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he long e m impac o Dayligh
Sa ing ime egula ions in daily li e
a se e al ci cles o la i ude
José Ma ía Ma ín-olalla
We analyze la ge scale (N ~ 10000)  ime use su eys in Uni ed S a es, Spain, I aly, F ance and G ea
B i ain o asce ain seasonal a ia ions in he sleep/wake cycle and he labo cycle a e dayligh sa ing
ime  egula ions ha e s ood up  o  a  leas   o y yea s. Tha  is, no   he usual sea ch  o   he impac  o   he
biannual  ansi ions, bu  a sea ch  o  how indus ialized socie ies ha e answe ed  o DST  egula ions a
di e en  ci cles o  la i ude. Resul s show  ha   he labo  cycle is equally dis ibu ed  h ough seasons i
measu ed in local ime. i is an e e yday expe ience which is a majo ou come o DS . he sleep/wake
cycle displays dis u bances punc ua ed by sola  e en s: sun ise, sunse  and noon. In week-ends, unde
ee p e e ences, sleep onse  delays in summe , opposing  o  he  egula ion and  ollowing  he delay in
sunse   ime, while sleep o se  ad ances, despi e clock  ime al eady ad anced in  he sp ing  ansi ion.
This ad ance s ill  ollows  he ad ance in sun ise  imes. The bes  explana ion  o   hese  indings is  ha
human cycles a e no  misaligned by  he size and di ec ion o  DST  egula ions, which explains  he
success o   ha  p ac ice. The sleep/wake cycle in G ea  B i ain and F ance exhibi   ewe  s a is ically
signi ican  excu sions  han  he sleep/wake cycle in Spain, I aly and Uni ed S a es, despi e ligh  and da k
seasonal de ia ions a e la ge . ha could be indica ing ha he p e e ence o a seasonal egula ion o
ime dec eases wi h inc easing la i ude abo e 47°. The p e e ences  o  a seasonal  egula ion o  clocks
and o he choice o pe manen summe ime o pe manen win e ime a e ske ched om a p e ious
epo on human ac i i y.
Legisla i e bodies in Ame ica and Eu ope a e cu en ly ponde ing he con inui y o Dayligh Sa ing Time egula-
ions —DST—, also known as Summe Time A angemen s. They consis o a o wa d change o clocks in sp ing,
which is e e sed in au umn. They ha e become a pa o e e yday li e in some indus ial, u ban socie ies since i s
incep ion one hund ed yea s ago, amids Wo ld Wa One, o since he 1970s, amids he ene gy c isis.
DST egula ions a e con enien ly desc ibed as a ime zone shi — o ins ance om UTC + 1 o UTC + 2 in
Cen al Eu ope a he sp ing ansi ion— howe e , i no hing else change, hey a e simply a seasonal egula ion in
he phase o human cycles, all equal o a seasonal egula ion o opening imes. As an example in 1810, well be o e
he s anda diza ion o ime, he Spanish Na ional Assembly s a ed sessions a 10 am om Oc obe o Ap il bu
a 9 am om May o Sep embe 1.
Ei he way, he seasonal egula ion o human ac i i y in indus ialized, u ban socie ies synced o clocks mee s
he biannual ansi ions ha cha ac e izes DST. Physiologis s and medical doc o s hink o hese ansi ions as
a dis up ion o ou ci cadian sys em2,3. A se ies o s udies has ied o un eil hei impac in he s ocks ma ke s4,
in suicide a es5, in he a es o myoca dial in a c ion6, in acciden a es7, in acciden and eme gency isi s and
e u n isi s8 o in he a e o au opsies9. Gene ally speaking haza ds happen o inc ease immedia ely a e he
sp ing ansi ion. Physiologis s hen ad oca e o discon inuing DST10–12 and se ing win e ime pe manen ly o ,
in p ac ical e ms, delaying summe ac i i y by one hou . Howe e , and almos inad e en ly, hey also acknowl-
edge he con enience o he p ac ice, a leas o some people13.
The “bene i s” o DST ha e been usually summa ized in ex ended ou doo leisu e ac i i ies and ma ginal
sa ings in ene gy consump ion. Some economis s, decision-make s push o ex end hese bene i s o win e , by
discon inuing DST in he “pe manen summe ime” mode14–16. I no hing else changes his choice would ad ance
human ac i i y by one hou in win e pushing o s a imes ahead o sun ise in win e . The na u al abho ence
o ge ing ac i a ed in he da k plays agains his choice. When physiologis s ad oca e o pe manen win e ime
hey a e p e en ing agains his kind o s ess on he ci cadian sys em11,12. To be socially accep ed an ea ly s a
Uni e sidad de Se illa, Facul ad de Física, Depa amen o de Física de la Ma e ia Condensada, ES41012, Se ille,
Spain. email: [email p o ec ed]
open
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o human ac i i y equi e angible ou comes which usually come in he o m o inc easing sco es o end imes
ahead o win e sunse .
