a probabilistic approach to estimating species pools from...

- A probabilistic approach to estimating species pools from large compositional matrices - 191

Journal of Vegetation Science 13: 191-198, 2002© IAVS; Opulus Press Uppsala. Printed in Sweden

Abstract. Species pools are increasingly recognized as impor-tant controls of local plant community structure and diversity.While existing approaches to estimate their content and sizeeither rely on phytosociological expert knowledge or on sim-ple response models across environmental gradients, the pro-posed application of phytosociological smoothing accordingto Beals exploits the full information of plant co-occurrencepatterns statistically. Where numerous representative com-positional data are available, the new method yields robustestimates of the potential of sites to harbour plant species.

To test the new method, a large phytosociological databankcovering the forested regions of Oregon (US) was subsampledrandomly and evenly across strata defined by geographicregions and elevation belts. The resulting matrix of speciespresence/absence in 874 plots was smoothed by calculatingBeals’ index of sociological favourability, which estimates theprobability of encountering each species at each site from theactual plot composition and the pattern of species co-occur-rence in the matrix. In a second step, the resulting lists ofsociologically probable species were intersected with com-plete species lists for each of 14 geographical subregions.Species pools were compared to observed species composi-tion and richness. Species pool size exhibited much clearerspatial trends than plot richness and could be modelled muchbetter as a function of climatic factors. In this framework thegoal of modelling species pools is not to test a hypothesis, butto bridge the gap between manageable scales of empiricalobservation and the spatio-temporal hierarchy of diversitypatterns.

Keywords: Beals smoothing; Biodiversity; Biogeography;Climate; Databank; Phytosociology; Plant community; Spatialscale.

A probabilistic approach to estimating species poolsfrom large compositional matrices

Ewald, Jörg

Fachhochschule Weihenstephan, Fachbereich Wald und Forstwirtschaft, D-85350 Freising, Germany;E-mail [email protected]

Introduction

Plant ecologists have recently stressed the role ofspecies pools in shaping local community compositionand diversity (Eriksson 1993; Wisheu & Keddy 1996;Pärtel et al. 1996; Zobel 1997; Zobel et al. 1998; Canteroet al. 1999; Lord & Lee 2001). It is increasingly ac-knowledged that available species pools have to betaken into account, if effects of both natural factors andexperimental treatments on diversity are to be inter-preted in a meaningful way (Grace 1999; Rajaniemi &Goldberg 2000) and translated into successful manage-ment (Zobel et al. 1998). However, there appears to beno straightforward way of defining, measuring or mod-elling species pools (Eriksson & Ehrlén 1992; Dupré2000). In fact, their determination requires knowledgeabout the ecology and distribution of all species in entirefloras – a condition that is hard to meet in most parts ofthe world.

Two components are crucial for the estimation oflocal species pools: the flora and the environmentalfilter (Zobel et al. 1998). A flora lists all species in arestricted geographical area, in which they form thepool for any plant communities; its richness was termedg-diversity by Whittaker (1960, 1972). The environ-mental filter defines what fraction of species in a floraare capable of establishing populations under the envi-ronmental conditions prevailing in a habitat, i.e. whichspecies have niches overlapping with the local realiza-tion of environmental state space (Hutchinson 1957).Because an exhausting definition of niches and environ-mental state space is impractical (if not unattainable),realized niches must be estimated from empirical coin-cidence data (Austin 1999).

Pärtel et al. (1996) based species pool estimation ona list of plant indicator values for Central Europe(Ellenberg et al. 1991, a compilation of expert know-ledge on presumed ecological optima). They proposedto extract ecological preferences from the phytosocio-logical literature as an alternative. Applying both typesof environmental filters to the flora of Swedish grass-lands and forests Dupré (2000) found that ecological

192 Ewald, J.

indicator values for light, temperature, moisture, soil pHand nitrogen availability were less efficient in definingrealistic community pools than the phytosociologicalapproach based on Oberdorfer’s (1994) flora of Ger-many, that classifies species as ‘character species’ ofcommunity types and mentions other suitable habitats.Both approaches rely on a particular regional traditionof phytosociology and its unusually large body of em-pirical, largely descriptive expert knowledge. Conse-quently, their implementation is impractical anywhereoutside of Central Europe and its immediate vicinity.

