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Abstract

Questions: Which environmental factors influence fine-grain beta diversity of vegetation and do they vary among taxonomic groups? Location: Palaearctic biogeographic realm. Methods: We extracted 4,654 nested-plot series with at least four different grain sizes between 0.0001 m² and 1,024 m² from the GrassPlot database, covering a wide range of different grassland and other open habitat types. We derived extensive environmental and structural information for these series. For each series and four taxonomic groups (vascular plants, bryophytes, lichens, all), we calculated the slope parameter (z-value) of the power-law species–area relationship (SAR), as a beta diversity measure. We tested whether z-values differed among taxonomic groups and with respect to biogeographic gradients (latitude, elevation, macroclimate), ecological (site) characteristics (several stress-productivity, disturbance and heterogeneity measures, including land use) and alpha diversity (c-value of the power-law SAR). Results: Mean z-values were highest for lichens, intermediate for vascular plants and lowest for bryophytes. Bivariate regressions of z-values against environmental variables had rather low predictive power (mean R² = 0.07 for vascular plants, less for other taxa). For vascular plants, the strongest predictors of z-values were herb layer cover (negative), elevation (positive), rock and stone cover (positive) and the c-value (u-shaped). All tested metrics related to land use (fertilisation, livestock grazing, mowing, burning, decrease in naturalness) led to a decrease in z-values. Other predictors had little or no impact on z-values. The patterns for bryophytes, lichens and all taxa combined were similar but weaker than those for vascular plants. Main conclusions: We conclude that productivity has negative and heterogeneity positive effects on z-values, while the effect of disturbance varies depending on type and intensity. These patterns and the differences among taxonomic groups can be explained via the effects of these drivers on the mean occupancy of species, which is mathematically linked to beta diversity.
J Veg Sci. 2021;32:e13045.    
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https://doi.org/10.1111/jvs.13045
Journal of Vegetation Science
wileyonlinelibrary.com/journal/jvs
Received:6December2020 
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  Revised:1M ay2021 
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  Accepted:12May2021
DOI: 10.1111/jvs.130 45
SPECIAL FEATURE: MACROECOLOGY
OF VEGETATION
Fine- grain beta diversity of Palaearctic grassland vegetation
Iwona Dembicz1,2,3 | Jürgen Dengler2,3,4 | Manuel J. Steinbauer5|
Thomas J. Matthews6,7 | Sándor Bartha8,9 | Sabina Burrascano10 |
Alessandro Chiarucci11 | Goffredo Filibeck12 | François Gillet13 |
Monika Janišová14 | Salza Palpurina15,16 | David Storch17,1 8 | Werner Ulrich19 |
SvetlanaAćić20 | Steffen Boch21 | Juan Antonio Campos22 |
Laura Cancellieri23 | Marta Carboni24 | Giampiero Ciaschetti25 |
Timo Conradi3| Pieter De Frenne26 | Jiri Dolezal27 | Christian Dolnik28|
Franz Essl29 | Edy Fantinato30 | Itziar García- Mijangos22 |
Gian Pietro Giusso del Galdo31 | John- Arvid Grytnes32 | Riccardo Guarino33 |
Behlül Güler34 | Jutta Kapfer35 | Ewelina Klichowska36|ŁukaszKozub1|
Anna Kuzemko37 | Swantje Löbel38| Michael Manthey39 |
Corrado Marcenò15,22 | Anne Mimet40,2 | Alireza Naqinezhad41 |
Jalil Noroozi42 | Arkadiusz Nowak43,44 | Harald Pauli45,46 | Robert K. Peet47 |
Vincent Pellissier40 | Remigiusz Pielech48,49 | Massimo Terzi50 |
EminUğurlu51 | Orsolya Valkó52 | Iuliia Vasheniak53 | Kiril Vassilev16 |
Denys Vynokurov37 | Hannah J. White54 | Wolfgang Willner42 |
Manuela Winkler45,46 | Sebastian Wolfrum55,56 | Jinghui Zhang57, 3 |
Idoia Biurrun22
1Department of Ecology and Environmental Conservation, Institute of Environmental Biology, Faculty of Biology, University of Warsaw, Warsaw, Poland
2VegetationEcologyGroup,InstituteofNaturalResourceSciences(IUNR),ZurichUniversit yofAppliedSciences(ZHAW),Wädenswil,Switzerland
3Plant Ecology, Bayreuth Center of Ecology and Environmental Research (BayCEER), University of Bayreuth, Bayreuth, Germany
4GermanCentreforIntegrativeBiodiversityResearchiDiv)Halle-Jena-Leipzig,Leipzig,Germany
5Sport Ecology, Department of Sport Science & Bayreuth Center of Ecology and Environmental Research (BayCEER), University of Bayreuth, Bayreuth,
Germany
6CE3C–CentreforEcology,EvolutionandEnvironmentalChanges/AzoreanBiodiversityGroup,Univ.dosAçores,Açores,Portugal
7GEES (School of Geography, Earth and Environmental Sciences) and Birmingham Institute of Forest Research, University of Birmingham, Birmingham, UK
8GINOPSustainableEcosystemsGroup,CentreforEcologicalResearch,Tihany,Hungary
9InstituteofEcologyandBotany,CentreforEcologicalResearch,Vácrátót,Hungary
10DepartmentofEnvironmentalBiology,SapienzaUniversityofRome,Rome,Italy
11BIOMELab,DepartmentofBiological,GeologicalandEnvironmentalSciences(BiGeA),AlmaMaterStudiorum–Universit yofBologna,Bologna,Italy
12DepartmentofAgricultureandForestSciences(DAFNE),UniversityofTuscia,Viterbo,Italy
13UMRChrono-environnement,UniversitéBourgogneFranche-Comté,Besançon,France
ThisisanopenaccessarticleunderthetermsoftheCreativeCommonsAttributionLicense,whichpermitsuse,distributionandreproductioninanymedium,
provided the original work is properly cited.
©2021TheAuthors.Journa l of Vegetation SciencepublishedbyJohnWiley&SonsLtdonbehalfofInternationalAssociationforVegetationScience
Thisar ticleisapartoft heSpecialFeat ureMacroecol ogyofvegetation,edi tedbyMeelisPär tel,Fr ancescoMariaS abatini,NaiaM oruet a-Holme,H olgerKreftan dJürgenDengler.
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Journal of Vegetation Science DEMBIC Z Et al.