The seasonal egula ion o human ac i i y —and also DST egula ions— ques ions when human ac i i y
should s a in iew o he seasonal sp ead o sun ise imes, sunse imes, day ime and noon insola ion. Tha is,
upon which condi ions indi iduals and socie ies synced o clock ime would p e e seasonally a ying opening
imes ins ead o yea ound opening imes, e en hough annoying biannual ansi ions would be needed in he
o me . The answe o his ques ion may depend on a numbe o issues ha includes ch ono ype —p e e ence
o mo ningness e sus e eningness— o economic sec o —ou doo e sus indoo ac i i ies—. F om he poin
o iew o he physical science he answe is domina ed by la i ude, a ole ha is i ually omi ed in DST discus-
sions17. Fo ins ance DST egula ions ha e ne e been a choice in he T opics, because he e seasonal a ia ions
a e small. Likewise, he p e e ence o ad ancing human ac i i y ela i e o win e sun ise is mo e equen a high
la i ude jus because he e sun ise delays he mos and sunse ad ances he mos in win e . Gene ally speaking
e e y ci cle o la i ude exhibi s a dis inc pa e n o seasonal ligh and da k cycle and human ac i i y adap s o
ha acco dingly18–20.
The ole o la i ude is o he u mos impo ance in he Eu opean Union, whe e popula ion and decision-make s
sp ead om 35° la i ude —Mal a, C e e and Cyp us— o 70° la i ude —Finnish Lapland— exhibi ing i idly di -
e en na u al condi ions21. Howe e , and based on in e nal ma ke e iciency, he Eu opean Commission has
been pushing o synch onous DST a angemen s, p e en ing membe s a es om op ing-ou . The Commission
conside ed he impac o six possible scena ios in which a ew membe s ha e asynch onous a angemen s22.
Howe e no scena io simula ed ha he p e e ence o DST egula ions could s a i y wi h la i ude. In sha p
con as his p e e ence does s a i y wi h la i ude in Aus alia, B azil and Chile.
Time zone and ime zone egula ion only se a bi a y e e ences o ime. They ha e s ood up unchanged o
almos one hund ed yea s in G ea B i ain, I eland, Po ugal, signi ican ci ies o Uni ed S a es; and o some i y/
o y yea s elsewhe e in Eu ope and Ame ica. These se ings allow people o make decisions based on clock ime
which a e a ionally linked o he cycle o ligh and da k19.
This manusc ip is aimed o inspec how hese egula ions impac ed in human li e h ough sensi i e decisions.
Time use su eys —la ge scale s udies (N ~ 104) which y o asce ain how people sha e a s anda d day23— a e
he app op ia e ool o ha . This pape will analyze he case o i e indus ialized coun ies (Uni ed S a es, Spain,
I aly, F ance and Uni ed Kingdom), whe e seasonal ime a angemen s ha e occu ed in he o y yea s p io
o he da e o he su ey. The wo mos basic daily cycles will be s udied: he sleep/wake cycle — egula ed by
ou physiology— and he labo cycle —s ongly ela ed o ou social li e—. The basic goal is o assess seasonal
de ia ions in hese cycles including hei s a is ical signi icance and a ske ch o he impac o la i ude. I mus be
emphasized ha his manusc ip will ocus on he long e m —seasonal— e ec s o he egula ion o ime, no on
e ec s a ound he ansi ions.
No coun e ac ual will be conside ed he e. The ob ious choice is a simila analysis o he ime use su eys in
independen coun ies whe e DST has no been applied egula ly. The Republic o Ko ea and Japan a e he bes
candida es.
Me hods
he da a se s. Mic oda a om ime use su eys in Spain24 and Uni ed S a es25 a e eely a ailable a he
in e ne . Mic oda a om su eys in I aly26, F ance27, G ea B i ain28 could be ob ained a e pe i ion o public
au ho i ies in 2014.
E e y esponden o a ime use su ey illed a dia y which consis ed o N0 = 144 ime slo s —each one ep-
esen ing en minu es— o indexes. I is possible o disc imina e he da e o he dia y a leas o he le el o a
imes e and he day o he week. In his wo k he yea will be pa i ioned in o wo semes e s o seasons: summe
(Ap il o Sep embe , imes e s wo and h ee) and win e (Oc obe o Ma ch, imes e s one and ou ). No ice
ha Oc obe is coun ed in he win e season al hough egula ions a he ime o he su eys ex end summe ime
un il end o Oc obe (Eu ope) o un il s a o No embe (Uni ed S a es). I is also assumed ha seasonal pa i ion
does no in oduce a bias in he dis ibu ion o ch ono ypes and economic sec o s.
Dia ies will be g ouped in ou i ems: (1) week day (Monday o F iday) dia ies ha epo some wo king ac i -
i y; (2) week day dia ies ha do no epo any wo king ac i i y; (3) week-end (Sa u day and Sunday) dia ies ha
epo some wo king ac i i y; and (4) week-end dia ies ha do no epo any wo king ac i i y.