Grace & Pugesek (1997) defined species pools onthe basis of joint ecological measurements and speciesoccurrences with respect to a salinity gradient, i.e. asingle extreme environmental factor bearing strongly onthe physiological tolerances (fundamental niches) ofspecies. This approach requires extensive sampling ofvegetation and soils and is less useful in differentiatingmesic habitats, where community composition stronglydepends on biotic interactions and, as a consequence,multidimensional realized rather than simple funda-mental niches have to be estimated.

This contribution proposes a shortcut to definingplant species pools that is both practical and versatile.Beals (1984) introduced an ‘index of sociologicalfavourability’, that was subsequently termed ‘Bealssmoothing’ by McCune (1994). It has passed unnoticedthat Brisse et al. (1980) in France had developed anidentical matrix operation earlier as an extension of fidel-ity in the sense of Braun-Blanquet (1964). Designed torelieve the ‘zero truncation problem’ in sparse commu-nity matrices, it replaces presences/absences in a plot-by-species matrix with probabilities of occurrence esti-mated on the basis of observed plot composition. In thisrespect, it resembles Pärtel’s and Dupré’s indicatorspecies approach to species pool estimation, in which amean indicator value is calculated on the basis of ob-served composition and species with optima close tothat value are searched for. It differs in relying on themultidimensional structure of real data rather than on astrongly simplified expert system such as Ellenberg indi-cator values. Despite being a phytosociological method itavoids subjectivity and simplification, because it operateswithout classifications and presupposed gradients.

This paper presents a new application of Bealssmoothing to the study of species richness. Exploiting alarge phytosociological databank of coniferous forestsin the American Pacific Northwest, numerical floristicand environmental filters are applied. The environmentalfilter is treated as a probabilistic model, which cancreate various outcomes depending on the parametersused. Alternative species pool models are evaluated bycomparing them to raw data and to each other, bycreating maps and relating them to climatic conditions.

Material and Methods

An existing large phytosociological data set cover-ing forests throughout the entire state of Oregon, USA(Ohmann & Spies 1998) was screened for plot data withcomplete sampling of vascular species (trees, woodyand herbaceous understorey), resulting in a total of 8425plots (each 500-800 m2). As this sample was largelyrestricted to public lands with high conservation priorityand contained only occasional plots from young forests,the study was limited to 6,984 mature and late succes-sional stands (> 60 yr) based on estimates of age re-corded on the ground by the surveying teams. Thetaxonomical data were made compatible by checking allrecorded names in regional manuals (Peck 1961;Hitchcock et al. 1969; Hickman 1993) and adjustingnomenclature to the level of 1180 accepted speciesgiven in the reference list of the Plants national database

Fig. 1. Vascular plant richness in 874 forest communities ofOregon ( = ecoregions; ----- = subregions); top: regionalspecies pool size (g-diversity, estimated for standardized sam-pling intensity); centre: observed plot richness (a-diversity);bottom: modelled species pool size (0.1 cut-off probability).


(Anon. 1999). The 5 forested ecoregions defined byOhmann & Spies (1998) were further subdivided into 14subregions (Fig. 1; Table 1). A spatially and orographi-cally balanced subsample of 874 plots containing 636species was obtained by randomly sampling 38 strata(2-3 elevational belts in 14 subregions, each representedby 23 plots).

That matrix served as a basis for applying an envi-ronmental filter in the definition of species pools. Thematrix was transformed to presence/absence andsmoothed by calculating Beals’ (1984) index of socio-logical favourability (PC-Ord 4; McCune & Mefford1999), which estimates the probability of encounteringspecies at a site from the actual species composition inthe plot and the pattern of species co-occurrence in thematrix:

(1)

where bij is the estimated probability of species j tooccur in sample i, Si the number of species in sample i,Mjk the number of joint occurences of species j and k andNk the number of occurrences of species k in the wholematrix. The transformed matrix was re-imported intothe related database, where it was subjected to queries.Several alternative extracts of those species with a po-tential of occurring at each of the given sites (A’ in Fig.2) were created by querying all species scoring bij valuesexceeding thresholds of 0 up to 0.4. Increasing thisprobability threshold amounts to tightening the criteriaof the environmental filter or, in other words, to focussingthe angle of vision on multivariate compositional space.Corresponding to the 10 thresholds, this step resulted in

10 alternative matrices listing all species with a minimumprobability of occurrence in the environments repre-sented by each of the 874 plots.

