Publisher Correction: Seasonal synchronization of sleep timing in industrial and pre-industrial societies

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Sleeping and being awake are probably the most basic human activities entrained to Earth's rotation period = T 24 h -the definition of hour-and the light/dark (LD) cycle. A sleep-independent circadian mechanism 1 links wakefulness to the photoperiod (light) and sleep to the scotoperiod (dark). A sleep-dependent homeostatic mechanism 1 limits our propensity to being awake to roughly = T 2 /3 16 h of continued wakefulness. At the Equator the shares of light and dark are = T /2 12 h, Earth's obliquity ε = .°23 5 alters them with latitude and seasons. The shares of the LD cycle and the shares of the sleep/wake cycle are then different and wakefulness must occur during the scotoperiod or sleep must occur during the photoperiod.
It is a wide understood that artificial light and industrialization has reshaped the human sleep/wake cycle 2 by altering the way humans receipt light during the scotoperiod. To which extend is still a matter of discussion. Much of the contemporary concern is focused in one issue: sleep deprivation caused by artificial light 3 .
In the past few years several studies have addressed the sleep timing in societies with different degrees of industrialization, trying to find clues which help understanding the way modern artificial light has altered sleep timing.
Three of these studies analyzed hunter-gatherer, horticulturalist, pre-industrial societies 4-6 and reported similar or shorter sleep durations compared with industrial societies. In contrast another group of four studies reported data on homogeneous pre-industrial communities with and without access to electricity 7-10 and reported later sleep onset times and shorter sleep duration with increasing urbanization. This manuscript will not address the impact of artificial light on sleep duration. Instead it will discuss the sources of synchronization in sleep timing, which quantities related to the sleep/wake cycle remain stationary and which not. The study will analyze a rather eclectic collection of reports that covers industrialized countries -data coming from eight national time use surveys-and pre-industrial societies -data coming from the seven previously cited references. For so doing sleep timing and the LD cycle will be contrasted. The analysis will address the seasonal characterization of sleep timing, the dependence of sleep timing on latitude and the role of Daylight Saving Time (DST) in synchronizing sleep timing.
www.nature.com/scientificreports www.nature.com/scientificreports/ The dependent variable, outcome or response in this analysis will be human sleep timing. It will be parameterized by the distance to solar noon, which can be evaluated from local time measurements if longitude and local time zone are known: where τ i is a local time (relative to midnight), Δ is the local time zone offset relative to UTC (Coordinated Universal Time) and λ is local longitude relative to UTC prime meridian and =°C 360 is one cycle. The time offset δ is the time distance from solar noon to midday. The LD cycle will be characterized by the shortest photoperiod, which is that of the winter solstice. In this work "winter" or "winter solstice" will always be used in absolute form: it can indistinctly mean the Northern Solstice (June) or the Southern solstice (December) depending on the hemisphere. Calendar references will not be used.
The shortest photoperiod is the time distance from winter sunrise (WSR) to winter sunset (WSS): the time distance from the latest sunrise to the earliest sunset. It is a proxy for absolute latitude φ | |, the angular distance to Equator, irrespective of the hemisphere, to which is related by 11 : 2 cos sin sin sin cos cos (2) w c 1 where = − .°z 0 83 c is a critical solar altitude relative to the horizon, which defines sunrise and sunset. Winter is non-zero below polar circles; above polar circles D w is just set to zero (permanent scotoperiod).
The shortest photoperiod is straightforwardly related to winter sunrise and winter sunset times by: where time is given as a distance to solar noon. This simple relation suffices to understand the role of the shortest photoperiod as a predictor or independent variable in the forthcoming analysis. Except for minor corrections due to finite angular size of the solar disk and to atmospheric refraction, the shortest scotoperiod equals the shortest photoperiod. Summer sunrise (SSR) and sunset (SSS) times are then given by ±D w /2, if time is given as a distance to midnight. Therefore the limiting boundaries of the LD cycle are characterized by a unique gradient β = = − 1/2 30 min h 1 if D w is the predictor. The gradient reads thirty minute in advance/delay of winter/summer sunrise/sunset per hour change in D w . Events that delay with increasing distance to the Equator -winter sunrise or summer sunset-take the negative value β = − m . Events that advance with increasing distance to the Equator -winter sunset and summer sunrise-take the positive value β = + m . Unlike boundaries, the midpoints of the LD cycle are characterized by stationary values ( = m 0). Solar noon happens at = t 0, irrespective of latitude. Yearly averaged values of sunrise times and of sunset times yield values close to  6 h, irrespective of latitude. Table 1 lists the societies whose sleep timing will be analyzed in this work. It also lists geographical data relevant for the analysis and the sample size of each study. Figure 1 displays the societies on Earth's surface.