Responden s in g oups 1 and 3 will be labeled as “employees” he ea e . G oups 2 and 4 will only conside
dia ies illed by esponden s aged a leas wen y yea s; hey will be labeled as “non-employees”.
G oup 1 encloses wo king esponden s in a week day. They a e leas p one o ee p e e ences and mos p one
o igh social iming, including he use o ala m clocks o ge ing ac i a ed. G oup 4 is he mos popula ed in
e e y su ey. I encloses non-wo king esponden s in a week-end. I does no dis inguish be ween hose who
wo ked du ing week days and hose who no . Ei he case, esponden s in his g oup a e mos p one o ee p e e -
ences — o ins ance ising up a hei will—. Con as ingly G oup 3 is he leas popula ed since he labo ac i i y
in week-ends is compa a i ely small. Table1 lis s sample sizes o e e y su ey and g oup analyzed.
In he cases o Spain, F ance and Uni ed S a es only con iguous egions will be analyzed. Also A izona
esponden s will no en e in he s udy since his s a e does no obse e DST egula ions.
E en ually he seasonal index will be pe mu ed, e-sampled o e-shu led and wo pa i ions o he pe mu ed
samples will be compa ed o he unshu led, seasonal, o iginal pa i ion o se he s a is ical signi icance o sea-
sonal de ia ions.
he ma hema ical amewo k. The sleep/wake cycle —being awake o sleeping— and he labo cycle
—being wo king o no wo king— will be s udied. Fo ei he cycle wo kind o magni udes will be cha ac e ized:
(1) he daily hy hm R(i) — he sha es o esponden s doing a p esc ibed ac i i y on a gi en index— and (2) he
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expe imen al (sample) cumula i e dis ibu ion unc ion P(i) and sample a e age alue E o a se o i e s ochas ic
a iables which cha ac e izes each cycle o e e y indi idual. Figu eS.1 in Supplemen a y Ma e ial ske ches his
se which is composed o :
• The daily du a ion o he ac i i y d1: he daily wo king ime and he daily sleep o wake ime.
• The cen e o g a i y 2: he momen when hal he daily du a ion has been consumed and hal emains.
• The i s occu ence o he ac i i y 1 o onse ime.
• The las occu ence o he ac i i y 3 o o se ime.
• The dis ance om onse o o se d2.
Fo hese quan i ies he cycle begins a 4 am, a ound he poin o daily minimum human ac i i y. I he cycle
is unimodal —jus one pe iod o ac i i y, wi h no b eaks— he cen e o g a i y ma ches o he midpoin om
onse o o se .
The domain o any o hese s ochas ic a iables consis s o he N0 indexes ha ill one cycle (day). The e o e
hey all a e disc e e a iables.
Seasonal di e ences will be ob ained by sub ac ing esul s om win e esponden s o esul s o m summe
esponden s. The s a is ical signi icance o he seasonal de ia ions Rs(i) − Rw(i) will be de e mined by he Welch’s
- es o unequal a iances29. The s a is ical signi icance o Ps − Pw and Es − Ew will be de e mined by analyzing
andom pe mu a ions o he seasonal index. The size o he pe mu a ion es will be M =107 , much smalle han
Time Use Su ey
Time La i ude Rise/se Inso e iciency Sample size Ra io
o se φsp ead cosθw/cosθsN NwNsNs/Nw
Nh
G ea B i ain25 6 min 52.3° 04 h39 m 25/88
1. Mon-F i (employees) 4081 1745 2336 1.34 44.7
2. Mon-F i (non-
employees) age ≥20 3768 1481 2287 1.54 42.4
3. Sa -Sun (employees) 1378 599 779 1.30 26.0
4. Sa -Sun (non-
employees), age ≥20 6473 2611 3862 1.48 55.8
F ance24 50 min 47.8° 03 h37 m 32/91
1. Mon-F i (employees) 6243 2872 3371 1.17 55.7
2. Mon-F i (non-
employees) age ≥20 6095 2622 3473 1.32 54.7
3. Sa -Sun (employees) 1890 877 1013 1.16 30.7
4. Sa -Sun (non-
employees), age ≥20 8544 3729 4815 1.29 64.8
I aly26 11 min 43.6° 03 h11 m 39/94
1. Mon-F i (employees) 5576 2784 2792 1.00 52.8
2. Mon-F i (non-
employees) age ≥20 5390 2719 2671 0.98 51.9
3. Sa -Sun (employees) 3596 1805 1791 0.99 42.4
4. Sa -Sun (non-
employees), age ≥20 15707 7698 8009 1.04 88.6
Spain27 72 min 40.4° 02 h49 m 44/96
1. Mon-F i (employees) 4271 2053 2218 1.08 46.2
2. Mon-F i (non-
employees) age ≥20 4889 2364 2525 1.07 49.4
3. Sa -Sun (employees) 971 505 466 0.92 22.0
4. Sa -Sun (non-
employees), age ≥20 4965 2431 2534 1.04 49.8
Uni ed S a es28 8 min 38.5° 02 h36 m 47/97
1. Mon-F i (employees) 36498 18629 17869 0.96 135.1
2. Mon-F i (non-
employees) age ≥20 25589 13014 12575 0.97 113.1
3. Sa -Sun (employees) 14775 7631 7144 0.94 85.9
4. Sa -Sun (non-
employees), age ≥20 47877 24408 23469 0.96 154.7
Table 1. Lis o pa icipan coun ies wi h geophysical in o ma ion: ime o se , la i ude φ, he sp ead o
sun ise/sunse imes and he e iciency o insola ion a noon in win e cosθw and summe cosθs. No ice ha DST
egula ionsappa en ly inc ease he sp ead o sunse imes by one hou , dec ease he sp ead o sun ise imes by
one hou . Also ime o se inc eases by one hou a e DST onse . The able also lis s he sample size o e e y
g oup o esponden s. N is he whole numbe o esponden s in g oup, Ns s ands o he numbe o summe
esponden s, Nw is he numbe o win e esponden s, Ns/Nw is he a io and
Nh
is he squa e oo o he
ha monic mean o Ns and Nw.