14InstituteofBotany,PlantScienceandBiodiversit yCenter,SlovakAcademyofSciences,BanskáBystrica,Slovakia
15DepartmentofBotanyandZoology,FacultyofScience,MasarykUniversity,Brno,CzechRepublic
16NationalMuseumofNaturalHistory,BulgarianAcademyofSciences,Sofia,Bulgaria
17CenterforTheoreticalStudy,CharlesUniversit y,Praha1,CzechRepublic
18Depar tmentofEcology,FacultyofScience,CharlesUniversity,Praha2,CzechRepublic
19Depar tment of Ecology and Biogeography, Faculty of Biology and Environmental Protection, Nicolaus Copernicus University, Torun, Poland
20Depar tmentofAgrobotany,FacultyofAgriculture,UniversityofBelgrade,Belgrade-Zemun,Serbia
21Biodiversity&Conser vationBiology,WSLSwissFederalResearchInstitute,Birmensdorf,Switzerland
22PlantBiologyandEcology,UniversityoftheBasqueCountr yUPV/EHU,Bilbao,Spain
23Depar tmentofAgriculturalandForestr ySciences(DAFNE),UniversityofTuscia,Viterbo,It aly
24Department of Science, University of Roma TRE, Rome, Italy
25BotanicalOffice,MajellaNationalPark,Sulmona,Italy
26Forest&NatureLab,GhentUniversity,Gontrode,Belgium
27InstituteofBotany,CzechAcademyofSciences,Pruhonice,CzechRepublic
28Ecology Centre Kiel, Kiel University, Kiel, Germany
29DivisionofConservationBiology,VegetationandLandscapeEcology,UniversityVienna,Vienna,Austria
30Department of Environmental Sciences, Informatics and Statistics, Ca' Foscari University of Venice, Venice, Italy
31Department of Biological, Geological and Environmental Sciences, University of Catania, Catania, Italy
32Department of Biological Sciences, University of Bergen, Bergen, Norway
33Dipartimento di Science, Università degli studi di Palermo, Palermo, Italy
34BiologyEducation,DokuzEylulUniversity,Buca,İzmir,Turkey
35DivisionforGeographyandStatistics,DepartmentofLandscapeMonitoring,NorwegianInstituteofBioeconomyResearch,Tromsø,Norway
36InstituteofBotany,FacultyofBiology,JagiellonianUniversit y,Kraków,Poland
37Depar tmentofGeobotanyandEcology,M.G.KholodnyInstituteofBotany,NationalAcademyofSciencesofUkraine,Kyiv,Ukraine
38LandscapeEcologyandEnvironmentalSystemsAnalysis,InstituteofGeoecology,TUBraunschweig,Braunschweig,Germany
39InstituteofBotanyandLandscapeEcology,GreifswaldUniversity,Greifswald,Germany
40ComputationalLandscapeEcology,HelmholtzCenterforEnvironmentalResearch,Leipzig,Germany
41Depar tmentofPlantBiology,FacultyofBasicSciences,UniversityofMazandaran,Babolsar,Iran
42Depar tmentofBotanyandBiodiversityResearch,UniversityofVienna,Vienna,Austria
43BotanicalGardenCenterforBiologicalDiversityConservationinPowsin,PolishAcademyofSciences,Warsaw,Poland
44Institute of Biology, University of Opole, Opole, Poland
45Depar tmentofIntegrativeBiologyandBiodiversit yResearch,GLORIACo-ordination,UniversityofNaturalResourcesandLifeSciencesVienna(BOKU),
Vienna,Austria
46GLORIACo-ordination,InstituteforInterdisciplinaryMountainResearch,AustrianAcademyofSciences,Vienna,Austria
47Depar tmentofBiology,UniversityofNorthC arolina,ChapelHill,NorthCarolina,USA
48DepartmentofForestBiodiversity,FacultyofForestry,UniversityofAgricultureinKraków,Kraków,Poland
49FoundationforBiodiversityResearch,Wrocław,Poland
50Institute of Biosciences and Bioresources (IBBR), Italian National Council of Research (CNR), Bari, Italy
51Forest Engineering, Faculty of Forestry, Bursa Technical University, Yildirim, Turkey
52CentreforEcologicalResearch,InstituteofEcologyandBotany,MTA-ÖKLendületSeedEcologyResearchGroup,Vácrátót ,Hungary
53Faculty of Chemistry, Biology and Biotechnologies, Vasyl' Stus Donetsk National University, Vinnytsia, Ukraine
54School of Biology and Environmental Science, Earth Institute, University College Dublin, Dublin 4, Ireland
55ChairofOrganicAgricultureandAgronomy,Weihenstephan,TechnischeUniversitätMünchen,Freising,Germany
56InstituteofOrganicFarming,SoilandResourceManagement(IAB),BavarianStateResearchCenterforAgriculture(LfL),Freising,Germany
57SchoolofEcologyandEnvironment,InnerMongoliaUniversity,Hohhot,China
Correspondence
JürgenDengler,VegetationEcologyGroup,
Institute of Natural Resource Sciences
(IUNR),ZurichUniversityofApplied
Sciences(ZHAW),Grüentalstr.14,8820
Wädenswil,Switzerland.
Email:juergen.dengler@zhaw.ch
Abstract
Questions: Whichenvironmental factorsinfluence fine-grain betadiversity of veg-
etation and do they vary among taxonomic groups?
Location: Palaearctic biogeographic realm.
Methods: Weextracted 4,654 nested-plot serieswith at least four different grain
sizesbetween0.0001m²and1,024m²fromtheGrassPlotdatabase,coveringawide
    
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Journal of Vegetation Science
DEMBIC Z Et al.
1 | INTRODUCTION
One of the central aims of ecology and evolutionary biology is to
understand the drivers of biological diversity at different spatial and
temporalscales(Allanet al., 2011;Isbell et al.,2011).Acrucialdi-
mension of biological diversity is β-diversity,thevariabilityinspecies
compositionbetweenlocalcommunities(Andersonetal., 2011).At
large spat ial grain sizes (≥ 100 km ²) and along lat itudinal and e le-
vation gradients, important drivers of β-diversityare macroclimate
anddispersalbarriers(Qian,2009;Qianetal.,2013;Pinto-Ledezma
et al., 2018). At medium (0.01 km² to <100 km²) and small spatial
grainsizes(<0.01kor1ha;grainsizeclassificationmodifiedf rom
Field et al., 2009), the drivers are much less understood, although
microclimateandsoilvariability areknowntoinfluencesmall-scale
communitycomposition(Opedalet al., 2015; Ulrichetal.,2017).A
betterunderstandingofdriversoffine-grainβ-diversitywouldsup-
port a more informed application of this biodiversity dimension in
vegetation ecology, conservation and management measures, and
allow more reliable inter- and extrapolations of species richness
to other fine grain sizes. Transferring results from coarse-grain
β-divers ity studies is n ot possible, as sever al studies have show n
strong changes in patterns and drivers of β-diversity across grain
sizes(Veech&Crist,2007;Sreekaretal.,2018).
Species–arearelationships(SARs)describingtheincreaseofspe-
cies richness with area are another major research focus of ecology
and biogeo graphy (Connor & Mc Coy,1979; Dra kare et al., 200 6;
Dengler, 20 09). SARs can be co nstructe d in various ways, a mong
them, wi th nested and no n-nested samp ling units (Den gler et al.,
2020a). There is growing evidence that among the numerous pro-
posedSARfunctions(Tjørve,2003;Dengler,2009),thepowerfunc-
tion (S = c Az log S = log c + z log A; where S is species richness,
A is area, and c and z are fitted parameters) provides the best fit in
most cases(Connor&McCoy, 1979;Dengler,2009; Triantis etal.,
2012; Matt hews et al., 2016; Den gler et al., 2020 a). The param e-
tersofSARfunctions(andspecificallytheexponentz of the power
law)arewidelyusedforcomparingtheshapeofSARsoftaxonomic
groups with different dispersal abilities (Patiño et al., 2014), assess-
ing the impact of anthropogenic disturbance on species assemblages
(Tittensor et al., 2007), and quantifying the expected species loss
duetohabitatareareduction(He&Hubbell,2011).
Funding information
TheBavarianResearchAlliance(viathe
BayIntAnscheme)andtheBayreuthCenter
of Ecology and Environmental Research
(BayCEER) funded the initial GrassPlot
workshop during which the database was
established and the current paper was
initiated(grantstoJDe).WUacknowledges
suppor t from the Polish National Science
Centre (grant 2017/27/B/NZ8/00316). IB,
JACandIG-MwerefundedbytheBasque
Government(IT936-16).GFcarriedout
theresearchintheframeoftheMIUR
initiative“Departmentofexcellence”(Law
232/2016). SBa was suppor ted by the
G I N O P - 2 . 3 . 2 - 1 5 - 2 0 1 6 - 0 0 0 1 9  p r o j e c t . 
CMwassupportedbytheCzechScience
Foundation(grantno.19-28491X)and
theBasqueGovernment(IT936-16).ID
was supported by the Polish National
ScienceCentre(grantDEC-2013/09/N/
NZ8/03234) and by a Swiss Government
ExcellenceScholarshipforPostdocs(ESKAS
No.2019.0491).MJwassupportedbythe
SlovakAcademyofSciences(grantVEGA
02/0095/19).ANwassupportedbya
“MasterPlanProject”intheUniversityof
Mazandaran,Iran.DSwassupportedby
theCzechScienceFoundation(grantno.
20-29554X).AK,IVandDVweresupported
by the National Research Foundation
of Ukraine (project no. 2020.01/0140).
JDowassupportedbytheCzech
ScienceFoundation(GA17-19376S)and
LTAUSA18007
Co-ordinating Editor:HolgerKreft
range of different grassland and other open habitat types. We derived extensive
environmental and structural information for these series. For each series and four
taxonomic groups (vascular plants, bryophytes, lichens, all), we calculated the slope
parameter (z-value)ofthepowerlawspecies–arearelationship(SAR),asabetadiver-
sity measure. We tested whether z-valuesdifferedamongtaxonomicgroupsandwith
respect to biogeographic gradients (latitude, elevation, macroclimate), ecological (site)
characteristics (several stress– productivity, disturbance and heterogeneity measures,
including land use) and alpha diversity (c-valueofthepowerlawSAR).
Results: Mean z-values were highest for lichens, intermediate for vascular plant s
andlowestfor bryophytes.Bivariateregressions of z-values against environmental
variables had rather low predictive power (mean R² = 0.07 for vascular plants, less
for other taxa). For vascular plants, the strongest predictors of z-values wereherb
layer cover (negative), elevation (positive), rock and stone cover (positive) and the c-
value(U-shaped).Alltestedmetricsrelatedtolanduse(fertilization,livestockgrazing,
mowing, burning, decrease in naturalness) led to a decrease in z-values.Otherpredic-
tors had little or no impact on z-values.Thepatternsforbryophytes,lichensandall
taxa combined were similar but weaker than those for vascular plants.