Data sets.
Societies are grouped in three categories: industrial, pre-industrial without access to electricity and pre-industrial with access to electricity. Incidentally, all industrial societies lie in the Northern Hemisphere. All pre-industrial societies lie in the Southern Hemisphere, except Fondwa (FON). Table 2 lists sleep timing in industrial and pre-industrial societies in the winter season. Table 3 lists summer values.
Sleep timing in industrial societies was computed from time use surveys. They are a fundamental tool for understanding social behavior and try to ascertain when people do basic activities like sleeping, eating or working in a standard day. This work will study results from eight national time use surveys. Six are located in Europe: Denmark 12 , Ireland 13 , United Kingdom 14 , France 15 , Italy 16 and Spain 17 . Two are located in America: Canada 18 and United States 19 . Countries are labeled according to iso-3166 alpha-3 codes.
A time survey usually takes 144 time-slots in a day, each representing ten minutes. Respondents are asked to indicate their main activity in every time-slot. The daily rhythm of an activity is the number of respondents which reported doing an activity at a given time-slot scaled by the number of respondents (see ref. 20 for a detailed description). Therefore a daily rhythm averages the myriad of individual decisions that shapes a society.
The daily rhythm of the sleep/wake activity looks like a smoothed rectangular function with the vast majority of respondents awaken by noon and sleeping by midnight. Therefore it shows the preference of contemporary societies for monophasic sleep, only slightly modified in Spain and Italy by the siesta (nap), a short sleep at mid afternoon.
Two transitions -one in the morning, one at night (see Fig. 1 in ref. 20 )-from the sleep to wake state and vice-versa are observed. A threshold located at half the range of the daily rhythm -which is close to 50%-will help identifying sleep offset and sleep onset. They can be viewed as an average of individual wake up times and bedtimes. The average of sleep onset and sleep offset will define the midpoint of sleep (or wake).
www.nature.com/scientificreports www.nature.com/scientificreports/ Number of respondents in a time survey is usually in the range of thousands and differ in age, sex and social issues. Here sleep timing was computed for laborers in a weekday (Monday to Friday) and non-working population age 25 year in a week day. Tables 2 and 3 lists the average value of these quantities.
Time use surveys usually collect data during at least one calendar year. Only the Danish and Irish surveys did not do so. Yet, there are not significant differences for the winter (here meaning autumn and winter) and summer (here meaning spring and summer) season. Modern societies entrain to clock time. Hence seasonal variations in extratropical, industrial societies are mostly induced by Daylight Saving Time (DST) onset and offset. It must be noted that DST rules do not prevent people from further advancing their timing after DST onset, or from delaying it, which would fight against DST onset. Industrial societies do not do either of them. They keep synced to clock timing year round. That way DST is the main source of seasonality in these societies.
Previous works on pre-industrial societies include Knutson 4 which reported sleep patterns in fifty-eight persons living in the community of Fondwa in Haiti. They have no access to electricity. The study was conducted in January-February (winter) of 2003 using wrist actimetry. Tables 2 and 3 collect data contained in the abstract of the manuscript, which also reports a standard deviation of 40 min.
