Ma zian, Johannes; Laabs, Julian; Mülle , Johannes; Requa e, Tilman
A icle — Published Ve sion
Inequali y in ela ional weal h wi hin he uppe socie al
segmen : e idence om p ehis o ic Cen al Eu ope
Humani ies and Social Sciences Communica ions
P o ided in Coope a ion wi h:
Kiel Ins i u e o he Wo ld Economy – Leibniz Cen e o Resea ch on Global Economic Challenges
Sugges ed Ci a ion: Ma zian, Johannes; Laabs, Julian; Mülle , Johannes; Requa e, Tilman (2024) :
Inequali y in ela ional weal h wi hin he uppe socie al segmen : e idence om p ehis o ic Cen al
Eu ope, Humani ies and Social Sciences Communica ions, ISSN 2662-9992, Sp inge Science and
Business Media LLC, Be lin, Vol. 11, Iss. 1, pp. 1-12,
h ps://doi.o g/10.1057/s41599-024-03053-x
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ARTICLE
Inequali y in ela ional weal h wi hin he uppe
socie al segmen : e idence om p ehis o ic
Cen al Eu ope
Johannes Ma zian1,2,7✉, Julian Laabs3,4,7, Johannes Mülle 4,5,6 & Tilman Requa e2
While ou unde s anding o long- e m ends in ma e ial weal h inequali y in p ehis o ic
socie ies has expanded in ecen decades, we know li le abou long- e m ends in o he
dimensions o weal h and abou social de elopmen s wi hin pa icula socie al segmen s. This
pape p o ides he fi s e idence o inequali y in ela ional weal h wi hin he uppe socie al
segmen o a sup a- egional ne wo k o communi ies in p ehis o ic Cen al Eu ope o e he
fi s ou millennia BCE. To his end, we compiled a no el da ase o 5000 single- une al
bu ial mounds and employed bu ial mound olume as a p oxy o he bu ied indi idual’s
ela ional weal h. Ou analysis e eals a consis en ly high le el o inequali y among he bu ied
indi iduals, showing a wa e-like pa e n wi h an inc easing end o e ime. Addi ionally, ou
findings show empo al shi s in he size o he uppe socie al segmen . Based on a e iew o
a cheological and paleo-en i onmen al e idence, he empo al change in inequali y may be
explained by echnological p og ess, clima e and popula ion dynamics, ade and social
ne wo ks, and/o sociopoli ical ans o ma ions.
h ps://doi.o g/10.1057/s41599-024-03053-x OPEN
1Kiel Ins i u e o he Wo ld Economy, Kiel 24118, Ge many. 2Depa men o Economics, Kiel Uni e si y, Kiel 24118, Ge many. 3Depa men His o y, Leipzig
Uni e si y, Leipzig 04107, Ge many. 4CRC 1266 Scales o T ans o ma ion, Kiel Uni e si y, Kiel 24118, Ge many. 5Depa men o P e- & P o ohis o y, Kiel
Uni e si y, Kiel 24118, Ge many. 6Clus e o Excellence ROOTS, Kiel Uni e si y, Kiel 24118, Ge many.
7
These au ho s con ibu ed equally: Johannes Ma zian,
Julian Laabs. ✉email: [email p o ec ed]
HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | (2024) 11:557 | h ps://doi.o g/10.1057/s41599-024-03053-x 1
1234567890():,;
In oduc ion
Fo decades, esea che s ha e been ying o lea n abou he
e olu ion o social inequali y in humani y’s deep pas .
Empi ical ad ances ha e been made in unde s anding
inequali y in mode n and p eindus ial as well as ancien socie ies
(Al ani, 2021; Milano ic, 2016; Pike y, 2014; Pike y and Saez,
2014; Scheidel, 2017; McGui e, 1983; Bogaa d e al., 2019; Bo -
ge ho Mulde e al., 2009; Fochesa o e al., 2019,2021; Kohle
e al., 2017; Windle e al., 2013). Especially ou knowledge abou
he de elopmen and d i e s o ancien inequali y has g ea ly
imp o ed in ecen yea s. Bu , he li e a u e o en ocusses on
explaining inequali y in he en i e socie y. To gain a comp e-
hensi e unde s anding o (ancien ) inequali y, howe e , i is also
c ucial o examine inequali y wi hin specific socie al segmen s,
such as he e y ich o e y poo .
Cu en esea ch emphasizes he impo ance o unde s anding
inequali y dynamics wi hin so-called “eli es,”as in a-eli e
inequali y and conflic s can po en ially des abilize en i e socie-
ies (Tu chin, 2023). Howe e , such conflic s and subs an ial
socie al changes ypically occu only e e y ew decades. The e-
o e, adop ing a long- e m pe spec i e and s udying social
dynamics in ancien socie ies can p o ide aluable lessons o he
p esen and u u e.
A his poin , we s ill lack long- un da a on inequali y
wi hin “eli es”o , mo e b oadly, wi hin an “uppe socie al
segmen .”Fu he mo e, when s udying his segmen , we need
o look beyond ma e ial weal h inequali y and explo e o he
ypes o inequali y. The eason is ha membe s o an uppe
socie al segmen exe powe no only h ough hei ma e ial
weal h bu also h ough, o example, hei social ies and
ne wo ks.
In his pape , we ake an ini ial s ep in p o iding long- un
e idence om p ehis o ical Cen al Eu ope ega ding he
de elopmen o inequali y wi hin an uppe socie al segmen .
In pa icula , we ocus ou analyses on inequali y in ela ional
weal h and changes in he size o he uppe socie al segmen .
In his con ex , we conside he ela ional weal h o an indi-
idual as i s endowmen wi h social ies and ne wo ks (Bo -
ge ho Mulde e al., 2009). To s udy ela ional weal h
inequali y among indi iduals in p ehis o ical Cen al Eu ope,
we cons uc ed a da ase o ~5000 single- une al bu ial
mounds ha da e back o he fi s ou millennia BCE. Cen al
Eu ope is a cheologically well s udied, bu a de ailed quan i-
a i e assessmen o inequali y in he longue du ée is s ill
lacking.
