand patchiness of habitat may affect the similarity betweenreplicates and, thus, the initial slope of the curve. Moreover,the slow accumulation and consequently, the larger numberof replicates required to reach the plateau in the soft bottomsample may be linked to the number of rare species present, aswell as to the sensitivity of the sampling method.

Despite the extensive differences between the samples cho-sen with regard to size of sampling area, patchiness of habitator age of community, the performance of the estimatorsapplied to the described data sets was comparable. This may beindicative of a remarkable robustness of the observed pattern.The fact that the six estimators underestimated the asymptoticspecies richness is consistent with other studies that use thesame and other estimators (e.g., Petersen and Meier 2003;Brose and Martinez 2004; Cao et al. 2004). Beyond the generalsimilarity among estimator’s performances, Jack2 was moreaccurate and less biased for all habitats in almost all replica-tion levels. In contrast, MM exhibited a high precision in allhabitats. At low sampling effort, MM and Jack2 performed bestin terms of bias, accuracy, and precision for the natural andartificial hard-bottom communities. For the soft-bottom com-munity, Jack2 was clearly the least biased and the most accu-rate estimator at all levels of replication. For estimations basedon larger samples, both Chao1 and ACE seem to performslightly better than MM but worse than Chao2 and both Jack-knifes. These findings are comparable to some previouslyreported results. For instance, the study by Walther and Moore(2005) found that Chao2 (Chao 1987) performed best whileJack2, Jack1, and Chao1 ranked second, third, and fourth,respectively. The MMMean and ACE estimators were reportedto perform worse (Walther and Moore 2005). Although theydid not evaluate the performances of ACE, MM, and Jack2,Foggo et al. (2003) concluded that amongst 6 different tech-niques to estimate marine benthos species richness, Chao1represented the best nonparametric alternative for a limitednumber of survey units. In contrast, Ugland and Gray (2004)argue that Chao1 severely underestimates the true richness in

Fig. 3. Percentages of asymptotic species richness estimated by MM,Chao1, ACE, Chao2, Jack1, and Jack2 using variable replicate numbers forthe (A) soft-bottom, (B) natural hard-bottom, and (C) artificial hard-bot-tom habitats. Means and 95% confidence intervals are indicated (n = 10).Dashed line indicates the asymptote of the SAC given by the UGE index.*In panel B at replicate level 52 confidence intervals are zero as there wasonly one set of 52 replicates.


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benthic assemblages of the Norwegian continental shelf. Intheir study, Chao1 predicted approximately 1100 species froma data-set with 809 species. Nevertheless, when surveyinglarger areas of the shelf than the ones they use in their analy-sis (see their Table 1), over 2500 species were found (Uglandand Gray 2004). The large underestimation by Chao1 iscaused by infrequent species (Ugland and Gray 2004). In arecent evaluation of 15 different estimators using arthropodsabundances, Hortal et al. (2006) concluded that the perform-ance of 10 estimators were highly dependent on the level ofreplication. In that study, Chao1 and ACE showed a higherprecision at low replication but the superiority of these twoestimators over the rest decreases with increasing sample size.Conversely, in a study using Monte Carlo simulations, Broseand Martinez (2004) showed that ACE, Chao1, Chao2, andJack2 were positively biased under high replication. However,in some of the previously mentioned studies, true richness wasestimated based on inventories, experts, simulated landscapemodels, or museum collection data (Brose et al. 2003; Petersenand Meier 2003; Brose and Martinez 2004; Cao et al. 2004;Hortal et al. 2006) and not on real and numerous communitysub-units, as done in this study. If incomplete lists suggest alower-than-real regional richness, apparent overestimations

may result. Only one of the previously mentioned studies hasestimated true richness based on the asymptote of the speciesaccumulation curve (Foggo et al. 2003).

