ARTICLE
En i onmen al d i e s and spa ial scaling o species
abundance dis ibu ions in Palaea c ic g assland ege a ion
We ne Ul ich
1
| Thomas J. Ma hews
2,3
| Idoia Biu un
4
|
Juan An onio Campos
4
| Pa yk Czo ek
5
| Iwona Dembicz
6
|
F anz Essl
7
| Go edo Filibeck
8
| Gian-Pie o Giusso del Galdo
9
|
Behlül Güle
10
| Ali eza Naqinezhad
11
| Pé e Tö ök
12,13,14
|
Jü gen Dengle
15,16
1
Depa men o Ecology and Biogeog aphy, Nicolaus Cope nicus Uni e si y, To u
n, Poland
2
GEES (School o Geog aphy, Ea h and En i onmen al Sciences) and Bi mingham Ins i u e o Fo es Resea ch, Uni e si y o Bi mingham,
Bi mingham, UK
3
cE3c –Cen e o Ecology, E olu ion and En i onmen al Changes/Azo ean Biodi e si y G oup/CHANGE –Global Change and Sus ainabili y
Ins i u e and Uni e sidade dos Aço es (FCAA), Ang a do He oísmo, Po ugal
4
Depa men o Plan Biology and Ecology, Uni e si y o he Basque Coun y UPV/EHU, Bilbao, Spain
5
Białowieża Geobo anical S a ion, Facul y o Biology, Uni e si y o Wa saw, Białowieża, Poland
6
Depa men o Ecology and En i onmen al Conse a ion, Ins i u e o En i onmen al Biology, Facul y o Biology, Uni e si y o Wa saw,
Wa saw, Poland
7
Bioin asions, Global Change, Mac oecology G oup, Depa men o Bo any and Biodi e si y Resea ch, Uni e si y o Vienna, Vienna, Aus ia
8
Depa men o Ag icul u e and Fo es Science (DAFNE), Uni e si y o Tuscia, Vi e bo, I aly
9
Depa men o Biological, Geological and En i onmen al Sciences, Uni e si y o Ca ania, Ca ania, I aly
10
Biology Educa ion, Dokuz Eylul Uni e si y, _
Izmi , Tu key
11
Depa men o Plan Biology, Facul y o Basic Sciences, Uni e si y o Mazanda an, Mazanda an, I an
12
MTA-DE Lendüle Func ional and Res o a ion Ecology Resea ch G oup, Uni e si y o Deb ecen, Deb ecen, Hunga y
13
Polish Academy o Sciences, Bo anical Ga den - Cen e o Biological Di e si y Conse a ion in Powsin, Wa szawa, Poland
14
Depa men o Ecology, Uni e si y o Deb ecen, Deb ecen, Hunga y
15
Vege a ion Ecology, Ins i u e o Na u al Resou ce Managemen (IUNR), Zu ich Uni e si y o Applied Sciences (ZHAW), Wädenswil, Swi ze land
16
Plan Ecology, Bay eu h Cen e o Ecology and En i onmen al Resea ch (BayCEER), Uni e si y o Bay eu h, Bay eu h, Ge many
Co espondence
We ne Ul ich
Email: [email p o ec ed]
Funding in o ma ion
Aus ian Science Founda ion, G an /
Awa d Numbe : I 3757-B29; Basque
Go e nmen , G an /Awa d Numbe :
IT936-16; HAS Momen um P og am,
G an /Awa d Numbe s: NKFIH K 119225,
K 137573; MIUR Ini ia i e, G an /Awa d
Numbe : Law 232/2016; Na odowe
Abs ac
Species abundance dis ibu ions (SADs) link species ichness wi h species
abundances and a e an impo an ool in he quan i a i e analysis o ecological
communi ies. Niche-based and sample-based SAD models p edic di e en
spa ial scaling p ope ies o SAD pa ame e s. Howe e , empi ical esea ch on
SAD scaling p ope ies is la gely missing. He e we ex ac ed pe cen age co e
alues o all occu ing ascula plan s as p oxies o hei abundance in 1725
10-m
2
plo s om he G assPlo da abase, co e ing 47 egional da a se s o
Recei ed: 26 Oc obe 2021 Re ised: 2 Ma ch 2022 Accep ed: 7 Ma ch 2022
DOI: 10.1002/ecy.3725
This is an open access a icle unde he e ms o he C ea i e Commons A ibu ion License, which pe mi s use, dis ibu ion and ep oduc ion in any medium, p o ided
he o iginal wo k is p ope ly ci ed.
© 2022 The Au ho s. Ecology published by Wiley Pe iodicals LLC on behal o The Ecological Socie y o Ame ica.
