Suicide risk could be proportional to SCN tau above a zero suicide risk set-point of 24.05 hours

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Schwartz This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9152191/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract Suicide is the 10th leading cause of death and varies seasonally, suggesting involvement of the suprachiasmatic nucleus (SCN) and photoperiod, which both modulate suicide risk and tau, the free-running period of the SCN. This study hypothesized that tau linearly scales suicide risk. The CDC’s 22-year monthly suicide data were fitted with non-linear/cosine curves; annual means m and amplitudes d were extracted; extant tau values were extracted from the literature. The 22-year average annual suicide rhythm was indistinguishable from a pure sinusoid with a late-spring peak, implicating the photoperiod and SCN. Highly correlated variables m and d implicated SCN tau as the proportional driver of both and yielded a zero tau-related suicide risk set-point = 24.05 hours, above which tau-related suicide risk increased proportionally. The population attributable fraction estimated that >73% of all USA suicides were theoretically preventable by reducing tau, which could be the main risk factor for suicide. Health sciences/Diseases Health sciences/Medical research Health sciences/Risk factors suicide suprachiasmatic circadian photoperiod sunspots Race Sex genetic Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Introduction Suicide is the 10th leading cause of death worldwide 1 and a is horrific human tragedy like no other. The causes of suicide are multifactorial (e.g. social, interpersonal, economic, psychiatric, genetic) 1 , 2 . Although post-mortem studies of suicide victims initially converged on several brain regions (e.g. prefrontal cortex) that abnormally express certain genes, mRNA, protein levels, or radioligand binding 3 , 4 , any such promising pathogenic suicide risk loci have mostly eluded replication 5 . Thus, any critical clues about the brain’s regional vulnerabilities and mechanisms of suicide risk still remain dishearteningly obscure. One very conspicuous clue to the brain’s regulation of suicide risk happens to be the oldest and most replicated finding in the suicide literature, namely, the late-spring peak and the late-fall trough in suicides 6 , 7 . French sociologist Emile Durkheim first described the remarkable sinusoidal annual rhythm of suicides with a late-spring peak that paralleled the photoperiod (daylength) in each of three European countries before the widespread societal use of Edison’s electric light bulb (p. 111–116) 6 . Since then, during the modern electric light era, this sinusoidal annual rhythm in suicide risk has appeared variably somewhat obscured 7 . Unfortunately, no progress has been made in elucidating the neurobiology underlying this enduring seasonal suicide risk factor, and novel approaches are desperately needed. The obvious brain locus for potentially mediating this annual rhythm in suicide risk is the master biological clock in the suprachiasmatic nucleus (SCN) 8 – 10 . In the Pittendrigh and Daan ‘clock for all seasons’ model of circadian rhythmicity 11 , Evening (E) and Morning (M) circadian oscillators track dusk and dawn, respectively, thereby changing their mutual phase angle (y EM ) according to the changing photoperiod in both nocturnal rodents 11 , 12 and diurnal humans 13 , 14 . In rodents, changes in photoperiod result in changes in both y EM and its mechanistically linked free-running locomotor period tau 11 , 15 , 16 —which reflects the free-running period tau of the whole SCN in vivo 17 , 18 . These observations suggest that naturalistically in humans, SCN tau —which displays incremental plasticity as a function of prior photic history 19 —could also vary sinusoidally with the photoperiod. Consistent with this hypothesis, in preliminary ultradian forced desynchrony 20 and free-running temporal isolation 21 , 22 protocols, tau peaked in the late-spring and summer, respectively. Thus, if tau is causally related to suicide risk, any such photoperiod-induced sinusoidal rhythms in tau could potentially be associated with parallel sinusoidal annual rhythms in human suicides. Consistent with the possibility of an even broader influence of tau on suicide, the rank order of groups by their mean annual suicide risk (White people > Black people; Males > Females) 2 has also been found identically—albeit in very different types of forced desynchrony protocols—in their SCN tau (White people > Black people 23 , 24 ; Males > Females 25 ). In the gold standard forced desynchrony protocol 8 , humans live for 3–4 weeks in an experimental room devoid of time cues except that they adhere to a dim light/dark schedule (e.g. 18.67 hours wakefulness and 9.33 hours sleep = 28 hour “days”) that is outside the limits of entrainment (synchronization) of their SCN-driven physiologic rhythms (e.g. core body temperature, melatonin) which therefore all free-run together at the individual’s characteristic near-24 hour SCN intrinsic tau . These observations suggest that variations in tau may contribute not only to the photoperiodic cycles in suicide risk, but also to the very wide and puzzling variations between Races and Sexes in mean annual suicide risk 2 . Indeed, ample evidence already links aspects of human circadian rhythms (e.g. seasonality, chronotype, genetics) with suicidal behavior 26 – 29 . The present study hypothesized that subgroup differences in annual means and amplitudes of suicide risk are linearly scaled to tau according to Race, Sex, and photoperiod gradients. The USA Center for Disease Control’s monthly suicide database from 1999–202030 was interrogated by the eight Race:Sex subgroups, and extant tau values were extracted from the gold standard protocols in the literature. Annual means and amplitudes of suicide risk were mapped onto the subgroup’s corresponding SCN tau values. Any coherent relationships derived between these variables could shed important new light on the regulation of suicide risk. Methods Extraction of suicide numbers CDC WONDER suicide data are ultimately derived from the death certificates submitted by families and officials to the local and state Vital Records offices, which then submits these data to the National Center for Health Statistics (NCHS). The NCHS marks all cases of suspected suicide as provisional for 26 weeks pending further investigation, before submitting the final data to the National Vital Statistics System (NVSS). The CDC then compiles these NVSS data into the CDC WONDER database 30 . The monthly suicide numbers were extracted using the “Underlying Cause of Death” databases (1999 – 2020), using ICD-10 codes X60 – X84 for “Intentional self-harm.” The monthly adult (ages 25 – 84) 22-year suicide time series were divided into 8 subgroups according to the CDC’s current categories for Sex (Male and Female) and Race (White, Black, Asian/Pacific Islander, and American Indian/Alaskan Native peoples; abbreviated herein as WM, WF, BM, BF, APIM, APIF, AIANM, and AIANF) 30 . In the 85+ age range, only White Males had sufficient numbers of reportable suicides for all 264 months, so this age bracket was excluded from the adult analyses. Reporting of Race is mandatory on the USA census. The API subgroup is an aggregated and particularly heterogeneous Race category that is defined as peoples whose origins are from the Far East, Indian subcontinent, or Southeast Asia (who also identified on the 2010 census as Chinese 24%, Indian 20%, Filipino 18%, Vietnamese 11%, Korean 10%, Japanese 5%, Pakistani 3%…) 31 . All subgroups had valid suicide data for the entirety of their 264 months except for AIANF, who only had 14% non-suppressed monthly data and who therefore had to be excluded from all analyses. The total number of suicides for these 7 remaining subgroups from 1999 – 2020 was 700,881. Demographics The subgroup percentages of the USA adult population in 1999 (2020) were WM 41% (39%), WF 43% (40%); BM 5% (6%), BF 6% (7%); APIM 2% (3%), APIF 2% (4%); and AIANM 0.4% (0.7%), AIANF 0.4% (0.7%). Each subgroup’s 22-year average Fractional Population (FP) was taken as the average of their 1999 and 2020 fractional populations percentages. Non-linear analysis of the subgroup’s suicide risk profiles The 7 subgroup-specific Individual suicide risk profiles R i (t) were obtained by first dividing each respective subgroup’s raw monthly suicide totals by the number of days per month (including adjustment for leap years) and by the subgroup’s populations per month (linearly interpolated from their yearly populations—the results did not change whether the interpolations were anchored in January or July), then multiplied by 10,000,000 for a tractable analysis (i.e. units for R i ( t ) = (suicides/day/subgroup population) * 10 -7 . To characterize each subgroup’s time series, a non-linear/one-harmonic cosine function was tested for suitability, whereby Individual suicide risk R i (t) = a + bt + ct 2 + d * cos[(2p( t – e )/12)], where t is month (January 1999 = 1). All analyses were performed using the on-line “Non-linear Least Squares Regression” software program from Statpages.org 32 , which is the same program that is included in “R”. The 22-year mean annual suicide risks m i were also extracted from each subgroup i ’s fitted curve. Prespecified subgroup-specific individual suicide risk parameters of interest were mean annual suicide risk m , seasonal amplitude of suicide risk d , and phase e. The model-derived subgroup-specific parameter estimates m , d and e were compared using 95% confidence intervals (mean ± 1.96 * SE). In order to more closely examine the hypothesis that the annual variation in suicide rates is related to the photoperiod, a further “yearly waveshape analysis” was conducted for each subgroup by 1) detrending each 22-year time series by subtracting its linear and quadratic components, 2) averaging the yearly data over the 22 years, and 3) fitting these data with the curve a + b * cos(2p( t – e )/12). An additional exploratory “residual analysis” was then conducted by subtracting each subgroup’s means from the detrended raw 22-year suicide data. Because each subgroup’s residual data exhibited obvious sinusoidal multi-year rhythmicity that oscillated around a zero baseline, they were also fitted with cosine curves of the form Residual suicide risk = A * cos(2p( t – E )/ T ), where t = month (1 – 264), and A , T , and E are amplitude, period, and phase, respectively. Mapping of the WM and WF suicide data onto the extant WM and WF SCN tau data The hypothesis that SCN tau scales suicide risk necessarily invokes a mapping of the suicide risk data from deceased suicide victims onto the SCN tau data from healthy humans. The unique Duffy et al. 25 tau data for both healthy White Males (N = 105, mean ± SE, 24.19 ± 0.02) and Females (N = 52, mean ± SE, 24.09 ± 0.03) are 1) normally distributed and hence are consistent with tau being normally distributed in the entire White population, 2) the only gold standard estimates for human SCN tau in vivo at present and possibly for the foreseeable future 33 , and 3) derived from forced desynchrony studies that spanned over 25 years, the last ~12 of which overlapped with the present study, making them valid long-term mean tau estimates for healthy WM and WF. In addition, insofar as 1) up to 60% of all USA suicide victims have no known prior history of mental illness, 34,35 and 2) there is currently no evidence that mental distress of any kind modifies SCN tau in vivo 36 , these Duffy et al. mean tau values for healthy WM and WF represent the best approximations for the mean tau values for these hundreds of thousands of White suicide victims in the present study. Therefore, mapping the suicide data onto the tau data was warranted as an initial approach to this neurobiologically quite defensible hypothesis, although concerns about a possible “ecological fallacy” (e.g. drawing inferences about individual biological processes from their correlated population biological measures) should not be dismissed. The actual mapping is described below (see Results, SCN proportional control of suicide risk ). Population attributable fraction The partial Population Attributable Fraction for a given subgroup is defined herein as the proportion of incident cases (i.e. the Incidence Risk IR) of suicide that would not have occurred had each subgroup i not been exposed to its pathogenic “dose” tau , or PAF i = (IR exposed – IR unexposed )/IR exposed 37,38 . A PAF with repeated IR’s that can be averaged over time—which in the present study was 264 measurements—provides a better overall PAF estimate than a PAF based on just a single IR 39 . Each subgroup’s 22-year average IR estimate was thus taken as their 22-year mean annual suicide risk m i . Because each subgroup’s photoperiodic variation in suicide risk oscillated sinusoidally with amplitudes d i around their respective means, the PAFcalculations could be validly based solely on m i . Because there was no zero-risk unexposed subgroup, the subgroup-specific partial PAF i ’s were calculated relative to the subgroup with the minimum m and then weighted by their fractional population percentage (FP i ), and summed, such that the overall PAF = S PAF i = S [FP i* ( m i – m min )/ m i ]. In addition, since the hypothesis specifies that D m = k 1* D tau , then the validity of the PAF requires that the PAF i terms ( m i – m min )/ m i ≈ [( tau i – tau min )/ tau i ] or the PAF is rendered invalid 37,39,40 . Two assumptions went into this PAF calculation: 1) each subgroup was continuously exposed more or less stably to their characteristic pathogenic dose of intrinsic tau throughout the 22-years; and 2) any subgroup-specific variabilities due to non- tau -related suicide risk (e.g. environmental, socioeconomic, non-SCN brain regions, genetic) would be exhibited as additional variabilities “away from” the linear tau -related suicide risk variabilities. Results Non-linear model fits and acrophase analysis Fig. 1 and Table 1 depict the non-linear model fits, which appeared quite acceptable, especially in the more populous subgroups. The single harmonic sinusoidal component was statistically significant in all subgroups except in BF ( p = 0.18) and APIF ( p = 0.054). As expected, the rank orders of the 22-year mean annual suicide risk m —and surprisingly also for d —were W > B; M > F. The subgroup’s acrophases e were all around May-June and did not differ significantly between any subgroups. The grand mean phase e for the entire sample was June 5 (May 28 to June 12), which was 4.44 SE before the summer solstice. Table 1. Model parameters for the 7 subgroups. Significant differences were found between all subgroups for both m and d , with rank orders: m , WM > AIANM > BM > APIM > WF > APIF > BF; d , WM and AIANM > APIM and BM and WF > APIF and BF. There were no significant differences between subgroups in the timing of their acrophases. Sbgrp Model m d Acrophase WM r = 0.92 7.834 (7.792 to 7.818) 0.474 (0.414 to 0.534) Jun 3 (May 27 to Jun 10) WF r = 0.90 2.112 (2.094 to 2.131) 0.128 (0.102 to 0.154) Jun 13 (Jun 7 to Jun 19) BM r = 0.65 3.385 (3.346 to 3.426) 0.143 (0.0867 to 0.199) Jun 1 (May 24 to Jun 9) BF r = 0.55 0.672 (0.655 to 0.689) 0.0164 (-0.00790 to 0.0407) May 3 (Feb 8 to Jul 28) APIM r = 0.47 2.920 (2.867 to 2.977) 0.160 (0.0820 to 0.238) May 12 (Apr 14 to Jun 9) APIF r = 0.19 1.148 (1.098 to 1.195) 0.0400 (-0.00416 to 0.0803) Jun 14 (Apr 16 to Aug 13) AIAM r = 0.50 5.980 (5.833 to 6.132) 0.476 (0.264 to 0.688) Jun 11 (May 16 to Jul 6) AIAF NA NA NA NA Sample r = 0.93 4.384 (4.361 to 4.406) 0.258 (0.226 to 0.290) Jun 5 (May 28 to Jun 12) Waveshape analysis In the most populous subgroups, the 22-year “stationary” average annual suicide rhythm could not be distinguished from a pure sinusoid (Fig. 2). Notably, there appeared what could only be the signature protective effect of Christmas on suicides in December for subgroups who were either the more populous and/or traditionally of Christian faith, as well as a seemingly smaller rebound in those same subgroups in January. Multi-year sinusoidal suicide risk rhythms and their correlates with solar sunspot activity Presiding over the years of this study were Solar Cycles 23 (~12.3 years) and 24 (~11.0 years) 41 , during which all subgroups exhibited significant multi-year sinusoidal suicide risk rhythms that had multiple and consistent correlates in the Schwabe sunspot cycles (Figs. 3, 4, Supplementary Table S1). The subgroup’s periods fell into three mostly distinct period bands of ~8, ~12, and ~16 years. The periods of the two ~12-year band members (AIANM and APIM) found a major correlate in the ~12-year period of the prevailing Schwabe sunspot cycle 42 . The amplitudes of the two ~12-year band members exhibited ~40% reductions from Cycle 23 to 24, which was similar to the ~35% drop in the amplitudes of sunspot numbers 43 (Fig. 5). A related solar amplitude correlate was also found in all subgroups, whose solar sunspot amplitudes SA were correlated with their solar photoperiod amplitudes d ( SA vs. d : r = 0.83, p = 0.02; slope = 0.55; intercept CI’s: d -axis -0.15 to 0.21; SA axis -0.74 to 0.81). The ~8-year band members found their solar period correlate in the prominent ~8-year sunspot asymmetry cycle 44-47 , which was mysteriously conspicuous during the solar Maunder minimum of 1645 – 1715 48,49 . Sunspot asymmetry has been conceptualized and measured in many different ways, making acrophase estimates difficult to ascertain, but may have been near 2001, 2011, and 2017 44,47,50 , which approximate the acrophases—perhaps recorded with even more fidelity—for WM (2001, 2009, 2017) and the phase-lagged BF (2003, 2011, 2018), but somewhat less so for slightly speedier APIF (2004, 2010, 2016). SCN proportional control of suicide risk Fig. 6 depicts that the seven subgroup’s epidemiologic ( m , d ) coordinates were highly linearly correlated ( r = 0.97, p = 0.0004; slope = 0.071, CI = 0.050 to 0.093; m -intercept CI = -1.06 to +1.52; d -intercept CI = -0.13 to +0.055), suggesting an important causal biological relationship between these two global measures of suicide risk, such that the regression line could pass through the origin (0, 0) where average annual suicide risk vanishes. What biological mechanisms could possibly explain these two quite conspicuous findings? The hypothesis (see Introduction) stipulates that both m and d vary linearly with SCN tau . As such, the first finding—the tight correlation between m and d —could be due to the fact that both m and d are scaled separately and proportionally to SCN tau . Regarding the second finding—that both m and d could simultaneously reduce to zero—the hypothesis must now include the existence of a zero tau -related suicide risk set-point. In order to formally test these two hypotheses, the Duffy et al. WM and WF ( m , d ) 2D coordinates were mapped onto their respective WM and WF ( tau , m , d ) 3D coordinates (see Methods). If these two hypothesis are true, then these two points will define a line in 3D space that must 1) intersect the tau axis in the vicinity of the hypothetical zero suicide risk set-point ( tau set , 0, 0), and 2) have orthogonal linear projections in the ( tau , d ) and ( tau , m ) planes with slopes ( d/tau and m/tau ) that preserve the original d / m ratio in their mutual slope ratio = ( d/tau )/( m/tau ) = d / m , independent of any dihedral angle between the two planes. Fig. 7 depicts the results of this mapping. Consistent with the predictions, ( tau , m ) and ( tau , d ) both intersected the suicide risk zero intercept precisely at tau set = 24.053. In addition, the original d / m slope ratio was preserved (Fig. 6 d / m = 0.071 (0.050 to 0.093); Fig. 7 d / m = 0.060). It’s a miraculous bullseye! In White people, 1) the magnitude of individual suicide risk appears to be proportional to ( tau – tau set ), and 2) tau set = 24.05 marks the zero tau -related suicide set-point where both m and d simultaneously reduce to zero (see Methods for limitations). This SCN circadian and photoperiodic formulation of suicide risk is entirely consistent with the established role of the SCN in the daily and seasonal regulation of affect, mood, and suicide risk 51-55 . Fig. 7 therefore yields Equations for Individual monthly suicide risk R i ( t ) due to tau i , R i ( t ) = a 1* ( tau i – tau set ) + a 2* ( tau i – tau set ) * cos[(2p t /12) + e ] tau i > tau set R i (t) = 0 tau i ≤ tau set where a 1 and a 2 are the scaling factors (57.22 and 3.46) for m and d , respectively, t is day of the year, e is the phase that is assumed here to be common to every subgroup i , and tau set is the zero tau -related suicide risk set-point = 24.05 hours. Validity checks on the PAF calculation Suicide risk was hypothesized to increase linearly with the pathogenic dose of tau , or D m = k * D tau . Thus, if the PAF is valid, the partial PAF term ( m i – m min )/ m i must approximate the SCN term [( tau i – tau min )/ tau i ] (see Methods). Substituting the WM and WF m and tau values into this PAF formula yields the partial PAF term [( m WM – m WF )/ m WM ] = 0.728, which is extremely close to the SCN term [( tau WM – tau set ) – ( tau WF – tau set )/( tau WM – tau set )] = 0.730, bolstering the validity of both the PAF model and the hypothesis of linear scaling of m to tau . The two assumptions that went into the PAF are now discussed below. The continuous exposure of each subgroup i to their extrapolated 22-year mean tau i . The Duffy et al. tau data were collected over the course of ~25 years, ~12 of which overlapped with the present study interval. It was therefore assumed that the Duffy et al. mean tau estimates for WM and WF were accurate long-term estimates and could reasonably be extrapolated identically for the entire ~22 years. That tau indeed acted continually and proportionally on both m and d throughout these 22 years was demonstrated in a separate model (see SM, section S2). Absence of any non-tau-related major exogenous or endogenous confounders. This was validated insofar as there were no obvious subgroup-specific variabilities that were exhibited “away from” the tight ( m , d ) regression line in Fig. 6. In fact, the AIANM subgroup was the subgroup that was located farthest away from the regression line, and this deviation could almost entirely be accounted for by their unusually high solar photoperiod amplitude d relative to their m (which was also biologically consistent with their very high sunspot amplitude). The PAF calculation The valid PAF was thus calculated as follows: PAF = S PAF i = S [( m i – m min )/ m i ] * PF i = WM ((7.79 – 0.67)/7.79) * 0.40 + WF ((2.12 – 0.67)/2.12) * 0.415 + BM ((3.39 – 0.67)/3.39) * 0.055 + APIM ((2.93 – 0.67)/2.93) * 0.025 + APIF ((1.15 – 0.67)/1.15) * 0.03 + AIANM ((5.95 – 0.67)/5.95) * 0.0055 = 73.0% of all USA non-BF suicides from 1999 – 2020 would not have occurred had each subgroup manifested the enviable low tau of BF. From another perspective, Fig. 7 suggests that all subgroups, including the resilient BFs, could have their tau -related suicide risk reduced to close to zero if their tau were reduced to 24.05 hours. Discussion The most straightforward explanation for the annual sinusoidal suicide risk rhythm is that it reflects the direct effect of the Earth’s annual sinusoidal photoperiod cycle (or alternatively, the Earth’s annual sinusoidal dawn or dusk cycles) on the human brain at latitudes of the USA. Because of Earth’s axial tilt and its Keplerian motion around the sun, the earliest sunrise (e.g. Washington DC) occurs around June 13 at 5:42 am, but the latest sunset occurs around June 27 at 8:37 pm, even though the longest day still occurs around the summer solstice on June 21 56 . Therefore, the fact that the suicide risk rhythm acrophase of June 5 (May 29 to June 12) was significantly (4.44 SE) before the summer solstice suggests that this rhythm was not merely passively following total photon count but rather was actively entrained in large part by the SCN Morning oscillator that was tracking the earliest solar dawn. Presumably, even with eyelids closed and shades drawn, most people slumber in bedrooms that still allow sufficient solar irradiation at dawn in order for the SCN M oscillator to entrain the suicide rhythm by retinal mechanisms 57,58 . It is inspiring that a social-religious zeitgeber can have such clear suppressive effect on suicide and suggests that a spirited “all-hands-on-deck” approach to the management of actively suicidal individuals is a worthy acute therapeutic strategy until treatment is secured. Large previous studies have also shown a protective effect of various aspects of religious affiliation on suicide risk, although smaller studies have shown negative results 59–61 . Given the multiple and consistent period and amplitude correlates, it is hard not to infer that human suicide risk is causally modulated by variations in the Schwabe sunspot cycle. Indeed, several prior studies are consistent with these present sunspot-suicide findings. In Lithuania (1989– 2013, N = 33,072 suicides) 62 , a positive correlation was found between sunspot numbers and suicides. In Finland (1979–1999, N = 27,469 suicides) 63 , a significant 3% increase in suicides was found during years of maximum sunspot activity that approximates the magnitudes found in the present study. In Taiwan (1991–2008, N = 4857 suicides) 64 , significant sunspot suicide rhythms with periods of ~ 5- and ~ 16-years were found in both Males and Females. In addition, it is difficult to even imagine another etiologic agent(s) that could produce such long-term synchronous antiphase sinusoidal suicide rhythms other than some non-visual effects of sunspot cycles on the phase of a biological oscillator like the SCN. Many factors influence SCN tau and hence suicide risk, including 1) light intensity and duration 58,65–67 , 2) SCN neuronal network structure and synchronization 68–74 , 3) SCN GABA-mediated attractive and repulsive forces that modulate the phase angle between the E and M oscillators (y EM ) 75–77 , 4) gonadal hormones 78 , and 5) SCN circadian gene transcription-translation feedback loops and their influences on SCN neuronal electrical activity 79,80 . In the present context, the various Race:Sex subgroup’s ( m , d ) coordinates in Fig. 6 are of great interest and are presumably due to genetic factors resulting from evolutionary pressures operating on tau for the different subgroups at different latitudes, environmental temperatures, and light sensitivities 23,24,26,28 . From another perspective, these Racial differences in tau also provide a compelling explanation for the longstanding and perplexing USA “Suicide Race Paradox,” which struggles to explain why the persecuted Black race paradoxically has a significantly far lower suicide rate than the persecutor White race 81 . The hypothesized acrophase in tau during the late-spring predicts that the prevalence and suicidality of the long tau 82–84 delayed chronotype (i.e. late to bed, late to rise) should also peak in the late-spring. While no such definitive epidemiologic studies exist, considerable evidence supports this hypothesis. Delayed chronotype 1) is associated with long tau in rigorous forced desynchrony studies 82–84 , 2) becomes more prevalent with the later evening sunlight that occurs across latitudes within a single time zone with equal clock times 85 , 3) exhibits rank orders in prevalence rates for Race (W > B) 86 and Sex (Males > Females) 87 that are parallel to the Race and Sex gradients in tau and suicide risk in the present study, 4) is associated with a greater suicide risk than less-delayed chronotypes 88 as well as non-delayed chronotypes in both unipolar 89,90 and bipolar 91 mood disorders, and 5) correlates positively with free-running tau in a diurnal rodent model of chronotype 92 . By contrast, two studies found no increase in delayed chronotype with seasons—one was a theoretical study using a fixed tau model 93 , while the other was a clinical study that did not adjust for daylight savings time 94 . Thus, the current evidence is consistent with the hypothesis that the prevalence and suicidality of long tau delayed chronotype should increase with later evening sunlight along Race-, Sex-, and photoperiod gradients. How can we reconcile the present model with the known tau - lengthening 95–97 anti-suicidal effects of lithium 98–100 ? In a seminal study using dispersed human skin fibroblasts—which have similar, but not identical, molecular rhythms compared with the whole SCN 101 —patients with bipolar disorder who were lithium responders ( n = 44) tended to shorten their tau in response to lithium treatment compared with lithium non-responders, who tended to have longer fibroblast tau ( n = 15) 102 . These findings were replicated in a preliminary study using neuronal precursor cells 103 . Another study using fibroblasts also found that in patients with bipolar disorder ( n = 32), longer tau was associated with poorer response to lithium 104 . Thus, there may be a subset of patients with relatively longer (but not the longest) tau who are uniquely clinically responsive to the tau -shortening effect of lithium. Given that lithium’s overall tau -increasing effect does not apparently increase global suicide risk in patients with mood disorders, it is possible that for unknown reasons, lithium doesn’t lengthen tau in lithium non-responders 102,103 . The data in this study have yielded the conclusion that increases in photoperiod (i.e. increases in the amount of visible light in the light/dark LD cycle) result in increases in tau in diurnal humans (see SM, section S4 for discussion of Aschoff’s