The regional species pools (for mature and old-growth forests, g-diversity) in each of the 14 ecoregionswere defined as all species included in random subsam-ples of 142 plots (the number of quadrats available in themost sparsely sampled subregion, western Klamath,Table 1). This procedure is a compromise between anattempt to define regional pools as complete as possiblebased on a maximum of available observations and the

Table 1. Stratification of the study area based on subdivision of ecoregions (Ohmann & Spies 1998); forested area based on Landsat30 m ¥ 30 m pixel data; note that sampling intensity (number of quadrats) did not depend on forest area (R2 = 0.027, n.s.).

Region No. of quadrats Land area (km2) Forest area (km2) % forest

Blue Mountains 898 46335.0 23533.9 50.8central 206 14295.3 8637.8 60.4eastern 513 14505.7 5795.6 40.0

western 179 17534.0 9100.5 51.9Cascades 3187 30025.2 26035.6 86.7

central 1432 10372.7 9103.0 87.8northern 1122 7984.2 6756.3 84.6southern 633 11668.3 10176.3 87.2

Coast Ranges 818 27591.5 20486.5 74.2northern 218 16449.5 10629.3 64.6southern 600 11142.0 9857.2 88.5

Eastern Cascades 624 29450.5 17754.4 60.3northern 258 11673.1 6819.3 58.4

southeastern 185 10132.1 5551.9 54.8southwestern 181 7645.3 5383.2 70.4

Klamath 1457 16103.6 13412.4 83.3northeastern 710 7130.6 5811.5 81.5southeastern 605 4953.4 3901.1 78.8

western 142 4019.6 3699.8 92.0

Fig. 2. Intersection of floristic sets; F = flora; R = regionalspecies pool (all species occurring in a subregion); A' =‘environmental’ species pool modeled by Beals smoothing;A = modelled species pool (R « A’); B = plot composition;c = species common to plot composition and species pool(B « A).

bS

M

Niji

jk

kk

=ÊËÁ

ˆ¯̃Â1

194 Ewald, J.

need to avoid bias due to uneven sampling intensityacross regions. Equal sub-sampling did not introduceanother bias, because the number of available quadratswas largely independent of the subregions’ forest area(Table 1). Note, that for the purposes of this study it wascrucial to obtain taxonomically explicit regional speciespools (R in Fig. 2) for intersection with pools derived byapplying environmental filters (A’ in Fig. 2).

Community species pools for each site (A in Fig. 2)were then modelled by intersecting the lists of all speciespresent in the subregion (regional pool R) with the listsof all species with a minimum probability of occurrencein the plot environment (A’). This combination ofchorological (floristic) and environmental (phyto-sociological) filters accords to the logic of the speciespool concept.

The relationships between the respective sets ofspecies in plot data (B), the modelled community pool(A) and the regional species pool (R) formed the basis ofassessment of the outcomes of various species poolmodels (Fig. 2): Sørensen’s similarity index

(2)

expresses the overall match between observation andmodel. Inclusiveness c/B*100 describes the proportionof observed species that were included in the modelledpools (the complement to ‘error type I’ sensu Dupré2000) and saturation (c/A*100) the percentage of mod-elled species that were observed (complement to ‘errortype II’). Mean coefficients for all 874 plots were calcu-lated to compare model performance. The Spearmancorrelation coefficient (Statistica 5.5; Anon. 1984-2000)between observed and modelled richness expresses theability of the modelled pool to reproduce the observedrank order of species richness.