Ecology. 2022;103:e3725. h ps://onlinelib a y.wiley.com/ /ecy 1o 16
h ps://doi.o g/10.1002/ecy.3725
Cen um Nauki, G an /Awa d Numbe :
2017/27/B/NZ8/00316; Ba a ian Resea ch
Alliance
Handling Edi o : Helmu Hilleb and
19 di e en g asslands and o he open ege a ion ypes o he Palaea c ic bio-
geog aphic ealm. Fo each plo , we i ed he Weibull dis ibu ion, a model
ha is able o e ec i ely mimic o he dis ibu ions like he log-se ies and log-
no mal, o he species–log abundance ank o de dis ibu ion. We calcula ed
he skewness and ku osis o he empi ical dis ibu ions and linked hese
momen s, along wi h he shape and scale pa ame e s o he Weibull dis ibu-
ion, o plo clima ic and soil cha ac e is ics. The Weibull dis ibu ion p o ided
excellen i s o g assland plan communi ies and iden i ied ou basic ypes o
communi ies cha ac e ized by di e en deg ees o dominance. Shape and scale
pa ame e alues o local communi ies on poo e soils we e la gely in acco -
dance wi h log-se ies dis ibu ions. P opo ions o subdominan species ended
o be lowe han p edic ed by he s anda d logno mal SAD. Successi e accu-
mula ion o plo s o he same ege a ion ype yielded nonlinea spa ial scaling
o SAD momen s and Weibull pa ame e s. This scaling was la gely indepen-
den o en i onmen al co ela es and geog aphic plo posi ion. Ou indings
cau ion agains simple gene aliza ions abou he mechanisms ha gene a e
SADs. We a gue ha in g asslands, logno mal- ype SADs end o p e ail
wi hin a wide ange o en i onmen al condi ions, including mo e ex eme
habi a s such as a id en i onmen s. In con as , log-se ies dis ibu ions a e
mainly es ic ed o compa a i ely species- ich communi ies on humid and
e ile soils.
KEYWORDS
logno mal dis ibu ion, log-se ies dis ibu ion, Palaea c ic g assland, plan co e , spa ial
scaling, species abundance, Weibull dis ibu ion
INTRODUCTION
Mo e han 80 yea s a e he seminal wo k o Mo omu a
(1932), he concep o he species abundance dis ibu ion
(SAD) in ecological communi ies emains a ocus o eco-
logical in e es (Ma hews & Whi ake , 2014; McGill
e al., 2007; Ul ich e al., 2010). SADs link species ich-
ness wi h ela i e species abundances and exhibi a con-
sis en gene al o m wi h many a e and ew abundan
species (McGill e al., 2007). They a e impo an in he
quan i a i e analysis o ecological communi ies, pa icu-
la ly in he quan i ica ion o a i y (Kunin, 1997), com-
pe i i e hie a chies (Mac Nally e al., 2014), niche
pa i ioning (Sugiha a e al., 2003; Tokeshi, 1999),
changes in species unc ional ai s (Dan as de Mi anda
e al., 2019), and he concep o neu al communi y
assembly (Hubbell, 2001; May, 1975). Recen in e es has
shi ed om s a is ical dis ibu ion i ing (Alonso
e al., 2008; Bald idge e al., 2016; Mo lon e al., 2009;
Ul ich e al., 2010) and he es ing o he unde lying
niche-based and s ochas ic heo ies (Connolly
e al., 2005; Magu an & Hende son, 2003) owa d he
analysis o obse ed and p edic ed changes in ela i e
abundances ac oss spa ial (Bo da-De-
Agua, e al., 2012;
Fe ei a de Lima e al., 2020;Šizling e al., 2009) and em-
po al (Tomašo ých & Kidwell, 2010) scales. A g ea e
unde s anding o he scaling o SADs and he unc ional
consequences o SAD scaling pa e ns a e no jus o he-
o e ical in e es , and will likely be use ul in biodi e si y
managemen (Ma hews & Whi ake , 2015).
Compe i i e and niche-o ien a ed app oaches ha e
o en assumed SADs o be gene ic p ope ies o ecological
communi ies de e mined by species in e ac ions (Cen u i
on
&L

opez Gappa, 2011;Tokeshi,1999)andnichepa -
i ioning (Sugiha a, 1980). Niche-o ien a ed SAD model
pa ame e s a e de e mined by species ichness and he
speci ic pa e n o niche di ision, bu no by he empo al
o spa ial dynamics o communi y assembly. Howe e ,
sample-based heo e ical wo k has demons a ed ha he
pa ame e s o impo an SAD models change wi h inc eas-
ing sample size (G een & Plo kin, 2007;Šizling e al., 2009)
and pa e ns o spa ial agg ega ion (Do nelas & Connolly,
2008).Thesemodelsinclude heexponen ialse ies,cha ac-
e ized by iden ical p opo ions o species along he g adien
2o 16 ULRICH ET AL.
o log- ans o med species abundance (Mo omu a, 1932),
he log-se ies sample dis ibu ion, cha ac e ized by a ew
highly abundan species and an excess o species ep esen-
ed by a single indi idual (Fishe e al., 1943), and he log-
no mal dis ibu ion, cha ac e ized by a compa a i ely high
numbe o species wi h in e media e abundance and simila
numbe s o ela i ely abundan and a e species (Gas on &
Blackbu n, 2000;P es on,1948). Impo an ly, Locey and
Whi e (2013)demons a ed ha heshapeo SADsisde e -
mined by he in e play o he o al numbe s o indi iduals
and species. Bo h inc ease wi h inc easing sample a ea.