The ocal poin o ou inequali y analyses is he olumes o
he bu ial mounds, which we employ as p oxies o he ela-
ional weal h o he bu ied indi iduals. We assume ha he
la ge he olume o he bu ial mound, he g ea e he indi-
idual’s ela ional weal h. In o he wo ds, an indi idual who
possessed a la ge bu ial mound had a highe economic and
poli ical abili y o mobilize people and esou ces wi hin i s
(social) ne wo k o accomplish specific goals han an indi i-
dual wi h a small bu ial mound. I is impo an o no e ha
hese ne wo ks we e ypically confined o local communi ies/
socie ies and did no ex end ac oss he en i e egion o Cen al
Eu ope. None heless, we assume ha he espec i e commu-
ni ies/socie ies we e economically and socially highly in e -
connec ed, o ming pa o a sup a- egional ne wo k. This
pe spec i e is suppo ed by exis ing a cheological e idence
(Pa ke Pea son, 2003; K is iansen and La sson, 2005;
Milisauskas, 2011; Ke ig and Shennan, 2015; Fu hol , 2021).
Despi e po en ial a ia ions in social–cul u al o ma ions
wi hin p ehis o ic socie ies, indi iduals wi h g ea e access o
esou ces and ne wo ks cons i u e he uppe socie al segmen . O
cou se, he p opo ion o indi iduals holding highe social s a us
in compa ison o he en i e popula ion may a y due o di e -
ences in social p ac ices. Howe e , as bu ial mounds we e p e-
dominan ly ese ed o hose indi iduals who had a high social
s a us, hese da a o e us a unique oppo uni y o analyze
inequali y be ween hose socially dis inguished indi iduals ha
o med he uppe socie al segmen o he men ioned sup a-
egional ne wo k (Capelle, 2000; Egge , 1999). To analyze
inequali y among hese indi iduals, we employ inequali y indices
such as he Gini index o he da a. We in e p e he esul ing
alues as measu es o inequali y among bu ied indi iduals’
le e age o make use o hei esou ces and ne wo ks.
In addi ion o he bu ial mound da a, we collec ed in o ma ion
on he numbe o indi iduals bu ied in fla and collec i e bu ials.
F om hese da a, we can es ima e he sha e o indi iduals bu ied
in bu ial mounds o e ime. This sha e gi es us an idea abou
how many people we e able o exp ess hei ela ional weal h ia
bu ial mounds. O , o pu i di e en ly, his sha e ells us abou
he size o he uppe socie al segmen .
Ou analyses e eal wokeyfindings abou p ehis o ic
inequali y. Fi s , he e is a wa e-like end in he sha e o
indi iduals who had su ficien ela ional weal h o he con-
s uc ion o a bu ial mound. This finding indica es a changing
size o he uppe socie al segmen in Cen al Eu ope o e ime.
Second, he le el o inequali y in ela ional weal h be ween
hese indi iduals was high h oughou he en i e pe iod.
Howe e , i was no cons an bu s eadily changed wi h an
inc easing end o e ime—especially du ing he las 1200
yea s BCE. F om an a cheological pe spec i e, ac o s ha
help o a ionalize ou esul s a e he es ablishmen o new
echnologies and hei social implica ions (Bose up, 1981;
Childe, 1957;O’B ien and Shennan, 2010), imp o emen o
de e io a ion o wea he and clima e condi ions (Robe s,
1998; E dkamp and Manning, 2021), changes in he size and
composi ion o he popula ion (Johnson, 1982;Be encou
e al., 2007; Mülle , 2013a; Zimme mann, 2012), he eme -
gence and ea angemen s o ade and social ne wo ks
(Fu hol , 2014;Feinman,2017; K is iansen e al. 2018), and
shi s in he sociopoli ical s uc u e (Fu hol e al., 2020;
Kienlin and Zimme mann, 2012).
Bu ial mound olume as a p oxy o ela ional weal h
Ea h mounds a e among he mos well-known a cheological
s uc u es in Eu ope (Ha ding, 2000;Johansene al.,2004;
Bou geois, 2013). They ep esen a complex social p ac ice
in ol ing economic, ideological, and poli ical eali ies and a e
conside ed as he g a es o indi iduals wi h a dis inguished
social s a us (Capelle, 2000; Assmann, 2013; Mülle -Scheeßel,
2013; End igkei , 2014; Osbo ne, 2014;Mülle ,2018). To assess
he social s a us o a bu ied indi idual, we use he olume o i s
bu ial mound as a p oxy o i s ela ional weal h (Bo ge ho
Mulde e al., 2009; Beck and Quinn, 2023). The ela ional
weal h o an indi idual ep esen s i s economic and poli ical
abili y o mobilize people and esou ces in i s (social) ne wo k
o achie e ce ain goals. Since he bu ied indi idual is dead a
he ime when he bu ial mound is e ec ed, we conside he
e ec ion as a pos humous o m o i s ela ional weal h. Fu -
he mo e, s udies on e hnoa cheological documen ed commu-
ni ies show ha cons uc ing a monumen o en in ol es a
la ge kinship g oup ha ex ends beyond he indi idual
household (Jeunesse, 2018;Mille ,2021; Wunde lich e al.,
2021). In his con ex , he cons uc ion o a bu ial mound can
also be unde s ood as a social signal symbolizing a long- e m
in es men o he deceased and he associa ed g oup (Bliege
Bi d and Smi h, 2005; Quinn, 2019). Hence, bu ial mounds
ARTICLE HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | h ps://doi.o g/10.1057/s41599-024-03053-x
2HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | (2024) 11:557 | h ps://doi.o g/10.1057/s41599-024-03053-x
demons a ed he economic and poli ical abili y o he indi i-
dual and g oup o compe e and collabo a e wi h o he indi i-
duals and g oups in he local and egional ne wo k (Pa ke
Pea son, 2003; Leach, 1979).
In ou analyses, we only use bu ial mounds dedica ed o a
single indi idual. The e o e, i is possible o in e p e he con-
s uc ion o a bu ial mound as di ec ly ela ed o an indi idual’s
ela ional weal h. Hence, he la ge he bu ial mound, he weal-
hie , mo e powe ul, and he be e in eg a ed he bu ied indi-
idual in o local and egional ne wo ks. Fu he mo e, we use a
bu ial mound’s olume ins ead o i s floo a ea o measu e ela-
ional weal h. The easoning is as ollows: I we assume ha he
e o equi ed o build a bu ial mound is p opo ional o i s floo
a ea, his will mean ha a bu ial mound wi h a la ge floo a ea
would ha e he same heigh as one wi h a small floo a ea. Gi en
he obse ed shapes o bu ial mounds, his ela ionship does no
seem easonable. Since we canno obse e he olume o each
bu ial mound in he da ase , we make a cheologically easonable
assump ions abou a bu ial mound’s shape o compu e he
espec i e olumes. We explain he compu a ion p ocedu e in he
me hods sec ion in mo e de ail.