The effect of smoothing on the detectability of thespatial diversity pattern was assessed by fitting polyno-mial trend surfaces (Legendre & Legendre 1998) toobserved and modelled richness. Spatial models weredeveloped by removing insignificant 2nd and 3rd orderpolynomial terms of centered geographic coordinates ina backward stepwise regression (Statistica 5.5; Anon.1984-2000). Correspondingly, predictions of richnessfrom annual precipitation (based on the model by Dalyet al. 1994) and annual temperature (model by Dodson& Marks 1997) were assessed by regressing observedand modelled richness against siginificant 1st to 3rdorder polynomial terms of the standardized climaticvariables – a procedure allowing non-linear responsesurfaces to be fitted.

Results

In the stratified data set observed richness variedbetween 2 and 58 vascular plant species per plot with amean of 21. Plot richness was only broadly related to theregional richness in forest floras. The richest plots didoccur in the floristically most diverse regions of thesouthwestern Klamath Mountains (Fig. 1, top and cen-tre). On the other hand, forest stands were moderatelyspecies-rich in the floristically depauperate Coast Rangesand often species-poor in Oregon’s dry interior regionswith their relatively diverse floras.

Species pools modelled by smoothing and sub-sequent intersection with regional flora were as largeas ca. 200 species if all species with even the smallestprobability of occurrence were included and declinedhyperbolically with an increasing threshold probabil-ity (Fig. 3). Beyond a cut-off value of 0.3 meanmodelled species pool size dropped below observedrichness. The proportion of observed species whichwere correctly included in modelled pools (inclusive-ness) dropped almost linearly at cut-off probabilitiesabove 0.1. Correspondingly, the proportion of mod-elled species that were actually observed in plots (satu-ration) increased. Floristic similarity between modeland observation was a hump-shaped optimum functionof cut-off probability with the closest match (61%) at acut-off of ca. 0.275. The rank correlation betweenobserved and modelled richness rose from 0.4 to maxi-mum values of 0.61 and tapered off at probabilitiesabove 0.2.

Observed species richness was highly variable ingeographic space (Fig. 1, middle). Only 15.6% of thevariation was accounted for by a polynomial trendsurface. Species pool size formed the clearest spatialpattern, when the probability threshold was set to 0(Fig. 3). This version of the model largely reproducesregional richness, resulting in 14 rather discrete speciespool sizes corresponding to g-diversity in Fig. 1 (top).Imposing an increasingly tight environmental filter byincreasing cut-off probability caused a linear, but shal-low decline in fit to the spatial trend surface. Evenspecies pools modelled without regional constraints(A’ in Fig. 1) could be modelled reasonably well (R2 =0.41). Consequently, maps of potential richness weremuch easier to interpret (Fig. 1, bottom) than theobserved data (top).

Precipitation and temperature explained a slightlylarger fraction of observed richness than geographiclocation (R2 = 0.184). Modelled species pools ap-peared to reflect climatic space much more closely(Fig. 3): Variance explained by climate was highest(58.6%) at a cut-off level of 0.25. In the model withoutregional constraints (A’ in Fig. 2) R2 = 0.283. Richness

SIc

A B=

+2

100*


generally increased with mean temperature and re-sponded unimodally to precipitation under warm, butwas invariably low under cold, conditions (Fig. 4). Themodels for species pools placed the expected maximum

richness in a drier climate and suggested a slightlystronger differentiation of richness with moisture atlow temperatures.

Fig. 3. Evaluation of species pools modelled with varying cut-off probabilities of species occurrence for 874 forest communities throughoutOregon; curves show mean values for all plots, bars show standard deviation; where appropriate dashed horizontal lines indicatecorresponding mean for observed plot data.

196 Ewald, J.

Discussion

Beals smoothing of phytosociological data, as ap-plied in this study, enhances our ability to see andinterpret patterns of species richness in geographic andenvironmental space as it improves the detection ofcompositional gradients (McCune 1994). As in otherderivations of species pools (Pärtel et al. 1996; Dupré2000) geographical information on the available flora iscombined with an ecological filter that allows listing ofall species that appear adapted to occur in a givencommunity. In Oregon, as in most other parts of theworld, there is only sparse information available to dothis. There is no comprehensive compilation of distribu-tions below the state level, no list of Ellenberg indicatorvalues and no phytosociological flora listing habitatpreferences for all species. However, where forests areconcerned, there is a large databank of quadrat descrip-tions, which the proposed method exploits to derivetentative forest flora and model species pools.