Conclusions: We conclude that productivity has negative and heterogeneity posi-
tive effects on z-values,while the effect of disturbance varies depending on type
and intensity. These patterns and the differences among taxonomic groups can be
explained via the effects of these drivers on the mean occupancy of species, which is
mathematically linked to beta diversity.
KEY WORDS
disturbance,elevation,fine-grainbetadiversity,heterogeneity,landuse,macroecology,mean
occupancy, Palaearctic grassland, productivity, scale dependence, species– area relationship
(SAR),z-value
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While β-diversity and SARs are widely studied, there is little
awarenessthatthese twoconceptsarecloselyrelated. MacArthur
(1965) implicitly suggested that the slope parameter z of nested
SARscanbeusedasameasureofβ-diversityandtheinterceptasa
measure of α-diversity,butthiswaslaterdismissedbyConnor and
McCoy (1979). Koleff et al. (2003) demonstrated mathematically
that the exponent z of the power function is indeed a direct mea-
sure of β-diversity.Similarly,Ricotta etal. (2002)proposedtheuse
of the slope parameter b1ofspeciesaccumulationcurves(SACs;for
differences fromSARs,see Dengler et al.,2020a) modelledwith a
logarithmic function (S = b0 + b1 log A) as a measure of multiplicative
β-diversity.Jurasinskietal.(2009)listedslopeparametersofnested
SARsasthethirdconceptofproportionaldiversity,nexttoadditive
and multiplicative β-diversity,butindicatedthattheyareonlyrarely
applied.
More recen tly,P olyakova et al. (2016; see al so Sreekar et al.,
2018)re-introducedz-valuesasavalidmeasureofmultiplicativeβ-
diversityincontinuoushabitats.IftheSARismodelledwithapower
function, the slope parameter z is calculated by:
where S2 and S1arethesp eciesrichn essvalu esofthegr ainsizesA2 and
A1, respectively, with A2 > A1. Therefore, if the sampling takes place in
nested plots, S2 can be interpreted as γ-diversityandS1 as (averaged)
α-diversity:
Defining multiplicative β-diversityas
it follows that
Accordingly,z-valuesarethelogarithmsof“conventional”multi-
plicative β-diversity,dividedbythelogarithmoftheratioofthecon-
sidered areas. The advantage of this approach is that the resulting
value allows direct comparison of β-diversityvaluesirrespective of
the relative increase in area between the α-andγ- l e v e l .
The slope zofnestedpowerfunctionSARswithinacontinuous
habitat(incontrasttoislandSARswhereeacharearepresentsadif-
ferent, spatially separate unit) is also linked to the average sparsity
of species (Storch, 2016) in terms of the proportion of occupied sub-
plots: the sparser the species are on average in the sampling plots
(i.e.thelowertheirmeanoccupancyis),thesteepertheSARslope.
Intuitively, if all species occur in each subplot of a larger plot, the
SAR slope approacheszero, while if all species exclusivelyoccupy
just one subplot, the slope approaches one. There is a mathematical
relationship between mean species’ occupancy and the SAR slope
(Šizling&Storch,2004),butthepredictionofSARslopeswouldre-
quire complete information on all species occupancies within a given
plot (i.e. the total number of occupied subplots for each species),
whichisnotavailableinmostnested-plot data(usuallyonly a very
small subset of all potential subplots ofsmallergrainsize within a
larger plot is sampled, thus precluding a realistic estimate of occu-
pancy). Still, one can predict that any factor affecting mean species
occupan cy in a sampling d esign will also infl uence the SAR slo pe
(Šizling & Storc h, 2004). This f inding enables t he investigatio n of
the effects of taxonomic group and ecological factors on species
occupancyandthusSARslopes.Resultsofthefew,mostlyregional,
empiricalstudiesondriversoffine-grainz-valuesinvegetationare
largely i diosyncrat ic and inconclu sive (Appen dix S1).Fo r instance,
certaintypesofdisturbances,likegrazing,mayselectivelydecrease
the occupancy of grassland plant species, creating opportunities for
others (Loucougarayet al.,2004), thuspossibly increasing the SAR
slope. In contrast, other disturbances may selectively eliminate the
sparsest species, increasing overall mean species occupancy, and
thus decreasing theSARslope.Inthis context of multiple possible
responses,acomparativeempiricalstudyofSARslopesisneededto
shed light on the causal pathways through which individual environ-
mentalfactorsaffectspeciesoccupanciesandSARslopes.
Grasslands are inherently fine-grain communities with the
maximum compositional variability appearing at very fine scales,
usually b elow 1 m² (Bart ha et al., 200 4, 2011). The vegetatio n of
Palaearcticgrasslandsisparticularlysuitableforstudyingfine-grain
β-diversityasitregularlycontainsthreetaxonomicgroupswithcon-
trasting ecological properties (vascular plants, bryophytes, lichens).
Moreover,suchgrasslandsoccurunderverydiversesiteconditions
(e.g. from sea level to more than 5,000 m a.s.l., from very wet to
verydrysites)andmanagementregimes(e.g.natural,semi-natural,
intensified; Dengler et al., 2020b). Since Palaearctic grasslands are
known toexhibitextremevariationinsmall-scale species richness,
from monospecific systems to the world records in vascular plant
species richnessbelow 100 m² (Wilsonetal.,2012; Dengler et al.,
2016a),weexpectthatfine-grain β-diversity values willalsocover
a broad range.
Here, we usethe extensiveGrassPlot database (Dengler etal.,
2018), which prov ides multi-scal e species richnes s data of grass-
landsandothernon-forestedhabitatsacrossthewholePalaearctic
biogeographicrealm,totesthowfine-grainβ-diversity(measuredas
z-valuesofnested-plotsSARs)isrelatedtomultiplepotentialdrivers.
Weexpectedthathigherfine-grainheterogeneitywillincreasefine-
grain β-diversity, but the oretical pred ictions for the r ole of other
environmental factors were unclear due to their possible contradic-
tory ef fects (se e Appendix S1). Thus , we addressed th e following
research questions:
1. How do z-values differ among three taxonomic groups (vascular
plants, bryophytes, and lichens)?
(1)
z
=
log
(
S2
S1
)
log
(
A2
A
1)
(2)
z
=
log
(
𝛾
𝛼
)
log
(
A𝛾
A
𝛼)
(3)
𝛽
mult =
𝛾
𝛼
(4)
z
=
log(
𝛽mult
)
log
(
A𝛾
A
𝛼)
    
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DEMBIC Z Et al.
2. Howdoz-valuesvaryinrelationtolarge-scalebiogeographic char-
acteristics, such as latitude, elevation and macroclimate?
3. Howare z-valuesrelatedtosmall-scaleecological characteristics,
related to stressproductivity, disturbance and heterogeneity?
4. Howarez-valuesrelatedtoα- diversity?
2 | METHODS
2.1 | Vegetation-plotdata
Weusedplotdatafromthe collaborativevegetation-plotdatabase
GrassPlot (Biurrun et al., 2019; Dengler et al., 2018; https://edgg.
org/databases/GrassPlot) registered as EU-00-003 in the Global
Index of Vegetation-Plot Databas es (GIVD; Dengler et al., 2011).
GrassPlotassemblesvegetation-plotdata,togetherwithmethodo-
logical, environmental and structural information from grasslands
and other n on-forest veget ation type s (rocks and scre es, deser ts,
ruderal communities etc.) from the Palaearctic biogeographic realm.
GrassPlotspecificallycollectsmulti-scaledatasetsfromnested-plot
sampling schemes (e.g. Dengler et al., 2016b) with areas from 0.0 001
to1,024m².
Weretrievedallnested-plotseriesfromGrassPlot(v.2.04on20
March2020)thatcontainedatleastfourdifferentgrainsizes(4,654
serie s,consistingof16 4,578individualplots).Allserieshadinforma-
tion on vascular plants,890onterricolous(soil-dwelling)bryophytes,
894 on terricolous lichens, and 862 on all three taxonomic groups,
i.e. the total species richness of the vegetation (hereafter termed
complete vegetation). We refer to the four categories (complete veg-
etation, vascular plants, bryophytes, lichens) together as the four
taxonomic groups.