Measu ing p ehis o ic inequali y wi h bu ial mound da a
To cons uc ou da ase , we collec ed in o ma ion on he size
o bu ial mounds om ex ensi e a cheological ca alogs. Ou
da ase p o ides in o ma ion on 4986 bu ial mounds in Cen al
Eu ope. I co e s he fi s ou millennia BCE and includes
bu ial mounds om he Neoli hic up un il he appea ance o
he Romans in Cen al Eu ope. Addi ionally, we collec ed da a
on he p e alence o indi iduals bu ied in fla and collec i e
bu ials. In ou analysis, we measu e inequali y in ela ional
weal h be ween indi iduals in he en i e geog aphic a ea o
Cen al Eu ope, which yields he mos ime-g anula pe spec-
i e. Al hough ou da ase ’s spa ial g anula i y allows o sub-
egional analyses, we lea e hem o u u e esea ch. Such
analyses equi e a ho ough discussion o he egional a che-
ological backg ound, which is beyond he scope o his a icle.
SI, Sec ions 1 and 2 display all a iables included in ou da ase
and he addi ional da a, along wi h a concise desc ip ion o
hei meaning. The e e ences o he p ima y a cheological
ca alogs om which we compiled he da a a e a ailable in SI,
Sec ion 8.
Gi en ha he da ing in e als o he bu ial mounds a y
be ween 10 and 4700 yea s, we decided o limi ou analysis o
bu ial mounds wi h a maximum da ing in e al o 600 yea s.
This es ic ion educes he size o ou da ase , bu i ensu es
mo e p ecise esul s. None heless, i is wo h no ing ha limi s
beyond 600 yea s do no significan ly al e ou findings (see SI,
Sec ion 7). Hence, ou esul s a e mainly d i en by he well-
da ed bu ial mounds. Finally, we spli ou obse a ion pe iod
in o in e als o 200 yea s and assign each bu ial mound o one
o he in e als acco ding o he a e age o he ini ial and final
alue o i s da ing in e al. The choice o 250- and 300-yea
in e als, again, does no subs an ially al e he esul s (see SI,
Sec ions 5 and 6).
Figu e 1displays maps wi h he spa ial loca ion o he bu ial
mound si es in each 200-yea in e al. To a oid con usion abou
small sample sizes, we no e ha some si es consis o mul iple
bu ial mounds. Howe e , o he in e als 0–200 BCE, 2800–3000
BCE, and 3000–3200 BCE, he numbe o bu ial mounds is oo
low o a c edible analysis (see SI, Sec ion 4). Al hough he bu ial
mound si es a e spa ially dispe sed wi hin he 200 in e als, we
conside he en i e s udy egion o be cha ac e ized by high
economic and social connec i i y (Pa ke Pea son, 2003; K is-
iansen and La sson, 2005; Milisauskas, 2011; Ke ig and Shennan,
2015; Fu hol , 2021). Fu he mo e, we iew he communi ies
wi hin his egion as pa s o a sup a- egional ne wo k ha spans
ac oss Cen al Eu ope.
To assess he deg ee o inequali y in ela ional weal h be ween
he indi iduals o he uppe socie al segmen o he sup a-
egional ne wo k, we use he Gini index and indices om he
class o Gene alized En opy Measu es (Kohle e al., 2017;
Windle e al., 2013; Cowell, 2000).
1
I is impo an o emphasize
ha he es ima es ob ained o he indices a e subjec o s a is ical
unce ain y. A ypical me hod o calcula e he s anda d e o o
an index is he use o asymp o ic heo y, no ably boo s apping.
In he p esen da ase , howe e , he summa y s a is ics in SI,
Sec ion 4 show ha we ace “hea y- ailed”dis ibu ions, a eason
why boo s apping is no su ficien (Da idson and Flachai e,
2007; Cowell and Flachai e, 2015; Du ou e al., 2019). We,
he e o e, apply pe mu a ion es s o assess he s a is ical sig-
nificance o di e ences be ween wo inequali y es ima es (Du ou
e al., 2019).
Me hods
Compu a ion o a Bu ial Mound’s Volume om i s
G ound A ea. As a gued in he sec ion “Bu ial Mound Volume
as a P oxy o Rela ional Weal h,”we use a bu ial mound’s
olume ins ead o i s floo a ea as a p oxy o he bu ied indi-
idual’s weal h. Since we canno obse e he olume o each
bu ial mound, we employ a non-linea ans o ma ion o i s floo
a ea and in o ma ion abou i s shape o econs uc he olume. I
is impo an o men ion ha he da ase con ains bu ial mounds
o fi e di e en geome ic shapes ( iewed om a bi d’s eye iew):
ound, ound-o al, o al, ec angula , and apezoid. Fo he
ans o ma ion, we summa ize he shapes ound, ound-o al, and
o al as “ ound”and he shapes ec angula and apezoid as
“ ec angula .”
S a ing wi h ound-shaped bu ial mounds, he p ocedu e is as
ollows: Le be he adius o a ci cle and a sphe e, Abe he a ea
o he ci cle, and Vbe he olume o he sphe e. Then
A¼π 2
and
V¼4
3π 3
:
Supposing ha he olume o a ound-shaped bu ial mound
can be app oxima ed by he o mula o a hemisphe e
V ound ¼2
3π 3
and ha he heigh o he bu ial mound is p opo ional o i s
adius, hen e o mula ing V
ound
yields:
V ound ¼2
3π 3¼2
3
π0:5
π0:5π 3¼2
3π0:5π1:5 3¼2
3π0:5π 2
1:5¼2
3π0:5A
1:5
:
Mul iplying he olume by an a bi a y cons an would no
influence he ou comes o he inequali y indices in his pape
since hey all sa is y he scale in a iance axiom (Cowell, 2000).
Hence, i all ound-shaped bu ial mounds ha e a hemisphe e
shape, ans o ming he floo a ea o each bu ial mound by an
exponen o 1.5 yields i s olume.