The precision of species pool modelling at the re-gional and environmental levels increases with the sizeof the available database, because coverage of rarespecies depends on sampling intensity. While this sug-gests that as many plots as possible should be included,it should not be done at the cost of spatial or environ-mental bias. Counteracting spatial lumping – as in theOregon forest database (Table 1) – by stratified sub-sampling greatly reduces dataset size in non-systematicsamples. Once a suitable database has been compiled, itis recommended to re-iterate the whole process pro-posed in this paper, including model evaluation, beforechoosing a particular species pool model.

Following Brisse et al. (1995) one can say thatBeals’ smoothing of phytosociological data calibrates amultidimensional plant indicator system. Much as in themodel proposed by Pärtel et al., actual composition isused to position a plot in ecological space, which is thensearched for species with preferences close to that posi-tion. The differences are that Beals smoothing leaves

Fig. 4. Polynomial trend surfaces of observedspecies richness (top, R2 = 0.184) and modelledspecies pools (below, R2 = 0.586) as a function ofclimate variables precipitation and temperature;light dots denote plot positions.


ecological (or phytosociological) space unreduced, andthat preferential species are queried by applying variousprobability thresholds instead of fixing an arbitrary defi-nition of species pool. Thus, the idea of the species poolas a concrete set that can, at least in principle, be sharplydelimited is replaced by the view that we can only giveprobabilities of species occurrence. Interpreting thegraphs of model outcomes (Fig. 3) gives clues to whichconcrete set of pools to choose for a particular purpose.In the Oregon case, a cut-off of 0.2 performs close tooptimal in several respects. If, on the other hand,inclusiveness of rarer species and spatial smoothness ofthe pools seem more important, one may want to choosea cut-off of 0.1 (Fig. 1).

Smoothing aggregates information on a coarser leveland reduces noise. The proposed procedure deals mainlywith environmental and geographic space. Less obvi-ously, combination of many replicate samples fromsimilar sites reduces the temporal noise that metapopu-lation dynamics of dispersal, recruitment and local ex-tinction impose on individual communities (Rosenzweig& Ziv 1999). For similar reasons, statistical averagingof diversity is a common practice in community ecol-ogy: Thus, the hump-shaped biomass-richness curves(Al-Mufti et al. 1977; Grime 1979) are usually based onmean values (Grace 1999) and richness is averaged forgroups of plots with similar positions on ecologicalgradients (Whittaker 1960; del Moral 1972; Zobel et al.1976). Besides reducing random variation, smoothingand averaging amount to shifting to a higher hierarchi-cal systems level (Allen & Starr 1982). Likewise, spe-cies pool theory and the metacommunity model (Hubbell2001) relegate the explanation of properties at the com-munity level to external controls operating at coarserspatial (and temporal) scales.

Attributing the concentration on plot scale diversityto a merely ergonomic ease of sampling and manipu-lating, Allen & Starr (1982) recommended searching foran appropriate scale coarser than the community tountangle biodiversity – an agenda that is finally pursuedin the recent literature on species pools and meta-communities. The probabilistic model of species poolsallows searching for the most appropriate scales inunderstanding floristic and ecological information inlarge data sets. Thus, the relationships of species poolsize with observed richness and with climatic variableswere tightest at intermediate cut-off probabilities – i.e.intermediate angles of vision on compositional space. Itshould not be overlooked how crucial and yet howdifficult it is to acquire field data that cover a range ofscales from stands to entire ecoregions. Phytosociologi-cal databases such as the one used in this example (seeEwald 2001 for a worldwide review) and electronicatlases of plant distribution (e. g. British Isles Monitor-

ing Scheme: Palmer & Bratton 1995; German VascularPlant Databank: Schönfelder 1999; Atlas FloraeEuropaeae: Anon. 2000) hold great promise in thisrespect.