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he whole numbe o pe mu a ions (≈10N) and la ge enough o he pu pose. The p- alue will be he ac ion o
andom pe mu a ions which yields la ge de ia ions han he es ed seasonal alue, hus ques ioning whe he he
obse ed di e ence is seasonal o andom. Signi icance will be se a he s anda d le el α = 5%. This es will be
one- ailed o assess i s -o de s ochas ic o de ing.
I should be no iced ha o R, 1, 2 and 3 he seasonal de ia ion will compa e o − 1h i is gi en as a uni-
e sal ime and DST egula ions apply.
Fo he pu pose o compa ing samples wi h di e en sizes Rs − Rw will be scaled by a iance and sample size o
ge he Welch’s s a is ics o he de ia ions and Ps − Pw will be scaled by sample size o ge he Kolmogo o -Smi no
s a is ics o he de ia ions. In Supplemen a y ma e ial he ma hema ical amewo k is ho oughly desc ibed (see
Sec ion S.1).
he geophysical amewo k. Summe ime a angemen s a e ela ed o seasons, which a ises om he
obliqui y ε = 23.5° o Ea h’s o a ion axis ela i e o he e olu ion axis. Wi hou obliqui y he e would be no
seasons. The Sun would climb up o he same zeni h angle day a e day. Sun ises and sunse s will happen wi h a
ecu ence o T = 24h (Ea h’s o a ion pe iod) due Eas (dawn) and due Wes (dusk) yea ound.
Wi h non-ze o obliqui y e e y o hese magni udes change om da e o da e in a quan i y p esc ibed solely
by la i ude. Table1 lis s ime o se , la i ude φ, he sp ead o sun ise/sunse imes om summe o win e , and
he cosine o he sola zeni h angle a noon in win e θw and summe θs. Ins ead o he ba e angle θ, i s cosine is
a mo e sensi i e magni ude o unde s anding human beha io since insola ion is p opo ional o i . Figu e1
summa izes he sp ead o sun ise and sunse imes a ou ep esen a i e ci cles o la i ude helped by clocks wi h
24-H analog dial.
In Supplemen a y ma e ial (Sec ion S.2) he seasonal a ia ions a e ho oughly desc ibed.
No ice ha as pe DST egula ions, ime o se inc eases by one whole hou in sp ing, and se s back o he
alue lis ed in Table1 in au umn; he sp ead o sun ise appa en ly dec eases by one whole hou as measu ed local
ime, while he sp ead o sunse appa en ly inc eases by one whole hou .
Resul s
No malized seasonal di e ences o daily hy hms a e shown in Fig.2. As Supplemen a y Ma e ial seasonal daily
hy hms om which seasonal di e ences we e compu ed a e shown in Fig.S.3. The e, seasonal di e ences a e
usually ha d o isualize. Sleep/wake daily hy hm looks like a window unc ion showing he o e whelming
p e e ence o monophasic sleep —one con inued pe iod o sleep, ollowed by one con inued pe iod o wake pe
day— and a g ea deal o coo dina ion in he ansi ions, wi h he wake ied o sun ise and sleep de e mined by
homeos asis20. The only de ia ion om his beha io occu s in I aly and Spain; i is due o sies a, an a e noon,
sho ake o sleep. Labo daily hy hms a e no ably mo e complex.
Seasonal de ia ions in hi y daily hy hms a e shown in Fig.2. They a e a anged in 5 × 4 panels. On e e y
ow a ime use su ey is p esen ed; on e e y column a daily hy hm: sleep/wake in a week-day (g oups 1 and 2),
labo in a week-day (g oup 1) and hen he same o a week-end. Da ke lines e e o employees, ligh e lines
o non-employees. Sola epheme ides —sun ise, noon and sunse — a e no ed by do ed e ical lines and ange
om summe o win e alues.
