The Monthly Rhythm of Incidence and Age at Menarche: Thirty Fi Ve Years of Research. the Circa-vacation-study Expectancy Rhythm of Incidence and Age at Menarche

The hypothesis that the vacation-study-expectancy scholar regime produces most of the monthly rhythm of the age at menarche (AaM) was tested. Studies on monthly menarche incidence (MI) refuted climatic factors as a main factor in this rhythm, and indicated that the main factor of this rhythm is the succession of expectancies of study (Stu-months) or vacation (Vac-months) months within a year. Thus the hypothesis of seasonal circa-annual rhythm should be modifi ed to the circa-[vacation (fi esta)]-[study (non-fi esta)]-expectancies rhythm for the MI and age at menarche annual rhythms. In several countries Vac-months had higher MI than Stu-months. The high MI of Vac-months was followed by a large decrease when girls started their studies and a MI increase occurred as vacations approached. The hypothesis proposes that at the end of vacations and at the beginning of the study period the AaM should be lowest, and then the mean of AaM should increase because of the menarche delay of girls whose menarche was arrested by the initiation of school work. This pattern was found in four independent samples, from Chile, Colombia, USA and Brazil. The probability that this result be due to random fl uctuation of means is extraordinarily low (P<10-8). I conclude that the infl uence of the expectancy of vacation and study periods on the monthly rhythm of the age at menarche is a real process that accounts for most of this rhythm.