The e o e, he sample beha io o SADs should au oma i-
cally ansla e in o changes in SAD shape ac oss spa ial
scales. The si ua ion is complica edby he ac ha local
communi ies a e no simply andomsamples om he
la ge egional species pools. Ins ead, hey esul om h ee
basic p ocesses: species-speci ic dispe sal, habi a il e ing,
and local species in e ac ions (e.g., D’Amen e al., 2017;
Tö ök e al., 2018;Vellend,2016). These h ee p ocesses
ope a e di e en ly a di e en spa ial scales. As such, o
his eason, we also canno expec SADs o be in a ian o
spa ial scale.
A spa ial ex en s abo e he local communi y, wo
con as ing heo e ical app oaches p edic di e en SAD
shapes. Neu al app oaches gene ally p edic ha log-
se ies SADs will cha ac e ize egional species pools
(Hubbell, 2001), as epo ed by Wu e al. (2019). In con-
as , Connolly e al. (2005) epo ed scale-in a ian log-
no mal egional SADs o exhaus i ely sampled ma ine
ish and co al ee communi ies, a guing ha he
obse ed in a iance esul s om he co esponding scal-
ing o mul iple ecological p ocesses ha o ce SADs in o
a logno mal shape. We no e ha Šizling e al. (2009)
a gued agains exac scale in a iance o logno mal SADs.
These au ho s showed ha , i he SAD a one scale is log-
no mal, he SADs a o he scales con e ge on igh -
skewed dis ibu ions ha can appea oughly logno mal,
esul ing in appa en scale in a iance.
Ac oss axa, s udies ha e epo ed changes in he
(i) pa ame e s o he models ha bes i local SADs wi h
inc easing spa ial scale and (ii) ype o SAD model ha
p o ides he mos accu a e ep esen a ion o he empi i-
cal dis ibu ion (in wha ollows e e ed o as he SAD
shape). Fo example, Bo da-de-
Agua e al. (2017)
epo ed ha he a iance and skewness o a h opod
SADs changed p edic ably acco ding o an allome ic
unc ion along spa ial g adien s. Wu e al. (2019) ound
consis en di ec ional empo al changes in ini ially a i-
ably shaped local o es ee SADs owa d egional log-
se ies dis ibu ions as p edic ed by neu al, dispe sal-
d i en models (Hubbell, 2001). Fe ei a de Lima
e al. (2020) iden i ied a dec easing hie a chy o ac o s
ha igge a iabili y in B azilian A lan ic o es SAD
shapes ac oss spa ial and empo al scales: sample size,
conspeci ic agg ega ion, and β-di e si y. An ˜
ao e al. (2021)
ound ha Poisson logno mal models, including hose
wi h mul iple modes, p o ided he bes i o la ge-scale
SADs o mul iple axa ( he log-se ies ne e p o ided he
bes i o he la ges -scale SADs), whe eas a mix o log-
se ies and Poisson logno mal models p o ided he bes
i s o he SADs o smalle a eas.
This p io wo k has no esol ed he ques ion o
whe he obse ed changes in SAD shapes wi h g ain
size and in esponse o he a o emen ioned h ee
basic p ocesses (in e ac ions, il e ing, dispe sal) occu
in a p edic able way and whe he hey a e axon- o
communi y-speci ic. I also emains unclea whe he
SAD scaling in ol es g adual changes in pa ame e
alues wi hin he same ype o dis ibu ion o , ins ead,
la ge and ab up shi s (i.e., b eakpoin s) in pa ame e
alues and hus swi ching be ween di e en ypes o
dis ibu ions. Sample heo y (G een & Plo kin, 2007)
assumes g adual changes in SAD model pa ame e alues
wi hin he same gene al dis ibu ion shape, whe eas ce ain
neu al models (e.g., Hubbell, 2001) p edic la ge shi s
om egional log-se ies SADs owa d local logno mal- ype
dis ibu ions, depending on he deg ee o dispe sal limi a-
ion. Such changes in ela i e abundance ha e s ong impli-
ca ions o he scaling o he ecological p ocesses ha
de e mine he hie a chy o species abundances. An empi i-
cal assessmen o he ype o scaling and he espec i e scal-
ing pa ame e s would allow o an imp o ed ex apola ion
o obse ed abundance dis ibu ions.