Da ke ho izon al g ay bands highligh he egion whe e Welch’s - es would sus ain he null hypo hesis H0:
Rs(i) − Rw(i) = 0 a he s anda d le el o signi icance. Ligh e bands highligh he egion whe e 10−7 < p < α. As
Supplemen a y Ma e ial Fig.S.4 shows he co esponding alues p(i) o hese seasonal de ia ions, and Table2
epo s he occu ence o signi ican de ia ions p(i) < α in mo ning and a e noon hou s.
Likewise, Fig.3 (sleep/wake) and Fig.4 (labo ) show he no malized seasonal de ia ions o he s ochas ic a -
iables ob ained om each cycle. As Supplemen a y ma e ial Fig.S.5 (sleep/wake cycle) and Fig.S.6 (labo cycle)
Figu e 1. The seasonal cycle o ligh and da k depic ed in ou clocks wi h 24-H analog dial. Clocks a e
loca ed a ci cles o la i ude φ = 15°, 40°, 52°, 60°. E e y clock loca es mo ning hou s on he igh hal , om
0 (midnigh ) o 12 (noon); a e noon hou s (12–24), on he le hal . The equinoc ial nigh is loca ed on he
op hal , om 18 (sunse ) o 6 (sun ise) and he equinoc ial day ime, on he bo om hal . The ed ink displays
pe manen nigh , he yellow ink displays pe manen day ime, and he pink ink displays he egion whe e ligh
and da k al e na e seasonally. Poin z deno es summe sunse ; x, summe sun ise;Y, win e sunse ; w, win e
sun ise; and he numbe in wn anno a es hou s be o e win e sun ise. No ice ha w and z a e sepa a ed by
some 12h i espec i e o la i ude. Clock aces display mean sola ime and local ime a ime me idians. Time
o se —see Table1— mus be added o ind local ime alues o , al e na i ely, clock aces mus be u ned
coun e clockwise one deg ee pe e e y ou minu es o ime o se .
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show he seasonal sample cumula i e dis ibu ion unc ions om which seasonal di e ences we e compu ed; in
mos o he ci cums ances seasonal di e ences a e ha d o isualize.
Figu e3 displays one-hund ed seasonal de ia ions and Fig.4, i y. They a e a anged in 5 × 5 panels each
showing esul s om ou g oups (sleep/wake) and wo g oups (labo ). Ve ically, panels display he esul s o one
Figu e 2. No malized seasonal de ia ions
Δ= ⋅−KNRRs()/2
wsw ms
. Blueish inks display week-day
s a is ics (g oups 1 and 2). G eenish inks display week-end s a is ics (g oups 3 and 4). Da ke lines apply o
employees (g oups 1 and 3); ligh e lines o non-employees (g oups 2 and 4). The da ke ho izon al g ay band
highligh he egion whe e he Welch’s - es sus ains he null hypo hesis H0: Rs − Rw = 0 a he s anda d le el o
signi icance α = 5%. The ligh e ho izon al g ay bands highligh he egion 10−7 ≤ p < α. Fo ΔKw = 6 he p-
alue equals o 10−8.69. Ve ical lines show sola epheme ides (sun ise, noon and sunse ) in win e and summe
as measu ed in local ime. Da ke sun applies o summe .

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s ochas ic a iable: i s h ee columns display ime ma ks, las wo columns du a ions; along a ow panels display
he esul s o one ime use su ey. On e e y panel he ho izon al axis displays he a iable —ei he a local ime o
an elapsed ime— and he e ical axis displays he Kolmogo o -Smi no dis ance, see Eq. (S8).
As in Fig.2 blueish lines e e o week-day g oups; g eenish lines o week-end g oups; da ke lines e e o
employees; ligh e lines o non-employees. Finally, boxes loca e he i s , median and hi d qua ile o he dis ibu-
ions; and o ime-ma ks — h ee igh mos columns— he panel also displays sola epheme ides: sun ise, sunse
and noon in win e and summe ( e ical do ed lines).
Unlike in Fig.2, he di ec ion o de ia ions in Figs.3 and 4 is easy o add ess: posi i e excu sions (Ps > Pw)
indica e ha he summe dis ibu ion ad ances ela i e o he win e dis ibu ion: ea lie imes o ime-ma ks,
sho e du a ions o elapsed imes. Nega i e excu sions (Ps <Pw) indica e he opposi e. One single peak usually
indica es a shi in he mean o he dis ibu ions.
The da ke g ay band highligh s he egion whe e he null hypo hesis H0: Ps − Pw = 0 would sus ain a he
s anda d le el o signi icance i he dis ibu ion we e con inuous, which was ne e he case he e. The ligh e g ay
s ip highligh he egion whe e 10−7 < p < α s ill in he con inuous case.