Yetish et al. 5 reported the sleep timing in three hunter-gatherer, horticulturalist societies: the San (SAN) in Namibia, the Tsimané (TSI) in Bolivia and the Hadza (HAD) in Tanzania. None of them has access to electricity. Tables 2 and 3 collect sleep timing listed in Table S2 of the reference, which includes winter and summer data for the San and Tsimané. Authors reported standard deviations range from 0.5 h to 1 h.  Table 1. Overview of the relevant geographical information. Geographical data in industrial countries are population-weighted median values extracted from the database of cities with a population larger than 1000 inhabitants at http://www.geonames.org; labels are ISO 3166-1 alpha-3 codes. The shortest photoperiod is a function of φ | | and Earth's obliquity. Winter sunrise WSR time and winter sunset WSS time are given as a distance to solar noon in decimal hours. The variation of sunrise times is the difference between summer rise time and winter sunrise time. Time offset is the difference between solar noon and local time midday (rounded to one minute). In summer one hour must be added in industrial societies to account for DST rules. Univariate analysis sample average, sample range and the variability expressed as twice the sample standard deviation are shown for all three categories combined. See Fig. 1  www.nature.com/scientificreports www.nature.com/scientificreports/ Samson et al. 6 studied sleep timing in a small-scale agricultural society named Mandena (MAN) in Madagascar. The study was conducted from July to August (winter). Tables 2 and 3 collect data reported in Table 1 of the cited reference. Characteristically this society exhibited fragmented sleep at night but reported standard deviation amounts to 3.5 h for sleep onset and only 1 h for sleep offset.
Moreno et al. 7 analyzed sleep timing from rubber tappers in the Chico Mendes Amazon Extractive Reserve (Acre, Brazil). The study was conducted from September to November (spring) on a community without access to electricity (CMN) and a community with access to electricity (CME). Tables 2 and 3 collect workday values of sleep timing obtained from Fig. 1 of the cited reference which reports standard errors of mean values in the range of 10 min.
De la Iglesia et al. 8 analyzed sleep timing in two communities of the Toba/Qom -one with access to electricity (TQE), the other one without access (TQN)-in summer and winter. They live in the province of Formosa, the most Equatorial in Argentina. Tables 2 and 3 collect rise times and bedtimes from Table 1 of the reference which reports standard error of the mean in the range of 10 min.
Beale et al. 9 described sleep timing in two neighboring communities in Mozambique: Milange (MIL, urban) and Tengua (TEN, rural). The study was conducted from April to June (autumn-winter). Tables 2 and 3 collect  sleep timing from Table 1 of the cited reference, which reports standard errors of the mean also in the range of 10 min.
Finally, Pilz et al. 10 Table 2 collects sleep timing presented in Table S2 (winter, actimetry data) of the cited reference, which reports standard deviations in the range from 30 min to 120 min. The seven locations have been grouped according to: locations with no access to electricity or which gained access only recently (two, Bombas and Areia Branca, label QBN); locations which gained access to Figure 1. Locations of the societies whose sleep timing is analyzed in this manuscript, see Table 1 to decode labels. Rounded symbols display industrial societies; triangles and crosses, pre-industrial societies. Solid symbols display societies with access to electricity; open symbols display societies without access to electricity; crosses display pairs with and without access to electricity. Circles of latitude are the Equator, the Tropics (at φ ε = ± ) and the Polar Circles (at φ ε = ±|°− | 90 ). Continental and lake polygons were taken from http:// www.naturalearthdata.com/. Supplementary Material contains a version of this picture with both Hemispheres lying on a unique hemisphere.
Only two studies 5,8 reported data in winter and in summer. Four of the five remaining studies report winter-autumn data, and only Moreno et al. 7 reported data in spring-summer only. Except for the Quilombolas 10 -who live at 30° where the variation of sunrise times climbs close to two hours (see Table 1)-data will be used indistinctly in winter and summer analysis.

Results
This section will put forward the seasonal differences in sleep timing and will contrast sleep timing against the natural gradients = m 0 and β = ± m through three different methods: first a visualization of data (Fig. 2); then multiple binning analyses (Fig. 3); and finally univariate analyses (which are included in Tables 2 and 3) and multiple bivariate analyses (Table 4).

