Environmental drivers and spatial scaling of species abundance distributions in Palaearctic grassland vegetation

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 Ul ich, W., T. J. Ma hews, I. Biu um, J. A. Campos, P. Czo ek, I. Dembicz, F. Essl, e al., 2021. “G assland Plan Rela i e Abundances.”Figsha e. h ps://doi.o g/10.6084/m9. igsha e. 16870641. Vellend, M. 2016. The Theo y o Ecological Communi ies. P ince on: P ince on Uni e si y P ess. Wang, X., M. D. F. Ellwood, D. Ai, R. Zhang, and G. Wang. 2018. “Species Abundance Dis ibu ions as a P oxy o he Niche–Neu ali y Con inuum.”Jou nal o Plan Ecology 11: 445–52. Wilson, J. B. 1993. “Would we Recognise a B oken-S ick Commu- ni y i we Found One?”Oikos 67: 181–3. Whi ake , R. H. 1965. “Dominance and Di e si y in Land Plan Communi ies.”Science 147: 250–60. Wu, A., X. Deng, H. He, X. Ren, Y. Jing, W. Xiang, S. Ouyang, W. Yan, and X. Fang. 2019. “Responses o Species Abundance Dis- ibu ion Pa e ns o Spa ial Scaling in Sub opical Seconda y Fo es s.”Ecology and E olu ion 9: 5338–47. Zhou, J., and D. Ning. 2017. “S ochas ic Communi y Assembly: Does i Ma e in Mic obial Ecology?”Mic obiology and Molec- ula Biology Re iews 81: e00002–17. 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, Pa yk Czo ek, Iwona Dembicz, F anz Essl, e al. 2022. “En i onmen al D i e s and Spa ial Scaling o Species Abundance Dis ibu ions in Palaea c ic G assland Vege a ion.”Ecology 103(8): e3725. h ps://doi.o g/10.1002/ecy.3725 16 o 16 ULRICH ET AL.