Conce ning ec angula -shaped bu ial mounds, he p ocedu e
is e y simila . Le lbe he leng h o a ec angula , wi s wid h, A
i s a ea, and le Vbe he olume o a co esponding cuboid wi h
leng h l, wid h w, and heigh h. Then
A¼lw
HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | h ps://doi.o g/10.1057/s41599-024-03053-x ARTICLE
HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | (2024) 11:557 | h ps://doi.o g/10.1057/s41599-024-03053-x 3
and
V¼lwh:
Fu he mo e, suppose ha he olume o a cuboid V
ec
—
which co esponds o an a ea A
ec
—app oxima es he olume o
a ec angula -shaped bu ial mound. Also, assuming ha he
leng h o his cuboid is p opo ional o i s wid h l:¼c1w
,and
ha he heigh o he cuboid is p opo ional o i s wid h
(h:=c
2
w), hen
A ec ¼c1w
|{z}
l
w¼c1w2
and
A ec ¼c1w
|{z}
l
wc2w
|{z}
h
Re o mula ing V ec yields
V ec ¼c0:5
1
|{z}
c0:5
1
c1w
|{z}
l
wc2w
|{z}
h
¼c1:5
1w3c2
c0:5
1
¼ðc1w2Þ1:5c2
c0:5
1
¼A1:5
ec
c2
c0:5
1
:
Again, mul iplying he olume by an a bi a y would no
ma e o he compu a ion o he inequali y indices. Hence, i all
ec angula -shaped bu ial mounds ha e a cuboid shape, wi h
hei leng h and heigh p opo ional o hei wid h, ans o ming
he floo a ea o each bu ial mound by an exponen o 1.5 yields
i s olume as well.
Ma hema ical o mulas o he inequali y indices and hei
asymp o ic s anda d e o s. The ollowing h ee exp essions
p esen o mulas o compu ing he indices om he class o
gene alized en opy measu es Ic;I0;I1
he Gini index (G), and
he no malized Gini index (G*) Cowell (2000).
Ic¼1
n
1
cc1ðÞ
∑
n
i¼1
xi
x
c1
8c≠0;1
I0¼1
n∑
n
i¼1log
x
xi
o c¼0
I1¼1
n∑
n
i¼1
xi
x
log xi
x
o c¼1
G¼1
2n2
x∑
n
i¼1
∑
n
j¼1xixj
G¼n
n1G
The no a ion is as ollows: ndeno es he numbe o bu ial
mounds in he sample, iand jspecific bu ial mounds, x
i
and x
j
he olume o bu ial mounds i,j,
x he a i hme ic mean o x, and
ca sensi i i y pa ame e .
The ollowing exp ession s a es he o mula o he asymp o ic
s anda d e o (ASE) ha is alid o all indices om he GEM
Fig. 1 Spa ial dis ibu ion o he bu ial mound si es in each o he 200-yea in e als o he analysis. A g een do shows he geog aphical posi ion o a
bu ial mound si e.
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class (Cowell and Flachai e, 2015).
ASE Ic
¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
n2∑
n
i¼1Zi
Z
2
Z
i
deno es a e m ha di e s o pa icula alues o he
sensi i i y pa ame e c, and
Zis he a e age o all Z
i
. Using he
same no a ions as in he p e ious o mulas, he ollowing h ee
exp essions gi e he espec i e Z
i
o di e en alues o c.
Zi¼1
c2c
xi
x
ccxi
x
Icþ1
c2c
8c≠0;1
Zi¼xi
x
log xi
o c¼0
Zi¼xi
x
log xi
x
I11
o c¼1
Rega ding he no malized Gini index, he subsequen exp es-
sion displays a o mula o i s asymp o ic s anda d e o (ASE)
wi h he no a ion being as be o e (Cowell and Flachai e, 2015).
ASE G
ðÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
n
xðÞ
2∑
n
i¼1Zi
Z
2
s
Co espondingly, he nex exp ession defines he o mula o
he Z
i
, whe e xiðÞ deno es he i h elemen o he o de ed sample.
The obse a ions in he o de ed sample a e anked by ascending
magni ude o hei bu ial mound olume.
Zi¼Gþ1ðÞxiðÞþ2i1
n
xiðÞ2
n∑
i
j¼1xj
ðÞ
P ocedu e o pe o ming pe mu a ion es s. A p ima y me h-
odological objec i e o his pape is o p esen a sui able ool o
es ing he s a is ical significance o a di e ence in wo alues o
an inequali y. In he p esence o hea y- ailed dis ibu ions, he
mos app op ia e ool o his exe cise is pe mu a ion es s
(Du ou e al., 2019). The heo e ical ounda ions o he pe mu-
a ion es da e back o he ea ly 20 h cen u y (Pi man, 1937), bu
he ecen wo k o Du ou e al. (2019) demons a es hei
supe io i y in es ing di e ences in inequali y. The e o e, his
sec ion aims o p o ide a s ep-by-s ep p ocedu e o conduc ing
pe mu a ion es s based on hei wo k. Conce ning mo e de ail
on he me hod’s echnical ounda ions, we e e o he
espec i e pape .
Suppose he e a e wo popula ions, Aand B. Fo example,
popula ion Acould be he popula ion o all bu ial mounds in he
Neoli hic in Cen al Eu ope, while popula ion Bcould be he
popula ion o all bu ial mounds in he B onze Age in Cen al
Eu ope. The p ima y pu pose lies in de e mining i he deg ee o
inequali y di e s be ween hese wo pe iods. To measu e he
deg ee o inequali y, we can use an inequali y index θ. Hence, he
“ ue”popula ion deg ee o inequali y in he Neoli hic is θ
A
and
in he B onze Age θ
B
. Howe e , since i is impossible o obse e
he en i e popula ion o bu ial mounds in each pe iod, we canno
de e mine θAand θB. Thus, bo h alues a e unknown. The e o e,
elying on obse able sample da a, we need o es ima e hem o
ge an idea abou hei alues. The ec o XA¼xA
1;xA
2; :::; xA
m
con ains he sample da a om he Neoli hic, and he ec o XB¼
xB
1;xB
2; :::; xB
n
he sample da a om he B onze Age. The e a e m
bu ial mounds in he sample XAand nbu ial mounds in he
sample XB. The elemen s xA
1;xA
2; :::; xA
ma e he co esponding
olumes o obse ed bu ial mounds in he Neoli hic, and he
elemen s xB
1;xB
2; :::; xB
na e he co esponding olumes o obse ed
bu ial mounds in he B onze Age. Ideally, hese samples a e
ep esen a i e o hei espec i e popula ions. Using he olumes
in each sample, we can compu e ^
θAand ^
θB;whe e ^
θAis he
deg ee o inequali y in he sample XAand ^
θB he deg ee in sample
XB. Bo h ^
θAand ^
θBa e es ima es o he ue bu unknown
popula ion deg ee o inequali y. F om his pe spec i e, i is
e iden why s a is ical unce ain y su ounds he es ima es ^
θAand
^
θBand why compu ing he di e ence be ween ^
θAand ^
θBdoes no
answe he ques ion i he deg ee o inequali y be ween he
popula ion di e s. A mo e app op ia e answe o his ques ion is
o pe o m hypo hesis es ing using, o example, pe mu a ion
es s. The mos app op ia e pe mu a ion es o es ing
di e ences in inequali y p oceeds as ollows:
1. Se up a pai o hypo heses: H0:θA¼θB s. H1:θA≠θB.
The null hypo hesis H0s a es ha employing inequali y
index θ o assess he deg ee o inequali y in popula ion A
and B, inequali y does no di e be ween hem. In con as ,
he al e na i e hypo hesis H
1
s a es he deg ee o inequali y
di e s.
2. To es his pai o hypo heses, he pe mu a ion es uses he
sample da a om XAand XB. To gua an ee he asympo i c
alidi y o he pe mu a ion es , i is necessa y o scale he
samples XAand XBusing hei espec i e sample means
xA
and
xB. Hence, he scaled samples a e XA¼xA
1
xA;
xA
2
xA; :::;
xA
m
xA
and XB¼xB
1
xB;
xB
2
xB; :::;
xB
m
xB
.
3. Unde H0, i does no ma e om which sample he da a
o compu ing ^
θAand ^
θBs ems. The e o e, he pe mu a ion
es me ges XAand XB o ob ain a combined sample
XC¼xA
1
xA;
xA
2
xA; :::;
xA
m
xA;
xB
1
xB;
xB
2
xB; :::;
xB
m
xB
.XCcon ains mþnbu -
ial mound olumes.
4. The nex exe cise is o pe mu e XC:In o al, he e exis
mþn
ðÞ
!di e en pe mu a ions.
5. The p oblem is ha he la ge he sample sizes mand n, he
la ge he numbe o possible pe mu a ions. The e o e, he
pe mu a ion es andomly d aws Ko hese mþnðÞ!
pe mu a ions wi hou eplacemen . Hence, including he
ini ially combined da a XC, he e a e Kþ1 pe mu a ions
a ailable o he analysis.
6. Subsequen ly, we need o choose a sui able es s a is ic o
es ing he di e ence in he deg ee o inequali y be ween he
wo popula ions. In his case, S¼^
θA^
θB
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
^
VθA
ðÞ
þ^
VθB
ðÞ
pis an
app op ia e es s a is ic. ^
VθA
and ^
VθB
a e es ima es
(asymp o ic/boo s ap) o he a iance o ^
θAand ^
θB. I he
samples a e dependen , i is necessa y o adjus he
denomina o by including he co a iance o he samples.
7. Using he o mula o he es s a is ic om 6., as well as he
da a om he o iginal samples XAand XB, he pe mu a ion
es compu es he obse ed es s a is ic Sobs.
8. The nex s ep spli s each o he Kpe mu a ions in o wo
samples o size mand n. Fo example, he fi s mbu ial
mound olumes o m he elemen s o he sample o
popula ion A, whe eas he emaining nbu ial mound
olumes o m he elemen s o he sample o popula ion B.
9. The compu a ion o he es s a is ic om 6—using he da a
om he spli samples o he Kpe mu a ions—yields K
alues o he es s a is ic.
10. Finally, compa ing he alues o he K es s a is ics wi h he
ini ially obse ed es s a is ic Sobs yields he pe mu a ion
es ’sp- alue. The o mula o he p- alue is he ollowing:
p alue ¼2 min
∑
K
j¼1IS
j≤Sobs
ðÞ
þ1
Kþ1;
∑
K
j¼1IS
j≥Sobs
ðÞ
þ1
Kþ1
8
<
:9
=
;
.Sjis he
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HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | (2024) 11:557 | h ps://doi.o g/10.1057/s41599-024-03053-x 5
es s a is ic’s alue co esponding o pe mu a ion Kand
IðÞ is an indica o unc ion aking on he alue 0 i he
condi ion wi hin he b acke s is no ue and 1 i he
condi ion is ue.
In addi ion o he impo ance o escaling he samples, he e is
ano he condi ion unde which pe mu a ion es s a e asymp o-
ically alid. This condi ion holds when he sample sizes a e
equal, o he unde lying dis ibu ions ha e he same asymp o ic
a iance. Howe e , i has been shown ha e en o e y unequal
sample sizes and hea y- ailed dis ibu ions, pe mu a ions es s
ou pe o m boo s ap and asymp o ic es ing p ocedu es (Du ou
e al., 2019). I has also been shown ha pe mu a ion es s a e
supe io o o he es ing p ocedu es om a size and powe
pe spec i e (Du ou e al., 2019). The e o e, hey a e he bes
op ion o es ing di e ences in inequali y in ou da ase .
A ime-g anula pe spec i e on social inequali y
Figu e 2shows he esul s o he empo ally fine-g ained analysis
o inequali y in ela ional weal h be ween indi iduals o he uppe
socie al segmen , he sum o bu ied indi iduals (indi iduals
bu ied in bu ial mounds, fla bu ials, and collec i e bu ial), and
he sha e o indi iduals bu ied in bu ial mounds. Since he esul s
a e e y simila ac oss he ou inequali y indices (see SI, Sec ion
4), we discuss ou findings conside ing he Gini index. We use he
sha e o indi iduals bu ied in bu ial mounds o ge an idea abou
he size o he uppe socie al segmen . To calcula e his sha e, we
di ide he numbe o single- une al bu ial mounds by he sum o
indi iduals bu ied in collec i e and fla bu ials and bu ial
mounds.