be found in MI of months belonging to antithetical seasons (summer and winter) and the similarities that should be found in months of diff erent seasons with similar climatic conditions (autumn and spring); 5) the similarity of the rhythm that should be found in regions with the same latitude, altitude and geographical conditions.With all these expected situations we refuted conclusively the seasonality of the circa-annual rhythm of MI; for example: 1) marked rhythms were found in samples from tropical or equatorial zones where the rhythm was not expected (Chennai in India and Medellín in Colombia); 2) in all the examined samples strong diff erences were found among months of the same season or with the same photoperiod and temperature; it was frequent to fi nd a peak of MI followed by a trough of MI in contiguous months (Valenzuela et al., 1996a(Valenzuela et al., , 1996b(Valenzuela et al., , 1999;;Valenzuela 2004, Valenzuela 2006); 3) samples from contiguous regions belonging to diff erent countries show diff erent MI rhythms.One of the most striking diff erences in the menarche incidence (MI), between Hemispheres was found in Feb, with a peak in Santiago (summer) and a trough in Europe (winter, Valenzuela et al. 1991Valenzuela et al. , 1993Valenzuela et al. , 1996aValenzuela et al. , 1996b)).This could be produced by climatic factors, but this is refuted because in most countries of Europe, Jan and Dec (winter months as Feb) showed a peak, but Feb showed a trough.In Santiago we observed for Dec-Jan-Feb a peak-peak-peak series, in Europe a peak-peak-trough series.This correlated very well with the quality of months being a vacation (Vac) or a study (Stu) month; in Santiago a Vac-Vac-Vac series and in Europe a Vac-Vac-Stu series occurred for Dec-Jan-Feb, respectively.This discovery was realized independently by Prof. Csoknyay in Hungary, Prof. Srikumari in India, Prof. Pineda in Colombia and by our group in Santiago, because in the four countries Stu-months and Vac-months showed lower and higher MI, respectively (Valenzuela et al., 1996a(Valenzuela et al., , 1996b(Valenzuela et al., , 1999)).We decided to test the hypothesis that Stu-months and Vac-months implied low and high MI, respectively.With four samples from Chennai (ancient Madras, India), Debrecen (Hungary), Medellín (Colombia) and Santiago (Chile) we found only 5 out of 48 months that disagreed with the hypothesis, thus the agreement was highly signifi cant (P<10 -8 , Valenzuela et al., 1999).We hypothesized that vacations associated with fi esta (or relaxation) expectancy elicited menarche and that study, associated with non-fiesta (or stress) expectancy, delayed (inhibited) menarche.This does not mean only the relationship with the school-vacation-study period, but with the socio-cultural yearly periodicity that involves students, workers, travelers and most human annual activities.This seems to explain the preliminary conclusion of Nakamura et al. (1986) in Japan that there was not a relationship of the secular changes in the monthly rhythm of MI and secondary school periods.They found annual rhythms with peaks in Apr and Aug since 1891 until now, and a third peak in Jan since 1960.They argued that by 1900 around 1% of girls attended secondary school after the age of 12. From our perspective, this is a premature conclusion because there is the possibility that general social vacations used to coincide with primary school vacations, but no data was provided to test this hypothesis.Also, the two described peaks maintained for more than 90 years agree well with social vacation-work periods.We postulated that the "annual expectancy" or a "long term expectancy" of a "climate" of celebration was the "zeitgeber" (http://en.wikipedia.org/wiki/Zeitgeber)"time giver" or "synchronizer" of the MI annual rhythm, and not the seasonal climate (Valenzuela et al., 1999;Valenzuela, 2004).Thus the following test was to examine the days of celebrations (feasts) for the girls in Medellín and Santiago for which we knew the holidays or, more precisely the days of fi esta.Very signifi cant peaks of MI were found for the birthday and fi esta days that were signifi cant for girls, but not for holidays without special signifi cance for them (a revision of specifi c days is found in Valenzuela, 2004, where the memory bias was also tested and refuted) or in current holidays of the week (Saturday and Sunday), which did not show a peak of menarche (Valenzuela, 2004).Thus we discarded defi nitively the refuted hypothesis of the circa-annual seasonal monthly MI and worked with the circa-[vacation (fi esta)]-[study (non-fi esta)] expectancies rhythm as the primary cause of the circa-annual menarche rhythm.This hypothesis proposes that the calendar rhythm of general vacation (fi esta) -study (non-fi esta) lived by girls, year by year since their birth (or even prenatally, remember that the hypothesis proposes a general vacation-study rhythm for everybody not only for girls having menarche) generates a circa-annual rhythm of expectancies of fi esta-non-fi esta that leads to increase MI by the expectancy of a fi esta-period and to stop or delay menarche by the expectancy of a non-fi esta period.Vacation months are associated with a high increase of MI and study months with a trough of MI.
With this in mind, the hypothesis of infl uence of the fi estavacation versus non-fi esta-study on the age at menarche was a logical expectancy.Previously, the age at menarche was related to the season (Gueresi, 1997), but since the relationship found was rather for vacation-study periods, the study of MI and age at menarche according to seasons blurs the relationship of MI with Vac-Stu months and hides the true origin of the menarche rhythm.It seems that our refutation of the seasonal factors presented as early as 1991 (Valenzuela et al., 1991(Valenzuela et al., , 1993) ) was not accepted by researchers working in this fi eld.Matchock et al. (2004) insisted on seasonal factors as the cause of the MI rhythm.Their data show several conclusive refutations of seasonal or climatic factors.They found that May and July (one month before and after the summer solstice, respectively, with similar photoperiod and temperature) had a signifi cant trough (p<0.001) and peak (p<0.0001) of menarche, respectively.Also, they found that Jan and Feb, two winter months, had a signifi cant peak (p<0.01) and trough (p<0.01),respectively.These facts refute conclusively the climatic or seasonal hypothesis; but they agree perfectly with our Vac-Stu fi estanon-fi esta hypothesis.If Dec-Jan are months with vacations as well as Jul-Aug, and Feb (or including middle-end Jan) and Jun (or including beginning-middle Jul) is a month of study, as we know, in general, from the USA vacation-study calendar, the results of Matchock et al ( 2004) fi t perfectly our vacationstudy hypothesis.To better understand our hypothesis on the circa-vacation-study age at menarche, let us work with the Chilean school rhythm.In Dec, Jan and Feb (Vac-months) higher MI were found, but in Mar (fi rst Stu-month) a fall in the incidence occurs.This lower incidence continues until Jun; it begins to increase until Dec, where a peak is again observed.The expected annual rhythm of the age at menarche is easy to predict from such a rhythm of incidence.In Mar until Jun lower means of menarche age should be observed (menarche refractory to study delay); the monthly mean should increase from Jun to Dec (the delayed menarche during the Stu-months) as the Vac-months approach.This pattern was seen in Santiago (temperate zone S Hemisphere), Medellín (equatorial zone, N. Hemisphere) and Riberão Preto (Brazil, temperate zone, S. Hemisphere) and published previously (Valenzuela 2004(Valenzuela , 2006)).The present study intends to test formally the hypothesis of the infl uence of Stu-months and Vac-month on the age at menarche.The expectancy of studies can delay menarche but it cannot suppress it defi nitively.Soon or later, according to the impressionableness (in face of the expectancy of fi esta or non-fi esta) of each girl, menarche is going to occur.Those girls that should have had menarche in a certain month (due to their natural sexual maturation) and were delayed by studies (stress) are going to have it in the following months at a higher age of menarche.