Table3 lis s he occu ences o he ou possible ou comes o he one- ailed pe mu a ion es : Ps = Pw,
Ps ≠ Pw, Ps > Pw, and Ps < Pw. A sco e is ob ained a e assigning +1 o Ps > Pw, −1 o Ps < Pw and 0 o he wise. As
Supplemen a y ma e ial TableS.1 (sleep/wake) and TableS.2 (labo ) lis he esul s o he pe mu a ion es o
e e y o he 100 (sleep/wake) and 50 (labo ) analyses.
The occu ence o ou comes o he es on he a e age alues Es − Ew is no di e en om esul s in Table3
sa e o he ac ha inequali ies a e shi ed: Ps > Pw leads o Es < Ew and con e sely. As Supplemen a y ma e ial
TableS.3 (sleep/wake cycle) and TableS.4 (labo cycle) lis s he esul s o e e y o he analyses. P obabili y di e -
ences Ps(i) − Pw(i) — e ical di e ences in Fig.S.5— can be ansposed in o quan ile o “ho izon al” di e ences.
As Supplemen a y ma e ial and o he sake o comple eness TableS.5 (sleep/wake) and TableS.6 (labo ) lis
qua ile di e ences.
Discussion
Figu e2 highligh s he s abili y o he labo cycle in week-days —column 2— and week-ends —column 4—.
Seasonal de ia ions seldom climb up o 2 and he null hypo hesis H0: Rs(i) − Rw(i) = 0 is seldom ejec ed a he
s anda d le el o signi icance, see Table2. Labo cycle in a week-end (g oup 3) is sligh ly mo e p one o seasonal
al e a ions, al hough i mus be aken in o accoun ha week-end labo cycle di e s signi ican ly om week-day
labo cycle, see Fig.S.3 and ha sample sizes a e smalle in g oup 3 by a ac o anging om 2 o 8, see Table1.
In he same way Fig.4 displays modes seasonal de ia ions in a iables ela ed o he labo cycle, which do
no b eak he null hypo hesis H0: Ps − Pw = 0 (see Table3) a he s anda d le el o signi icance as deduced om a
pe mu a ion es o size M = 107. Also i is seldom he case ha he null hypo hesis H0: Es − Ew = 0 (see TableS.4)
is ejec ed. The e o e labo cycle is equally dis ibu ed h ough seasons in en i onmen s unde DST egula ions.
The s abili y o he labo cycle is p obably he main silen goal and he main ou come o summe ime egu-
la ions. Indeed ime egula ions ha e always been aimed owa ds social li e, o which wo king hou s is one o i s
mos signi ican examples.
I is a ques ion o unde s and he seasonal de ia ions in he labo cycle o coun ies wi h he same deg ee
o social de elopmen , la i ude and no exposed o seasonal clock changing. The ob ious choices would be
ΔKw b eakdown
G oup 1 G oup 2 G oup 3 G oup 4
All g oups
Mon-F i Mon-F i Sa -Sun Sa -Sun
employees non-employees employees non-employees
p < αam/pm am/pm am/pm am/pm o al
Sleep/wake
G ea B i ain 17/20 16/16 4/4 31/3 111
F ance 14/21 13/11 31/24 7/21 142
I aly 16/17 7/26 11/19 43/32 171
Spain 6/44 13/48 0/26 18/39 194
Uni ed S a es 21/44 12/34 7/15 45/24 202
Labo
G ea B i ain 13/0 22/2 37
F ance 0/3 48/16 67
I aly 31/4 6/1 42
Spain 10/9 2/13 34
Uni ed S a es 4/7 1/4 16
Table 2. B eakdown o s a is ically signi ican de ia ions in ΔKw a e a Welch’s - es o unequal a iance was
pe o med. Signi icance is aken a he s anda d le el α = 5%. E e y g oup o esponden s spli s occu ences
in mo ning/a e noon (am/pm) indexes. The emaining indexes up o a o al o 72/72 sus ained he null
hypo hesis H0: Rs(i) − Rw(i) = 0. The igh -mos column lis he whole numbe o excu sions p < α, om a o al
o 4N0 = 576 (sleep/wake) and 2N0 = 288 (labo ) analysis. In Spain am/pm di ide was se a 1 pm local ime, see
ime o se in Table1.
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he Republic o Ko ea and Japan. I espec i e o ha he so es conclusion o he p eceding esul s is ha he
labo cycle ole a es a seasonal shi o i s phase equal o one hou in he di ec ion p esc ibed by he egula ions
(ad ance in sp ing, delay in au umn). I is ou o he scope o his manusc ip o co ela e his p ac ice wi h eco-
nomic ou comes like he G oss Domes ic P oduc .