Rule and light’s effects on tau in LL and LD in nocturnal and diurnal organisms) 105 . It is also possible that some as yet unidentified non-visual band of electromagnetic radiation pollution 106 could be contributing, for example, to these long-term linear and parabolic variations in suicide rates 107 . In this regard, Wever famously “guaranteed at a high level of significance” that his artificial 10 Hz electric field was capable of modifying tau 22 (p. 205), raising the possibility that a treatment such as repetitive transcranial magnetic stimulation (rTMS) could be a rapidly acting tau -reducing treatment for individuals with acute suicide risk. Perhaps more quickly within therapeutic reach would be mathematically derived tau -shortening light/dark treatments with specified light intensities and schedules, which could hold great promise for treating suicidal individuals 19,58 . The present SCN tau -based model of suicide risk implies that the suicidogenic effects of emotional stress are ultimately channeled into the SCN—the “final common pathway”—which then determines whether suicide risk crosses the suicide threshold according to its error signal ( tau – tau set ) and its d / m ratio. Certainly, very few people die by suicide without incurring some type of terrible emotional distress, but how does such emotional distress modulate the SCN’s regulation of suicide risk? The effects of emotional stress on the circadian system in general and on SCN tau in particular are only beginning to be clarified 108,109 . Reconciling this SCN final common pathway model of emotional stress with the known and sometimes wide national, historical, and long-term variations in suicide rates might seem challenging. Durkheim’s European pre-electric-light 1870’s suicide data are instructive here (Fig. 9). Each of the three countries (probably > 98% White, but definitive sources do not exist) exhibited robust sinusoidal suicide rhythms with remarkably constant “relative amplitudes” (fitted cosine amplitudes: France 26.2% Italy 26.7%, Prussia 25.9%; Fig. 9A). By contrast, Durkheim’s mean annual suicide rates were only somewhat less than those in the present study (crude suicide rates per 100,000 population: France 16.0; Italy 3.8; Prussia 15.2; USA range, WM 22.3, BF 2.5). In Fig. 9B, Durkheim’s data show that the 1870’s SCN regression line also likely passes through the origin (compare Fig. 9B to Fig. 6). These data therefore permit the inference that suicide risk in the absence of artificial light in 1870’s White Europe was also governed by an SCN that had 1) a larger d and a 3.7-fold larger d / m ratio than today 110 , 2) a zero tau -related suicide risk set-point—possibly also different than today, and 3) a very major effect on suicide rates. The very low suicide rate of 1870’s Italy are instructive given the sometimes quite large inter-national differences in suicide rates that have been observed over time 1 . In Fig. 9B, the fact that Italy’s lowest m fell exactly along the SCN regression line indicates that SCN tau was still involved in regulating Italy’s low suicide risk. But how could such a ~ 4-fold difference in m between geographically similar White populations be solely a function of SCN tau ? It seems unlikely that White Italy tau —or more exactly ( tau – tau set )—was ~ 4-fold lower than White France and White Prussia tau . In a post-hoc analysis, the White 85 + subgroup exhibited the maximum suicidal risk which was double that of the rest of WM adults, yet their extremely high ( m , d ) coordinates (14.367, 1.0135)—like the extremely low ( m , d ) coordinates of 1870’s Italy—also stayed exactly on the SCN regression line. While this 2-fold elevation in suicide rates of WM 85 + compared with the rest of adult WM tau could be explained if WM 85 + mean tau = 24.33 hours [i.e. ( tau – tau set ) = (24.33–24.05) = 0.28 = 2 * (24.19–24.05)], a tau ≥ 24.33 was seen in only < 25% of the Duffy et al. over 65 age range 25 , requiring that a long tau ≥ 24.33 for this very suicidal WM 85 + subgroup also confers some sort of preferential longevity such that they become the majority of the remaining living members of this WM 85 + subgroup, which seems rather improbable. Thus, something other than differences in tau must also be influencing suicide rates such that low Italy and high WM 85 + remained on the SCN regression despite their extreme and disparate distances from the zero set-point. There is really only one way that this could occur. Most studies have found that various of the multifaceted measures of hope (e.g. spirituality, social cohesion, religious affiliation—collectively referred to hereafter as H) are the most significant individual protective factors against suicide 59–61,111 . Could H somehow be involved in the SCN’s regulation of the suicide risk? What if instead of suicidal risk being proportional to the error signal ( tau – tau set ), suicide risk now becomes proportional to ( tau – tau set – H), where positive H counteracts suicide risk by reducing the suicide error signal that is due to ( tau – tau set ), thereby maintaining a nation’s linear scaling of suicide risk ( m , d ) coordinates on the SCN regression line. H can be positive or negative. H was high in 1870’s Italy, whereas H reaches its absolute minimum in the downtrodden and isolated elderly, whose suicide rates increase rapidly after 70 all the way up to the human maximum 1 . The habenula regulates futility-related affects and has circadian and photoperiodic clocks that respond to light and maintain bidirectional neural connections with the SCN and hence could encode the level of H and relay it to the SCN, which ultimately determines suicide risk 112–114 . It is likely that both tau set and the d / m ratio are intrinsic parameters of this exquisitely precise SCN master clock 8,11,115 . In light of these considerations, the PAF now takes its final form: In the USA from 1999–2020, assuming that all subgroups had had the same national H, then > 73% of all non-BF suicides could have been prevented if their SCN tau had been equal to that of the resilient morning-type BF. The two main limitation of the present study are that 1) the zero tau -related suicide risk set-point was based solely on the tau of WM and WF (see SM, section S3 and Methods), and 2) the suicide data from deceased suicide victims were mapped onto the tau data from healthy subjects. Of course, the WM and WF ( tau , m , d ) data in Fig. 7 are not merely “two datapoints” but rather are population estimates obtained from decades of methodologically large (from a physiological perspective) sample sizes of White people. In addition, 1) up to 60% of suicide victims appear to have had no documented prior psychiatric illness 34,35 , and 2) there was no evidence for a subgroup-specific differential effect of genetics that was located “away from” the “SCN regression line” in Fig. 6, suggesting that these healthy tau values from Duffy et al. could well reflect those of suicide victims. Another cautionary note is that up to ~ 25% of humans have a circadian tau < 24.0 hours 8,116,117 , which Fig. 7 suggests would be associated with a tau -related suicide risk of zero. Insofar as at least some of these individuals presumably still die by suicide, it is again recognized that there may be “other-than- tau -related” factors that alone can also influence suicide risk. Accordingly, it is virtually certain that the ~ 30% of the extra- tau variance in suicide risk due to emotional factors (e.g. maintenance of H) plays a critical role in determining whether an individual falls prey to suicide. In summary, all of the data in this study are fully consistent with the SCN tau -based proportional control model such that suicide risk is 1) scaled proportionally to ( tau – tau set – H) according to Race:Sex gradients, 2) has a zero tau -related suicide risk set-point = 24.05 hours, and 3) is modified by the Earth’s photoperiod rhythms, the solar sunspot rhythms, and by emotional stress and Hope. The PAF suggests that > 73% of all suicides in the USA from 1999–2020 may have been due to the variations in the operation of this remarkably precise and increasingly well-characterized suprachiasmatic nucleus and hence were theoretically preventable. The quest to discover scalable measures of SCN tau 33 and practical tau -reducing treatments 118 now has urgency. Declarations Data Availability. The data that supports this investigation are freely available on-line from CDC WONDER at https://wonder.cdc.gov/mcd-icd10html. Competing Interests: The author reports no competing interests. Acknowledgment. The author expresses appreciation to the CDC and affiliated agencies involved in the long-term collection and curating of these exquisite and life-saving suicide data. Funding Declaration. The author received no funding for the study. Human Ethics and Consent to Participate Declaration. Not applicable. Author Contribution . The author was the sole agent in this manuscript’s conception, data analysis, and writing. References Ilic, M. & Ilic, I. Worldwide suicide mortality trends (2000-2019): a joinpoint regression analysis. World J Psychiatry 12 , 1044-1060 (2022). https://doi.org/10.5498/wjp.v12.i8.1044 Martínez-Alés, G., Jiang, T., Keyes, K. M. & Gradus, J. L. The recent rise of suicide mortality in the United States. Annu. Rev. 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International Journal of Bipolar Disorders 12 , 6 (2024). https://doi.org/10.1186/s40345-024-00326-x Tondo, L., Vazquez, G. H. & Baldessarini, R. J. Suicidal behavior associated with mixed features in major mood disorders. Psychiatr. Clin. North Am. 43 , 83-93 (2020). Brown, S. A. et al. The period length of fibroblast circadian gene expression varies widely among human individuals. PLoS Biol. 3 , e338 (2005). https://doi.org/10.1371/journal.pbio.0030338 McCarthy, M. J. et al. Chronotype and cellular circadian rhythms predict the clinical response to lithium maintenance treatment in patients with bipolar disorder. Neuropsychopharmacology 44 , 620-628 (2019). https://doi.org/10.1038/s41386-018-0273-8 Mishra, H. K. et al. Circadian rhythms in bipolar disorder patient-derived neurons predict lithium response: preliminary studies. Mol. Psychiatry 26 , 3383-3393 (2021). https://doi.org/10.1038/s41380-021-01048-7 Sanghani, H. R. et al. Patient fibroblast circadian rhythms predict lithium sensitivity in bipolar disorder. Mol. Psychiatry 26 , 5252-5265 (2021). https://doi.org/10.1038/s41380-020-0769-6 Bano-Otalora, B. et al. Bright daytime light enhances circadian amplitude in a diurnal mammal. Proc. Natl. Acad. Sci. U. S. A. 118 , e2100094118 (2021). https://doi.org/10.1073/pnas.2100094118 Bandara, P. & Carpenter, D. O. Planetary electromagnetic pollution: it is time to assess its impact. Lancet Planet Health 2 , e512-e514 (2018). Schwartz, P. J. Electromagnetic fields and circadian rhythms. JAMA 269 , 868 (1993). https://doi.org/10.1001/jama.1993.03500070047019 Landgraf, D., McCarthy, M. J. & Welsh, D. K. Circadian clock and stress interactions in the molecular biology of psychiatric disorders. Curr Psychiatry Rep 16 , 483 (2014). https://doi.org/10.1007/s11920-014-0483-7 Helfrich-Forster, C. Interactions between psychosocial stress and the circadian endogenous clock. Psych J 6 , 277-289 (2017). https://doi.org/10.1002/pchj.202 Wehr, T. A., Giesen, H. A., Moul, D. E., Turner, E. H. & Schwartz, P. J. Suppression of men’s responses to seasonal changes in day length by modern artificial lighting. American Journal of Physiology 269 , R173-R178 (1995). Dmitriev, A. On determinants of national suicide rates: evidence from Baysian model averaging. Applied Economics 56 , 8838-8845 (2023). https://doi.org/10.1080/00036846.2023.2294272 Huang, L. et al. A visual circuit related to habenula underlies the antidepressive effects of light therapy. Neuron 102 , P128-142 (2019). https://doi.org/10.1016/j.neuron.2019.01.037 Marks, R. B. et al. The role of the lateral habenula in suicide: a call for further exploration. Front. Behav. Neurosci. 16 , 812952 (2022). https://doi.org/10.3389/fnbeh.2022.812952 Salaberry, N. L., Hamm, H., Felder-Schmittbuhl, M.-P. & Mendoza, J. A suprachiasmatic-independent circadian clock(s) in the habenula is affected by Per gene mutations and housing light conditions in mice. Brain Struct. Funct. 224 , 19-31 (2019). https://doi.org/10.1007/s00429-018-1756-4 Wehr, T. A. A ‘clock for all seasons’ in the human brain. Prog. Brain Res. 111 , 321-342 (1996). https://doi.org/10.1016/S0079-6123(08)60416-1 Wyatt, J. K., Ritz-De Cecco, A., Czeisler, C. A. & Dijk, D. J. Circadian temperature and melatonin rhythms, sleep, and neurobehavioral function in humans living on a 20-h day. Am. J. Physiol. 277 , R1152-1163 (1999). https://doi.org/10.1152/ajpregu.1999.277.4.r1152 Wright Jr, K. P., Hughes, R. J., Kronauer, R. E., Dijk, D. J. & Czeisler, C. A. Intrinsic near-24-h pacemaker period determines limits of circadian entrainment to a weak synchronizer in humans. Proc. Natl. Acad. Sci. U. S. A. 98 , 14027-14032 (2001). https://doi.org/10.1073/pnas.201530198 Jewett, M. E., Forger, D. B. & Kronauer, R. E. Revised limit cycle oscillator model of human circadian pacemaker. J. Biol. Rhythms 14 , 493-499 (1999). Additional Declarations No competing interests reported. Supplementary Files SupplementaryMaterial.docx Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 16 Apr, 2026 Reviewers agreed at journal 31 Mar, 2026 Reviewers invited by journal 24 Mar, 2026 Editor assigned by journal 19 Mar, 2026 Submission checks completed at journal 18 Mar, 2026 First submitted to journal 17 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9152191","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":612250257,"identity":"39e8f97b-8d52-42ac-bb13-63a6e842d691","order_by":0,"name":"Paul J. Schwartz","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/ElEQVRIiWNgGAWjYFCCAwzMEAZjw4EEAxsQo/EAUVp4GJgbH3yoSIPoJWQPVAt7s+GMM4ehxuAB5ozHH34ubLPLt+c/2CbN23bebm37YaAtNTbRuLRYNpwxlp7ZlmzZwwDWcjt525lEoJZjabkNOLQYHDjDxsy7jdmAh7ERosXsAFALY8NhPFqOPwNqqTfgYWYEaTmXbHb+ISEtB8yAWg4b8LAxgrx/wM7sBgFbwH7h/XfcgOcMIyiQkxPMbgBtScDjF3MJYIjxnKk2YO8//gAYlXb2ZufTHz74UGOD22ESB1AFEsEqE3AoB2vhRzPMHo/iUTAKRsEoGKEAAD7EZwuciCqoAAAAAElFTkSuQmCC","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Paul","middleName":"J.","lastName":"Schwartz","suffix":""}],"badges":[],"createdAt":"2026-03-17 19:53:46","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9152191/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9152191/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105567136,"identity":"2c6c1868-e2b1-49df-aaa7-87e6ec19de4d","added_by":"auto","created_at":"2026-03-27 12:58:25","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":231142,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRaw time series and fitted curves for the Individual suicide risk profiles.