For those n ested-plot ser ies with more th an one plot for cer-
taingrainsizes,weaveragedrichnessvaluespergrainsize.Thus,we
obtainedone single richness valueforeachgrain sizewithin each
nested-plot series a nd for each taxon omic group. The p lots were
distributed across 34 different countries from 28.5° N to 70.0° N
and 16.2° W to 161.8° E, and covered an elevation gradient from
0mto 4,387 m a.s.l. (Figure 1 and Appendix S2).They includeda
wide range of different vegetation types (natural grasslands, sec-
ondarygrasslands,azonalcommunities,dwarfshrublands,tallforb
and ruderal communities andsemi-desert s); in fact, the selection
criteria of GrassPlot (Dengler et al., 2018) include 63% of all distin-
guished h abitat typ es in the Europea n part of the rea lm (Janssen
etal.,2016).FIGURE1 Densityandspatialdistributionofthe4,654
nested-plotseries in thePalaearctic biogeographicrealm contain-
ing information on vascular plant species that were analysed in this
study. The colour scale indicates the number of available series per
10,000-km²grid cell.The mapuses theLambert Azimuthal Equal-
Areaprojection.
2.2 | SARmodelling
We fitted a power function to each data set representing a taxo-
nomicgroupwithinanested-plotseries,usingthenon-transformed
S-space”(S = c Az, where S is species richness, Aisareain m²,and
c and z are fitted parameters) and the “logarithmic S-space”(log10
S = log10 c + z log10 A). Both approaches are valid, have been widely
used in the literature, and have different strengths and limitations
(see Dengler, 2009; Dengler et al., 2020a). Due to the different
treatment of the error structure, the parameter estimates in the two
mathematical spaces usually deviate. Generally, fitting in S- s p a c e 
givesmoreweighttogoodfitatlargergrainsizes,whereasfittingin
log S-spacegivesmoreweighttogoodfitatsmallergrainsizesand
typically reduces heteroscedasticity in the residuals.
To fit the power model in log S-space,weusedlinearregression
and the standard ‘lm’ function in R (R Core Team, 2018). The fit-
ting in S-spacefollowedtheapproachofDengleretal.(2020a; see
alsoMatthewsetal.,2019a).Weappliednon-linearregressionusing
the ‘mle2’ function in the bbmle R package (Bolker & R Core Team,
2017). Starting parameter values were derived from fitting the linear
model in log S-space.Inasmallnumberofcaseswheretheresultant
S-spacemodeldidnotconverge,weiteratedacrossarangeofdiffer-
ent starting parameter values to achieve convergence (see Dengler
et al., 2020a). To avoid problems with fitting in log S-space, we as-
signed small non-zero values to any subplot with observed values
of S = 0 (see Dengler et al., 2020a). For both the S-space andlog
S-spacefittedmodels,westoredthez-andc-values.
FIGURE1 Densityandspatialdistributionofthe4,654nested-
plot series in the Palaearctic biogeographic realm containing
information on vascular plant species that were analysed in this
study. The colour scale indicates the number of available series per
10,000-km²gridcell.ThemapusestheLambertAzimuthalEqual-
Areaprojection
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2.3 | Predictorvariables
In addition to the taxonomic group, we used a wide range of plot
characteristics available from GrassPlot and related to our re-
searchquestions(forfurtherdetailsandreferences,seeAppendix
S3, for the number of plots used in each analysis see Appendix
S6). We grouped them into three categories: biogeographic char-
acteristics, ecological characteristics and α- diversity. The ecological
characteristics were further subdivided into those related to the
stress– productivity and disturbance axes (Grime, 1977; Huston,
2014) as well as to heterogeneity (Lundholm , 2009; Stein et al .,
2014), in order to conn ect with well-es tablished th eories of α-
diversity.However,weacknowledgethatsomevariablesareonly
weakly connected to the respective group or might contain ele-
ments of more than one group.
Asbiogeographic characteristics, we used two variables related to
major biogeographic theories (latitude and elevation) and four major
climatic variables (mean annual temperature, temperature seasonality,
mean annual precipitation, precipitation seasonality). While latitude
and most of the elevation data were provided by the original data
set collectors, missing elevation data and the other four variables
were derived from external sources using the plot coordinates (for
details,seeAppendixS3).
The stress– productivity variables refer to the stress– productivity
axis of Gri me (1977; product ivity in Huston , 2014): We used soil
pH and soil depth mean as soil-related stress measures,assuminga
U-shapedrelationshipofstress withsoilpH(nutrientuptakeislim-
itedatbothhighandlowpH,withadditionaltoxicityeffectsatlow
pH;see Lambers etal.,2008)and a negative relationship withsoil
depth(seeAppendixS1).Further,weclassifiedplotsintothosethat
receive (anthropogenic) fertilization vs those that do not. Finally,
we used herb layer cover as a proxy of productivity. While at cover
values below 90% there should be a reasonably good correlation of
standing biomass with herb layer cover (Ónodi et al., 2017), we ac-
knowledge that for very high cover values the relationship likely will
disappear as the biomass then mainly is determined by vegetation
height.
The disturbance variables refer to disturbance sensu Grime
(1977)andHuston(2014),meaningdestructionorremovalofac-
cumulatedbio-and necromass.Therefore, litter cover was used
asanadverseproxy of disturbance(Appendix S1).Wealso con-
sider slope inclination as related to disturbance because erosion
increases with inclination. Furthermore, we extracted the follow-
ing measures of anthropogenic disturbance from GrassPlot: nat-
uralness (at two levels) and presence of the management types
livestock grazing, mowing and burning. Naturalness at coarse level
indicates whether grassland is natural or secondary, while natu-
ralness at fine level refers to the intensity of human impact on
vegetation within each of the two coarse categories (for details,
seeAppendixS3).
The heterogeneityv ariables are tho se that describe t he small-
scale variability of stress– productivity and/or disturbance, usually
determined withinthe largest orsecond-largestgrainplot of each
nested series: Soil depth CV indicates the variability of soil depth
within a plot; microtopography refers to deviations from a smooth
plane, which couldlead to small-scale differencesin soil moisture;
rock and stone cover is related to variation in soil depth, microclimate
and erosion; shrub layer cover is related mainly to variation in light
and moisture conditions.
As a measure of α- diversity, we used the c- value fromthe SAR
modelling (see above). The c- value is the predicted average species
richnessattheunitarea,i.e.inourcasein1m².
2.4 | Analysesofthez- values
We tested how the modelled z-value s of the power funct ion de-
pended on our four groups of predictors: taxonomic group, bio-
geographic characteristics, ecological (site) characteristics and
α-diversity.Weexcluded nested-plot series with no reported spe-
cies for the investigated taxonomic group as well as the very few
nested-plotseries where the model fitting didnotconvergeorre-
sulted in theoretically impossible values of z > 1 (Williamson, 2003).
In consequence, for S- space we had esti mated z-values for 4 ,554
series for vascular plants, 716 for bryophytes, 400 for lichens and
862 for complete vegetation (numbers differ slightly for log S-space).
As only a small fractionof our data set contained all variables
of interest, we decided to test the effect of each of them inde-
pendently, similar to the study of Drakare et al. (2006) for z-values
and Deng ler et al. (2020a) for sh apes of SARs. From a s tatistical
point of view multiple regressions, which analyse a multitude of
predictors simultaneously, including potential interactions, might be
considered advantageous. However,inour case such an approach
would have drastically reduced the spatial coverage or forced us
to restrict ourselves to those variables that can be retrieved from
globaldatabasesatcoarsergrainsinsteadofusingourin-situdeter-
mined fine grain data. For the continuous variables(see Appendix
S3), we used bivariate linear regressions to test for their potential in-
fluence on the z-valuesofthethreetaxonomicgroupsandcomplete
vegetation.Toaccountforpotentialhump-shapedorU-shapedrela-
tionships,weimplementedasecond-orderpolynomialfunctionbut
removed thequadraticterm if non-significant.Toallow fortheas-
sessmentofmorecomplexnon-linearrelationships,weadditionally
visualize d a polynomial su rface using l ocal fitt ing as implemen ted
in the R package stats by the ‘loess’ function (with smoothing pa-
rameter αsetto0.8). For categoricalpredictors(seeAppendixS3),
weappliedanalysisofvariance (ANOVA),followedbyTukey'spost
hoc test (R package stats) and multcompView (Graves et al., 2019) to
identify homogeneous groups. The comparison of taxonomic groups
wasadditionallycarriedoutforonlythosenested-plotserieswhere
all three t axonomic groups had been recorded simultaneously. In this
case,weusedamixed-effectsmodelwithplotseriesIDasarandom
factor(intercept).Themixed-effectsmodelwasimplementedusing
the R package lme4(version1.1-19;Batesetal.,2015)followedbya
Tukey's post hoc test as implemented in the function ‘glht’ of the R
package multcomp(version1.4-8;Hothornetal.,2008).
    
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3 | RESULTS
The results obtained for S-spaceandlogS-spacewerequalitatively
similar; in log S-spaceonaveragethemodelledz-valueswereslightly
higher and R²adj about 25% higher than in S-space (for n, R²adj, pa-
rameter estimates and p-values in both S-spaces, see Appendix
S6). Thus (and to be consistent with Dengler et al., 2020a), we re-
port here the results in S-spaceindetail(results inlogS-spaceare
showninAppendixS5).Wefocusedprimarilyontheresultsforvas-
cular plants, for which we have the most comprehensive data set.