Rationale
After examining data on the monthly MI we found that the monthly incidence rhythm accounted for the relationship of menarche and the condition Stu-month (low incidence) or Vac-month (high incidence).By assuming that the study regime decreases the MI and delays menarche of susceptible girls, we proposed a hypothesis on the monthly rhythm of the age at menarche (Valenzuela, 2006).The hypothesis proposed that the last month(s) of the long vacation period (with a high MI) and the following Stu-months (with a low MI) should present the lowest means of the age at menarche.In the last Vac-months no more delayed girls are present and in the initial Stu-months only refractory girls for the factors that delayed menarche menstruate at the earliest ages.In the following Stu-months the low incidence and mean age of menarche are maintained or grow slowly, but a tendency to increase the mean age at menarche should be seen until a Vac-month, where a higher incidence of menarche should be observed with a high mean of menarche age (induction of delayed menarche).This increase in the menarche age occurs in the initial Vac-months until all the delayed girls have their menarche; at this point a dramatic fall in the age of menarche should be observed, conserving the high MI that is the characteristic of Vac-months.The expected random monthly incidence of menarche was calculated as the quotient between the number of days of each month and 365.25 (Feb = 28.25 days).As pointed out in the Introduction, our studies showed that it was not properly the fi esta period or holidays, but rather the expectancy of fi esta or holidays is the factor that increases the MI.It was evident that the environment or circumstances related to the expectancy of fi esta (relaxation or reward) or non-fi esta (stress or unwanted situation) could impress strongly the neuro-psycho-endocrine system, so as to change the age of circa-vital events such as menarche (Valenzuela et al., 1999;Valenzuela, 2004Valenzuela, , 2006)).I think that the expectancy of the event, and not necessarily the event itself was the cause of the rhythm, because of the left-biased bell shaped distribution of menarche around the event.This precluded a recruitment distribution where menarche increases its incidence in the previous days (or weeks or months) of the event (Vac-months) and decreases drastically after the event (Valenzuela et al., 1999;Valenzuela, 2004Valenzuela, , 2006)).We have called the factor of the rhythm fi esta as a preliminary approach.We do not know whether entering school is a stress factor, but I use this term in a colloquial mode, leaving its demonstration for further research.Hard work is necessary to discover the specifi c neuro-psycho-endocrine factor.It is important to remark that in Chile the two weeks of winter vacation often occurs in July, but it is not a fi xed period; it is defi ned year to year and it may range from the last week of June to the fi rst week of August.Thus, the winter vacation in Chile cannot produce a clear expectancy of fi esta as fi xed holidays or vacations can.We found a strong confi rmation of this condition examining MI in the Christian celebration of the Holy Week that is variable in the calendar year to year; as expected the Holy Week did not have a menarche peak (not published).The midyear vacations in Medellín (Colombia), Riberão Preto (Brazil) and in USA (mid-Atlantic states, Matchock et al., 2004) are fi xed periods of vacation, thus the fi esta-expectancy for the mid-year vacation does really occur.

DATA AND METHODS
Published data of age at menarche from Santiago, Chile (two samples, 1978 and 1990-1), Medellín, Colombia (1990) and Riberão Preto, Brazil (1998) were studied (Tavares et al., 2000(Tavares et al., , 2004;;Valenzuela, 2006).The condition of Vac-month or Stumonth is in these cited articles.The monthly incidence and the mean age at menarche in a calendar month were indicated as over (+) or under (-) the expected incidence or the total mean age, respectively.Months were classifi ed as Vac-month if they had a week or more of vacation days, when it was indicated in the literature or if it was considered as a Vac-month by the authors; otherwise it was considered as a Stu-month.A more recent sample from USA was included (Matchock et al., 2004); however, this study did not present the age at menarche for each month but the result of the analysis clustering months by season.