Offset
Midpoint Onset

Univariate analysis for all three categories combined (N = 22)
Sample average  Table 2. Sleep timing in industrial and in pre-industrial societies with and without electricity. Times are expressed in decimal hours as a distance to solar noon t i or a distance to winter sunrise (WSR) In the first case, the time offset (see Table 1) and T/ = 2 12 h must be added to obtain local times. Winter solar altitude WSA at sleep offset is also shown. Finally sleep onset also lists the distance to next sleep offset. Univariate analysis for all three categories combined is also listed. It includes samples average, sample range and sample variability defined as twice the sample standard deviation. Variabilities smaller than 70 are highlighted in bold. Starred societies mark studies conducted in the summer/spring season.
www.nature.com/scientificreports www.nature.com/scientificreports/ photoperiod in the vertical axis. This setting is geographical: it mimics Fig. S1 in Supplementary Material. The vertical axis is absolute latitude but displays straight values of D w (right axis); the horizontal axis is longitudedistance to noon, see Equation (1)-. That way the curvilinear line of shadow becomes straight (see Equation (3)). However, notice that geometrically the predictor = x D w is displayed on the vertical axis, while responses = y t t t { ; ; } 1 2 3 are displayed on the horizontal axis. Therefore, gradients will be described relative to the upright ( = m 0).
Each panel of Fig. 2 must be understood as a three layer picture. The deepest layer shows the LD cycle: the lighter background is the photoperiod; the darker background is the scotoperiod. Dotted lines display solar altitude starting at −18° (outer most) in steps of 6°.
The middle layer is human sleep timing. Solid symbols refer to people with access to electricity; open symbols, to people without access to electricity. Circles display industrial values; triangles pre-industrial societies; squares in top panel refers to data obtained in the summer season; squares in bottom panel refers to data obtained in the winter season.
Horizontal error lines in industrial data span from sleep timing for laborers in a week day (earliest bound) to sleep timing for non-laborers in a week day aged 25 years or more (latest bound). Error lines for sleep onset are too short to be displayed.
The aboveboard layer shows straight lines with gradients β = − m (dash-dot), = m 0 (solid) and β = + m (dash-dot-dot). They represent the natural gradients associated to the boundaries of the LD cycle ( β = ± m ) and to noon ( = m 0). Adjacent straight lines in Fig. 2 are always separated by one whole hour. They bin data points within the interval of one hour. Bin position is uniquely determined by the center of the bin. Bins can move along the horizontal axis and the number of counts inside the bin can be recorded.  Table 3. Sleep timing in industrial and in pre-industrial societies with and without electricity during the summer season. Times are expressed in decimal hours as a distance to solar noon t i or a distance to winter sunrise (WSR) In the first case, the time offset (see Table 1) and T/ = 2 12 h must be added to obtain local times, one more hour must be added to industrial values due to DST. Summer solar altitude SSA at sleep offset and sleep onset distance to next sleep offset are also listed. Univariate analysis for all three categories combined is also listed. It includes samples average, sample range and sample variability defined as twice the sample standard deviation. Variabilities smaller than 70 min are highlighted in bold. Starred societies mark studies conducted in the autumn/winter season.
www.nature.com/scientificreports www.nature.com/scientificreports/ This technique can be used to put forward which gradient best collects data. Results are shown in Fig. 3. In winter (top panels) gradient β = − m gets the narrowest and highest peak, positioning sleep timing one hour before sunrise (offset), seven hours after sunrise (midpoint) and eight hours before sunrise (onset). Gradient = m 0 displays a high peak for sleep offset but it is wider than peak for β = − m . Gradient β = + m poorly interacts with data.
In summer (bottom panels) it is = m 0 which exhibits the best coherence. Sleep offset is located six hours before noon, the midpoint is two hours after noon and sleep onset occurs nine hours after noon. Gradients β = − m and β = + m display lower and smeared peaks. Nonetheless, sleep onset is located some two hours after sunset and sleep offset is locate around sunrise.
Graphical information shown in Fig. 3 can also be described by the univariate analysis of sleep timing listed in Table 2 (winter) and Table 3 (summer). The point to note is the variability. In winter, variability decreases by if sleep timing is measured relative to sunrise β − t D i w , compared to measurements relative to noon t i . In summer, it is just the opposite. Values shown in bold highlight this change over. www.nature.com/scientificreports www.nature.com/scientificreports/ Finally Table 4 shows bivariate analysis -multilinear regression analysis-in which D w is the predictor and sleep timing is the response. It should be stressed that no regression lines are displayed on Fig. 2 which, for the sake of simplicity, only shows lines whose gradient is related to the LD cycle.