S udying ou esul s and accompanied a cheological e i-
dence, we ecognize a epea ing, wa e-like pa e n in he sha e
o indi iduals bu ied in bu ial mounds o e ime. The pa e n
consis s o wo phases. In he ini ial phase, only a ew indi i-
duals we e bu ied in bu ial mounds, whe eas in he second
phase, many mo e we e bu ied in bu ial mounds. In each o he
wo phases, we obse e fluc ua ions in inequali y in ela ional
weal h be ween he indi iduals o an uppe socie al segmen
ha ollow an inc easing, o e a ching end. The pa e n
eme ges fi s om abou 3800 BCE o 3300 BCE and second
om 3300 BCE o 2200 BCE. Then, he hi d and ou h ime, i
eme ged om oughly be ween 2200 BCE and 1200 BCE and
om 1200 o 200 BCE. We a ionalize he con ex o he pa e n
and i s wo phases based on he ich co pus o li e a u e on he
eme gence o (ancien ) inequali y and social s a ifica ion
(Bo ge ho Mulde e al., 2009;Kohle e al.,2017; Kienlin and
Zimme mann, 2012;Lenski,1966; P ice and Feinman,
1995,2010;S anish,2017;ThomasandMa k,2013):
The pa e n’sfi s phase (1) is cha ac e ized by he occu ence
o inno a ions, such as new p oduc ion echniques and echnol-
ogies in he o m o new ools, me als, o c ops. This occu ence
o en goes along wi h he eme gence o new o shi ing o e -
egional ade and exchange ne wo ks. Goods being exchanged
o e such ne wo ks a e no only commodi ies and esou ces bu
also knowledge. Ini ially, only a ew people ake pi o al posi ions
in hese ne wo ks and make use o he incoming inno a ions. The
managemen o he flow o in o ma ion and esou ces in hei
ne wo k also helps hese ew people consolida e hei social
posi ion o e ime. This se up can hen be used o u he gain
economic and poli ical powe . As a esul , he ela ional (and
ma e ial) weal h o hose indi iduals s eadily inc eases and makes
hem pa o he uppe socie al segmen . Those who ha e nodal
posi ions in egional and in e -communi y exchange ne wo ks a e
likely pa o a local manage ial eli e (S anish, 2017). A he end o
phase (1) and du ing he ansi ion p ocess o phase (2), he
inno a ion becomes es ablished and is mo e widely used in
socie y; bu key ne wo k posi ions a e s ill held by a ew
indi iduals.
A he s a o he pa e n’s second phase (2), dis up i e e en s
such as mig a ion, cul u al ans o ma ion, o en i onmen al
change igge a ea angemen o la ge-scale ade and exchange
ne wo ks es ablished in phase (1). This ea angemen o e s
Fig. 2 De elopmen o inequali y in ela ional weal h be ween he membe s o he uppe socie al segmen using ime in e als o 200 yea s. The ed
and black lines connec ing inequali y es ima es and he sha es o indi iduals bu ied in bu ial mounds o consecu i e ime slices a e linea in e pola ions
and no ac ual obse a ions. A “x”on op o each line connec ing he inequali y es ima es indica es i he di e ence in he es ima es be ween wo pe iods is
s a is ically significan (p- alue < 0.1). In con as , a “o”indica es a s a is ically insignifican di e ence (p- alue ≥0.1). The numbe s on op o he inequali y
es ima es show he sample size. The g een ba s ep esen he sum o bu ied indi iduals (bu ial mounds, fla g a es, and collec i e g a es) in he espec i e
ime in e als cap u ed by ou da a. The black line displays he sha e o indi iduals bu ied in bu ial mounds, which gi es us an idea abou he ela i e size o
he popula ion’s uppe socie al segmen and social mobili y and s uc u es. SI, Sec ions 4 and 7 con ain he nume ical esul s o his figu e.
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mo e indi iduals he oppo uni y o ins all hei own and mo e
localized ne wo ks. These ne wo ks a e la ge enough o indi i-
duals o accumula e su ficien ela ional weal h ha sepa a es
hem om indi iduals om o he pa s o socie y. Howe e , he e
a e s ill indi iduals who can ake pi o al posi ions in agg ega ed
localized ne wo ks. These posi ions allow hem o accumula e a
high le el o ela ional weal h.
This wo-phase pa e n epea s wi h he occu ence o ano he
se o inno a ions and can be accele a ed due o ad ances in
anspo a ion and in as uc u e. O e ime, he sp ead o ce ain
inno a ions aises ag icul u al p oduc i i y, which can inc ease
o e all p ospe i y and migh induce changes in popula ion size
(Tu chin e al., 2022). Th oughou hese wo phases, changes in
echnology, p ospe i y, and popula ion size migh esul in
compe i ion be ween he indi iduals o he uppe socie al seg-
men o aspi e o mo e influence. All hese changes may al e he
pace o in e ac ion wi hin and he densi y o ne wo ks, which lead
o inc easing, bu fluc ua ing le els o inequali y in ela ional
weal h. A comp ehensi e o e iew o ou p oposed pa e ns is
desc ibed in he ollowing pa ag aphs and summa ized in Table
1. The ends in ne wo k s uc u es shown in Table 1a e de i ed
om he modeled size o collec i ely ac ing g oups
(Zimme mann, 2012), he influences o he inno a ions and
ans o ma ion igge s lis ed in Table 1, and he findings o he
ci ed wo ks.
The fi s occu ence o he pa e n (P1, 3800–3300 BCE)
s a ed wi h he eme gence o new ag icul u al echnologies such
as animal ac ion and he a d a ound 3800–3400 BCE (Bakke e
al., 1999; Whi ehouse and Ki leis, 2014). The fi s phase (Ph 1.1,
3800–3500 BCE) is connec ed o long and ound bu ial mounds
wi h conside able size di e ences, which explain he high alues
o he Gini index. Howe e , he la ge inequali y es ima es in he
No h and Cen al egion o ou esea ch a ea pa ly con adic
ou iews on he cha ac e o hese Neoli hic socie ies (Mülle ,
2001). Ins ead, hey co espond o a highe deg ee o social
s a ifica ion and a e consis en wi h he unexpec ed ex en o
egional coope a ing ne wo ks (Sø ensen, 2014). In addi ion o
changes in he subsis ence economy, he e we e ad ances in
coppe me allu gy, and ea ly coppe i ems became aluable
p es ige goods (B ozio e al., 2023).