STATISTICS
The agreement and disagreement with the hypothesis, given in the Rationale, was indicated for each month by (+) and (-), respectively and a sign test was applied to calculate the statistical signifi cance, under the binomial expected probability of 0.5 for (+) and 0.5 for (-) signs.Since the condition of agreement and disagreement may be diffi cult to evaluate for a reader who does not know the hypothesis, an example is developed.Feb in Santiago is the last summer Vac-month, thus according to the hypothesis it should present a high MI (Vacmonth) but a low mean age at menarche because it happens after two months of vacations where all the delayed girls have had their menarche.If this is found in Santiago a + sign is given to Feb; however, Feb in Medellín (Colombia) or Riberão Preto (South Brazil) is the fi rst school month, after the Dec-Jan vacations so it should present a low MI and a low mean age at menarche.In this example the MI is mentioned to orient the reader, but it was tested in previous articles, thus in the present analysis only the expected mean age at menarche was used to assign the agreement or disagreement with the hypothesis.

RESULTS
The agreement and disagreement with the hypothesis is shown in Table 1 for samples from Santiago (1978 and1990) and in Table 2 for samples from Medellín (1990) and Riberão Preto (1998).In Table 2 a sample from the mid-Atlantic states of USA (Matchock et al., 2004) is included to test the agreement of MI with the sample from Medellín, because the samples from the Northern Hemisphere share a very similar pattern of vacationstudy regime and coincide in having the National Day in July (4 th for USA, and 20 th for Colombia).However, the samples diff er completely in the climatic conditions.While in the Mid-Atlantic States of USA there are four clearly demarked seasons, in Medellín, an equatorial city with eight solar seasons, an "eternal" spring occurs.Diff erences between the samples also agreed with diff erences in vacation-study condition of months.Dec in Medellín showed the second peak of MI, but it did not show a signifi cant increase in MI in USA; this also agrees with the hypothesis because in Medellín Dec is a full vacation month, but it is a partial vacation month in USA.Also, the midyear vacation in Medellín includes days of Jun and fi nishes in Jul (at the 20 th Jul National Day), but the midyear vacation in USA begins in Jul and fi nishes in Aug; we see a shift toward Aug in the USA sample in relation to Medellín.In the comparison of samples from Medellín and USA a signifi cant correlation was found for the MI (r = 0.6869; p = 0.014).
In Santiago, in 1978 Mar was a Vac-month and in 1990-1 it was a Stu-month; Sep was Stu-month in 1978 and Vacmonth in 1990-1.The standard deviation is missing in the Brazilian sample, so the standard error could not be calculated.The standard error is important because the agreementdisagreement with the hypothesis is interpreted between two consecutive months by their signifi cant diff erence (more than two standard errors) in the MI (previous analyses) or in the mean age at menarche.The Brazilian sample is rather small, so a large variance and standard error are expected in the monthly incidence of and mean age at menarche, this implies that the tendency of the monthly mean of the age at menarche cannot be precisely evaluated as it can in the other samples.In the Chilean and Colombian samples there was a complete

TABLE 2
Incidence, mean age at menarche and agreement or disagreement with the hypothesis of the infl uence of the vacation-study condition on the age at menarche.Samples from Medellín (Colombia, Valenzuela et al., 1999) and Riberão Preto (Brazil, Tavares et al., 2004).Monthly incidence of menarche in a USA sample (Matchock et al., 2004).

TABLE 1
Incidence, mean age at menarche and agreement or disagreement with the hypothesis of the infl uence of the vacation-study condition on the age at menarche.Chilean girls from Santiago sampled in 1990-1 and 1978 (Valenzuela et al., 1999;Valenzuela, 2006).Brazil 1998, Dec = 152.7, Feb = 144.3 (dif = 8.4, the probability cannot be calculated because the standard deviation is not known, but this diff erence is surely signifi cant, because the standard deviation in all the samples is near 14 months).

Age at menarche in months
In complete agreement with our hypothesis, and in disagreement with the seasonal hypothesis, the USA sample showed a late menarche for girls having it in Dec and an early menarche in girls having it in Feb (Matchock et al., 2004).