Generally, the results for bryophytes, lichens and complete vegeta-
tion were similar; thus, we mention them only when there were im-
portant deviations. As we tested numerous bivariate relationships
with large amounts of observations, the results of significance tests
should be viewed with caution. While we report all significant rela-
tionships in the Results, we focus the Discussion on those relation-
ships with a relevant amount of explanatory power (mostly R2
adj >
0.02).
3.1 | Taxonomicgroups
The z-valuesofthetaxonomicgroupsdifferedsignificantly,whether
testedacrossallavailabledatasets(ANOVA)oronlyforthosedata
sets in which vascular plants, bryophytes and lichens were sampled
simultaneously(mixed-effectsmodelwith plot ID asarandomfac-
tor; Figure 2). The highest z-valu es across all dat a sets in S- s p a c e 
were found in lichens (mean ± standard deviation: 0.28 ± 0.14, me-
dian: 0.25), followed by vascular plants (0.23 ± 0.10, median: 0.21)
and bryophytes (0.19 ± 0.11, median: 0.17). The order was the same
whenconsideringonlynested-plotserieswhereallthreetaxonomic
groups had data, with lichens (0.29 ± 0.15, median: 0.26) followed
by vascular plants (0.22 ± 0.05, median: 0.21) and br yophytes
(0.20 ± 0.11, median: 0.18).
3.2 | Biogeographiccharacteristics
For vascular plants and bryophytes, z-valueshadaU-shaped,slightly
negative relationship with latitude and a positive relationship with
elevation (Figure 3 and Ap pendix S4). Fo r lichens, the r elationship
between z-valuesandelevation was slightlyhump-shaped,andthe
relationship with latitude was not significant (Appendix S4). For
complete vegetation, only latitude showed a significant relationship,
whichwasdecreasingtoslightlyU-shaped(AppendixS4).
WefoundU-shapedrelationshipsformean annual temperature,
temperature seasonality and precipitation seasonality in the case of
vascularplantsandbryophytes(Figure3andAppendixS4).Lichen
z-values showed a U-shaped relationship only with temperature
seasona lity (Appe ndix S4). By contr ast, the z-values of complete
vegetation were negatively related to temperature seasonality
andshowedaU-shapedrelationshipwithprecipitationseasonality
(Appe ndix S4). Onl y vascular pla nt z-values showedasignificant,
hump-shapedrelationshipwithmean annual precipitation (Figure 3,
AppendixS4).
3.3 | Ecologicalcharacteristics
For vascular plants and complete vegetation, z-values hadhump-
shaped relationships with soil pH (Figure 3, Appendix S4), while
bryophytes and lichens did not show a significant pattern with this
variable (Appendix S4). For vascularplants and complete vegeta-
tion, z-valueshadanegativeandinthelattercaseslightlyU-shaped
FIGURE2 Differences in z-values(modelledinS-space)amongthethreetaxonomicgroups:vascularplants,br yophytesandlichens,and
allthesegroupspooledtogether(a)acrossallavailablenested-plotseriesand(b)fortheserieswithsimultaneousdataofallgroups(note
that the number of replicates in [b] is lower than for complete vegetation in [a] as in many plots bryophytes and lichens were considered, but
absent).Thevaluesontopindicatethenumbersofnested-plotseriesused,whilethebluelowercaselettersindicatesignificantdifferences
among groups (p <0.05)astestedwithaTukeyposthoctestwithANOVAfor(a)andalinearmixedeffectmodelwithplotseriesIDas
random effect (on intercept) for (b)
Complete
Vascular pl
.
Bryophytes
Lichens
z
(a) All plot series (b) Plot series with z in all groups
Complete
Vascular pl.
Bryophytes
Lichens
0.00.2 0.40.6 0.81.0
862 4554 716 400
bca
349 349 349 349
bca
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Journal of Vegetation Science DEMBIC Z Et al.
relationship with soil depth (Figure 3, Appendix S4). By contrast,
z-values of br yophytes and l ichens were not relat ed to soil depth
(AppendixS4). Fertilized grasslands had significantly lower z-values
in vascular plants than unfertilized ones (mean values: 0.15 vs 0.23;
AppendixS4;nosignificantpatternsintheothergroupsduetothe
low number of replicates). For vascular plant s, z-valueshadastrongly
decreasingandslightly U-shaped relationship with herb layer cover
(Figure 3), while the relationship was insignificant for bryophytes,
increasing for lichens and hump-shaped for complete vegetation
(AppendixS4).
Acrossalltaxonomicgroups,z-valueswere positivelyrelatedto
slope inclination (Figure 3, App endix S4). However, the smo othed
curve for vascular plants shows that in the flattest areas (slope in-
clination <7°), the relationship was negative (Figure 3). The z-values
FIGURE3 z-Valuesforvascularplants(modelledinS-space)inrelationto:(a)latitude,(b)elevation,(c),meanannualtemperature,(d)
meanannualprecipitation,(e)temperatureseasonality,(f)precipitationseasonality,(g)soilpH,(h)soildepthmean,(i)slopeinclination,
(j) litter cover, (k) soil depth CV, (l) microtopography, (m) rock and stone cover, (n) shrub layer cover, (o) herb layer cover, and (p) c-value(=
modelledrichnessat1m²,asmeasureofα-diversity).Redlinesindicatesignificantlinear,hump-shapedorU-shapedrelationships(p < 0.01)
with confidence intervals, while the blue lines represent local polynomial regression with confidence intervals
0.00
0.25
0.50
0.75
30 40 50 60 70
Latitude [°]
z
R0.06
2∗∗∗
(a)
0.00
0.25
0.50
0.75
010002000 3000 4000
Elevation [m a.s.l.]
z
R0.15
2∗∗∗
(b)
0.00
0.25
0.50
0.75
01020
Mean annual temperature [°C]
z
R0.06
2∗∗∗
(c)
0.00
0.25
0.50
0.75
500 1000
Mean annual precipitation [mm]
z
R< 0
2.01∗∗
(d)
0.00
0.25
0.50
0.75
010002000
Te mperature seasonality [°C]
z
R0.01
2∗∗∗
(e)
0.00
0.25
0.50
0.75
30 60 90
Precipitation seasonality [%]
z
R0.01
2∗∗∗
(f)
0.1
0.2
0.3
0.4
0.5
46810
Soil pH
z
R0.01
2∗∗
(g)
0.2
0.4
0.6
0255075 100
Soil depth mean [cm]
z
R0.02
2∗∗∗
(h)
0.0
0.2
0.4
0.6
0.8
0204060
Slope inclination [°]
z
R0.01
2∗∗∗
(i)
0.0
0.2
0.4
0.6
0.8
0255075100
Litter cover [%]
z
R0.03
2∗∗∗
(j)
0.1
0.2
0.3
0.4
050100 150
Soil depth CV [%]
z
R< 0
2.01∗
(k)
0.1
0.2
0.3
0.4
0255075 100
Microtopography [cm]
z
R0.01
2∗∗
(l)
0.0
0.2
0.4
0.6
0.8
0255075100
Rock and stone cover [%]
z
R0.14
2∗∗∗
(m)
0.0
0.2
0.4
0.6
0.8
0204060
Shrub layer cover [%]
z
R0.02
2∗∗∗
(n)
0.0
0.2
0.4
0.6
0.8
0255075 100
Herb layer cover [%]
z
R0.41
2∗∗∗
(o)
0.00
0.25
0.50
0.75
0204060
c
z
R0.11
2∗∗∗
(p)
    
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 9 of 15
Journal of Vegetation Science
DEMBIC Z Et al.
of vascular plants had a U-shaped relationship with litter cover,
with a strongly negative influence of this factor in the range from
0% to 20% indicated by the smoothing function (Figure 3). There
wasasimilarU-shapedrelationshipforbryophytes,increasingfrom
20% cover (A ppendix S4), whi le the relationshi p was positive for
lichens an d complete veget ation (App endix S4). Natural grasslands
had significantly higher z-values than secondary ones for vascular
plants a nd complete veget ation (Figure 4). M oreover, for vascular
plants, there was a strong and consistent decrease in z-valueswith
increasing land use intensity both within the natural and the sec-
ondar y grasslands (Appendix S4). The z-val ues of vascular plant s
were clearly influenced by livestock grazing and mowing, with the
highest valuesfoundin unusedgrasslands,followedbyonlygrazed
and only mown grasslands and finally those subject to both manage-
ment techniques (Figure 5). For the two other taxonomic groups and
the complete vegetation, the patterns were less pronounced, but
with a tendency toward higher z-values in grazed-only grasslands
(Figure 5). For burning, we did not find an effect on z-values,except
in bryophytes where unburned grasslands had significantly lower
valuesthanburnedones(AppendixS4).