Results in Table 4 are shown line by line. They include: (1) sample gradient m s and (2) its confidence interval CI both measured in units of β = − 30 min h 1 , except when the response is solar altitude, in which case they are measured in degrees per hour, the parentheses show half the amplitude of the confidence intervals; (3) the probabilistic value (p-value); (4) the coefficient of determination; and (5) possible outliers -experimental data whose confidence residual excludes zero. Significance is always taken at the level α = 5%. Probabilistic values smaller than this level are highlighted in bold along with the corresponding sample correlation coefficient. In these cases the null hypothesis "response does not depend on the predictor" is rejected. Gradients and confidence intervals for the regression relative to winter sunrise are not displayed: they can be obtained just by adding 1 to numerical values shown for the regression relative to noon.
For the winter season sleep timing gets a gradient close to β: and probabilistic values are smaller that α. Therefore the null hypothesis "sleep timing -offset, midpoint and onset-distance to noon does not depend on the shortest photoperiod" is rejected in winter. That means sleep timing depends on the predictor. Taking into account that the range of the predictor is 300 min (see Table 1), the predicted lag in the phase of the sleep/wake cycle from the Equator to φ | | =°55 amounts to × Δ ∼ m D 120 min s w or two hours. However, if sleep timing is measured relative to winter sunrise then the probabilistic values are larger than the significance level. Therefore the null hypothesis "sleep timing -offset, midpoint, and onset-distance to winter sunrise does not depend on the shortest photoperiod" sustains at the significance level.
Also interestingly, winter solar altitude at sleep offset sustains the null hypothesis ( = . p 0 73), which means winter solar altitude at sleep offset is stationary with the shortest photoperiod. The average value ∼ −°z 9 w (see Table 2) is located in the middle of the winter nautical twilight.
Still in winter, sleep onset to sleep offset − − t t T p 0 38 larger than the significance level. Therefore the null hypothesis "sleep onset to sleep offset does not depend on the shortest photoperiod" sustains at the significance level. This result comes from the fact that sleep offset and sleep onset follow similar trends: the difference offsets the trend. www.nature.com/scientificreports www.nature.com/scientificreports/ As far as the summer season is concerned the conclusions are again reversed: the null hypothesis "sleep timing distance to noon does not depend on the shortest photoperiod" sustains at the significance level with probabilistic values = . .

Discussion
The two process model of sleep 1,21,22 describes the sleep/wake cycle with three gold standards: (1) the circadian regulation of sleep (process C) creates a photoreceptive propensity for wakefulness during the day; therefore people tend to abhor waking up before sunrise; (2) it also creates a scotoreceptive propensity for sleep at night; hence people tend to abhor going to bed before sunset. Likewise, (3) the homeostatic regulation of sleep (process S) creates a propensity for sleep with increasing duration of wakefulness, which generally saturates (and triggers sleep) when duration is close to = T 2 /3 16 h. All three standards meet in Fig. 2 within the range of observed latitudes.
In winter (see top panel) the first process photoreceptively aligns sleep offset to sunrise -the ancient time reference-, instead of noon -the modern time reference-. Bivariate analysis (see Table 4) reports stationary values of winter solar altitude at winter sleep offset, and stationary values of sleep offset distance to winter sunrise. They are a supporting evidence for the photoreceptive regulation of winter sleep offset along a wide range of latitudes. Below ∼ D 7 h w (or above φ | | ∼°55 ) winter sunrise is so delayed that people may wake up long before it, induced by process S. Evidences based in the "sleep and other personal care" cycle suggest 20 this cross-over.
A scotoreceptive (photoreceptive) circadian (C) regulation of sleep onset in Fig. 2 (top panel) can only be dictated by the gradient β = + m , shown by dash-dot-dotted lines in the figure, whose distance to winter sunset is stationary. This gradient poorly interact with data (see Fig. 3 top, right). However pre-industrial societies without electricity (open triangles in Fig. 2) can be binned inside a one-hour width bin delayed δ = .
t 3 5 h s from winter sunset. In this category only Mandena sleep onset is not binned as a result of their preference for segmented sleep. Toba/Qom, Milange/Tengua and Chico Mendes locations, which pair societies with and without access to electricity find the member without electricity on the near side of the photoreceptive bin, and the member with electricity on the far side of the bin. The Quilombola location without electricity meets the far side of the bin but those with electricity lie well outside the bin.