\u003c/strong\u003e The subgroup-specific curve fits were modeled as Individual suicide risk \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(t)\u003c/em\u003e = \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e + \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003cem\u003et + c\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003cem\u003et\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e + d\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e*\u003c/sub\u003ecos[(2p(\u003cem\u003et – e\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e)/12)], where \u003cem\u003et\u003c/em\u003e is month (January 1999 = 1). Note the linear and quadratic trends in the various subgroups. Model parameters are listed in Table 1.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-9152191/v1/d3e93c5701f33086e320db57.png"},{"id":105499706,"identity":"a0546375-1760-4ca3-a8e6-6991ba04a8af","added_by":"auto","created_at":"2026-03-26 17:14:25","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":196307,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDetrended 22-year average Individual suicide risk profiles for the 7 subgroups and their fitted curves.\u003c/strong\u003e The Christmas effect appears more consistently in Males. Data are double plotted for visual clarity.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-9152191/v1/1ef9331830048144e7e73127.png"},{"id":105499711,"identity":"181f3db8-30d5-4086-b6b1-2e9660dafd99","added_by":"auto","created_at":"2026-03-26 17:14:25","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":247107,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eIndividual sunspot suicide risk rhythms for the 7 subgroups.\u003c/strong\u003e The detrended sunspot suicide rhythms were modeled as \u003cem\u003eIndividual sunspot suicide risk\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e = \u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e*\u003c/sub\u003ecos(2p(\u003cem\u003et\u003c/em\u003e – \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e)/\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e). The subgroups displayed three relatively distinct period bands of ~8, ~12, and ~16 years, as well as ~12- and ~16-year antiphase rhythms (see Fig. 4).\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-9152191/v1/e41714269a4264484d73776c.png"},{"id":105499703,"identity":"41201eb3-a55f-4ec8-9c09-ed5544bcc716","added_by":"auto","created_at":"2026-03-26 17:14:25","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":46452,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThree mostly distinct period bands for the residual multi-year suicide rhythms.\u003c/strong\u003e Mean subgroup population-weighted periods for the three bands are 7.8, 12.0, and 15.7 years. Within each of the three Race subgroups, the ratios of the M:F (or F:M) periods were very close the integer 2 (WF:WM 15.8/8.0 = 1.98; BM:BF 15.5/7.4 = 2.09; APIM:APIF 11.9/6.1 = 1.98), suggesting an effect of Sex on a 2:1 entrainment pattern.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-9152191/v1/0a2de970edbddc3ac8537031.png"},{"id":105499705,"identity":"72d32ddb-6e3a-44d3-b663-f5cc793cdd87","added_by":"auto","created_at":"2026-03-26 17:14:25","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":79053,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCorrelations between the peaks of the ~12-year suicide risk cycle and of Schwabe sunspot activity for Solar Cycles 23 and 24. \u003c/strong\u003eThe amplitude of sunspot numbers decreased by about 35% from Solar Cycles 23 to 24, as did the amplitude of suicide peaks for both subgroups in the ~12-year band (AIANM 45%; APIM 40%). Similar such reductions could not be found in any of the other subgroups. Data were smoothed using a 12-month averaging window.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-9152191/v1/ee1d20cc0b8b321719d13470.png"},{"id":105566655,"identity":"7b324db1-9693-49f8-a3ad-b2ddb3115227","added_by":"auto","created_at":"2026-03-27 12:56:54","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":52065,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e\u003cstrong\u003em\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e and \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003ed\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e are regulated proportionally with a possible zero suicide risk set-point = (0, 0). \u003c/strong\u003eThe regression line has a slope of \u003cem\u003ed\u003c/em\u003e/\u003cem\u003em\u003c/em\u003e = 0.071 and could pass through the origin (0, 0). Note that within each Race, the Sex gradient in \u003cem\u003em\u003c/em\u003e may not be the same (WM:WF = 3.71, BM:BF = 5.04, APIM:APIF = 2.54; see also Supplementary Figs. S2, S3).\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-9152191/v1/6ee1ddf1b7a4dba7e18f3551.png"},{"id":105499712,"identity":"dc5032dd-55e5-4ecc-a5c8-4cf46cdc8c2c","added_by":"auto","created_at":"2026-03-26 17:14:25","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":63107,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eValidation of the SCN proportional control model of suicide risk with a zero \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003etau\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-related suicide risk set-point.\u003c/strong\u003e As required and predicted by the hypothesis, (\u003cem\u003etau\u003c/em\u003e, \u003cem\u003em\u003c/em\u003e) and (\u003cem\u003etau\u003c/em\u003e, \u003cem\u003ed\u003c/em\u003e) intersected at a zero \u003cem\u003etau\u003c/em\u003e-related suicide risk set-point (24.05 hours) and the \u003cem\u003ed\u003c/em\u003e/\u003cem\u003em\u003c/em\u003e ratio was maintained.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-9152191/v1/9d99ff9d94a7f9c3bddf5959.png"},{"id":105499708,"identity":"cfdc5cf5-e85f-4b74-8c9e-b76024dc0468","added_by":"auto","created_at":"2026-03-26 17:14:25","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":47834,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe SCN model of proportional control of Individual suicide risk with a zero \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003etau\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-related suicide risk set-point.\u003c/strong\u003e Three hypothetical subgroups are depicted. Subgroup-specific mean annual suicide risks \u003cem\u003em\u003c/em\u003e (horizontal red segments) and monthly suicide risks \u003cem\u003ed\u003c/em\u003e (blue closed circles) are plotted on the same grid. The linearly graded subgroup-specific \u003cem\u003etau\u003c/em\u003e-related differences in \u003cem\u003em\u003c/em\u003e that were derived from Table 1 are represented by the sloped red regression line. The amplitudes of the three sinusoidal annual suicide risk rhythms were all scaled up by the same arbitrary constant for visual clarity. Note the decay and eventual death of the annual suicide rhythm as \u003cem\u003etau\u003c/em\u003e is reduced to the set-point. While this schematic does not capture the linear and quadratic trends seen in Fig. 1, an additional analysis was performed that showed continuous proportional modulation of \u003cem\u003em\u003c/em\u003e and \u003cem\u003ed\u003c/em\u003e over the course of the 22 years (Supplementary Fig. S1), indicating that the subgroup’s average \u003cem\u003em\u003c/em\u003eand \u003cem\u003ed\u003c/em\u003e indeed reflect 22-year measures.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-9152191/v1/e019bbce2cda6c6d4b30ad44.png"},{"id":105499707,"identity":"7ba4e9d7-d0a5-47b8-a6dd-d2a3957acbab","added_by":"auto","created_at":"2026-03-26 17:14:25","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":85545,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDurkheim’s pre-electric-light European suicide data. \u003c/strong\u003eA\u003cstrong\u003e. \u003c/strong\u003eAll three countries exhibited sinusoidal suicide rhythms with remarkably similar relative amplitudes and phases, despite their data being based on far shorter time intervals and much lower N than the present study. Monthly data are normalized to 1000 suicides/year, and the horizontal line is the mean monthly suicide count of 1000/12 = 83.33. Data are double plotted for visual clarity. B. The 1870’s SCN regression line is analogous that of Fig. 6. The \u003cem\u003ed\u003c/em\u003e values were the fitted cosine amplitudes from A, while the \u003cem\u003em\u003c/em\u003e values for Italy and Prussia had to be obtained from the closest reported date ranges to those in A (compare the A and B legends; Durkheim commented on the long-term stability of suicide rates within each of these countries). As in Fig. 6, the confidence intervals for both the \u003cem\u003em\u003c/em\u003e- and \u003cem\u003ed\u003c/em\u003e-intercepts contain the origin (0, 0), indicating that back in 1870’s pre-electric light White Europe, suicide risk was likely governed by the SCN \u003cem\u003etau\u003c/em\u003e proportional controller.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-9152191/v1/812e1cccb44084f4d1f230dd.png"},{"id":105571064,"identity":"2aaeb045-e96e-4293-8bff-3463f44cd4d0","added_by":"auto","created_at":"2026-03-27 13:21:24","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2528188,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9152191/v1/cad908b7-085b-430e-852d-d6ca810b0375.pdf"},{"id":105499710,"identity":"6b3aa3eb-b149-43a7-8b2e-95682cf0f18e","added_by":"auto","created_at":"2026-03-26 17:14:25","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":397343,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryMaterial.docx","url":"https://assets-eu.researchsquare.com/files/rs-9152191/v1/a94c93360546f79aab1e38d8.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Suicide risk could be proportional to SCN tau above a zero suicide risk set-point of 24.05 hours","fulltext":[{"header":"Introduction","content":"\u003cp\u003eSuicide is the 10th leading cause of death worldwide\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e and a is horrific human tragedy like no other. The causes of suicide are multifactorial (e.g. social, interpersonal, economic, psychiatric, genetic)\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Although post-mortem studies of suicide victims initially converged on several brain regions (e.g. prefrontal cortex) that abnormally express certain genes, mRNA, protein levels, or radioligand binding\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e,\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e, any such promising pathogenic suicide risk loci have mostly eluded replication\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. Thus, any critical clues about the brain\u0026rsquo;s regional vulnerabilities and mechanisms of suicide risk still remain dishearteningly obscure.\u003c/p\u003e \u003cp\u003eOne very conspicuous clue to the brain\u0026rsquo;s regulation of suicide risk happens to be the oldest and most replicated finding in the suicide literature, namely, the late-spring peak and the late-fall trough in suicides\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. French sociologist Emile Durkheim first described the remarkable sinusoidal annual rhythm of suicides with a late-spring peak that paralleled the photoperiod (daylength) in each of three European countries before the widespread societal use of Edison\u0026rsquo;s electric light bulb (p. 111\u0026ndash;116)\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. Since then, during the modern electric light era, this sinusoidal annual rhythm in suicide risk has appeared variably somewhat obscured\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. Unfortunately, no progress has been made in elucidating the neurobiology underlying this enduring seasonal suicide risk factor, and novel approaches are desperately needed.\u003c/p\u003e \u003cp\u003eThe obvious brain locus for potentially mediating this annual rhythm in suicide risk is the master biological clock in the suprachiasmatic nucleus (SCN)\u003csup\u003e\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. In the Pittendrigh and Daan \u0026lsquo;clock for all seasons\u0026rsquo; model of circadian rhythmicity\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e, Evening (E) and Morning (M) circadian oscillators track dusk and dawn, respectively, thereby changing their mutual phase angle (y\u003csub\u003eEM\u003c/sub\u003e) according to the changing photoperiod in both nocturnal rodents\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e,\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e and diurnal humans\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. In rodents, changes in photoperiod result in changes in both y\u003csub\u003eEM\u003c/sub\u003e and its mechanistically linked free-running locomotor period \u003cem\u003etau\u003c/em\u003e\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e,\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e\u0026mdash;which reflects the free-running period \u003cem\u003etau\u003c/em\u003e of the whole SCN \u003cem\u003ein vivo\u003c/em\u003e\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. These observations suggest that naturalistically in humans, SCN \u003cem\u003etau\u003c/em\u003e\u0026mdash;which displays incremental plasticity as a function of prior photic history\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e\u0026mdash;could also vary sinusoidally with the photoperiod. Consistent with this hypothesis, in preliminary ultradian forced desynchrony\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e and free-running temporal isolation\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e protocols, \u003cem\u003etau\u003c/em\u003e peaked in the late-spring and summer, respectively. Thus, if \u003cem\u003etau\u003c/em\u003e is causally related to suicide risk, any such photoperiod-induced sinusoidal rhythms in \u003cem\u003etau\u003c/em\u003e could potentially be associated with parallel sinusoidal annual rhythms in human suicides.