Excep o he in luence o dispe sal, ew empi ical
s udies ha e deal wi h he ecological d i e s ha in lu-
ence he spa ial scaling o SADs, pa icula ly o plan s.
Global compa isons o woody (Ma hews e al., 2019;
Ul ich e al., 2018) and d yland plan s (Ul ich e al.,
2016) and local compa isons o o es gaps (Sal ado - an
Eysen ode e al., 2003) ha e highligh ed he impo ance
o clima ic a iabili y and en i onmen al s ess. Wo k on
o he plan g oups is lacking, as a e scaling analyses
ocused on ine, local-scale SAD da a. He e we ill his
knowledge gap by ocusing on ex a- opical g asslands
and o he open ege a ion communi ies. We use an
excep ionally la ge Palaea c ic da a se , he G assPlo
da abase (Biu un e al., 2019,2021; Dengle e al., 2018),
o add ess he ques ions a ound he scaling o abundance
dis ibu ions, using pe cen age co e es ima es as p oxies
o abundance. The G assPlo da a s em om di e se si e
condi ions (e.g., om sea le el o mo e han
5000 m abo e sea le el [a.s.l.], om e y we o e y d y
si es, and om humid o semia id clima es) and manage-
men egimes (e.g., na u al, semina u al, in ensi ied)
(Dengle e al., 2020). This a ia ion makes i possible o
link he obse ed changes in SAD pa ame e alues o
ECOLOGY 3o 16
en i onmen al cha ac e is ics. Impo an ly, ou da a
allow us o s udy he scaling o SADs wi hin iden ical
ege a ion ypes and o compa e he pa e ns o scaling
among ege a ion ypes.
Based on he p eceding discussion o empi ical and
sample heo e ical p edic ions, we examine (i) which
ypes o SADs a e ealized in ex a- opical g asslands,
(ii) how SAD shape changes ac oss en i onmen al g adi-
en s ac oss he Palaea c ic, and (iii) whe he and how he
scaling o SADs along spa ial g adien s migh in luence
in e ences o SAD a iabili y a la ge , geog aphical spa-
ial scales.
MATERIALS AND METHODS
Vege a ion-plo da a
We compiled da a om 3531 plo s ac oss 56 da a se s om
he collabo a i e ege a ion-plo da abase G assPlo
(Biu un e al., 2019; Dengle e al., 2018,h ps://edgg.o g/
da abases/G assPlo ). Using a minimum species ichness
h eshold o 20 o il e hese da a, we ex ac ed ascula
plan da a om 1725 single plo s ac oss 47 da a se s each
co e ing an a ea o 10 m
2
(da a se s, me ada a, and e e -
ences in Ul ich e al., 2021). In o al, hese plo s come om
20 di e en coun ies in Eu ope and Asia (Appendix S1:
Figu e S1) and co e 19 b oad ege a ion ypes (2nd le el
o he ecological-physiognomic ypology o G assPlo ;
Biu un e al., 2019). The lowe ichness bounda y
(20) allowed o su icien ly p ecise SAD i s and enabled
us o assess he change in communi y pa ame e s along
g adien s o inc easing ichness and abundance (c . Ul ich
e al., 2010). Abundances o all species in a plo we e
assessed by he pe cen age co e ( ypically used in plan
SAD s udies a he han ac ual abundances) (Ande son
e al. 2012; Chia ucci e al., 1999). Co e da a a e o en
mo e s ongly co ela ed wi h plan biomass han wi h he
numbe o ame s, ha is, single shoo s (Chia ucci
e al., 1999). The e o e, co e -based SADs a e pa icula ly
e ec i e a quan i ying he dis ibu ion o plan species bio-
mass wi hin and ac oss ege a ion plo s.
Fo he analysis o spa ial SAD scaling, we selec ed
40 plo clus e s om he da a se s, ha is, g oups o plo s
om he o iginal da a se wi h iden ical ege a ion ype
ha con ained a leas 15 indi idual plo s (in o al 1550
plo s) (Ul ich e al., 2021). Fo each clus e , we s a ed
SAD i ing wi h a andomly chosen plo o a leas 20 spe-
cies and g adually added he co e alues o all o he
plo s in andom o de o ob ain a cumula i e plo
sequence (CPS), which also e lec s inc easing sample
a ea. This addi i e p ocess implies ha cumula i e co e
alues migh be la ge han 100. We no e ha hese CPSs
do no o m sequences o spa ially con inuous ege a ion
bu a e agg ega ions o discon inuous plo s. O cou se,
he SAD a he s a ing poin and he speci ic o de ing o
plo s du ing accumula ion migh in luence he in e ed
scaling beha io and inc ease he a iance in scaling pa -
e ns ac oss hese CPSs. Howe e , we did no a e age
alues o se e al uns o andom accumula ion wi hin
each plo se ies because such a e aging would a i icially
smoo h he spa ial scaling and bias he pa e n owa d
wha is p edic ed om sample heo y in homogeneous
en i onmen s. The high numbe o indi idual plo s
wi hin each CPS gua an eed ha he assessmen o
changes in SAD pa ame e s ac oss a CPS would no be
in luenced by he o de ing o plo combina ion.