A homeostatic regulation (S) of sleep onset can only be dictated by the synchronizer of sleep offset ( β = − m , dash-dot lines in Fig. 2). Sleep onset in industrial societies can be homeostaticly binned with center at δ = .
T 8 3 h  Table 4. Multiple linear regression analyses for sleep timing in industrial and in pre-industrial societies.
Predictor is always the shortest photoperiod D w (see Table 1). Responses are listed in Table 2 (winter) and Table 3 (summer). Parentheses display half the amplitude of the confidence interval at the confidence level α − = 1 95%. Gradient and confidence interval are given in units of β = − 30 min h 1 , except starred values (WSA) which display units of degrees per hour. Gradients and confidence intervals for distance to WSR can be obtained adding 1 to numerical values listed for distance to noon. Probabilistic values smaller than the signficance level are highlighted in bold along with r 2 . Possible outliers are data whose confidence interval of residual at the significance level excluded zero. Latitude runs from 0° to 55° and the predictor, from 12 h to 7 h. Therefore regressions predict a change in the response (sleep timing to noon) × Δ ∼ m D 120 min www.nature.com/scientificreports www.nature.com/scientificreports/ to next sleep offset or 15.7 h from previous sleep offset. This behavior differs from the synchronization of working activity, whose start times (morning) syncs to the photoreceptive ( β = − m ) mechanism but whose end times (evening) again happens to be regulated by a photoreceptive mechanism, which now is β = + m 20 .
As observed in Fig. 2  . Interestingly pre-industrial sleep onset can be indistinctly binned by both mechanisms, perhaps characterizing homeostaticly and photoreceptively natural sleep onset in winter. However at the latitude of Spain and United States the homeostatic process is delayed by 2 h; at the latitude of France it makes 3 h, and at the latitude of the British Isles makes 4 h. The rate of increase equals the rate of decrease of the shortest photoperiod.
Ancient sleep onset in Europe may have been located anywhere between these two mechanisms. The lack of efficient, cheap artificial light, the temperature and the intense physical labor would have favored the circadian, photoreceptive mechanism. However, still in that case, the photoreceptive sleep onset comes only some 11 h after sunrise in Britain and only some 13 h after sunrise in Spain. In contrast, pre-industrial societies sustain at least 14 h of continued wake (see sleep onset to sleep offset in Table 2). The low value of continued wake would have played against the photoreceptive mechanism if the homeostatic process played also a role, as suggested by pre-industrial sleep timing. Very understandably, earlier sleep onset -somewhat bound to winter sunsetshould have led to segmented sleep 23,24 . Interestingly enough present day dinner times in Europe show synchronization with winter sunset times 20 and are placed within the photoreceptive strip shown in Fig. 2: some three hours after winter sunset.
There are only seven pre-industrial sleep timing available in the summer season (see triangles in Fig. 2 bottom panel or unstarred societies in Table 3). Only four of them (the Tsimané, the San and the two Toba/Qom) allow for a comparison with winter sleep timing. Two of them (the Tsimané and the San) live at φ | | =°15 where the seasonal variation of sunrise times amounts to 50 min or 0.88 h (see Table 1). Yet they exhibit markedly different behavior. The Tsimané do track solar variations: in summer they advance sleep offset and delay sleep onset by quantities smaller that 50 min. The San delay sleep timing, up to 70 min (sleep onset). This may be related to the impact of other quantities like temperature in a desertic environment 5 .
The Toba/Qom live at the Tropic where the seasonal variation of sunrise times exceeds one hour (see Table 1). Toba/Qom advance sleep offset by one hour in summer, irrespective of access/no access to electricity. Yet they wake up after sunrise (see Fig. 2 and Table 3). Sleep onset does not change (without electricity) or delays by half an hour (with electricity).
Industrial sleep timing is advanced by one hour induced by DST rules. The size of the change is similar to those discussed for pre-industrial sleep timing, but unlike them it is characteristically a change of phase: it equally advances sleep offset and sleep onset. It also should be mentioned that the variation of sunrise times amounts to 4 h on average.