\u003c/p\u003e \u003cp\u003eConsistent with the possibility of an even broader influence of \u003cem\u003etau\u003c/em\u003e on suicide, the rank order of groups by their mean annual suicide risk (White people\u0026thinsp;\u0026gt;\u0026thinsp;Black people; Males\u0026thinsp;\u0026gt;\u0026thinsp;Females)\u003csup\u003e2\u003c/sup\u003e has also been found identically\u0026mdash;albeit in very different types of forced desynchrony protocols\u0026mdash;in their SCN \u003cem\u003etau\u003c/em\u003e (White people\u0026thinsp;\u0026gt;\u0026thinsp;Black people\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e,\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e; Males\u0026thinsp;\u0026gt;\u0026thinsp;Females\u003csup\u003e25\u003c/sup\u003e). In the gold standard forced desynchrony protocol\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e, humans live for 3\u0026ndash;4 weeks in an experimental room devoid of time cues except that they adhere to a dim light/dark schedule (e.g. 18.67 hours wakefulness and 9.33 hours sleep\u0026thinsp;=\u0026thinsp;28 hour \u0026ldquo;days\u0026rdquo;) that is outside the limits of entrainment (synchronization) of their SCN-driven physiologic rhythms (e.g. core body temperature, melatonin) which therefore all free-run together at the individual\u0026rsquo;s characteristic near-24 hour SCN intrinsic \u003cem\u003etau\u003c/em\u003e. These observations suggest that variations in \u003cem\u003etau\u003c/em\u003e may contribute not only to the photoperiodic cycles in suicide risk, but also to the very wide and puzzling variations between Races and Sexes in mean annual suicide risk\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Indeed, ample evidence already links aspects of human circadian rhythms (e.g. seasonality, chronotype, genetics) with suicidal behavior\u003csup\u003e\u003cspan additionalcitationids=\"CR27 CR28\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe present study hypothesized that subgroup differences in annual means and amplitudes of suicide risk are linearly scaled to \u003cem\u003etau\u003c/em\u003e according to Race, Sex, and photoperiod gradients. The USA Center for Disease Control\u0026rsquo;s monthly suicide database from 1999\u0026ndash;202030 was interrogated by the eight Race:Sex subgroups, and extant \u003cem\u003etau\u003c/em\u003e values were extracted from the gold standard protocols in the literature. Annual means and amplitudes of suicide risk were mapped onto the subgroup\u0026rsquo;s corresponding SCN \u003cem\u003etau\u003c/em\u003e values. Any coherent relationships derived between these variables could shed important new light on the regulation of suicide risk.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cstrong\u003eExtraction of suicide numbers\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCDC WONDER suicide data are ultimately derived from the death certificates submitted by families and officials to the local and state Vital Records offices, which then submits these data to the National Center for Health Statistics (NCHS). The NCHS marks all cases of suspected suicide as provisional for 26 weeks pending further investigation, before submitting the final data to the National Vital Statistics System (NVSS). The CDC then compiles these NVSS data into the CDC WONDER database\u003csup\u003e30\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe monthly suicide numbers were extracted using the “Underlying Cause of Death” databases (1999 – 2020), using ICD-10 codes X60 – X84 for “Intentional self-harm.” The monthly adult (ages 25 – 84) 22-year suicide time series were divided into 8 subgroups according to the CDC’s current categories for Sex (Male and Female) and Race (White, Black, Asian/Pacific Islander, and American Indian/Alaskan Native peoples; abbreviated herein as WM, WF, BM, BF, APIM, APIF, AIANM, and AIANF)\u003csup\u003e30\u003c/sup\u003e. In the 85+ age range, only White Males had sufficient numbers of reportable suicides for all 264 months, so this age bracket was excluded from the adult analyses. Reporting of Race is mandatory on the USA census. The API subgroup is an aggregated and particularly heterogeneous Race category that is defined as peoples whose origins are from the Far East, Indian subcontinent, or Southeast Asia (who also identified on the 2010 census as Chinese 24%, Indian 20%, Filipino 18%, Vietnamese 11%, Korean 10%, Japanese 5%, Pakistani 3%…)\u003csup\u003e31\u003c/sup\u003e. All subgroups had valid suicide data for the entirety of their 264 months except for AIANF, who only had 14% non-suppressed monthly data and who therefore had to be excluded from all analyses. The total number of suicides for these 7 remaining subgroups from 1999 – 2020 was 700,881.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDemographics\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe subgroup percentages of the USA adult population in 1999 (2020) were WM 41% (39%), WF 43% (40%); BM 5% (6%), BF 6% (7%); APIM 2% (3%), APIF 2% (4%); and AIANM 0.4% (0.7%), AIANF 0.4% (0.7%). Each subgroup’s 22-year average Fractional Population (FP) was taken as the average of their 1999 and 2020 fractional populations percentages.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eNon-linear analysis of the subgroup’s suicide risk profiles\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe 7 subgroup-specific Individual suicide risk profiles \u003cem\u003eR\u003csub\u003ei\u003c/sub\u003e(t)\u003c/em\u003e were obtained by first dividing each respective subgroup’s raw monthly suicide totals by the number of days per month (including adjustment for leap years) and by the subgroup’s populations per month (linearly interpolated from their yearly populations—the results did not change whether the interpolations were anchored in January or July), then multiplied by 10,000,000 for a tractable analysis (i.e. units for \u003cem\u003eR\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e) = \u0026nbsp;(suicides/day/subgroup population)\u003csub\u003e*\u003c/sub\u003e10\u003csup\u003e-7\u003c/sup\u003e. To characterize each subgroup’s time series, a non-linear/one-harmonic cosine function was tested for suitability, whereby Individual suicide risk \u003cem\u003eR\u003csub\u003ei\u003c/sub\u003e(t)\u003c/em\u003e = \u003cem\u003ea\u003c/em\u003e + \u003cem\u003ebt + ct\u003csup\u003e2\u003c/sup\u003e + d\u003c/em\u003e\u003csub\u003e*\u003c/sub\u003ecos[(2p(\u003cem\u003et – e\u003c/em\u003e)/12)], where \u003cem\u003et\u003c/em\u003e is month (January 1999 = 1). All analyses were performed using the on-line “Non-linear Least Squares Regression” software program from Statpages.org\u003csup\u003e32\u003c/sup\u003e, which is the same program that is included in “R”. The 22-year mean annual suicide risks \u003cem\u003em\u003csub\u003ei\u003c/sub\u003e\u0026nbsp;\u003c/em\u003ewere also extracted from each subgroup\u003csub\u003ei\u003c/sub\u003e’s fitted curve. Prespecified subgroup-specific individual suicide risk parameters of interest were mean annual suicide risk \u003cem\u003em\u003c/em\u003e, seasonal amplitude of suicide risk \u003cem\u003ed\u003c/em\u003e, and phase \u003cem\u003ee.\u0026nbsp;\u003c/em\u003eThe model-derived subgroup-specific parameter estimates \u003cem\u003em\u003c/em\u003e, \u003cem\u003ed\u003c/em\u003e and \u003cem\u003ee\u003c/em\u003e were compared using 95% confidence intervals (mean ± 1.96\u003csub\u003e*\u003c/sub\u003eSE).\u003c/p\u003e\n\u003cp\u003eIn order to more closely examine the hypothesis that the annual variation in suicide rates is related to the photoperiod, a further “yearly waveshape analysis” was conducted for each subgroup by 1) detrending each 22-year time series by subtracting its linear and quadratic components, 2) averaging the yearly data over the 22 years, and 3) fitting these data with the curve \u003cem\u003ea\u003c/em\u003e + \u003cem\u003eb\u003c/em\u003e\u003csub\u003e*\u003c/sub\u003ecos(2p(\u003cem\u003et\u003c/em\u003e – \u003cem\u003ee\u003c/em\u003e)/12). An additional exploratory “residual analysis” was then conducted by subtracting each subgroup’s means from the detrended raw 22-year suicide data. Because each subgroup’s residual data exhibited obvious sinusoidal multi-year rhythmicity that oscillated around a zero baseline, they were also fitted with cosine curves of the form Residual suicide risk = \u003cem\u003eA\u003c/em\u003e\u003csub\u003e*\u003c/sub\u003ecos(2p(\u003cem\u003et\u003c/em\u003e – \u003cem\u003eE\u003c/em\u003e)/\u003cem\u003eT\u003c/em\u003e), where \u003cem\u003et\u0026nbsp;\u003c/em\u003e= month (1 – 264), and \u003cem\u003eA\u003c/em\u003e, \u003cem\u003eT\u003c/em\u003e, and \u003cem\u003eE\u003c/em\u003e are amplitude, period, and phase, respectively.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMapping of the WM and WF suicide data onto the extant WM and WF SCN \u003cem\u003etau\u003c/em\u003e data\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe hypothesis that SCN \u003cem\u003etau\u003c/em\u003e scales suicide risk necessarily invokes a mapping of the suicide risk data from deceased suicide victims onto the SCN \u003cem\u003etau\u003c/em\u003e data from healthy humans. The unique Duffy et al.\u003csup\u003e25\u003c/sup\u003e \u003cem\u003etau\u003c/em\u003e data for both healthy White Males (N = 105, mean ± SE, 24.19 ± 0.02) and Females (N = 52, mean ± SE, 24.09 ± 0.03) are 1) normally distributed and hence are consistent with \u003cem\u003etau\u0026nbsp;\u003c/em\u003ebeing normally distributed in the entire White population, 2) the only gold standard estimates for human SCN \u003cem\u003etau\u003c/em\u003e \u003cem\u003ein vivo\u003c/em\u003e at present and possibly for the foreseeable future\u003csup\u003e33\u003c/sup\u003e, and 3) derived from forced desynchrony studies that spanned over 25 years, the last ~12 of which overlapped with the present study, making them valid long-term mean \u003cem\u003etau\u003c/em\u003e estimates for healthy WM and WF. In addition, insofar as 1) up to 60% of all USA suicide victims have no known prior history of mental illness,\u003csup\u003e34,35\u003c/sup\u003e and 2) there is currently no evidence that mental distress of any kind modifies SCN \u003cem\u003etau\u003c/em\u003e \u003cem\u003ein vivo\u003c/em\u003e\u003csup\u003e36\u003c/sup\u003e, these Duffy et al. mean \u003cem\u003etau\u003c/em\u003e values for healthy WM and WF represent the best approximations for the mean \u003cem\u003etau\u003c/em\u003e values for these hundreds of thousands of White suicide victims in the present study. Therefore, mapping the suicide data onto the \u003cem\u003etau\u003c/em\u003e data was warranted as an initial approach to this neurobiologically quite defensible hypothesis, although concerns about a possible “ecological fallacy” (e.g. drawing inferences about individual biological processes from their correlated population biological measures) should not be dismissed. The actual mapping is described below (see Results, \u003cem\u003eSCN proportional control of suicide risk\u003c/em\u003e).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ePopulation attributable fraction\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe partial Population Attributable Fraction for a given subgroup is defined herein as the proportion of incident cases (i.e. the Incidence Risk IR) of suicide that would \u003cem\u003enot\u003c/em\u003e have occurred had each subgroup\u003csub\u003ei\u003c/sub\u003e not been exposed to its pathogenic “dose” \u003cem\u003etau\u003c/em\u003e, or PAF\u003csub\u003ei\u003c/sub\u003e = (IR\u003csub\u003eexposed\u003c/sub\u003e – IR\u003csub\u003eunexposed\u003c/sub\u003e)/IR\u003csub\u003eexposed\u003c/sub\u003e\u003csup\u003e37,38\u003c/sup\u003e. A PAF with repeated IR’s that can be averaged over time—which in the present study was 264 measurements—provides a better overall PAF estimate than a PAF based on just a single IR\u003csup\u003e39\u003c/sup\u003e. Each subgroup’s 22-year average IR estimate was thus taken as their 22-year mean annual suicide risk \u003cem\u003em\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e. Because each subgroup’s photoperiodic variation in suicide risk oscillated sinusoidally with amplitudes \u003cem\u003ed\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e around their respective means, the PAFcalculations could be validly based solely on \u003cem\u003em\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e. Because there was no zero-risk unexposed subgroup, the subgroup-specific partial PAF\u003csub\u003ei\u003c/sub\u003e’s were calculated relative to the subgroup with the minimum \u003cem\u003em\u003c/em\u003e and then weighted by their fractional population percentage (FP\u003csub\u003ei\u003c/sub\u003e), and summed, such that the overall PAF = S\u0026nbsp;PAF\u003csub\u003ei\u003c/sub\u003e = S [FP\u003csub\u003ei*\u003c/sub\u003e(\u003cem\u003em\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e – \u003cem\u003em\u003csub\u003emin\u003c/sub\u003e\u003c/em\u003e)/\u003cem\u003em\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e]. In addition, since the hypothesis specifies that D\u003cem\u003em\u003c/em\u003e = \u003cem\u003ek\u003c/em\u003e\u003csub\u003e1*\u003c/sub\u003eD\u003cem\u003etau\u003c/em\u003e, then the validity of the PAF requires that the PAF\u003csub\u003ei\u003c/sub\u003e terms (\u003cem\u003em\u003csub\u003ei\u003c/sub\u003e\u0026nbsp;\u003c/em\u003e– \u003cem\u003em\u003csub\u003emin\u003c/sub\u003e\u003c/em\u003e)/\u003cem\u003em\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e ≈ [(\u003cem\u003etau\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e – \u003cem\u003etau\u003csub\u003emin\u003c/sub\u003e\u003c/em\u003e)/\u003cem\u003etau\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e] or the PAF is rendered invalid\u003csup\u003e37,39,40\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eTwo assumptions went into this PAF calculation: 1) each subgroup was continuously exposed more or less stably to their characteristic pathogenic dose of intrinsic \u003cem\u003etau\u003c/em\u003e throughout the 22-years; and 2) any subgroup-specific variabilities due to non-\u003cem\u003etau\u003c/em\u003e-related suicide risk (e.g. environmental, socioeconomic, non-SCN brain regions, genetic) would be exhibited as additional variabilities “away from” the linear \u003cem\u003etau\u003c/em\u003e-related suicide risk variabilities.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e\u003cstrong\u003eNon-linear model fits and acrophase analysis\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFig. 1 and Table 1 depict the non-linear model fits, which appeared quite acceptable, especially in the more populous subgroups. The single harmonic sinusoidal component was statistically significant in all subgroups except in BF (\u003cem\u003ep\u003c/em\u003e = 0.18) and APIF (\u003cem\u003ep\u003c/em\u003e = 0.054). As expected, the rank orders of the 22-year mean annual suicide risk \u003cem\u003em\u003c/em\u003e\u0026mdash;and surprisingly also for \u003cem\u003ed\u003c/em\u003e\u0026mdash;were W \u0026gt; B; M \u0026gt; F. The subgroup\u0026rsquo;s acrophases \u003cem\u003ee\u003c/em\u003e were all around May-June and did not differ significantly between any subgroups. The grand mean phase \u003cem\u003ee\u003c/em\u003e for the entire sample was June 5 (May 28 to June 12), which was 4.44 SE before the summer solstice.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 1. Model parameters for the 7 subgroups.\u003c/strong\u003e Significant differences were found between all subgroups for both \u003cem\u003em\u003c/em\u003e and \u003cem\u003ed\u003c/em\u003e, with rank orders: \u003cem\u003em\u003c/em\u003e, WM \u0026gt; AIANM \u0026gt; BM \u0026gt; APIM \u0026gt; WF \u0026gt; APIF \u0026gt; BF; \u003cem\u003ed\u003c/em\u003e, WM and AIANM \u0026gt; APIM and BM and WF \u0026gt; APIF and BF. There were no significant differences between subgroups in the timing of their acrophases.