Soil depth CV had a weak h ump-shaped ef fect for z-values of
vascular plants, but a positive one on those of complete vegetation
(Figure 3, Appendix S4). Microtopography was a positive predictor
for z-valuesofvascular plants and complete vegetation,whilefor
bryop hytes the rel ationship was sl ightly hump-s haped, and fo r li-
chens, it wasnon-significant(Figure3,Appendix S4). Forvascular
plants, bryophytes and complete vegetation, z-values increased
monotonically with rock and stone cover, while there was no rela-
tionshipforlichens(Figure3,AppendixS4).Forvascularplantsand
bryophytes, z-values had a hump-shaped relationship with shrub
cover, while for lichens and complete vegetation it was positive
(Figure3,AppendixS4).
FIGURE4 Differences of z-
values (modelled in S-space)between
secondary and natural grasslands for
the four taxonomic groups: (a) complete
vegetation, (b) vascular plants, (c)
bryophytes, and (d) lichens. The numbers
ontopindicatethenumbersofnested-
plot series used, while different letters
indicate significant differences between
the groups
se
condary
natural
z
vegetationplants
(a) Complete (b) Vascular (c) Bryophytes (d) Lichens
natural
natural
natural
0.0 0.4 0.8
410 451
ba
2926 1584
ba
399 316 202 198
secondary
se
condary
secondary
FIGURE5 Effectofgrazingand
mowing on z-values(modelledinS-
space) for the four taxonomic groups:
(a) complete vegetation, (b) vascular
plants, (c) bryophytes, and (d) lichens. The
figures on top indicate the numbers of
nested-plotseriesused,whiledifferent
letters indicate significant differences
among groups according to the post
hoc test
grazed
and mown
unused
only grazed
only mown
z
graze
d and mown
unused
only grazed
only mown
grazed
and mown
unused
only grazed
only mown
grazed
and mown
unused
only grazed
only mown
(a) Complete
vegetation
(b) Vascular
plants (c) Bryophytes (d) Lichens
0.0 0.4 0.8
19384 259 144
ab acbc
3091752 1657 599
abcd
17281 244 138
aabab
171 159 29 0
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Journal of Vegetation Science DEMBIC Z Et al.
3.4 |α- diversity
Thez-valuesexhibitedastrongrelationshipwiththec- values of the
power model,i.e.themodelledrichnessat1m².Forvascular plants,
bryophytesandlichens individually,the relationshipwasU-shaped
with minima around 20 species for vascular plants and about 10 spe-
ciesforeachofthenon-vasculargroups(Figure3,AppendixS4).By
contrast, for complete vegetation, the relationship was linear nega-
tive(AppendixS4).
3.5 | Explanatorypowerofthedifferentpredictors
Overall, the explanatory power of the bivariate models was rela-
tively low, with R2
adj ranging from <0.01to0.41(AppendixS6).The
mean predictive power of the 16 bivariate regressions was 0.07 for
vascular plants, 0.02 for bryophytes, 0.02 for lichens and 0.03 for
completevegetation(Figure3,AppendixS4).Thehighestexplained
variance of z-values of vascular plants was found for herb layer
cover (R2
adj = 0.41), followed by naturalness at the fine level (0.18),
elevation(0.15),rockand stonecoveraswell as grazingand mow-
ing (both 0.14) and the c-value(0.11).Thevariablewiththehighest
R2
adj value for bryophyte and lichen z-valueswasthec-value(R2
adj
= 0.08 and 0.16, respectively), while all other predictors had R2
adj <
0.06(AppendixS6).ThevariableswiththehighestR2
adj for complete
vegetation were soil depth CV (R2
adj = 0.10), followed by inclination
andgrazing/mowing(both0.06).
4 | DISCUSSION
4.1 | Explanatorypower
Althoughmanyofthetested variables, representingbothbiogeo-
graphical and local habitat characteristics, were significant, the ex-
planatory power of these bivariate models was low, with only few
variables exceeding 10% explained variance. This is in striking con-
trasttomacroecologicalstudiesofcoarse-grainα-andβ-diversity,
which often find R²adj values above 50% with only one or a few
predictors(Pinto-Ledezmaetal.,2018).There areonlyfew large-
extent,fine-grainstudies inmacroecology(Becketal.,2012),and
thus few examples of how much explained variance one can expect.
Bruelheideetal.(2018),inaglobal studyofcommunity-weighted
means of traits, found that none of 30 tested environmental vari-
ables explained more than 10% of the total variance, and all 30
together only 10.8%. Reasons for the relatively low explained
variance in fine-grain macroecological studies include the possi-
ble effects of other unmeasured factors, such as legacy effects,
influences of the surroundings, and interspecific interactions, and
a spatial mismatch between the environmental predictors (mostly
derived from coarse- or at bes t medium-grain global databases)
andthefine-grainbiodiversityresponsevariables.Inthisrespect,
analyses based on GrassPlot have the advantage that, unlike those
in Bruelheide et al. (2018; based on sPlot), they contain numerous
well-curated in-situ determined predictor variables (soil, micro-
topography, heterogeneity, land use, vegetation structure), which
coincides with the relatively higher explained variance in our case.
However,forclim at icvariables,wealsoha dtorelyoncoarser-gr ain
data, despite it being known that temperature can strongly vary
across short distances, particularly in mountains (Opedal et al.,
2015).Aswetestednumerousvariablesthatcoverawiderangeof
different aspects, including many that typically yield high explan-
atory power for different facets of biodiversity, both in classical
macroecological (large extent, coarse grain) and vegetation ecologi-
cal (small extent, fine grain) studies, we doubt that other variables
individually would yield much higher R²values.Rather,weassume
that relatively low explained variance will be a typical outcome of
large-extent,fine-grainstudies.
4.2 | Mechanismsdrivingvariationinz- values
The relationships between β-divers ity and a wide r ange of pre-
dictorvariablesatanygrainsizeareinterpretablethroughthein-
fluence of these variables on mean occupancy, which determines
β-diversity (Storch, 2016). At fine spatial scales one candecom-
pose the spatial arrangement of plant communities into three dif-
ferent aspects that together make up mean occupancy: (a) total
cover; (b) mean size of individuals; and (c) similarit y of species
composition between adjacent subplots. While the relationships
between these three aspects and mean occupancy are mathemati-
cally self-evident (rightpart ofFigure 6,Appendix S7),the open
question prior to our study was how various environmental driv-
ers or species properties would influence one or several of these
aspects. Inspired by our findings and theoretical considerations,
we have developed a conceptual model (Figure 6), which is able to
explain some surprising outcomes of our study. For example, vari-
ables could have no or very weak effects when positive and nega-
tive influences on mean occupancy cancel themselves out, while
some “aggregated” variables could have unexpectedly strong ef-
fects when they influence mean occupancy consistently via more
than one pathway. While the left and middle parts of Figure 6 are
consistent with our findings, they should be seen as a set of test-
able hypotheses. In the following we will discuss our individual
findings in this framework.
4.3 | Taxonomicgroups
The z-values differed significantly among taxonomic groups (li-
chens > vascular plants >bryophytes).Astudyatmuchcoarser
grain sizes (regional to continental) by Patiño et al.(2014) found
similar z-valuesof0.18and0.21forthet wolineagesofbr yophytes
(i.e. liverworts and mosses) and 0.21 and 0.33 for the two lineages
of vascular plants (i.e. pteridophytes and spermatophytes). Patiño
etal.(2014)attributed theflatterSARsof liver worts,mossesand
    
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DEMBIC Z Et al.
pteridophytes to their higher long-distance dispersal capabilities
via spores compared to spermatophytes via seeds or other much
heavier diaspores. Dispersal limitation might also play a role at
short distances, particularly when considering that the majority
ofvascular plants are spreading clonally.Whileour small-grainz-
values forbryophytes(0.19)weresimilarto the coarse-grain val-
ues of Patiño et al. (2014), those for vascular plants (0.23) were
much lower than their coarse-grain results for spermatophytes
(the dominant group of vascular plants: 0.33). We are not aware
of any coarse -grain study of S ARs of lichens, b ut since they are
also mainly distributed via spores or small vegetative diaspores,
one should assume low z-valuessimilartothoseofbryophytesand
pteridophytes.Thefindingthatlichensshowthehighestfine-grain
z-values(0.28)amongthethreetaxaisprobablybecausetheyare
mostly restricted to a few microhabitats with reduced competition
by vascular plants and bryophytes, typically around rock outcrops
or on shallow, open soil (i.e. in patches with strong abiotic stress). In
such microhabitats, not only one but a whole array of lichen species
can occur,leading toa steep SAR (i.e. highz-value).Wethushy-
pothesizethatthetwomaintraitsinfluencingfine-grainβ-diversity
of species groups are their mean dispersal distance and their mean
nichebreadth(AppendixS7).