With all that in mind, discussing the role of the photoreceptive circadian mechanism in summer sleep timing is complicated. Sleep onset in pre-industrial values lie in a scotoreceptive bin located δ = .
t 2 5 h s after summer sunset. It is one hour earlier than the scotoreceptive bin observed in winter. Industrial sleep timing increasingly advance relative to this bin with increasing latitude. This may suggest that the photoreceptive circadian process is less efficient than the homeostatic process in regulating sleep timing through seasons. Notice that the photoreceptive mechanism is impacted by the seasonal variations of the LD cycle while the homeostatic mechanism is non-seasonal. Indeed, sleep onset to sleep offset is stationary with D w (or φ | |) both in summer and in winter (see Table 4).
Winter regulation of sleep timing through the photoreceptive and homeostatic mechanisms creates a lag in the phase of the sleep/wake cycle which amounts to 120 min at 55°. This lag is not intended to mean necessarily a circadian misalignment. The question is: can it survive to the opposite season?
DST rules regulate the phase of the sleep/wake cycle and offset the winter lag as observed in Fig. 2 and noted by the values of sample gradients for winter and summer bivariate analysis: β ∼ − m s (winter) and β ∼ − m s /3 (summer), see Table 4. It was previously argued 25 that DST changes are theoretically equivalent to a geographical translocation which moves industrialized timing "towards the Equator" (from Central Germany to Morocco without changing climate as authors said in a much narrower discussion than this one). However, it is the Sun that travels towards the observer from winter to summer and rises ε =°2 47 in the sky at extratropical latitudes. This is more than twice the difference in latitude from Germany to Morocco.
The point to note in Fig. 2 is the subsolar point. At the winter solstice (top panel) it lies beneath the bottom axis of the panel at φ | | = .°23 5 s . The winter angular distance to the subsolar point is simply φ φ | | + | | s . It increases with increasing latitude up to a remarkable value of ~80° for Denmark. That means the Sun only rises 10° above horizon at noon in winter.
By the summer solstice the subsolar point has traveled enough to be placed in the bottom panel (see the yellowish crossed circle). Now the angular distance to the subsolar point is φ φ | − | s . It is not dictated by the distance to the Equator (latitude) but by the distance to the Tropic. As a result summer solar altitude reaches at noon is ε°− = .°90 6 6 5 at the Equator and at φ | | =°47 as well -Switzerland in Europe, Nova Scotia and New Brunswick in America, and the Southern most tip of New Zealand lie on this circle of absolute latitude-as lines of solar elevation angles in Fig. 2 (bottom panel) reveals. Light conditions are then more homogeneous in summer than in winter. Therefore it should not be a surprise that sleep timing were also stationary.
Finally it should be discussed if either summer sleep timing could survive in winter or if winter sleep timing could survive in summer. The first option would mean permanent DST in industrialized, extratropical countries. The photoreceptive process (C) is then challenged with sleep offset occurring well before winter sunrise which breaks one of the golden rules.
www.nature.com/scientificreports www.nature.com/scientificreports/ Many times this is not socially welcome and the arrangement does not sustain too long as experiences in United Kingdom (1970s), Portugal (1970s and 1990s), Chile (2015) or Russia (2014) show. But, also, many times it is socially accepted: Alaska, Saskatchewan (1956), Iceland (1969) and, perhaps, Región de Magallanes in Chile (2016), all of them at φ =°50 or beyond. While culture plays a role in addressing this issue, latitude is also determining. First, as latitude increases and the winter photoperiod becomes short enough, the social propensity for waking up long before sunrise may increase, forecasting the delay in winter sunrise and the advance in winter sunset. Second, as latitude increases the rate of seasonal variations also increases, perhaps making harder to follow them. Helped by artificial light some societies at this range of latitudes are developing a non-seasonal behavior where people are just mere observers of the changes in the scotoperiod and photoperiod.