On i s way he sleep/wake cycle is mo e signi ican ly al e ed and i does so in di e en ways. Figu e2 —col-
umns 1 and 3— su ices o unde s and his idea: ΔKw climbs up o 4 o 6, some ime owa ds he posi i e side,
some ime owa ds he nega i e side, and excu sions p(i) < α a e mo e equen , see Table2. I is also wo hy o
men ion ha excu sions weigh on he a e noon, which makes sense aking in o accoun he di ec ion o DST
egula ions, which pushes o s abilizing mo ning imes only. Finally Table3 lis s occu ences o s ochas ic dom-
inance in he sleep/wake cycle and in he labo cycle, and p o ides a sco e: di e ences among bo h cycles a e sel
e iden , wi h he sleep/wake cycle hea ily exhibi ing s ochas ic dominance and labo cycle eluc an o ha .
Figu e 3. No malized seasonal de ia ions
Δ= ⋅−KNPP()
ks hsw
o he s ochas ic a iables ela ed o he
sleep/wake cycle. Along a ow a ime use su ey is shown, along a column one a iable is shown. Blueish lines
show week-day esponden s. G eenish lines show week-end esponden s. Da ke lines show employees; ligh e
lines, non-employees. Boxes loca e i s , second and hi d qua iles o he dis ibu ions. Fo sided es s on
con inuous samples, which is ne e he case he e, he da ke ho izon al g ay band highligh s he egion whe e
p < α; he ligh e band, he egion 10−7 < p < α; and o ΔKks = 6 he p- alue equals 10−15.7. In he le mos h ee
columns e ical do ed lines loca e sola epheme ides —sun ise, noon, sunse — in win e and summe .
Da kes sun applies o summe .
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Vi ually e e y sleep/wake cycle in Fig.2 is signaling a la ge excu sion by he ime o summe sunse , when he
pe manen nigh begins. Since, by hen, he daily hy hm is dec easing as mo e people is coming o bed, and he
excu sion goes owa ds he posi i e side, a delay in Rs is obse ed o Rs ades ou la e as a esul o la e sunse s.
In he mo ning, smalle bu s ill posi i e excu sions a e obse ed in some g oups, no ably in he week-end.
They occu in he ange when ligh and da k seasonally al e na e. Since, by hen, he daily hy hm is up ising, as
mo e people is ge ing up, he posi i e excu sion is now signaling an ad ance in Rs, which soa s ea lie .
Figu e3 shows hese esul s in he o m o p obabili y dis ibu ions. He e sleep onse has gene ally a nega-
i e excu sion, which leads o s ochas ic dominance Ps < Pw o Ps delays, while sleep o se display he opposi e
dominance Ps > Pw, o Ps ad ances. Table3 p o ides a summa y o his obse a ion: sleep o se ge s a posi i e
(ad anced) sco e; sleep onse , a nega i e nega i e (delayed) sco e.
As o du a ions a e conce ned, sleep ime and noc u nal sleep (onse o o se ime) mo e han o en dec eases
as a esul o ela i ely delayed sleep onse and sligh ly ad anced sleep o se . Bo h elapsed imes ge posi i e
(dec ease) sco es in Table3. Likewise he cen e o g a i y ends o delay only in a ew cases.
No ma e how s a is ically signi ican any o hese de ia ions can be, hey ha e li le signi icance in a e age
alues as seen in TableS.3: Es − Ew lie in he ange o ew minu es, much smalle han he size o clock changing
and he sp ead o sun ise ime and sunse ime. In he same way, qua ile di e ences a e mos equen ly equal o
less han one ime slo o en minu es, see TableS.5.
Figu e 4. Same as Fig.3 bu o he s ochas ic a iables ela ed o he labo cycle.
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No wi hs anding all his he ac ha sleep o se and sleep onse seasonal de ia ions a e opposi e mus be u -
he discussed in ela ion o he impac o DST. I sleep onse and sleep o se had go he same ype o s ochas ic
dominance —be ha an ad ance o a delay— hen i could be a gued ha he size o he seasonal change is oo
small —i bo h ended o ad anced, ampli ying he ad ance o clock ime— o oo la ge —i bo h ended o delay,
igh ing agains he ad ance o clock ime. Ei he way socie ies would be exp essing a global p e e ence o push-
ing o pulling he sleep/wake cycle. Wi h s ochas ic dominance leaning in opposi e di ec ions such a p e e ence
can no be iden i ied and DST can no be easily challenged. Indeed hey a e showing ha sun ise and sunse s ill
impac human beha iou , e en a e ha ing al e ed clocks, and ha he sleep/wake cycle is no misaligned by he
egula ions.
Since DST ad ances clocks only in sp ing, delays hem only in au umn, hus pushing o s abilizing sun ise
imes as measu ed local ime, mo ning esul s mus be u he discussed. As o he labo cycle is conce ned he
poin o no e is ha DST does no p e en employe s and employees om delaying hei iming a e he sp ing
ansi ion o om ad ancing hei iming a e he au umn ansi ion. Howe e esul s show ha his is seldom
he case. Also i is seldom he case ha hey need a u he ad ance in sp ing, o a u he delay in win e . In iew
o ha all, da a show seasonal egula ions o ime ope a e imely, easing he p e e ence o ea lie imes in summe
and he p e e ence o la e imes in win e . I also does so wi h a high deg ee o coo dina ion.