In this study, we estimated true regional richness by extrap-olation of the SAC given by the UGE index using the non-lin-ear Morgan-Mercer-Flodin (MMF) growth model (Morgan et al.1975). The MMF model was previously employed in two sur-veys on the diversity of deep sea and littoral nematodes (Lamb-shead and Boucher 2003; Mundo-Ocampo et al. 2007). Lamb-shead and Boucher (2003) estimated the marine nematodespecies richness in 16 locations. They have compared the esti-mations given by the MMF model with the non-parametricincidence-based coverage estimator (ICE - Lee and Chao 1994;Chazdon et al. 1998; Chao et al. 2000). In 88% of cases, theestimation given by the extrapolation was higher than the esti-mation provided by ICE. In one instance, both methods pro-vided identical estimates of nematodes species, in another oneICE produced higher numbers (Lambshead and Boucher 2003).Mundo-Ocampo et al. (2007) used the same approach to com-pare nematode biodiversity in two shallow, littoral locations ofthe Gulf of California. In both locations, the MMF extrapola-tion gave a higher estimation of nematode richness than ICE(Mundo-Ocampo et al. 2007). Both studies did not attempt toquantify the relationship between estimation error and lowreplication, as we do here. In opposition to these investigationswhere SAC were plotted as a function of the accumulated num-ber of individuals, our study uses SAC plotted against the accu-mulated number of samples. Deciding which type of curves touse depends on the nature of the data available (Gotelli andColwell 2001). If sample-based data are available, a SAC basedon samples is preferable, as it can account for natural levels ofsample patchiness (i.e., heterogeneity between replicates) inthe data (Gotelli and Colwell 2001). A further distinction of thepresent study from the investigations by Lambshead andBoucher (2003) and Mundo-Ocampo et al. (2007) is the use ofthe T-S curve (given by the UGE index) developed by Ugland etal. (2003) followed by the MMF model fitting to it. The result-ing extrapolation of the asymptotic richness is a more realisticestimation than the usual SAC (Ugland et al. 2003).

We demonstrate that the minimum sampling effort toreach a realistic estimation of true regional richness is variableamong communities or sampling methodology. Below thisthreshold sampling effort estimation is negatively biased. Theunavoidable estimation error caused by low replication can,

Fig. 4. Estimation error by Jack2 using variable replicate numbers for thesoft-bottom, natural hard-bottom, and artificial hard-bottom habitatsusing the logarithmic model y = a + b ln(x). Means and 95% confidenceintervals are indicated (n = 10).

Table 3. Quantification of the estimation error by Jack2*

Number of replicates

Habitat 2 4 8 16 32 52 y(0)

Soft-bottom 71.37 64.14 56.9 49.67 42.43 37.37 1865.43

Natural hard-bottom 62.74 54.02 45.31 36.60 27.88 21.78 294.13

Artificial hard-bottom 45.36 36.07 26.71 17.39 8.07 1.54 58.31*Based on the logarithmic model, we calculated the approximate estimation error by Jack2 (%) to compensate the bias caused by low replication. Withthe same model we also calculated for each habitat, the required sampling effort for the Jack2 estimator to be unbiased (y (0)).


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however, be quantified as shown in this paper. In addition, thelogarithmic function used to quantify the estimation erroralso informs at which sampling effort the estimationapproaches the asymptote of the SAC. Consequently, we pre-dict that if a weaker estimator in terms of performance is cho-sen, the logarithmic function will approach the x-axis far later,i.e., a greater amount of replicates would be required to equalthe asymptote of the SAC.

The extrapolation of the SAC is a computation and theshape of the curve is affected by the presence/absence of rarespecies in the samples as well as the amount of samples usedin the model. To assess how well the plateau reflects the “real”regional richness, we compared the plateau values obtained byour approach to the numbers provided by existing compre-hensive inventories in the three systems. (i) A 30-year-longsurvey of the soft-bottom macrofauna in the Kiel Bay, WesternBaltic Sea lists 184 species at the Station “Millionenviertel 14”(Rumohr, pers com). (ii) On Helgoland island, three extensivestudies in the same sub-habitats we used here, reported 53 ses-sile animal species (Janke 1986; Reichert 2003) and 39 speciesof macroalgae (Inka Bartsch, unpublished data). (iii) Finally,studies on the diversity of hard-bottom communities growingon artificial substrata conducted during three consecutiveyears in the south coast of Madeira Island (Jochimsen 2007;Canning-Clode et al. 2008, Manfred Kaufmann, unpublisheddata) reported a total of 44 species growing on the same typeof substrata, depth, and study site as the artificial hard-bottomdata-set in this analysis. Compared to these values, our extrap-olation still underestimates the “real” richness of the investi-gated habitats by 44% for the soft-bottom, 29% for the natu-ral hard-bottom, and 14% for the artificial hard-bottomhabitats. However, it should be noted that the reference listsinclude species from several seasons, years, and successionalstages, which, in contrast to our data set, do not necessarilyco-exist at the local scale. Regional species pools based on suchinventories may include species not susceptible to recruit intothe community considered because they are restricted to dif-ferent habitats and seasons.

We conclude that regional richness can be estimated fromsub-samples, that the quality of the estimation increases withsample size, and that the magnitude of the unavoidable esti-mation error can be quantified and, thus, corrected to someextent. We encourage further studies to include data frommore locations and then provide more robust correction val-ues to compensate the bias caused by low replication.

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Submitted 17 June 2008Revised 6 October 2008

Accepted 22 October 2008

limnology and oceanography: methods · rumohr for providing the soft-bottom data and mathieu cusson...

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