Fo each indi idual plo and each accumula ion s ep
o he CPS, we i ed he Weibull dis ibu ion o he spe-
cies ank–ln-abundance dis ibu ion (Whi ake ep e-
sen a ion) (Whi ake , 1965) using ln- ans o med
ela i e co e alues acco ding o s anda d p ac ice. The
inal s ep o each CPS p o ides a ough es ima e o he
abundance dis ibu ion o he egional species pool o
ha clus e . The comple e da a se , including i ed
pa ame e s and momen s o he SAD dis ibu ions, is
con ained in Ul ich e al. (2021).
En i onmen al a iables
The G assPlo da a se con ains a ange o en i onmen al
and geog aphical a iables known o be impo an d i e s
o plan di e si y and dis ibu ions; ce ain a iables a e
only a ailable o a subse o plo s. In his s udy, o all
plo s we used he geog aphical a iables la i ude, longi ude,
and ele a ion. Fo 1111 plo s, in o ma ion on mean soil
dep h, o 569 plo s in o ma ion on soil o ganic ma e con-
en (OMC), and o 338 plo s in o ma ion on soil C/N a io
was a ailable. Addi ionally, we e ie ed da a o a e age
annual empe a u e, annual p ecipi a ion, empe a u e
ange and p ecipi a ion a iabili y o all plo s om he
CHELSA clima e da abase (Ka ge e al., 2016). The com-
ple e geog aphical and en i onmen al aw da a o each
plo a e con ained in Ul ich e al. (2021).
Da a analysis
P io wo k on he a ia ion in SAD shape be ween si es
la gely elied on compa ing he i s o di e en s anda d
models. Howe e , eliable model compa isons need la ge
sample sizes, a leas on he o de o 20 species (Ul ich
e al., 2010; Wilson, 1993). The e o e, he e we ake a wo-
p onged app oach. Fi s , we ely on model-independen
momen s o SADs: he a iance (σ
2
, second momen ) as a
4o 16 ULRICH ET AL.
measu e o he ange in plan co e , he skewness
(γ, hi d momen ) as a measu e o an excess o ela i ely
a e o abundan species, and he ku osis (δ, ou h
momen ) as a quan i ica ion o he p opo ion o species
wi h ela i ely in e media e co e . Addi ionally, we i ed
he wo-pa ame e Weibull dis ibu ion o he obse ed
plan co e da a. Recen ly, Ul ich e al. (2018,2020) dem-
ons a ed ha his dis ibu ion is su icien ly lexible o
mimic a wide ange o obse ed SAD shapes. The model
allows o a con inuous acing o he changes in he wo
Weibull pa ame e alues (scale and shape) in o de o
assess he scaling p ope ies o obse ed SADs and o
ela e hese o en i onmen al co ela es.
Fi ing he Weibull model o empi ical SADs
The wo-pa ame e o m o he Weibull dis ibu ion has
he p obabili y densi y unc ion (PDF)
px>0;φ;λðÞ¼
φ
λ
x
λ

φ1ex
λ
ðÞ
φ
ð1Þ
whe e φis he shape and λ he scale pa ame e . The
Weibull shape pa ame e (φ) dec eases wi h inc easing
skewness o he dis ibu ion, and he scale pa ame e (λ)
inc eases wi h he obse ed ange in abundance (Ul ich
e al., 2018). Consequen ly, λand σ
2
a e posi i ely co e-
la ed (p esen da a: =0.73). The φ/λquo ien is mo e
closely ela ed o he empi ical a iance o he SAD by a
powe unc ion (c . Appendix S1: Figu e S2 o he p e-
sen da a se ). Shape pa ame e s a ound φ=2 mimic log-
no mal dis ibu ions, whe eas φ=1 e e s app oxima ely
o log-se ies dis ibu ions. When applied o species abun-
dances, he andom a ia e xmus con ain log-
ans o med abundances calcula ed o all species (S).