The second option would mean permanent winter time. Therefore the winter lag would sustain in the summer season, if nothing else changes. This is noted in Fig. 2 (bottom panel) by the surviving dash-dot lines with gradi- . Although the arrangement would look fine, from the point of view of the two model process a difference is worth to mention: sleep onset is now photoreceptively bound to sunset, while sleep offset is now homeostaticly bound to sleep onset. The surviving winter lag would allow then a new arrangement, one with advanced sleep timing.
The foremost evidence of this idea is the success of DST rules in many industrial, extratropical societies. Diurnal sleep is mandatory in summer at this range of circles of latitude, but the winter lag proved to be too much for the summer. The history of DST always shows some "clever" people in early 20th century trying to prevent others from resting in the summer mornings 26 . Long before that, in 1810, the Cádiz Cortes (Spanish first national assembly) seasonally advanced one hour the timing of their sitting from May to October -see http:// www.congreso.es/docu/blog/reglamento_cortes_1810.pdf (in Spanish)-. This change is equivalent to modern DST, including its transitions. That can be deduced from Equation (1), where the advance of τ or the advance of Δ leads to the same advance in t.
The solar altitude at noon, which is related to latitude, also influences the problem: the advance in summer sleep timing is a rational, efficient way of preventing insolation and overheating in the central hours of the summer day. This behavior is observed also in pre-industrial societies (see supplementary material in Yetish et al. 5 ). It likely plays a role in understanding early sleep offset in the Tsimané, the Hadza, Chico Mendes and Fondwa.
Looking in retrospect to Subtropical, pre-industrial data and to the cycle of light and dark, one hour of seasonal variation in human activity at extratropical latitudes is not an oddity. Once time was standardized, societies got entrained to non-seasonal clock time, one hour was the minimum available amount of change of time to adapt seasonally social timing either by setting DST rules or by moving social times. The impact of this change on the circadian system is a concern in terms of public health 27,28 after decades of analysis. However for that to be fully addressed it is also necessary to understand the impact of a non-seasonal behavior in public health.

Conclusions
Winter sleep timing in pre-industrial, hunter/gatherer-horticulturalist, Subtropical societies and in Extratropical, industrial societies remarkably accommodates to the cycle of light and dark across a wide range of angular distance to Equator (0° to 55°) and social development. Therefore, the phase of the sleep/wake cycle lags relative to noon/midnight as latitude increases up to 120 min at 55°. In summer, daylight saving time in industrial societies largely turns the phase of the sleep/wake cycle stationary with latitude.
Artificial light notably impacted the way in which people handle their wakefulness during the scotoperiod, after sunset. However it may not have misaligned the sleep/wake cycle since its phase is still governed by natural trends.
Daylight saving time is on public debate in Europe and America. The issue is governed by a trichotomy, which is influenced by latitude. First option is sleep timing should sustain noon synchronization year round -which identifies to permanent summer time-and, as a result, sleep offset would occur long before sunrise in winter at Extratropical latitudes. The second option is sleep timing should sustain winter synchronization year round -which identifies to winter time-and, as a result, the phase of the sleep/wake cycle should increasingly lag from noon with increasing latitude. This would increase the exposure in the central hours of the day at the hottest season of the year. The third option is sleep timing should seasonally swing to some extend. In this case DST is an appropriate option for contemporary societies bound to clock time, where the change of time can only proceed in steps of one hour.

Data Availability
Time Use Surveys are official surveys carried out by public Institutions. In US it is the Bureau of Labor Statistics and the United States Census Bureau. In UK it is the Office of National Statistics. They are a key tool for sociologists and economists to understand how we share time in a standard day. Any of them is a traceable, well-identified set of data.
Spanish, Dansih and American Time Use Survey microdata were freely available in the internet at the time of writing this manuscript. American Time Use Survey data can be obtained at https://www.bls.gov/tus/data.htm. A link to these surveys is provided in their corresponding references.
French, British, Italian, Canadian and Irish Time Use Survey microdata were obtained after a formal request was addressed to the institutions. The microdata were then sent to me by email, a hard-copy or as a downloadable link. In 2015, these institutions definitely were happy to send their microdata to any researcher who may need them.
Some other Institutions do not release their microdata, or request a fee for them, or request the researcher to visit the Institution if she needs access to them. In these cases I simply refused obtaining the microdata.
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