As o he sleep/wake cycle is conce ned he g oup mos p one o ee p e e ences —non-employees in a
week-end, g oup 4— exhibi s he la ges shi o sleep o se in summe wi h Ps > Pw in he i e su eys (see
Tables3 and S.1 in Supplemen a y Ma e ial). His o ically win e ime and win e ac i i y is aken as he no mal,
since ansi ions we e i s se on sp ing. Upon his iew, esul s sugges ha i ually no esponden in he su -
eys wan s o delay summe mo ning du ies, whe eas a numbe o people pushes o an ad ance in summe , e en
hough local ime was al eady ad anced by ime egula ions. This is compa ible wi h he spon aneous p e e ence
o pe manen summe ime in polls30, since he p ima y ou come o win e pe manen ime would be a delay in
summe human ac i i y i no hing else changes.
Wi h only i e su eys, he impac o la i ude in seasonal beha io can only be ske ched wi h some cau ion.
The mos appa en esul is epo ed in Table2: he occu ence o signi ican de ia ions (p(i) < α) in he sleep/
wake cycle inc eases wi h dec easing la i ude. In Figs.2 and 3 his is no ed by he s abili y o sleep/wake cycles in
G ea B i ain o F ance compa ed o hose elsewhe e, e en hough he sp ead o sun ise and sunse imes is la ge
he highe he la i ude. These esul s a e in acco dance wi h he impac o la i ude in pe iods o low calling ac i i y
in mobile phone da a o a la ge numbe (N ~ 106) o indi iduals o sho ange o la i udes18 (φ = {37°, 40°, 42.5°},
see Fig.2 in he Re e ence). The e he lowes la i ude showed he s onges seasonal a ia ions in he pe iods.
Coun s
G oup 1 G oup 2 G oup 3 G oup 4
All G oupsMon-F i employees Mon-F i non-employees Sa -Sun non-employees Sa -Sun employees
Ps↔PwSco e Ps↔PwSco e Ps↔PwSco e Ps↔PwSco e Ps↔PwSco e
< = ≠ > < = ≠ > < = ≠ > < = ≠ > < = ≠ >
Sleep o se 2 2 0 1 −0.2 1 2 1 1 0.0 0 3 0 2 +0.4 0 0 0 5 +1.0 3 7 1 9 +0.3
Cen e o
g a i y 3 2 0 0 −0.6 3 2 0 0 −0.60401+0.2 0 4 0 1 +0.2 6 12 0 2 −0.2
Sleep onse 4 1 0 0 −0.8 4 1 0 0 −0.82300−0.4 4 1 0 0 −0.5 14 6 0 0 −0.7
Onse o
o se 0 1 0 4 +0.8 1 0 1 3 +0.40104+0.8 0 0 0 5 +1.0 1 2 1 16 +0.8
Sleep ime 0 2 0 3 +0.6 1 2 0 2 +0.20302+0.4 0 0 0 5 +1.0 1 7 0 12 +0.6
All combined 9 8 0 8 0.0 10 7 2 6 −0.2 2 14 0 9 +0.3 4 5 0 16 +0.5 25 34 2 39 +0.1
Labo onse 0 4 0 1 +0.2 0302+0.4 0 7 0 3 +0.3
Cen e o
g a i y 0 5 0 0 0.0 0 5 0 0 0.0 0 10 0 0 0.0
Labo o se 0 5 0 0 0.0 0 5 0 0 0.0 0 10 0 0 0.0
Onse o
o se 0 50 00.0 2300−0.4 2 8 0 0 −0.2
Labo ime 0 50 00.0 2300−0.4 2 8 0 0 −0.2
All combined 0 24 0 1 0.0 4 19 0 2 −0.1 4 43 0 3 0.0
Su ey Sleep/Wake Labo
< = ≠ > Sco e < = ≠ > Sco e
G ea B i ain 3 12 0 5 +0.1 2701−0.1
F ance 5 5 2 8 +0.1 2701−0.1
I aly 5 7 0 8 +0.1 0 901+0.1
Spain 5 6 0 9 +0.2 0 10 0 0 0.0
Uni ed S a es 7 4 0 9 +0.1 0 10 0 0 0.0
All combined 25 34 2 39 +0.1 4 43 0 3 0.0
Table 3. Occu ences o hypo heses Ps > Pw, Ps ≠ Pw, Ps = Pw and Ps < Pw a e a pe mu a ion es o size M = 107
in he seasonal indexes was pe o med. De ailed esul s a e shown as Supplemen a y ma e ial in TablesS.1 and
S.2. The sco e is ob ained a e assigning +1, 0, 0, −1 o each ou come and scaling by he whole numbe o es s.