Looking at species pools as conceptual links in ahierarchy of complex systems transcends the issue ofthe circularity in their definition and of their testability(e.g. Herben 2000; Lepš 2001). In the framework pro-posed here, species pools are not neat independent pre-dictors resolving the complexity of community patterns,but a useful tool in studying the nested hierarchy ofspatial and temporal scales.

Acknowledgements. This research was funded by the MaxKade Foundation, New York. Thanks to the USDA ForestService and Janet Ohmann for providing the database and forsupplying additional GIS analyses. Bruce McCune, Jim Grace,Rune Økland, Meelis Pärtel and an anonymous reviewer helpedwith constructive remarks.

References

Anon. 1984-2000. Statistica kernel release 5.5. StatSoft Inc.,Tulsa, OK.

Anon. 1999. The PLANTS database (http://plants.usda.gov/plants). National Plant Data Center, USDA, NRCS, BatonRouge, LA.

Anon. 2000. Atlas florae europaeae: Distribution of vascularplants in Europe. Committee for Mapping the Flora ofEurope; http://www.helsinki.fi/kmus/afe.html.

Allen, T.F.H. & Starr, T.B. 1982. Hierarchy: perspectives forecological complexity. University of Chicago Press, Chi-cago, IL.

Al-Mufti, M.M., Sydes, C.L., Furness, S.B., Grime, J.P. &Band, S.R. 1977. A quantitative analysis of shoot phenol-ogy and dominance in herbaceous vegetation. J. Ecol. 65:759-791.

Austin, M. P. 1999. The potential contribution of vegetationecology to biodiversity research. Ecography 22: 465-484.

Beals, E.W. 1984. Bray-Curtis-ordination: an effective strat-egy for analysis of multivariate ecological data. Adv. Ecol.Res. 14: 1-55.

Braun-Blanquet, J. 1964. Pflanzensoziologie. 3. Aufl. Springer-Verlag, Wien, AT.

Brisse, H., Grandjouan, G., Hoff, M. & de Ruffray, P. 1980.Utilisation d’un critère statistique de l’écologie en phyto-sociologie – exemple des forêts alluviales en Alsace. Coll.Phytosociol. 9: 543-590.

Brisse H., de Ruffray, P., Grandjouan, G. & Hoff, M. 1995.The phytosociological database ‘SOPHY’. Part I: Calibra-tion of indicator plants. Part II: Socio-ecological classifi-cation of the relevés (English and French version). Ann.Bot. (Roma) 53: 177-223.

Cantero, J. J., Pärtel, M. & Zobel, M. 1999. Is species richnessdependent on the neighbouring stands? An analysis of thecommunity patterns in mountain grasslands of central

198 Ewald, J.

Argentina. Oikos 87: 346-354.Daly, C., Neilson, R.P. & Phillips, D.L. 1994. A statistical-

topographic model for mapping climatological precipita-tion over mountainous terrain. J. Appl. Meteorol. 33: 140-158.

del Moral, R. 1972. Diversity patterns in forest vegetation ofthe Wenatchee Mountains, Washington. Bull. Torrey Bot.Club 99: 57-64.

Dodson, R. & Marks, D. 1997. Daily air temperature interpo-lation at high spatial resolution over a large mountainousregion. Climate Res. 8: 2-20.

Dupré, C. 2000. How to determine a regional species pool: astudy in two Swedish regions. Oikos 89: 128-136.

Ellenberg, H., Weber, H.E., Düll, R., Wirth, V., Werner, W. &Paulißen, D. 1991. Zeigerwerte von Pflanzen in Mittel-europa. Scripta Geobot. 18: 1-248.

Eriksson, O. 1993. The species-pool hypothesis and plantcommunity diversity. Oikos 68: 371-374.

Eriksson, O. & Ehrlén, J. 1992. Seed and microsite limitationof recruitment in plant populations. Oecologia 91: 360-364.

Ewald, J. 2001. Der Beitrag pflanzensoziologischer Daten-banken zur vegetationsökologischen Forschung. Ber.Reinhold Tüxen Ges. 13: 53-69.

Grace, J.B. 1999. The factors controlling species density inherbaceous plant communities: an assessment. Perspect.Plant Ecol. Evol. Syst. 2: 1-28.