4.4 | Biogeographiccharacteristics
Among the climate variables, mean annual temperature had the
strongest influence on z-valueswithaU-shapedrelationship.This
could indicate that environmental stress leads to higher z-values.
Atthelowendofthegradient,coldnesswoulddirectlyrepresent
the stress, while at the high end drought effects might be the stress
factor. By contrast, z-values showed only very weakrelationships
with the other three climatic factors, which highlights that there
mightnotbeadirectrelationshipbetweenmacroclimateandfine-
grain z-values.
TheminimaoftheU-shapedrelationships ofz-valuesofvascu-
lar plants, bryophytes and complete vegetation with latitude were
around 5055°N. This finding differs substantially from the strong
negative relationship known for coarse-grain β-diversity in plants
(Qian & Ricklefs, 2007; Qian, 2009) as well as across taxa and scales
(meta-analysis by Drakare et al., 2006). Qiao et al. (2012), using
nested plots from forests in China, found a negative relationship be-
tween z-valuesandlatitudeforallvascularplants,treesandshrubs,
but not for herbaceous plants. The difference between our results
and the two studies (Drakare et al., 2006; Qiao et al. 2012) could
stem from the different ranges in latitude (Drakare et al., 2006:
FIGURE6 Conceptualfiguresummarizingourhypotheseshowdifferentdriverscouldinfluencefine-grainβ-diversityviachanging
meanoccupancyofspecies,basedonthefindingsofourstudyandtheoreticalconsiderations.Fine-grainβ-diversity(andlikewisefor
largergrainsizes)ismathematicallylinkedtomeanoccupancy,whichcanbedecomposedinto(i)totalcover;(ii)meansizeofindividuals;
and (iii) similarity of species composition between adjacent subplots. These three aspects of mean occupancy again are affected by the
environmental drivers: productivity, stress, disturbances as well as heterogeneity (green). Note that disturbance can have contrasting
effects depending on its type and intensity. To the very left we exemplify how two aggregated environmental parameters, land use
intensityandelevation(orange),viamultiplepathwayscouldinfluencefine-grainβ-diversity.Whatwemeanwiththethreeaspectsthat
make up mean occupancy is illustrated with a pair of figures showing to the left a situation with low and to the right with high value of the
respective aspect. The four different symbols represent individuals of four species distributed in a vegetation plot of a total extent of Aγ
=9andassessedalsoatagrainsizeofAα = 1. Influences of one parameter are indicated by the arrows with their + and – symbols, with
grey arrows corresponding to ecological hypotheses and black arrows to strict mathematical relationships. We did not aim to display all
possible relationships in this figure, but concentrated on those that we consider most important. The expected effect of a certain driver
oraggregatedenvironmentalparameteronfine-grainβ-diversitycanbeestimatedbymultiplyingthe+/-
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0– 60°; Qiao et al., 2012: 19– 52° vs 35– 70° in the present study).
The poleward decrease until ca. 50– 55° is consistent across all three
studies,whiletheincreasefromtheminimumtowardstheArcticwas
missed by the other studies because their gradients did not extend
so farpoleward. Moreover, specifically for grasslands, higher land
useintensityinthetemperatezone(mainlybetween45°Nand50°
N) could have contributed to the reduced z-valuesthere(seebelow).
Wefoundanincreaseinfine-grainβ-diversityofvascularplants
and bryophyteswith elevation,which contrasts withMoradietal.
(2020) for grasslands in Iran (2,00 0– 4,500 m a.s.l.), Kraft et al. (2011)
for forests in Ecuador (400– 2300 m a.s.l.; only trees) and Qiao et al.
(2012) for forests in China (300– 3,150 m a.s.l.), who found decreas-
ing z-values.However,itisinagreementwith findingsforz-values
ofvascularplantsintheKaroo,SouthAfrica(290–1800ma.s.l.;van
der Mer we & van Rooyen, 2011). We assume th at the increasing
fine-grainβ-diversitywithelevationcan be explained by (a)the in-
creased harshness of the climate with increasing elevation and re-
sulting stress for plants, possibly impacting spatial patterns of plants
(see above for latitude); (b) an increased role of facilitation leading
alsotoclustereddistributionsofspecies (Anthelmeetal.,2014);(c)
higher species turnover at small distances in an increasingly rugged
topogra phy and thus stro nger small-scal e gradients of soi l condi-
tions, water availability and microclimate, which are generally much
more pronounced at higher elevations (Körner, 2003); and (d) as for
latitude, the natural patterns possibly being amplified by higher land
use intensities at lower elevations.
4.5 | Stress–productivity
For vascular plants, the relationship with fertilization, soil depth
meanandherblayercovercanbeinterpretedasadecreaseinfine-
grain β-diversitywithhigherproductivity.Adecreaseinβ-diversity
means an increase in mean occupancy (Storch, 2016; Figure 6), which
can happen either if all species become more frequent or if the rar-
est species are dropped out from the community due to asymmet-
riccompetition.Indeed,Filibeck et al.(2019)found thatfine-grain
z-values in Italian limestonegrasslands were negativelycorrelated
with soil d epth, as deep-so il sites were colonized by co mpetitive
and patch-forming species, curtailing composition heterogeneity.
In addition, Chiarucci et al. (2006) found a negative relationship be-
tween z-valuesandgrasslandproductivityinItalyandGermany.By
contrast,DeMalachetal.(2019),studyingdrylandsworldwide with
a different measure of β-diversity, foundthe opposite pattern, i.e.
increasing β-diversity withhighercover.Thisdiscrepancyishardto
explain, but our data set is much more comprehensive in environ-
mental space and numbers; thus we trust that our findings are more
general. Finally, we only found a minimal effect of productivity-
related predictors on the z-valuesofbryophytesandlichens.Apos-
sible explanation could be that the direct effects of productivity
are counteracted by the opposing effects of increased herb layer
cover, which increases the stress for bryophytes through lower light
availability.
4.6 | Disturbance
Wefound thatnaturalgrasslands hadhigherfine-grain β-diversity
than secondary grasslands whose existence depends on anthropo-
genicbiomassremoval.Forvascularplants,grazingandmowingboth
affected z-values negatively, but more strongly for mowing. Thus,
weconcludethatlandusebyhumansonaveragereducesfine-grain
β-diversity in open vegetation. It is underst andable that mowing
particularly strongly decreases z-valuesasitremovesabove-ground
biomass non-selectively, thus reduces interspecific competition
(Wilson et al., 2012), thereby increasing stand homogeneity. Besides
ac tualdi stur bancee ffec t s,live s toc kgr azi ngc anc rea tesomehetero -
geneity in comparison to meadows, e.g. due to selective feeding, the
heterogeneous trampling intensity and patchy distribution of excre-
ments(Gilletetal.,2010;Tälleetal.,2016).Whilelanduseparame-
ters yielded R²adj values of up to 0.20, the explained variances of our
two other measures related to disturbance, slope inclination and lit-
ter cover were 0.03 or less, indicating that agricultural disturbances
have a different influence on z-valuesthanabioticdisturbances.
4.7 | Heterogeneity
Assumingthatheterogeneityincreasesz-values,weexpectedlarger
z-v aluestobeass oci atedwit hhighsoildepthC V,highmicroto pog ra-
phy, intermedia te rock and stone cover an d intermediate shr ub cover.
However,wemostlyfoundveryweakornoeffects,withexplained
variances of 0.02 or less, which contrasts with some geographically
orecologicallynarrowerstudies(Harner&Harper,1976;Polyakova
et al., 2016). Only rock and stone cover had a moderate effect in the
case of vascular plants (R²adj = 0.14) and complete vegetation (0.05),
but, contrary to our assumption, we found the highest z-valuesat
close to 100% rocks and stones. This is logical due to the negative
relationshipbetweenz-valuesand meanoccupancy:theless space
is available for plants to grow inside a plot, the lower the mean oc-
cupancyandlogically,butcounter-intuitively,thehigherthez-value.