The Fo an code used o asymp o ic o dina y leas -
squa es i ing o he Weibull dis ibu ion (using a
pa e n-seeking algo i hm) has al eady been p esen ed in
Ul ich e al. (2018) and is eely a ailable om he
co esponding au ho upon eques . As a measu e o
goodness o i we used he a e age sum o leas squa es:
i ¼1
SPS
1ln piln wj

2,whe e ln p
i
and ln w
j
deno e he
ln- ans o med obse ed and Weibull i ed ela i e abun-
dances, espec i ely. Ul ich e al. (2018) compa ed di e -
en ypes o SAD om small o in e media e sized
Japanese o es ee communi ies (<100 species) and
epo ed i alues <0.05 as being excellen , whe eas i
alues >0.3 we e conside ed poo . Figu e 1con ains six
ypical examples om he p esen da a se o excellen o
FIGURE 1 Six example i s o he Weibull dis ibu ion o g assland communi y species abundance dis ibu ions (SADs), wi h di e en
alues o he goodness-o - i measu e. Goodness o i was calcula ed as he a e age sum o leas squa es: i ¼1
SPS
1ln piln wj

2, whe e ln
p
i
and ln w
j
deno e ln- ans o med obse ed and Weibull i ed ela i e pe cen age co e alues. Le e s (e.g., RO_AP) e e o CPS plo code
(Appendix S1: Table S5) (Ul ich e al., 2021)
ECOLOGY 5o 16

poo i s and demons a es ha i alues <0.3 can s ill be
conside ed e y good. Weibull model i s o he SADs o
each plo , including obse ed and es ima ed co e alues
o each species oge he wi h espec i e SDs o he es i-
ma es, a e con ained in Ul ich e al. (2021).
S a is ical analysis
Fo each o he indi idual plo s and each accumula ion
s ep o he CPSs, we calcula ed he skewness (γ) and he
ku osis (δ) o he SAD. We no e ha a symme ic logno -
mal dis ibu ion has a skewness o γ=0, while a nega i e
skewness indica es an excess o ela i ely a e species
(no e ha his ega ds log-abundance dis ibu ions: dis i-
bu ions o aw abundances wi h an excess o a e species
a e igh skewed) (e.g., Šizling e al., 2009). A s anda d
logno mal dis ibu ion is cha ac e ized by a ku osis o
δ=3. Highe ku osis alues ma k an excess o species
wi h in e media e abundances. Addi ionally, we calcu-
la ed he p opo ional β-di e si y o each cumula i e plo
se ies as β¼1α=γ, whe e αis he a e age local (plo )
and γ he o al species ichness o he CPS.
G aphical compa isons o λ- alues o single plo s
(Figu e 2a)andCPS(Figu e3a) agains o al co e
indica ed he exis ence o ou clea ly sepa a ed g oups
o SADs. We op imized classi ica ion using k-means
clus e ing applied o he quo ien o λ/ln(co e alues)
and i ed o dina y loga i hmic leas -squa es eg es-
sions o each g oup indi idually. Disc iminan analysis
se ed o ela e hese g oups o en i onmen al a i-
ables. Nes ed linea mixed-e ec s modeling (GLM) and
pa ame ic ANOVA wi h pos hoc Tukey es s we e
used o ela e he SAD pa ame e s o communi y spe-
cies ichness, o al ln-abundance, and en i onmen al
a iables. To in e any nonlinea pa e ns wi h ega d
o changes in he a ious SAD momen s and pa ame-
e s (γ,δ,φ,λ) wi h spa ial scale, we included he
squa ed ze o cen e ed ln-co e e m (sepa a ely calcu-
la ed o each o he 40 CPSs in o he analysis). Because
he spa ial ex en o he s udy a ea, ha is, he a ea
encompassed by he plo s wi hin he CPSs, migh in lu-
ence he esul s we also added he a e age pai wise
plo dis ance wi hin each CPS as a co a ia e. We es i-
ma ed he impac s o p edic o a iables om pa ial η2
alues,
FIGURE 2 Plo s o (a, c) Weibull scale pa ame e λand (b, d) shape pa ame e φagains (a, b) o al plan co e alues and (c, d)
species ichness o all 1725 single plo s e u ned ou clea ly de ined g oups o plo s (A, B, C, D) wi h espec o he in e cep alue o λ.
G oups we e less clea ly de ined wi h espec o φ. Communi y membe ship o hese ou g oups is p o ided in Ul ich e al. (2021).
Reg ession lines e e o (a, b) o dina y leas -squa es loga i hmic and (c, d) linea eg essions. B oken lines in (a) indica e bounda ies o
g oup membe ship
6o 16 ULRICH ET AL.
pa ial η2¼SSe ec
SSe ec þSSe o ,
whe e SS deno es he sum o squa es. Calcula ions
we e unde aken using S a is ica 12.0.
We also applied polynomial o dina y linea segmen ed
leas -squa es eg ession o he SAD pa ame e alues e sus
ln-co e o each o he 40 CPSs, as implemen ed in
SigmaPlo 14. A signi ican b eakpoin indica es a nonlinea
scaling o he espec i e pa ame e s along he o al co e
alue (and he e o e a ea) axis o a gi en CPS. As he spa ial
dis ibu ion o he analyzed G assPlo plo s was clus e ed
and absolu e spa ial dis ances migh be impo an , we used
eigen ec o mapping and added he dominan eigen ec o
(EV1) o he Euclidean plo dis ance ma ix o he GLM
models as a co a ia e.