The second phase (Ph 1.2) da es be ween 3500 and 3300 BCE,
and due o he low numbe s o bu ial mounds and hei dec eased
di e en ia ion, a low Gini index is measu ed. A clima ic cold
e en (Bond −5.9 ka clima e e en ), da ing a ound 3500 BCE,
p obably a ec ed Cen al Eu opean socie ies as dec eases in
indica o s o human ac i i y show (Koláře al., 2022; Bond e al.,
2001; Hei z e al., 2021; Pa kinson e al., 2021). Fu he mo e, i is
easonable o assume ha he echnology o he wheel and he
inc easing use o animal ac ion in anspo and ag icul u e
became es ablished a ound 3500–3400 BCE (Klimscha, 2017;
Table 1 O e iew o he occu ences o he p oposed pa e ns wi h 2 phases and he co esponding size o he uppe socie al
segmen (gi en by he sha e o indi iduals bu ied in bu ial mounds; black line in Fig. 2), inequali y in ela ional weal h be ween
he indi iduals o he uppe socie al segmen , ne wo k s uc u e, and inno a ions/ igge s ha led o ans o ma ions in social
s uc u es and ne wo ks (see he ex o mo e de ails).
Pa e n Phase Da ing BCE Size in uppe
socie al segmen
Inequali y in uppe
socie al segmen
Ne wo k s uc u e Inno a ion/ igge s
P1 Ph 1.1 3800–3500 Medium High Mo e cen alized •Animal ac ion and he a d
•Ho icul u e
•Coppe me allu gy
Ph 1.2 3500–3300 Small Low Mo e localized •Bond −5.9 ka clima e e en
•Ag icul u e
•Wheel and he inc easing use o animal
ac ion in anspo and ag icul u e
P2 Ph 2.1 3300–2800 No da aaNo da aaMo e cen alized •Ca le: d a animal, dai y p oduc ion
•Long dis ance ade peak jade (wes )/
coppe ools (eas )
Ph 2.2 2800–2200 La ge Medium Mo e localized •New communica ion ne wo ks
•Influx o s eppe indi iduals
•Gende di e en ia ion
P3 Ph 3.1 2200–1600 Small High Cen alized •Bond −4.2 ka clima e e en
•Tin b onze echnology
Ph 3.2 1600–1200 La ge Medium Mo e localized •Tin b onze echnology gene ally
es ablished
•Socie al ans o ma ion in he Eas -
Medi e anean
•Changes in long-dis ance ade ne wo ks
P4 Ph 4.1 1200–800 Small High Mo e cen alized •Collapse o Medi e anean socie ies
•Changes in long-dis ance ade ne wo ks
•Mille
•Ho se and cha io
•Ideological changes (c ema ion as bu ial
i e, bi d symbolism)
Ph 4.2 800–400 Medium Ve y high Localized wi h
cen al hubs
•I on me allu gy
•Di ision o land
•Medi e anean ne wo ks
P5? Ph 5.1? 400–? Small Ve y high Localized wi h
cen al hubs
•Ea ly mone a y economy
•Oppida
aDue o collec i e bu ial adi ion, ou p oxy is no alid he e. Based on he inc eased size di e en ia ion o collec i e bu ials, we expec mo e inequali y be ween bu ial communi ies (Mülle , 2019;
Wunde lich e al., 2019).
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HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | (2024) 11:557 | h ps://doi.o g/10.1057/s41599-024-03053-x 7
Mischka, 2022). In con as o o he phases, a collec i e bu ial
adi ion eme ged in ou esea ch a ea (no he n pa s) o bu ials
in gene al became less isible (cen al pa ). Rela ional weal h, in
his phase, was less a ached o single indi iduals as labo
in es men s we e mos ly assigned o s uc u es o communal
cha ac e , such as collec i e megali hic g a es. Howe e , i is
easonable o expec communica ion o economic and ela ional
weal h be ween communi ies o ex ended sociopoli ical g oups
h ough he e ec ion o collec i e building endea o s (Gebaue ,
2014; Wunde lich, 2019). The megali hic g a es be ween 3500
and 3300 BCE show di e en ia ion in size, espec i ely, in labo
in es men , bu lowe compa ed o ea lie long ba ows. Fu -
he mo e, he e was an inc ease in he numbe o bu ial monu-
men s (Mülle , 2019; Wunde lich, 2019). The size o collec i e
ac ing g oups, compa ed o he p eceding phase (Ph 1.1),
dec eased (Zimme mann, 2012).
Especially be ween 3600 and 3000 BCE, megali hic ombs we e
buil in No he n Cen al Eu ope, which we e used o collec i e
bu ials o lineages o o he sociopoli ical g oups (Schulz Paulsson,
2016). This aises he ques ion o whe he ideology played a ole
in he adop ion o subsequen abandonmen o collec i e bu ial
p ac ices (Mülle , 2010; B ozio e al., 2019). To compu e he sum
o bu ied indi iduals, we assume in a e age 25–50 bu ials in one
collec i e bu ial (Schiesbe g, 2012), which led o he high num-
be s isible in Fig. 2.
Gi en he p edominan p ac ice o collec i e bu ials in ou
s udy a ea, he ini ial phase (Ph 2.1, 3300–2800 BCE) o he
second ins ance o he pa e n (P2, 3300–2200 BCE) p o es di -
ficul o cap u e wi h ou p oxy. In he ime in e als om 3200
o 2800 BCE, we only obse e 7 bu ial mounds in ou da a, which
is he eason why we do no compu e any inequali y index. In
phase Ph 2.1, he e a e mos ly collec i e megali hic g a es, bu he
ypes o monumen s al e ed om dolmen a ia ions o a chi-
ec u al elabo a e passage o galle y g a es. The la e ones show
highe di e en ia ion in size and labo in es men . Also, ewe
such monumen s we e buil , and he e was an inc ease in indi-
idual fla g a es (Mülle , 2019; Wunde lich e al., 2019;
Wunde lich, 2019). This demons a es he abili y o some com-
muni ies o acqui e mo e ela ional weal h han hei con-
empo a ies and is simila o he fi s phase o ou pa e n. Ph 2.1
is associa ed wi h a esu gence o human ac i i y obse ed in
many egions a ound 3300–3000 BCE (Pa kinson e al., 2021;
Koláře al., 2022). Du ing his phase, wo con empo a y ans-
egional ade ne wo ks o p es ige goods played a majo ole in
connec ing majo pa s o ou esea ch a ea–jade axes in he
Wes e n egion o ou s udy a ea and coppe ools in he Eas e n
egion (Klassen, 2004; Pé equin e al., 2012). In he subsis ence
economy ca le became impo an as d a animals as well as o
dai y p oduc s (Webe e al., 2020; E e shed e al., 2022). In his
espec , li es ock may ha e ac ed as mobile capi al.