\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"625\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\" style=\"width: 55px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSbgrp\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" style=\"width: 63px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eModel\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" style=\"width: 149px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003em\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" style=\"width: 185px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003ed\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" style=\"width: 173px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eAcrophase\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 55px;\"\u003e\n \u003cp\u003eWM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 63px;\"\u003e\n \u003cp\u003e\u003cem\u003er\u0026nbsp;\u003c/em\u003e= 0.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 149px;\"\u003e\n \u003cp\u003e7.834 (7.792 to 7.818)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 185px;\"\u003e\n \u003cp\u003e0.474 (0.414 to 0.534)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 173px;\"\u003e\n \u003cp\u003eJun 3 (May 27 to Jun 10)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 55px;\"\u003e\n \u003cp\u003eWF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 63px;\"\u003e\n \u003cp\u003e\u003cem\u003er\u0026nbsp;\u003c/em\u003e= 0.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 149px;\"\u003e\n \u003cp\u003e2.112 (2.094 to 2.131)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 185px;\"\u003e\n \u003cp\u003e0.128 (0.102 to 0.154)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 173px;\"\u003e\n \u003cp\u003eJun 13 (Jun 7 to Jun 19)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 55px;\"\u003e\n \u003cp\u003eBM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 63px;\"\u003e\n \u003cp\u003e\u003cem\u003er\u003c/em\u003e = 0.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 149px;\"\u003e\n \u003cp\u003e3.385 (3.346 to 3.426)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 185px;\"\u003e\n \u003cp\u003e0.143 (0.0867 to 0.199)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 173px;\"\u003e\n \u003cp\u003eJun 1 (May 24 to Jun 9)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 55px;\"\u003e\n \u003cp\u003eBF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 63px;\"\u003e\n \u003cp\u003e\u003cem\u003er\u0026nbsp;\u003c/em\u003e= 0.55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 149px;\"\u003e\n \u003cp\u003e0.672 (0.655 to 0.689)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 185px;\"\u003e\n \u003cp\u003e0.0164 (-0.00790 to 0.0407)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 173px;\"\u003e\n \u003cp\u003eMay 3 (Feb 8 to Jul 28)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 55px;\"\u003e\n \u003cp\u003eAPIM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 63px;\"\u003e\n \u003cp\u003e\u003cem\u003er\u0026nbsp;\u003c/em\u003e= 0.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 149px;\"\u003e\n \u003cp\u003e2.920 (2.867 to 2.977)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 185px;\"\u003e\n \u003cp\u003e0.160 (0.0820 to 0.238)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 173px;\"\u003e\n \u003cp\u003eMay 12 (Apr 14 to Jun 9)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 55px;\"\u003e\n \u003cp\u003eAPIF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 63px;\"\u003e\n \u003cp\u003e\u003cem\u003er\u003c/em\u003e = 0.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 149px;\"\u003e\n \u003cp\u003e1.148 (1.098 to 1.195)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 185px;\"\u003e\n \u003cp\u003e0.0400 (-0.00416 to 0.0803)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 173px;\"\u003e\n \u003cp\u003eJun 14 (Apr 16 to Aug 13)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 55px;\"\u003e\n \u003cp\u003eAIAM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 63px;\"\u003e\n \u003cp\u003e\u003cem\u003er\u003c/em\u003e = 0.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 149px;\"\u003e\n \u003cp\u003e5.980 (5.833 to 6.132)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 185px;\"\u003e\n \u003cp\u003e0.476 (0.264 to 0.688)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 173px;\"\u003e\n \u003cp\u003eJun 11 (May 16 to Jul 6)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 55px;\"\u003e\n \u003cp\u003eAIAF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 63px;\"\u003e\n \u003cp\u003eNA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 149px;\"\u003e\n \u003cp\u003eNA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 185px;\"\u003e\n \u003cp\u003eNA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 173px;\"\u003e\n \u003cp\u003eNA\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 55px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 63px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 149px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 185px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 173px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 55px;\"\u003e\n \u003cp\u003eSample\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 63px;\"\u003e\n \u003cp\u003e\u003cem\u003er\u0026nbsp;\u003c/em\u003e= 0.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 149px;\"\u003e\n \u003cp\u003e4.384 (4.361 to 4.406)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 185px;\"\u003e\n \u003cp\u003e0.258 (0.226 to 0.290)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\" valign=\"bottom\" style=\"width: 173px;\"\u003e\n \u003cp\u003eJun 5 (May 28 to Jun 12)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eWaveshape analysis\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn the most populous subgroups, the 22-year \u0026ldquo;stationary\u0026rdquo; average annual suicide rhythm could not be distinguished from a pure sinusoid (Fig. 2). Notably, there appeared what could only be the signature protective effect of Christmas on suicides in December for subgroups who were either the more populous and/or traditionally of Christian faith, as well as a seemingly smaller rebound in those same subgroups in January.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMulti-year sinusoidal suicide risk rhythms and their correlates with solar sunspot activity\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePresiding over the years of this study were Solar Cycles 23 (~12.3 years) and 24 (~11.0 years)\u003csup\u003e41\u003c/sup\u003e, during which all subgroups exhibited significant multi-year sinusoidal suicide risk rhythms that had multiple and consistent correlates in the Schwabe sunspot cycles (Figs. 3, 4, Supplementary Table S1). The subgroup\u0026rsquo;s periods fell into three mostly distinct period bands of ~8, ~12, and ~16 years. The \u003cem\u003eperiods\u003c/em\u003e of the two ~12-year band members (AIANM and APIM) found a major correlate in the ~12-year period of the prevailing Schwabe sunspot cycle\u003csup\u003e42\u003c/sup\u003e. The \u003cem\u003eamplitudes\u003c/em\u003e of the two ~12-year band members exhibited ~40% reductions from Cycle 23 to 24, which was similar to the ~35% drop in the amplitudes of sunspot numbers\u003csup\u003e43\u003c/sup\u003e (Fig. 5). A related solar amplitude correlate was also found in all subgroups, whose solar sunspot amplitudes \u003cem\u003eSA\u003c/em\u003e were correlated with their solar photoperiod amplitudes \u003cem\u003ed\u003c/em\u003e (\u003cem\u003eSA\u003c/em\u003e vs. \u003cem\u003ed\u003c/em\u003e: \u003cem\u003er\u003c/em\u003e = 0.83, \u003cem\u003ep\u003c/em\u003e = 0.02; slope = 0.55; intercept CI\u0026rsquo;s: \u003cem\u003ed\u003c/em\u003e-axis -0.15 to 0.21; \u003cem\u003eSA\u003c/em\u003e axis -0.74 to 0.81). The ~8-year band members found their solar \u003cem\u003eperiod\u003c/em\u003e correlate in the prominent ~8-year sunspot asymmetry cycle\u003csup\u003e44-47\u003c/sup\u003e, which was mysteriously conspicuous during the solar Maunder minimum of 1645 \u0026ndash; 1715\u003csup\u003e48,49\u003c/sup\u003e. Sunspot asymmetry has been conceptualized and measured in many different ways, making acrophase estimates difficult to ascertain, but may have been near 2001, 2011, and 2017\u003csup\u003e44,47,50\u003c/sup\u003e, which approximate the acrophases\u0026mdash;perhaps recorded with even more fidelity\u0026mdash;for WM (2001, 2009, 2017) and the phase-lagged BF (2003, 2011, 2018), but somewhat less so for slightly speedier APIF (2004, 2010, 2016).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSCN proportional control of suicide risk\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFig. 6 depicts that the seven subgroup\u0026rsquo;s epidemiologic (\u003cem\u003em\u003c/em\u003e, \u003cem\u003ed\u003c/em\u003e) coordinates were highly linearly correlated (\u003cem\u003er\u003c/em\u003e = 0.97, \u003cem\u003ep\u003c/em\u003e = 0.0004; slope = 0.071, CI = 0.050 to 0.093; \u003cem\u003em\u003c/em\u003e-intercept CI = -1.06 to +1.52; \u003cem\u003ed\u003c/em\u003e-intercept CI = -0.13 to +0.055), suggesting an important causal biological relationship between these two global measures of suicide risk, such that the regression line could pass through the origin (0, 0) where average annual suicide risk vanishes. What biological mechanisms could possibly explain these two quite conspicuous findings?\u003c/p\u003e\n\u003cp\u003eThe hypothesis (see Introduction) stipulates that both \u003cem\u003em\u003c/em\u003e and \u003cem\u003ed\u003c/em\u003e vary linearly with SCN \u003cem\u003etau\u003c/em\u003e. As such, the first finding\u0026mdash;the tight correlation between \u003cem\u003em\u003c/em\u003e and \u003cem\u003ed\u003c/em\u003e\u0026mdash;could be due to the fact that both \u003cem\u003em\u003c/em\u003e and \u003cem\u003ed\u003c/em\u003e are scaled separately and proportionally to SCN \u003cem\u003etau\u003c/em\u003e. Regarding the second finding\u0026mdash;that both \u003cem\u003em\u003c/em\u003e and \u003cem\u003ed\u0026nbsp;\u003c/em\u003ecould simultaneously reduce to zero\u0026mdash;the hypothesis must now include the existence of a zero \u003cem\u003etau\u003c/em\u003e-related suicide risk set-point. In order to formally test these two hypotheses, the Duffy et al. WM and WF (\u003cem\u003em\u003c/em\u003e, \u003cem\u003ed\u003c/em\u003e) 2D coordinates were mapped onto their respective WM and WF (\u003cem\u003etau\u003c/em\u003e, \u003cem\u003em\u003c/em\u003e, \u003cem\u003ed\u003c/em\u003e) 3D coordinates (see Methods). If these two hypothesis are true, then these two points will define a line in 3D space that must 1) intersect the \u003cem\u003etau\u003c/em\u003e axis in the vicinity of the hypothetical zero suicide risk set-point (\u003cem\u003etau\u003csub\u003eset\u003c/sub\u003e\u003c/em\u003e, 0, 0), and 2) have orthogonal linear projections in the (\u003cem\u003etau\u003c/em\u003e, \u003cem\u003ed\u003c/em\u003e) and (\u003cem\u003etau\u003c/em\u003e, \u003cem\u003em\u003c/em\u003e) planes with slopes (\u003cem\u003ed/tau\u0026nbsp;\u003c/em\u003eand \u003cem\u003em/tau\u003c/em\u003e) that preserve the original \u003cem\u003ed\u003c/em\u003e/\u003cem\u003em\u003c/em\u003e ratio in their mutual slope ratio = (\u003cem\u003ed/tau\u003c/em\u003e)/(\u003cem\u003em/tau\u003c/em\u003e) = \u003cem\u003ed\u003c/em\u003e/\u003cem\u003em\u003c/em\u003e, independent of any dihedral angle between the two planes.\u003c/p\u003e\n\u003cp\u003eFig. 7 depicts the results of this mapping. Consistent with the predictions, (\u003cem\u003etau\u003c/em\u003e, \u003cem\u003em\u003c/em\u003e) and (\u003cem\u003etau\u003c/em\u003e, \u003cem\u003ed\u003c/em\u003e) both intersected the suicide risk zero intercept precisely at \u003cem\u003etau\u003csub\u003eset\u003c/sub\u003e\u003c/em\u003e\u003csub\u003e\u0026nbsp;\u003c/sub\u003e= 24.053. In addition, the original \u003cem\u003ed\u003c/em\u003e/\u003cem\u003em\u003c/em\u003e slope ratio was preserved (Fig. 6 \u003cem\u003ed\u003c/em\u003e/\u003cem\u003em\u003c/em\u003e = 0.071 (0.050 to 0.093); Fig. 7 \u003cem\u003ed\u003c/em\u003e/\u003cem\u003em\u003c/em\u003e = 0.060). It\u0026rsquo;s a miraculous bullseye! In White people, 1) the magnitude of individual suicide risk appears to be proportional to (\u003cem\u003etau\u003c/em\u003e \u0026ndash; \u003cem\u003etau\u003csub\u003eset\u003c/sub\u003e\u003c/em\u003e), and 2) \u003cem\u003etau\u003csub\u003eset\u003c/sub\u003e\u003c/em\u003e = 24.05 marks the zero \u003cem\u003etau\u003c/em\u003e-related suicide set-point where both \u003cem\u003em\u003c/em\u003e and \u003cem\u003ed\u003c/em\u003e simultaneously reduce to zero (see Methods for limitations). This SCN circadian and photoperiodic formulation of suicide risk is entirely consistent with the established role of the SCN in the daily and seasonal regulation of affect, mood, and suicide risk\u003csup\u003e51-55\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eFig. 7 therefore yields Equations for Individual monthly suicide risk \u003cem\u003eR\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e) due to \u003cem\u003etau\u003csub\u003ei\u003c/sub\u003e,\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eR\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e)\u003cem\u003e\u0026nbsp;\u003c/em\u003e= \u003cem\u003ea\u003c/em\u003e\u003csub\u003e1*\u003c/sub\u003e(\u003cem\u003etau\u003csub\u003ei\u0026nbsp;\u003c/sub\u003e\u003c/em\u003e\u0026ndash; \u003cem\u003etau\u003csub\u003eset\u003c/sub\u003e\u003c/em\u003e) + \u003cem\u003ea\u003c/em\u003e\u003csub\u003e2*\u003c/sub\u003e(\u003cem\u003etau\u003csub\u003ei\u0026nbsp;\u003c/sub\u003e\u003c/em\u003e\u0026ndash; \u003cem\u003etau\u003csub\u003eset\u003c/sub\u003e\u003c/em\u003e)\u003csub\u003e*\u003c/sub\u003ecos[(2p\u003cem\u003et\u003c/em\u003e/12) + \u003cem\u003ee\u003c/em\u003e] \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u003cem\u003etau\u003csub\u003ei\u003c/sub\u003e\u0026nbsp;\u003c/em\u003e\u0026gt;\u003cem\u003e\u0026nbsp;tau\u003csub\u003eset\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eR\u003csub\u003ei\u003c/sub\u003e(t)\u0026nbsp;\u003c/em\u003e= 0 \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u003cem\u003etau\u003csub\u003ei\u003c/sub\u003e\u0026nbsp;\u003c/em\u003e\u0026le; \u003cem\u003etau\u003csub\u003eset\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003ewhere \u003cem\u003ea\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e and \u003cem\u003ea\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e are the scaling factors (57.22 and 3.46) for \u003cem\u003em\u003c/em\u003e and \u003cem\u003ed\u003c/em\u003e, respectively, \u003cem\u003et\u003c/em\u003e is day of the year, \u003cem\u003ee\u003c/em\u003e is the phase that is assumed here to be common to every subgroup\u003csub\u003ei\u003c/sub\u003e, and \u003cem\u003etau\u003csub\u003eset\u003c/sub\u003e\u003c/em\u003e is the zero \u003cem\u003etau\u003c/em\u003e-related suicide risk set-point = 24.05 hours.