RESULTS
Goodness o i
The majo i y o he g assland plan SADs we e e y well
i ed by he Weibull dis ibu ion ( i s in Ul ich
e al., 2021, Figu e 1; Appendix S1: Figu e S3). Among
he 1725 indi idual plo s, 400 (23.2%) had i alues <0.1,
indica ing excellen o e y good i s (e.g., Figu e 1a),
1135 plo s (65.8%) had i alues <0.3, indica ing e y
good i s (e.g., Figu es 1b, c), and only 196 (11.4%) we e
compa a i ely weakly i ed by he Weibull dis ibu ion
( i >0.75, e.g., Figu e 1e, ). Goodness o i di e ed sig-
ni ican ly be ween plo s (Appendix S1: Table S1). Species
ichness did no signi ican ly in luence goodness o i
(Appendix S1: Table S1).
Va iabili y in SAD pa ame e s be ween
SAD g oups
Wi h 868 indi idual plo s (50.3%) and 1263 CPS agg e-
ga ion s eps (81.5%), mos i ed SADs we e cha ac e -
ized by φ> 2.0, equi alen o logno mal- ype SADs.
Only 423 indi idual plo s (24.5%) and 47 o he CPS
agg ega ion s eps (3.0%) had φ<1.5, equi alen o a
log-se ies SAD. SAD skewness γdec eased wi h plo
abundance, indica ing an excess o a e species a
FIGURE 3 Plo s o (a, c) Weibull i scale pa ame e λand (b, d) shape pa ame e φagains (a, b) plan cumula i e co e and (c, d)
species ichness o all agg ega ion s eps o cumula i e plo se ies highligh he ou clea ly de ined g oups o plo s (A, B, C, D) wi h espec
o he in e cep alue o λ. G oups we e less clea ly de ined wi h espec o φ. Communi y membe ship o hese ou g oups is p o ided in
Ul ich e al. (2021). Reg ession lines e e o o dina y leas -squa es loga i hmic eg essions. B oken lines in (a) indica e bounda ies o g oup
membe ship
ECOLOGY 7o 16
highe o al co e alues (Appendix S1: Figu e S4c).
Ku osis δwas la gely independen o co e and ich-
ness (Appendix S1: Figu e S4d,h).
Plo s o φand λagains co e alues and species ich-
ness in combina ion wi h k-means clus e analysis
poin ed o ou dis inc g oups o g assland SADs di e -
en ia ed by he scaling o λwi h plan co e (Figu es 2a
and 3a; Appendix S1: Table S2). G oup di e en ia ion
was less ob ious wi h espec o φ(Figu es 2and 3;
Appendix S1: Table S2), al hough k-means clus e ing s ill
con i med >40.0% g oup membe ships (Figu es 2b,d
and 3b,d; Appendix S1: Table S2). The ou g oups did
no signi ican ly di e wi h espec o α-, β-, and
γ-di e si y o o local co e (Figu e 4a). One-way
ANOVA indica ed ha he e was a mode a e e ec o
ege a ion ype on g oup membe ship (pa ial
η2=0.08, p< 0.001). In pa icula , G oup B domina ed in
alpine, xe ic, ocky, and sandy d y g assland communi-
ies, while G oup C domina ed in meso-xe ic, mesic,
and Medi e anean g asslands, as well as in we lands
(Appendix S1: Figu e S3a).
Linea modeling de ec ed signi ican di e ences among
he ou SAD g oups wi h espec o he γand δo he SAD
dis ibu ion and he Weibull pa ame e alues (Table 1,
Figu e 4). G oups A and B SADs we e on a e age cha ac e -
ized by a sligh ly nega i e empi ical γ, indica ing an excess
o a e species (Figu e 4b), while he SADs o G oups C and
D we e signi ican ly igh skewed in acco dance wi h an
excess o abundan species (Figu e 4b). Fo all ou g oups,
δ anged be ween 2 and 3, wi h a dec ease owa d G oup D
(Figu e 4b). Weibull φwas lowes (<2.0) o G oup D com-
muni ies (Figu e 4b).
En i onmen al in luences
The clima ic a iables used he e, in addi ion o ele a-
ion and la i ude, did no signi ican ly in luence he
obse ed SAD shapes (Table 1; Appendix S1:
Figu e S5). φand λinc eased and γdec eased wi h soil
OMC (Appendix S1: Figu e S6e,g,h), while γinc eased
and λdec eased wi h soil C/N a io (Appendix S1:
Figu e S6i,l). Disc iminan analysis also did no de ec
any signi ican in luence o clima ic a iablesonSAD
g oup membe ship (Appendix S1: Table S3). Howe e ,
we ound a s ong indi ec in luence o soil cha ac e is-
ics on SAD g oup membe ship and he e o e on SAD
shape (Figu e 4c;AppendixS1:TableS3).G oupC
communi ies we e ela ed o deepe soils wi h
inc eased C/N a ios, while inc eased OMC was mos
common o G oup A communi ies (Figu e 4c). G oup
A communi ies domina ed a highe , and G oup D
communi ies a lowe , ele a ion (Figu e 4c).