The pa e n (P2) con inued in o he second phase (Ph 2.2.,
2800–2200 BCE). The shi om Ph 2.1 o Ph 2.2 is p o ound, as
he building o collec i e bu ials was abandoned, and a single
bu ial mound adi ion became es ablished (B ozio e al., 2019).
In p inciple, he inc ease in he size o he uppe socie al segmen
could esul om he low numbe o o al bu ials. Howe e ,
compa ing he absolu e numbe o bu ial mounds be ween 3800
and 2800 BCE and 2800 o 2200 BCE, he inc ease in he size o
he uppe socie al segmen seems eliable. The pe iod om 2800
BCE onwa d is closely associa ed wi h he subcon inen al cul u al
phenomenon o Co ded Wa e. The 3 d millennium BCE in
Eas e n and Cen al Eu ope is cha ac e ized by he c ea ion o
new and changing communica ion ne wo ks, including an influx
o indi iduals om he Cen al Eu asian s eppe (Fu hol , 2021;
K is iansen e al., 2017; Papac e al., 2021). The le el o inequali y
be ween he indi iduals o he uppe socie al segmen is high bu
also changed du ing ha pe iod. An in e es ing obse a ion is he
significan decline in he Gini index in 2600–2400 BCE which
canno be di ec ly linked o any majo ex e nal e en (e.g., cli-
ma e, mig a ion, disease). Ne e heless, he change could ela e o
he onse o he Bell Beake phenomena in Cen al Eu ope om
2600 BCE onwa d (Heyd, 2007; Olalde e al., 2018) and a decline
in popula ion numbe s beginning a ound 2500 BCE (Mülle ,
2013b). A u he possible indica o o high social di e en ia ion
o e he conside ed ime ame is he es ablishmen o clea
gende di e en ia ion om he beginning o he Final Neoli hic
(abou 2800 BCE), which consolida ed du ing he B onze Age
(Robb and Ha is, 2018).
The pa e n (P3) occu ed a hi d ime om 2200 o 1200 BCE,
wi h i s fi s phase (Ph 3.1) om 2200 o 1600 BCE. The Bond
−4.2 ka clima e e en las ing om abou 2350–1900 BCE—which
is a gued o ha e igge ed he collapse o he Akkadian empi e
(Cookson e al., 2019; B adley and Bakke, 2019)—did no ha e a
uni o m o s ongly isible e ec in ou s udy a ea (Kleijne e al.,
2020). Wi h he la e Ea ly B onze Age (2000–1600 BCE), in
b onze me allu gy became a ailable in nea ly all egions o ou
s udy a ea. Howe e , access o me als, such as coppe , in, and
gold, as well as o he p es igious objec s, was limi ed (Me zne -
Nebelsick, 2021; Mi nik e al., 2019; Radi oje iće al., 2019).
Mos o he bu ial mounds om 2000 o 1800 BCE belong o he
so-called “p incely”bu ials o he Úně ice g oups (2200–1600
BCE) in oday’s Eas e n Ge many (e.g., Helmsdo ) and Sou h-
Wes Poland (e.g., Łeki Małe) showing high di e en ia ion
be ween each o he . The size o he uppe socie al segmen was
small. The wo ld- amous “Sky Disc o Neb a”as well as ci cula
di ch enclosu es connec ed o as onomical obse a ion, hin a
he con ol o knowledge (Melle , 2019). Di e en ia ed house
sizes in densely popula ed bu no o ified se lemen s and o -
ifica ion ea u es a some se lemen s suppo he in e p e a ion
o a socially s onge di e en ia ion on communi y and egional
scale (Melle , 2019). The inequali y be ween he indi iduals o he
uppe socie al segmen is subs an ially highe han in he p e ious
pe iods. The o e all inc ease o inequali y om 2400–2200 BCE
o 2000–1800 BCE is significan (p- alue =0.002). Mo eo e , he
li e a u e poin s o a g ow h in communi y sizes and popula ion
in gene al (Zimme mann, 2012). In addi ion o he inc easing
long-dis ance ade, which was domina ed by he exchange o
me als, he ambe ade om he Bal ic Sou h shaped ans e-
gional ne wo ks in ou esea ch a ea (E née, 2016; Ling e al.,
2013). Be ween 2000 and 1200 BCE, in b onze became inc eas-
ingly a ailable, and imp o emen s in b onze me allu gy eme ged
(Radi oje iće al., 2019; K ause, 2003). These de elopmen s led
o he es ablishmen and inc eased use o b onze ools (e.g.,
sickles) o weapons (e.g., swo ds) om he Middle B onze Age
onwa d (Ho n and K is iansen, 2018; A noldussen and S eegs a,
2015). Wi h he significan d op in inequali y om 2000–1800
BCE o 1800–1600 BCE, he size o he uppe socie al segmen
g ew la ge as he inc eased numbe o bu ial mounds indica ed.
The second phase (Ph 3.2, 1600–1200 BCE) s a ed wi h a
su ge in bu ial mounds in ou da ase ha can be connec ed o
he phenomenon o he so-called “Tumulus Cul u e”(ca.
1600–1300 BCE) and he ea ly Olde No dic B onze Age (ca.
1750–1500 BCE). This ime ame is also cha ac e ized by majo
eo ganiza ions in long-dis ance ade ne wo ks as well as eco-
nomic and social changes o en associa ed wi h he end o he
Minoan socie y in he Medi e anean (Ha ding, 2000; Melle
e al., 2013). Fu he mo e, om 1600 o 1200 BCE, he size o
collec i ely ac ing g oups sh unk, bu we gene ally expec an
inc easing popula ion size o his phase (Zimme mann, 2012;
Mülle , 2013b; Nikulka, 2016). Compa ed o he p e ious sub-
phase (2200–1800 BCE), inequali y be ween he indi iduals o he
uppe socie al segmen s ayed cons an ly high h oughou he
ARTICLE HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | h ps://doi.o g/10.1057/s41599-024-03053-x
8HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | (2024) 11:557 | h ps://doi.o g/10.1057/s41599-024-03053-x