Grace, J.B. & Pugesek, B.H. 1997. A structural equationmodel of plant species richness and its application to acoastal wetland. Am. Nat. 149: 436-460.

Grime, J.P. 1979. Plant strategies and vegetation processes .John Wiley, Chichester, UK.

Herben, T. 2000. Correlation between species richness perunit area and the species pool cannot be used to demon-strate the species pool effect. J. Veg. Sci. 11: 123-126.

Hickman, J.C. (ed.) 1993. The Jepson manual – higher plantsof California. University of California Press, Berkeley,CA.

Hitchcock, C.L., Cronquist, A. & Ownbey, M. 1969. Vascularplants of the Pacific Northwest. Vols. 1-5. University ofWashington Publications in Biology, Seattle, WA.

Hubbell, S.P. 2001. The unified neutral theory of biodiversityand biogeography. Princeton University Press, Princeton,NJ.

Hutchinson, G.E. 1957. Concluding remarks. Cold SpringHarbor Symp. Quant. Biol. 22: 415-457.

Legendre, P. & Legendre, L. 1998. Numerical ecology. 2nded. Elsevier, Amsterdam, NL.

Lepš, J. 2001. Species-pool hypothesis: limits to its testing.Folia Geobot. 36: 45-52.

Lord, L.A. & Lee, T.D. 2001. Interactions of local and re-gional processes: species richness in tussock sedge com-munities. Ecology 82: 313-318.

McCune, B. 1994. Improving community analysis with theBeals smoothing function. Ecoscience 1: 82-86.

McCune, B. & Mefford, M.J. 1997. Multivariate analysis ofecological data version 3.04. MJM Software, GlenedenBeach, US.

Oberdorfer, E. 1994. Pflanzensoziologische Exkursionsflora.7th ed. Ulmer, Stuttgart, DE.

Ohmann, J.L. & Spies, T.A. 1998. Regional gradient analysisand spatial pattern of woody plant communities of Oregonforests. Ecol. Monogr. 68: 151-182.

Palmer, M.A. & Bratton, J.H. 1995. A sample survey of theflora of Britain and Ireland. UK Nature ConservationSeries 8, Peterborough, UK.

Pärtel, M., Zobel, M., Zobel, K. & van der Maarel, E. 1996.The species pool and its relation to species richness –evidence from Estonian plant communities. Oikos 75:111-117.

Peck, M.E. 1961. A manual of the higher plants of Oregon.2nd ed. Binfords & Mort, Portland, OR.

Rajaniemi, T.K. & Goldberg, D.E. 2000. Quantifying indi-vidual- and community-level effects of competition usingexperimentally-determined null species pools. J. Veg. Sci.11: 433-442.

Rosenzweig, M.L. & Ziv, Y. 1999. The echo pattern of speciesdiversity: pattern and processes. Ecography 22: 614-628.

Schönfelder, P. 1999. Mapping the flora of Germany. ActaBot. Fenn. 162: 43-53.

Whittaker, R.H. 1960. Vegetation of the Siskiyou Mountains,Oregon and California. Ecol. Monogr. 30: 279-338.

Whittaker, R.H. 1972. Evolution and measurement of speciesdiversity. Taxon 21: 213-251.

Wisheu, I.C. & Keddy, P. 1996. Three competing models forpredicting the size of species pools: a test using easternNorth American wetlands. Oikos 76: 253-258.

Zobel, D.B., McKee, A., Hawk, G.M. & Dyrness, C.T. 1976.Relationships of environment to composition, structureand diversity of forest communities of the central westernCascades of Oregon. Ecol. Monogr. 46: 135-156.

Zobel, M. 1997. The relative role of species pools in determin-ing plant species richness: an alternative explanation ofspecies coexistence. Trends Ecol. Evol. 12: 266-269.

Zobel, M., van der Maarel, E. & Dupré, C. 1998. Species pool:the concept, its determination and significance for com-munity restoration. Appl. Veg. Sci. 1: 55-66.

Received 20 April 2001;Revision received 26 December 2001;

Accepted 7 January 2002.Coordinating Editor: R.H. Økland.

a probabilistic approach to estimating species pools from...

Documents