4.8 |α- Diversity
The z-valuesshowedanunexpectedU-shapedrelationshipwiththe
c-values(exceptforcompletevegetation).Thissecondparameterof
the power function represents the intercept in the log– log repre-
sentation or, in other words, the species richness at the unit area (in
ourcase:1m²),whichonecouldcallα-diversity.Ifthetotalspecies
richness of whole plots (“γ-diversity”) wasconstant,ahighervalue
of the slope parameter would necessarily lead to a lower intercept,
so that the relationship between z and c would be negative. Since
γ-diversityvariesconsiderablyacrossthePalaearctic,morecomplex
patternsare possible.While moderately species-rich plots located
in suboptimal/stressful conditions indeed had the expected nega-
tive relationship between z and c, there were some plots character-
izedbyboth highcand z, which meansthat these plotsmust also
    
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DEMBIC Z Et al.
have exceptionally high total richness. This indicates that the most
species-richplotsarecharacterizedby aprevalenceofsubordinate
species with low mean occupancy. Our finding contrasts with the
strong negative relationships between z and c recently reported
for island SARs of archipelagos across the globe (Matthews et al.,
2019b), where γ-diversity also varied substantially.The reason for
the discrepancy is unknown, but it could be related to the differ-
encesinscaleandSARtype.
4.9 | Conclusionsandoutlook
While, before our study, there was only scattered and inconclusive
knowledgeandhardlyanytheoryaboutdriversoffine-grainz-values,
our comprehensive study has now enabled us to propose a theory
consisting of a set of hypotheses that are in agreement with our
findings(Figure6,AppendixS7).Inthefuture,thevalidityofthese
hypotheses should be tested with observational or, even better, ex-
perimental studies. While our findings partly concur with those from
coarse-grainβ-diversitystudies,wefoundsubstantialdifferencesfor
biogeographicvariables.Whereascoarse-grainβ-diversitytypically
declines with elevation (Tello et al., 2015; Sabatini et al., 2018) and
latitude(Qian &Ricklefs, 2007; Qian, 2009), fine-grainβ-diversity
increasedmonotonouslywithelevationandshowedaU-shapedre-
lationship with latitude. Similar scale dependence of drivers is well
known for α-diversity(Fieldetal.,2009;Siefertetal.,2012).Itwill
beinterestingtodetermineatwhichgrainsizethepositiveeffectof
elevationonfine-grainβ-diversityturnsintoanegativeeffect.
ACKNOWLEDGEMENTS
Weth anka llvege t ati o nsc ient istsw hoc a refu llycoll e cted them ulti-scale
plant diversity data from Palaearctic grasslands available in GrassPlot.
The Eurasian Dry Grassland Group (EDGG) and the International
Associ ation for Vegetatio n Science (IAVS) suppo rted the EDGG F ield
Workshops, which generated a core part of the GrassPlot data.
AUTHOR CONTRIBUTIONS
JDe conceived the idea of this paper andinitiatedthe datacollec-
tion.Mostauthorscontributeddata,whileJDeservedascustodian
andIBasdatabasemanageroftheGrassPlotdatabase.MJSandTJM
conducted the statistical analyses, ID and JDe led the writing. All
authors checked, improved and approved the manuscript.
DATA AVAIL AB I LI T Y STAT E MEN T
The data used in this paper are derived from the collaborative
vegetatio n-plot database G rassPlot (Dengle r et al., 2018; Biurrun
et al., 2019), version 2.02. They can be requested from GrassPlot
with a project proposal following the GrassPlot Bylaws (see https://
edgg.org/datab ases/Grass Plot).
ORCID
Iwona Dembicz https://orcid.org/0000-0002-6162-1519
Jürgen Dengler https://orcid.org/0000-0003-3221-660X
Manuel J. Steinbauer https://orcid.org/0000-0002-7142-9272
Thomas J. Matthews https://orcid.org/0000-0002-7624-244X
Sándor Bartha https://orcid.org/0000-0001-6331-7521
Sabina Burrascano https://orcid.org/0000-0002-6537-3313
Alessandro Chiarucci https://orcid.org/0000-0003-1160-235X
Goffredo Filibeck https://orcid.org/0000-0002-4187-9467
François Gillet https://orcid.org/0000-0002-3334-1069
Monika Janišová https://orcid.org/0000-0002-6445-0823
Salza Palpurina https://orcid.org/0000-0003-0416-5622
David Storch https://orcid.org/0000-0001-5967-1544
Werner Ulrich https://orcid.org/0000-0002-8715-6619
Svetlana Aćić https://orcid.org/0000-0001-6553-3797
Steffen Boch https://orcid.org/0000-0003-2814-5343
Juan Antonio Campos https://orcid.org/0000-0001-5992-2753
Laura Cancellieri https://orcid.org/0000-0002-0102-259X
Marta Carboni https://orcid.org/0000-0002-9348-4758
Giampiero Ciaschetti https://orcid.org/0000-0003-3314-8362
Timo Conradi https://orcid.org/0000-0003-2360-9284
Pieter De Frenne https://orcid.org/0000-0002-8613-0943
Jiri Dolezal https://orcid.org/0000-0002-5829-4051
Franz Essl https://orcid.org/0000-0001-8253-2112
Edy Fantinato https://orcid.org/0000-0003-0114-4738
Itziar García- Mijangos https://orcid.org/0000-0002-6642-7782
Gian Pietro Giusso del Galdo https://orcid.
org/0000-0003-4719-3711
John- Arvid Grytnes https://orcid.org/0000-0002-6365-9676
Riccardo Guarino https://orcid.org/0000-0003-0106-9416
Behlül Güler https://orcid.org/0000-0003-2638-4340
Jutta Kapfer https://orcid.org/0000-0002-8077-8917
Łukasz Kozub https://orcid.org/0000-0002-6591-8045
Anna Kuzemko https://orcid.org/0000-0002-9425-2756
Michael Manthey https://orcid.org/0000-0002-1314-6290
Corrado Marcenò https://orcid.org/0000-0003-4361-5200
Anne Mimet https://orcid.org/0000-0001-9498-436X
Alireza Naqinezhad https://orcid.org/0000-0002-4602-6279
Jalil Noroozi https://orcid.org/0000-0003-4124-2359
Arkadiusz Nowak https://orcid.org/0000-0001-8638-0208
Harald Pauli https://orcid.org/0000-0002-9842-9934
Robert K . Peet https://orcid.org/0000-0003-2823-6587
Vincent Pellissier https://orcid.org/0000-0003-2809-0063
Remigiusz Pielech https://orcid.org/0000-0001-8879-3305
Ma ssi mo Te rzi https://orcid.org/0000-0001-8801-6733
Emin Uğurlu https://orcid.org/0000-0003-0824-1426
Orsol ya Val https://orcid.org/0000-0001-7919-6293
Iuliia Vasheniak https://orcid.org/0000-0003-1020-3007
Kiril Vassilev https://orcid.org/0000-0003-4376-5575
Denys Vynokurov https://orcid.org/0000-0001-7003-6680
Hannah J. White https://orcid.org/0000-0002-6793-8613
Wolfgang Willner https://orcid.org/0000-0003-1591-8386
Manuela Winkler https://orcid.org/0000-0002-8655-9555
Sebastian Wolfrum https://orcid.org/0000-0003-0123-6720
Jinghui Zhang https://orcid.org/0000-0002-6217-7376
Idoia Biurrun https://orcid.org/0000-0002-1454-0433
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SUPPORTING INFORMATION
Additional supporting information may be found online in the
Supporting Information section.
AppendixS1.Summaryofpreviousfindingsforfine-grainβ-diversity
(z-values)inrelationshiptothepredictorsanalysedinourstudy
AppendixS2. Additionalinformation on theoriginofthe analysed
nested-plotseries
Appendix S3. Detailed overview of the considered predictor
variables
AppendixS4.AdditionalresultsinS- s p a c e
AppendixS5.Analysesofz-valuesmodelledinlogS - s p a c e
AppendixS6. The numeric outputs of all analyses in S-space and
log S - s p a c e
Appendix S7. Conceptual figure illustrating how different drivers
couldinfluencefine-grainβ-diversity(expandedversion)
How to cite this article:DembiczI,DenglerJ,SteinbauerMJ,
etal.Fine-grainbetadiversityofPalaearcticgrassland
vegetation. J Veg Sci. 2021;32:e13045. ht t p s : //do i .
org /10.1111/jvs.13045
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... Finally, when analysing the scale dependence of z values, we found a slight peak for the transition from 0.01 to 0.1 m 2 with decreases towards both the smaller and the larger grain sizes. These findings correspond to those in regional studies of Turtureanu et al. (2014), Polyakova et al. (2016) and Talebi et al. (2021), while other studies did not find a scale dependence of z values (Kuzemko et al. 2016;Dembicz et al. 2021b). This demonstrates that the scale dependence of z values in dry grasslands of the Palaearctic is generally weak, but if there is one, it always exhibits a peak at grain sizes clearly below 1 m 2 , pointing to a very fine-grained community organisation. ...
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