Spa ial scaling o SAD pa ame e s
The Weibull pa ame e s inc eased wi h inc easing cumu-
la i e co e alues (equi alen o inc easing a ea) in a
FIGURE 4 (a) A e age alues o α-, β-, and γ-di e si y, and
a e age local co e alues (C
local
) o cumula i e plo sequences (CPS)
wi hin he ou species abundance dis ibu ion (SAD) g oups
(uppe case le e s) iden i ied in Figu e 2. The e we e no signi ican
di e ences be ween ypes. (b) A e age alues o skewness (γ),
ku osis (δ), shape (φ), and scale (λ) pa ame e s o single g assland
SADs, wi hin he ou g oups. All g oup compa isons signi ican ly
di e ed wi hin each pa ame e . (c) A e age soil dep h, soil o ganic
ma e con en (OMC), soil C/N a ios, and plo ele a ion wi hin he
ou g oups. Fo soil dep h, G oups B and C signi ican ly di e ed
om G oups A and B; o OMC G oup A signi ican ly di e ed
om B, C, and D; o C/N a ios C and D di e ed om A and B; and
o ele a ion A and D di e ed and bo h di e ed om B and C. E o
ba s deno e SEs. Signi icances a he wo-sided 1% e o le el be ween
g oups we e es ed wi h one-way ANOVA and pos hoc Tukey es s
8o 16 ULRICH ET AL.
TABLE 1 Gene al linea modeling de ec ed signi ican di e ences in empi ical species abundance dis ibu ion (SAD) skewness (γ) and
ku osis (δ), and Weibull shape (φ) and scale (λ) pa ame e s, be ween ou g oups o g assland plan communi ies (as de ined in Figu e 2)
and be ween ege a ion ypes
Va iable d
γδφλ
Pa ial η2βPa ial η2βPa ial η2βPa ial η2β
SAD g oup 3 0.29*** …0.04*** …0.36*** …0.94*** …
Vege a ion ype 18 0.03*** …0.05*** …0.02*** …0.04*** …
T
mean
1 0.02*** 0.24 0.01** 0.23 0.03*** 0.32 <0.01 0.01
T
ange
1 <0.01 0.05 0.01** 0.20 0.01** 0.13 0.01** 0.04
P
mean
1 <0.01 0.06 <0.01 0.00 <0.01 0.03 <0.01 0.00
P
seasonali y
1 0.02*** 0.28 0.01** 0.18 0.04*** 0.33 <0.01 0.02
EV1 1 <0.01 0.02 <0.01 0.03 <0.01 0.02 <0.01 0.02
S 1 <0.01 0.01 <0.01 0.02 <0.01 0.04 0.01** 0.02
ln C 1 0.04*** 0.20 <0.01 0.04 0.03*** 0.17 0.34*** 0.20
2
…0.39*** …0.10*** …0.44*** …0.95*** …
No e:T
mean
,P
mean
, annual mean empe a u e and p ecipi a ion; T
ange
, empe a u e ange; P
seasonali y
, p ecipi a ion seasonali y; ln C, ln- ans o med co e
alues; S, species ichness; and he dominan eigen ec o o plo spa ial dis ances (EV1) se ed as me ic co a ia es.
Vege a ion ype en e ed he model as a andom e ec . Pa ial η2- and β- alues a e shown.
Pa ame ic signi icances: **p< 0.01, ***p< 0.001. N=1719 o all ou models.
FIGURE 5 Plo s o he ela ionships be ween species abundance dis ibu ion (SAD) skewness (γ), ku osis (δ), Weibull i shape (φ),
and scale pa ame e s (λ), and ln- ans o med co e alues o ou ep esen a i e cumula i e plo se ies. Red eg ession lines show
signi ican (p< 0.001) and g ay lines nonsigni ican (p> 0.10) piecewise eg essions. The o al in (o) deno es a s ep change in scale alue.
Si e in o ma ion o each o he ou si es can be ound in Ul ich e al. (2021).
ECOLOGY 9o 16
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SUPPORTING INFORMATION
Addi ional suppo ing in o ma ion may be ound in he
online e sion o he a icle a he publishe ’s websi e.
How o ci e his a icle: Ul ich, We ne , Thomas
J. Ma hews, Idoia Biu un, Juan An onio Campos,
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16 o 16 ULRICH ET AL.