DISCUSSION
It is important to remember that this hypothesis was proposed after seeing the distribution of the monthly incidence of menarche (MI).Thus there is no possibility of a circular epistemological procedure when we studied the age at menarche.We confi rm that the beginning of studies delays menarche in some girls, who are going to have it some months later when Vac-months approach.This result was observed in the four samples (and in the USA sample, as far as MI and age at menarche in Dec and Feb are concerned); when the vacation period is coming there is an increased number of girls having menarche at older ages.This occurs at midyear in Medellín and Riberão Preto (and it is expected for USA) with fi xed vacations in the middle of the school period.The pattern of MI has been also found in India and Hungary (and in USA as described), thus we can conclude that this is a very probable true culturalbiotic relationship.We confi rm our proposition that this is not a seasonal circa-annual rhythm, but a circa-[vacation (fi esta)]-[study (non-fi esta)] expectancies rhythm that is a systematic periodicity repeated year after year, caused by socio-cultural events with deep signifi cance for girls.The decay of the age at menarche from 5.5 to 8.4 months between December and February, in the four samples (and in the sample from USA, but without published values) is an extraordinary biotic process; this decay shows that the cultural-expectancy of important events for girls is a factor comparable to deep under nutrition (Leenstra et al., 2005), highly competitive physical training (Vadocz et al., 2002) or near 50 years in the secular trend of menarche age (Nakamura et al., 1986;Vecek et al., 2012;Woronkowicz et al. 2012).
Unfortunately the Brazilian sample is too small to study the infl uence of the daily MI or for a precise study of diff erences in the monthly MI (large standard errors), and the two disagreements with the hypothesis could be due to random fl uctuations.It is possible that some fi esta periods are not described in the article, as for example in April and around July-August.Also, the USA study (Matchock et al., 2004) did not provide fi gures for monthly means of menarche with which a fi ne test of our hypothesis could be done.However, Dec and Feb agree perfectly with our hypothesis as far as the authors informed qualitatively in the article.
These studies uncover important socio-cultural eff ects on the neuro-psycho-endocrine system.It is probable that boys are also submitted to such fi esta-expectancy infl uences, for example growth or sexual development could be accelerated in vacations in relation to the study period; we made some observations in the longitudinal follow up study, but these were not formalized or published.Unfortunately, studies are performed in relation to seasons and this does not allow answering this question.Our study provides a solid framework for psycho-somatic, bio-socio-cultural, socioendocrine and bio-psycho-anthropological studies.We point out one of these important socio-cultural-endocrine interactions.Dec 8 is a very important religious (Catholic) fiesta.Colombia and Chile are mostly Catholic countries in which the 8 Dec is a holiday and highly celebrated.However, while in Colombia Catholic girls receive often the first communion (an important family fiesta) on this day, the Catholic Church discontinued this practice in Chile.In Colombia several days presented signifi cant accumulation of menarche; among them 8 Dec presented the highest signifi cant peak of MI, but in Chile the MI on 8 Dec was not signifi cantly diff erent from any other day of December (Valenzuela, 2004).Again, we emphasize that it is not the fi rst communion that elicits menarche (in the girl that receives it), but the expectancy of a national and familial fi esta that elicits menarche in girls of these families who are in the time of their fi rst menstruation.Our study reveals that living year by year highly aff ectiveemotional cultural rhythms imprints dynamically the brain so as to condition deeply the neuro-psycho-endocrine axis that is compelled to follow these rhythms.Some cultural elements such as religious or national festivities are shown to have more psycho-endocrine infl uences than previously expected.
IS = incidence sign: + = over the expected monthly incidence; -under the expected monthly incidence; MAM = mean age at menarche; SE = standard error; MS = MAM sign; + = mean over the total mean; -= mean under the total mean; AHY = agreement (+) or disagreement (-) with the hypothesis.*In 1978 September was not a vacation month.agreementwith the hypothesis (36 months).In the Brazilian sample only two months disagreed with the expected situation.Thus in the total 48 months we found two disagreements, this occurs with probability P = 4.27x10 -12 .As proposed in the Rationale, one of the most relevant expected results of the hypothesis is the fall in the mean age at menarche between the fi rst month of vacations (long vacations), when a great number of girls with delayed menarche had it, and the last month of vacations or the fi rst month of study.