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eValidity checks on the PAF calculation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSuicide risk was hypothesized to increase linearly with the pathogenic dose of \u003cem\u003etau\u003c/em\u003e, or D\u003cem\u003em\u003csub\u003e\u0026nbsp;\u003c/sub\u003e\u003c/em\u003e= \u003cem\u003ek\u003c/em\u003e\u003csub\u003e*\u003c/sub\u003eD\u003cem\u003etau\u003c/em\u003e. Thus, if the PAF is valid, the partial PAF term (\u003cem\u003em\u003csub\u003ei\u003c/sub\u003e\u0026nbsp;\u003c/em\u003e\u0026ndash; \u003cem\u003em\u003csub\u003emin\u003c/sub\u003e\u003c/em\u003e)/\u003cem\u003em\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e must approximate the SCN term [(\u003cem\u003etau\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e \u0026ndash; \u003cem\u003etau\u003csub\u003emin\u003c/sub\u003e\u003c/em\u003e)/\u003cem\u003etau\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e] (see Methods). Substituting the WM and WF \u003cem\u003em\u003c/em\u003e and \u003cem\u003etau\u003c/em\u003e values into this PAF formula yields the partial PAF term [(\u003cem\u003em\u003csub\u003eWM\u003c/sub\u003e\u0026nbsp;\u003c/em\u003e\u0026ndash; \u003cem\u003em\u003csub\u003eWF\u003c/sub\u003e\u003c/em\u003e)/\u003cem\u003em\u003csub\u003eWM\u003c/sub\u003e\u003c/em\u003e]\u003csub\u003e\u0026nbsp;\u003c/sub\u003e= 0.728, which is extremely close to the SCN term [(\u003cem\u003etau\u003csub\u003eWM\u003c/sub\u003e\u003c/em\u003e\u003csub\u003e\u0026nbsp;\u003c/sub\u003e\u0026ndash; \u003cem\u003etau\u003csub\u003eset\u003c/sub\u003e\u003c/em\u003e) \u0026ndash; (\u003cem\u003etau\u003csub\u003eWF\u003c/sub\u003e\u003c/em\u003e \u0026ndash; \u003csub\u003e\u0026nbsp;\u003c/sub\u003e\u003cem\u003etau\u003csub\u003eset\u003c/sub\u003e\u003c/em\u003e)/(\u003cem\u003etau\u003csub\u003eWM\u003c/sub\u003e\u003c/em\u003e \u0026ndash; \u003cem\u003etau\u003csub\u003eset\u003c/sub\u003e\u003c/em\u003e)] = 0.730, bolstering the validity of both the PAF model and the hypothesis of linear scaling of \u003cem\u003em\u003c/em\u003e to \u003cem\u003etau\u003c/em\u003e. The two assumptions that went into the PAF are now discussed below.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eThe continuous exposure of each subgroup\u003csub\u003ei\u003c/sub\u003e to their extrapolated 22-year mean tau\u003csub\u003ei\u003c/sub\u003e.\u0026nbsp;\u003c/em\u003eThe Duffy et al. \u003cem\u003etau\u003c/em\u003e data were collected over the course of ~25 years, ~12 of which overlapped with the present study interval. It was therefore assumed that the Duffy et al. mean \u003cem\u003etau\u003c/em\u003e estimates for WM and WF were accurate long-term estimates and could reasonably be extrapolated identically for the entire ~22 years. That \u003cem\u003etau\u003c/em\u003e indeed acted continually and proportionally on both \u003cem\u003em\u003c/em\u003e and \u003cem\u003ed\u003c/em\u003e throughout these 22 years was demonstrated in a separate model (see SM, section S2).\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eAbsence of any non-tau-related major exogenous or endogenous confounders.\u003c/em\u003e This was validated insofar as there were no obvious subgroup-specific variabilities that were exhibited \u0026ldquo;away from\u0026rdquo; the tight (\u003cem\u003em\u003c/em\u003e, \u003cem\u003ed\u003c/em\u003e) regression line in Fig. 6. In fact, the AIANM subgroup was the subgroup that was located farthest away from the regression line, and this deviation could almost entirely be accounted for by their unusually high solar photoperiod amplitude \u003cem\u003ed\u003c/em\u003e relative to their \u003cem\u003em\u003c/em\u003e (which was also biologically consistent with their very high sunspot amplitude).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe PAF calculation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe valid PAF was thus calculated as follows: PAF = S\u0026nbsp;PAF\u003csub\u003ei\u003c/sub\u003e = S [(\u003cem\u003em\u003csub\u003ei\u003c/sub\u003e\u0026nbsp;\u003c/em\u003e\u0026ndash; \u003cem\u003em\u003csub\u003emin\u003c/sub\u003e\u003c/em\u003e)/\u003cem\u003em\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e] \u003csub\u003e*\u003c/sub\u003ePF\u003cem\u003e\u003csub\u003ei\u003c/sub\u003e\u0026nbsp;\u003c/em\u003e= WM ((7.79 \u0026ndash; 0.67)/7.79)\u003csub\u003e*\u003c/sub\u003e0.40 + WF ((2.12 \u0026ndash; 0.67)/2.12)\u003csub\u003e*\u003c/sub\u003e0.415 + BM ((3.39 \u0026ndash; 0.67)/3.39)\u003csub\u003e*\u003c/sub\u003e0.055 + APIM ((2.93 \u0026ndash; 0.67)/2.93)\u003csub\u003e*\u003c/sub\u003e0.025 + APIF ((1.15 \u0026ndash; 0.67)/1.15)\u003csub\u003e*\u003c/sub\u003e0.03 + AIANM ((5.95 \u0026ndash; 0.67)/5.95)\u003csub\u003e*\u003c/sub\u003e0.0055 = 73.0% of all USA non-BF suicides from 1999 \u0026ndash; 2020 would not have occurred had each subgroup manifested the enviable low \u003cem\u003etau\u0026nbsp;\u003c/em\u003eof BF. From another perspective, Fig. 7 suggests that all subgroups, including the resilient BFs, could have their \u003cem\u003etau\u003c/em\u003e-related suicide risk reduced to close to zero if their \u003cem\u003etau\u0026nbsp;\u003c/em\u003ewere reduced to 24.05 hours.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe most straightforward explanation for the annual sinusoidal suicide risk rhythm is that it reflects the direct effect of the Earth’s annual sinusoidal photoperiod cycle (or alternatively, the Earth’s annual sinusoidal dawn or dusk cycles) on the human brain at latitudes of the USA. Because of Earth’s axial tilt and its Keplerian motion around the sun, the earliest sunrise (e.g. Washington DC) occurs around June 13 at 5:42 am, but the latest sunset occurs around June 27 at 8:37 pm, even though the longest day still occurs around the summer solstice on June 21\u003csup\u003e56\u003c/sup\u003e. Therefore, the fact that the suicide risk rhythm acrophase of June 5 (May 29 to June 12) was significantly (4.44 SE) before the summer solstice suggests that this rhythm was not merely passively following total photon count but rather was actively entrained in large part by the SCN Morning oscillator that was tracking the earliest solar dawn. Presumably, even with eyelids closed and shades drawn, most people slumber in bedrooms that still allow sufficient solar irradiation at dawn in order for the SCN M oscillator to entrain the suicide rhythm by retinal mechanisms\u003csup\u003e57,58\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eIt is inspiring that a social-religious zeitgeber can have such clear suppressive effect on suicide and suggests that a spirited “all-hands-on-deck” approach to the management of actively suicidal individuals is a worthy acute therapeutic strategy until treatment is secured. Large previous studies have also shown a protective effect of various aspects of religious affiliation on suicide risk, although smaller studies have shown negative results\u003csup\u003e59–61\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eGiven the multiple and consistent period and amplitude correlates, it is hard not to infer that human suicide risk is causally modulated by variations in the Schwabe sunspot cycle. Indeed, several prior studies are consistent with these present sunspot-suicide findings. In Lithuania (1989– 2013, N = 33,072 suicides)\u003csup\u003e62\u003c/sup\u003e, a positive correlation was found between sunspot numbers and suicides. In Finland (1979–1999, N = 27,469 suicides)\u003csup\u003e63\u003c/sup\u003e, a significant 3% increase in suicides was found during years of maximum sunspot activity that approximates the magnitudes found in the present study. In Taiwan (1991–2008, N = 4857 suicides)\u003csup\u003e64\u003c/sup\u003e, significant sunspot suicide rhythms with periods of ~ 5- and ~ 16-years were found in both Males and Females. In addition, it is difficult to even imagine another etiologic agent(s) that could produce such long-term synchronous antiphase sinusoidal suicide rhythms other than some non-visual effects of sunspot cycles on the phase of a biological oscillator like the SCN.\u003c/p\u003e\n\u003cp\u003eMany factors influence SCN \u003cem\u003etau\u003c/em\u003e and hence suicide risk, including 1) light intensity and duration\u003csup\u003e58,65–67\u003c/sup\u003e, 2) SCN neuronal network structure and synchronization\u003csup\u003e68–74\u003c/sup\u003e, 3) SCN GABA-mediated attractive and repulsive forces that modulate the phase angle between the E and M oscillators (y\u003csub\u003eEM\u003c/sub\u003e)\u003csup\u003e75–77\u003c/sup\u003e, 4) gonadal hormones\u003csup\u003e78\u003c/sup\u003e, and 5) SCN circadian gene transcription-translation feedback loops and their influences on SCN neuronal electrical activity\u003csup\u003e79,80\u003c/sup\u003e. In the present context, the various Race:Sex subgroup’s (\u003cem\u003em\u003c/em\u003e, \u003cem\u003ed\u003c/em\u003e) coordinates in Fig. 6 are of great interest and are presumably due to genetic factors resulting from evolutionary pressures operating on \u003cem\u003etau\u003c/em\u003e for the different subgroups at different latitudes, environmental temperatures, and light sensitivities\u003csup\u003e23,24,26,28\u003c/sup\u003e. From another perspective, these Racial differences in \u003cem\u003etau\u003c/em\u003e also provide a compelling explanation for the longstanding and perplexing USA “Suicide Race Paradox,” which struggles to explain why the persecuted Black race paradoxically has a significantly far lower suicide rate than the persecutor White race\u003csup\u003e81\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe hypothesized acrophase in \u003cem\u003etau\u003c/em\u003e during the late-spring predicts that the prevalence and suicidality of the long \u003cem\u003etau\u003c/em\u003e\u003csup\u003e82–84\u003c/sup\u003e delayed chronotype (i.e. late to bed, late to rise) should also peak in the late-spring. While no such definitive epidemiologic studies exist, considerable evidence supports this hypothesis. Delayed chronotype 1) is associated with long \u003cem\u003etau\u003c/em\u003e in rigorous forced desynchrony studies\u003csup\u003e82–84\u003c/sup\u003e, 2) becomes more prevalent with the later evening sunlight that occurs across latitudes within a single time zone with equal clock times\u003csup\u003e85\u003c/sup\u003e, 3) exhibits rank orders in prevalence rates for Race (W \u0026gt; B)\u003csup\u003e86\u003c/sup\u003e and Sex (Males \u0026gt; Females)\u003csup\u003e87\u003c/sup\u003e that are parallel to the Race and Sex gradients in \u003cem\u003etau\u003c/em\u003e and suicide risk in the present study, 4) is associated with a greater suicide risk than less-delayed chronotypes\u003csup\u003e88\u003c/sup\u003e as well as non-delayed chronotypes in both unipolar\u003csup\u003e89,90\u003c/sup\u003e and bipolar\u003csup\u003e91\u003c/sup\u003e mood disorders, and 5) correlates positively with free-running \u003cem\u003etau\u003c/em\u003e in a diurnal rodent model of chronotype\u003csup\u003e92\u003c/sup\u003e. By contrast, two studies found no increase in delayed chronotype with seasons—one was a theoretical study using a fixed \u003cem\u003etau\u003c/em\u003e model\u003csup\u003e93\u003c/sup\u003e, while the other was a clinical study that did not adjust for daylight savings time\u003csup\u003e94\u003c/sup\u003e. Thus, the current evidence is consistent with the hypothesis that the prevalence and suicidality of long \u003cem\u003etau\u003c/em\u003e delayed chronotype should increase with later evening sunlight along Race-, Sex-, and photoperiod gradients.\u003c/p\u003e\n\u003cp\u003eHow can we reconcile the present model with the known \u003cem\u003etau\u003c/em\u003e-\u003cem\u003elengthening\u003c/em\u003e\u003csup\u003e95–97\u003c/sup\u003e anti-suicidal effects of lithium\u003csup\u003e98–100\u003c/sup\u003e? In a seminal study using dispersed human skin fibroblasts—which have similar, but not identical, molecular rhythms compared with the whole SCN\u003csup\u003e101\u003c/sup\u003e—patients with bipolar disorder who were lithium responders (\u003cem\u003en\u003c/em\u003e = 44) tended to \u003cem\u003eshorten\u003c/em\u003e their \u003cem\u003etau\u003c/em\u003e in response to lithium treatment compared with lithium non-responders, who tended to have longer fibroblast \u003cem\u003etau\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e = 15)\u003csup\u003e102\u003c/sup\u003e. These findings were replicated in a preliminary study using neuronal precursor cells\u003csup\u003e103\u003c/sup\u003e. Another study using fibroblasts also found that in patients with bipolar disorder (\u003cem\u003en\u003c/em\u003e = 32), longer \u003cem\u003etau\u003c/em\u003e was associated with poorer response to lithium\u003csup\u003e104\u003c/sup\u003e. Thus, there may be a subset of patients with relatively longer (but not the longest) \u003cem\u003etau\u003c/em\u003e who are uniquely clinically responsive to the \u003cem\u003etau\u003c/em\u003e-shortening effect of lithium. Given that lithium’s overall \u003cem\u003etau\u003c/em\u003e-increasing effect does not apparently increase global suicide risk in patients with mood disorders, it is possible that for unknown reasons, lithium doesn’t lengthen \u003cem\u003etau\u003c/em\u003e in lithium non-responders\u003csup\u003e102,103\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe data in this study have yielded the conclusion that increases in photoperiod (i.e. increases in the amount of visible light in the light/dark LD cycle) result in increases in \u003cem\u003etau\u003c/em\u003e in diurnal humans (see SM, section S4 for discussion of Aschoff’s Rule and light’s effects on \u003cem\u003etau\u003c/em\u003e in LL and LD in nocturnal and diurnal organisms)\u003csup\u003e105\u003c/sup\u003e. It is also possible that some as yet unidentified non-visual band of electromagnetic radiation pollution\u003csup\u003e106\u003c/sup\u003e could be contributing, for example, to these long-term linear and parabolic variations in suicide rates\u003csup\u003e107\u003c/sup\u003e. In this regard, Wever famously “guaranteed at a high level of significance” that his artificial 10 Hz electric field was capable of modifying \u003cem\u003etau\u003c/em\u003e\u003csup\u003e22\u003c/sup\u003e (p. 205), raising the possibility that a treatment such as repetitive transcranial magnetic stimulation (rTMS) could be a rapidly acting \u003cem\u003etau\u003c/em\u003e-reducing treatment for individuals with acute suicide risk. Perhaps more quickly within therapeutic reach would be mathematically derived \u003cem\u003etau\u003c/em\u003e-shortening light/dark treatments with specified light intensities and schedules, which could hold great promise for treating suicidal individuals\u003csup\u003e19,58\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe present SCN \u003cem\u003etau\u003c/em\u003e-based model of suicide risk implies that the suicidogenic effects of emotional stress are ultimately channeled into the SCN—the “final common pathway”—which then determines whether suicide risk crosses the suicide threshold according to its error signal (\u003cem\u003etau\u003c/em\u003e – \u003cem\u003etau\u003c/em\u003e\u003csub\u003e\u003cem\u003eset\u003c/em\u003e\u003c/sub\u003e) and its \u003cem\u003ed\u003c/em\u003e/\u003cem\u003em\u003c/em\u003e ratio. Certainly, very few people die by suicide without incurring some type of terrible emotional distress, but how does such emotional distress modulate the SCN’s regulation of suicide risk? The effects of emotional stress on the circadian system in general and on SCN \u003cem\u003etau\u003c/em\u003e in particular are only beginning to be clarified\u003csup\u003e108,109\u003c/sup\u003e. Reconciling this SCN final common pathway model of emotional stress with the known and sometimes wide national, historical, and long-term variations in suicide rates might seem challenging.\u003c/p\u003e\n\u003cp\u003eDurkheim’s European pre-electric-light 1870’s suicide data are instructive here (Fig. 9). Each of the three countries (probably \u0026gt; 98% White, but definitive sources do not exist) exhibited robust sinusoidal suicide rhythms with remarkably constant “relative amplitudes” (fitted cosine amplitudes: France 26.2% Italy 26.7%, Prussia 25.9%; Fig. 9A). By contrast, Durkheim’s mean annual suicide rates were only somewhat less than those in the present study (crude suicide rates per 100,000 population: France 16.0; Italy 3.8; Prussia 15.2; USA range, WM 22.3, BF 2.5). In Fig. 9B, Durkheim’s data show that the 1870’s SCN regression line also likely passes through the origin (compare Fig. 9B to Fig. 6). These data therefore permit the inference that suicide risk in the absence of artificial light in 1870’s White Europe was also governed by an SCN that had 1) a larger \u003cem\u003ed\u003c/em\u003e and a 3.7-fold larger \u003cem\u003ed\u003c/em\u003e/\u003cem\u003em\u003c/em\u003e ratio than today\u003csup\u003e110\u003c/sup\u003e, 2) a zero \u003cem\u003etau\u003c/em\u003e-related suicide risk set-point—possibly also different than today, and 3) a very major effect on suicide rates.\u003c/p\u003e\n\u003cp\u003eThe very low suicide rate of 1870’s Italy are instructive given the sometimes quite large inter-national differences in suicide rates that have been observed over time\u003csup\u003e1\u003c/sup\u003e. In Fig. 9B, the fact that Italy’s lowest \u003cem\u003em\u003c/em\u003e fell exactly along the SCN regression line indicates that SCN \u003cem\u003etau\u003c/em\u003e was still involved in regulating Italy’s low suicide risk. But how could such a ~ 4-fold difference in \u003cem\u003em\u003c/em\u003e between geographically similar White populations be solely a function of SCN \u003cem\u003etau\u003c/em\u003e? It seems unlikely that White Italy \u003cem\u003etau\u003c/em\u003e—or more exactly (\u003cem\u003etau\u003c/em\u003e – \u003cem\u003etau\u003c/em\u003e\u003csub\u003e\u003cem\u003eset\u003c/em\u003e\u003c/sub\u003e)—was ~ 4-fold lower than White France and White Prussia \u003cem\u003etau\u003c/em\u003e. In a post-hoc analysis, the White 85 + subgroup exhibited the maximum suicidal risk which was double that of the rest of WM adults, yet their extremely high (\u003cem\u003em\u003c/em\u003e, \u003cem\u003ed\u003c/em\u003e) coordinates (14.367, 1.0135)—like the extremely low (\u003cem\u003em\u003c/em\u003e, \u003cem\u003ed\u003c/em\u003e) coordinates of 1870’s Italy—also stayed exactly on the SCN regression line. While this 2-fold elevation in suicide rates of WM 85 + compared with the rest of adult WM \u003cem\u003etau\u003c/em\u003e could be explained if WM 85 + mean \u003cem\u003etau\u003c/em\u003e = 24.33 hours [i.e. (\u003cem\u003etau\u003c/em\u003e – \u003cem\u003etau\u003c/em\u003e\u003csub\u003e\u003cem\u003eset\u003c/em\u003e\u003c/sub\u003e) = (24.33–24.05) = 0.28 = 2\u003csub\u003e*\u003c/sub\u003e(24.19–24.05)], a \u003cem\u003etau\u003c/em\u003e ≥ 24.33 was seen in only \u0026lt; 25% of the Duffy et al. over 65 age range\u003csup\u003e25\u003c/sup\u003e, requiring that a long \u003cem\u003etau\u003c/em\u003e ≥ 24.33 for this very suicidal WM 85 + subgroup also confers some sort of preferential longevity such that they become the majority of the remaining living members of this WM 85 + subgroup, which seems rather improbable. Thus, something other than differences in \u003cem\u003etau\u003c/em\u003e must also be influencing suicide rates such that low Italy and high WM 85 + remained on the SCN regression despite their extreme and disparate distances from the zero set-point. There is really only one way that this could occur.\u003c/p\u003e\n\u003cp\u003eMost studies have found that various of the multifaceted measures of hope (e.g. spirituality, social cohesion, religious affiliation—collectively referred to hereafter as H) are the most significant individual protective factors against suicide\u003csup\u003e59–61,111\u003c/sup\u003e. Could H somehow be involved in the SCN’s regulation of the suicide risk? What if instead of suicidal risk being proportional to the error signal (\u003cem\u003etau\u003c/em\u003e – \u003cem\u003etau\u003c/em\u003e\u003csub\u003e\u003cem\u003eset\u003c/em\u003e\u003c/sub\u003e), suicide risk now becomes proportional to (\u003cem\u003etau\u003c/em\u003e – \u003cem\u003etau\u003c/em\u003e\u003csub\u003e\u003cem\u003eset\u003c/em\u003e\u003c/sub\u003e – H), where positive H counteracts suicide risk by reducing the suicide error signal that is due to (\u003cem\u003etau\u003c/em\u003e – \u003cem\u003etau\u003c/em\u003e\u003csub\u003e\u003cem\u003eset\u003c/em\u003e\u003c/sub\u003e), thereby maintaining a nation’s linear scaling of suicide risk (\u003cem\u003em\u003c/em\u003e, \u003cem\u003ed\u003c/em\u003e) coordinates on the SCN regression line. H can be positive or negative. H was high in 1870’s Italy, whereas H reaches its absolute minimum in the downtrodden and isolated elderly, whose suicide rates increase rapidly after 70 all the way up to the human maximum\u003csup\u003e1\u003c/sup\u003e. The habenula regulates futility-related affects and has circadian and photoperiodic clocks that respond to light and maintain bidirectional neural connections with the SCN and hence could encode the level of H and relay it to the SCN, which ultimately determines suicide risk\u003csup\u003e112–114\u003c/sup\u003e. It is likely that both \u003cem\u003etau\u003c/em\u003e\u003csub\u003e\u003cem\u003eset\u003c/em\u003e\u003c/sub\u003e and the \u003cem\u003ed\u003c/em\u003e/\u003cem\u003em\u003c/em\u003e ratio are intrinsic parameters of this exquisitely precise SCN master clock\u003csup\u003e8,11,115\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eIn light of these considerations, the PAF now takes its final form: In the USA from 1999–2020, assuming that all subgroups had had the same national H, then \u0026gt; 73% of all non-BF suicides could have been prevented if their SCN \u003cem\u003etau\u003c/em\u003e had been equal to that of the resilient morning-type BF.\u003c/p\u003e\n\u003cp\u003eThe two main limitation of the present study are that 1) the zero \u003cem\u003etau\u003c/em\u003e-related suicide risk set-point was based solely on the \u003cem\u003etau\u003c/em\u003e of WM and WF (see SM, section S3 and Methods), and 2) the suicide data from deceased suicide victims were mapped onto the \u003cem\u003etau\u003c/em\u003e data from healthy subjects. Of course, the WM and WF (\u003cem\u003etau\u003c/em\u003e, \u003cem\u003em\u003c/em\u003e, \u003cem\u003ed\u003c/em\u003e) data in Fig.\u0026nbsp;7 are not merely “two datapoints” but rather are population estimates obtained from decades of methodologically large (from a physiological perspective) sample sizes of White people. In addition, 1) up to 60% of suicide victims appear to have had no documented prior psychiatric illness\u003csup\u003e34,35\u003c/sup\u003e, and 2) there was no evidence for a subgroup-specific differential effect of genetics that was located “away from” the “SCN regression line” in Fig. 6, suggesting that these healthy \u003cem\u003etau\u003c/em\u003e values from Duffy et al. could well reflect those of suicide victims. Another cautionary note is that up to ~ 25% of humans have a circadian \u003cem\u003etau\u003c/em\u003e \u0026lt; 24.0 hours\u003csup\u003e8,116,117\u003c/sup\u003e, which Fig. 7 suggests would be associated with a \u003cem\u003etau\u003c/em\u003e-related suicide risk of zero. Insofar as at least some of these individuals presumably still die by suicide, it is again recognized that there may be “other-than-\u003cem\u003etau\u003c/em\u003e-related” factors that alone can also influence suicide risk. Accordingly, it is virtually certain that the ~ 30% of the extra-\u003cem\u003etau\u003c/em\u003e variance in suicide risk due to emotional factors (e.g. maintenance of H) plays a critical role in determining whether an individual falls prey to suicide.\u003c/p\u003e\n\u003cp\u003eIn summary, all of the data in this study are fully consistent with the SCN \u003cem\u003etau\u003c/em\u003e-based proportional control model such that suicide risk is 1) scaled proportionally to (\u003cem\u003etau\u003c/em\u003e – \u003cem\u003etau\u003c/em\u003e\u003csub\u003e\u003cem\u003eset\u003c/em\u003e\u003c/sub\u003e – H) according to Race:Sex gradients, 2) has a zero \u003cem\u003etau\u003c/em\u003e-related suicide risk set-point = 24.05 hours, and 3) is modified by the Earth’s photoperiod rhythms, the solar sunspot rhythms, and by emotional stress and Hope. The PAF suggests that \u0026gt; 73% of all suicides in the USA from 1999–2020 may have been due to the variations in the operation of this remarkably precise and increasingly well-characterized suprachiasmatic nucleus and hence were theoretically preventable. The quest to discover scalable measures of SCN \u003cem\u003etau\u003c/em\u003e\u003csup\u003e33\u003c/sup\u003e and practical \u003cem\u003etau\u003c/em\u003e-reducing treatments\u003csup\u003e118\u003c/sup\u003e now has urgency.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData Availability.\u003c/strong\u003e The data that supports this investigation are freely available on-line from CDC WONDER at https://wonder.cdc.gov/mcd-icd10html.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests:\u0026nbsp;\u003c/strong\u003e The author reports no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgment.\u0026nbsp;\u003c/strong\u003e The author expresses appreciation to the CDC and affiliated agencies involved in the long-term collection and curating of these exquisite and life-saving suicide data.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding Declaration.\u003c/strong\u003e The author received no funding for the study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eHuman Ethics and Consent to Participate Declaration.\u003c/strong\u003e Not applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contribution\u003c/strong\u003e. 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Rhythms\u003c/em\u003e \u003cstrong\u003e14\u003c/strong\u003e, 493-499 (1999).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-biological-timing-and-sleep","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [npj Biological Timing and Sleep](https://www.nature.com/npjbts)","snPcode":"44323","submissionUrl":"https://submission.springernature.com/new-submission/44323/3","title":"npj Biological Timing and Sleep","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"suicide, suprachiasmatic, circadian, photoperiod, sunspots, Race, Sex, genetic","lastPublishedDoi":"10.21203/rs.3.rs-9152191/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9152191/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Suicide is the 10th leading cause of death and varies seasonally, suggesting involvement of the suprachiasmatic nucleus (SCN) and photoperiod, which both modulate suicide risk and tau, the free-running period of the SCN. This study hypothesized that tau linearly scales suicide risk. The CDC’s 22-year monthly suicide data were fitted with non-linear/cosine curves; annual means m and amplitudes d were extracted; extant tau values were extracted from the literature. The 22-year average annual suicide rhythm was indistinguishable from a pure sinusoid with a late-spring peak, implicating the photoperiod and SCN. Highly correlated variables m and d implicated SCN tau as the proportional driver of both and yielded a zero tau-related suicide risk set-point = 24.05 hours, above which tau-related suicide risk increased proportionally. The population attributable fraction estimated that \u003e73% of all USA suicides were theoretically preventable by reducing tau, which could be the main risk factor for suicide.","manuscriptTitle":"Suicide risk could be proportional to SCN tau above a zero suicide risk set-point of 24.05 hours","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-26 17:14:14","doi":"10.21203/rs.3.rs-9152191/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-04-16T20:28:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"230948016071120058798706184668247705111","date":"2026-04-01T00:34:43+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-03-24T14:20:56+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-19T14:10:54+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-19T01:33:34+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Biological Timing and Sleep","date":"2026-03-17T19:45:49+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-biological-timing-and-sleep","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [npj Biological Timing and Sleep](https://www.nature.com/npjbts)","snPcode":"44323","submissionUrl":"https://submission.springernature.com/new-submission/44323/3","title":"npj Biological Timing and Sleep","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"c132b7bc-c161-4485-84bc-b7e74f9c76ed","owner":[],"postedDate":"March 26th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":65148535,"name":"Health sciences/Diseases"},{"id":65148536,"name":"Health sciences/Medical research"},{"id":65148537,"name":"Health sciences/Risk factors"}],"tags":[],"updatedAt":"2026-04-03T18:04:54+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-26 17:14:14","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9152191","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9152191","identity":"rs-9152191","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}