The Mathematics of the menstrual cycle

Abstract Attempts have been made to rebut criticisms by Professor Potter of a rhythm method of contraception described by the author. There is a correlation between the lengths of adjacent cycles within the menstrual histories of some women.     

The Mathematics of the menstrual cycle

Attempts have been made to rebut criticisms by Professor Potter of a rhythm method of contraception described by the author.

There is a correlation between the lengths of adjacent cycles within the menstrual histories of some women.     

Polygyny and Fertility among the Shipibo of the Peruvian Amazon

This report describes a study of the fertility experience of an Amazon Indian tribe that has shown evidence of having the highest documented fertility of any human group. The Shipibo, who live in the upper Peruvian Amazon, are experiencing rapid cultural change, including a decline in the prevalence of polygyny. This study tests the specific hypotheses that polygyny limits individual female and community fertility through the mechanism of post partum sexual abstinence and longer birth intervals. Total population counts in eight villages and reproductive histories of all females age 13+ show that mean birth interval lengths of polygynous women are four months longer than those of monogamous women. Fertility of polygynous women was lower, with 1.3 fewer term-births per reproductive span than that of monogamous women. The community general fertility rate is negatively associated with the proportion of polygynous birth intervals in the community. In this study, cultural change is strongly associated with higher fertility.     

U. S. population growth as an abstractly-perceived problem

Recent public opinion polls report that a majority of Americans consider the nation’s population growth rate to be a “serious” problem. Little systematic evidence exists on whether they view the problem as a factor that the individual married couple should consider in deciding on family size. A survey of 134 adult women living in a limited-income family housing project in a relatively small and isolated American community suggests: the view that continued population growth is a problem in the United States is endorsed more strongly than the view that the couple has a responsibility to limit its fertility because of overpopulation; and concern with population growth is only loosely associated with acceptance of the individual responsibility attitude. Among subgroups of respondents, Catholics were more likely to hold a negative attitude toward population growth than to possess the individual responsibility view and they exhibited a correlation between the two attitudes. Protestants were distinguished by no difference in or correlation between the acceptance of the two attitudes. A correlation between the attitudes was especially pronounced among Catholics with high achievement values. It is suggested that measures explicitly intended to control population growth probably cannot be adopted until there is a strong correlation between the two attitudes.     

Food limitation of population density in the orb-wed spider,Nephila clavata

Summary Field studies were conducted to clarify whether variation in food availability among habitats influences population density, and whether population density has a negative effect on foraging success in the orb-web spider,Nephila clavata. Lifetime food consumption per individual (i.e., foraging success) strongly correlated with mean body size of adult females and mean fecundity in populations. Also, there was a positive correlation between foraging success and population density. Since foraging success reflected potential prey availability in the habitat, food resource appeared to be a limiting factor for populations in this spider. Mean fecundity per individual correlated with population density of the following year, suggesting that decreased reproduction is a major component of food limitation on population density. Consistent defferences in mean body size between particular sites were observed over years, while such difference was less obvious in density. Thus, ranking of food abundance among habitats seems to be predictable between years. A field experiment revealed that an artificial increase in population density had no negative effect on the feeding rate of individuals, suggesting that intraspecific competition for food is not important in this species.     

The effect of variability in the fertility schedule on numbers of kin

"The kinship formulas developed by Goodman, Keyfitz, and Pullum (1974) are extended to encompass populations in which fertility varies among women. An expression is derived to determine the amount by which the number of sisters in a heterogeneous population exceeds that in a population with homogeneous fertility. This expression, which is a function of the variance in the gross reproduction rate of the population, can readily be applied to numbers of other kin, such as aunts and cousins. Several trial calculations indicate that calculations of average numbers of sisters based on an assumption of uniform fertility could result in a underestimate of about 13 percent." (SUMMARY IN FRE)     

The effect of variability in the fertility schedule on numbers of kin

The kinship formulas developed by Goodman, Keyfitz, and Pullum (1974) are extended to encompass populations in which fertility varies among women. An expression is derived to determine the amount by which the number of sisters in a heterogeneous population exceeds that in a population with homogeneous fertility. This expression, which is a function of the variance in the gross reproduction rate of the population, can readily be applied to numbers of other kin, such as aunts and cousins. Several trial calculations indicate that calculations of average numbers of sisters based on an assumption of uniform fertility could result in an underestimate of about 13 percent.     

The incidence of divorce within cohorts of American marriages contracted since the civil war

The proportion of marriages that end in divorce can be estimated from vital registration or from census data. The former source suggests considerably higher levels of divorce than does the latter. A new series, combining the two sources, is presented for annual marriage cohorts back to 1867. Actual experience to 1970 is traced and a projection beyond that point is made for cohorts with incomplete divorce histories. The cohort divorce series moves steadily upwards and shows much less variability than an equivalent series of period divorce rates. Factors related to high divorce within a cohort are armed service mobilization and high unemployment rates in the year of marriage, and slow national economic growth between pre- and post-marital periods.     

Variation in offspring size within a population of the web-building spiderAgelena limbata

Within a population of the web-building spiderAgelena limbata, the weight of the first instar nymphs ranged from 1.187 to 6.559 mg. Both intraclutch and interclutch variation were recorded. The mean weights were different among clutches and the coefficients of variation within a clutch ranged from 3.3 to 29.2%. Variation in the nymphal weight was certainly derived from variation in the egg weight because there was a high correlation between the two weights. Factors affecting interclutch variation in nymphal weight were examined by multiple regression analysis. Nymphal weight was positively correlated with the body size and food conditions of female parents, and negatively correlated with the clutch size. Among these three factors, the food conditions of female parents had the largest apparent effect on the interclutch variation. The results suggest that females with larger body size and more food produce larger offspring, and that there is a trade-off between offspring size and clutch size. Heavier nymphs had larger body size (carapace width) and may have larger energy reserves. Heavier nymphs survived experimental starvation for a significantly longer period.     

The nature of gender

I explain a biosocial model of women’s gendered behavior (behavior on which the sexes differ). This model integrates a macro sociological theory with a biological theory derived from primate behavior. The sociological model is designed to explain changes in the relationship between sex and behavior over time or between groups. The biological model is designed to explain individual within-sex variance and between-sex variance in gendered behavior in a cohort. Results from an original study are presented to demonstrate that within-sex variance in women’s gendered behavior is explained well by the primate model. I conclude that human nature is gendered. The implications of this conclusion are explored for demographic and other social science research.     

Spouse “Together Time”: Quality Time Within the Household

During the last decade more and more time-use data were gathered on a household level in stead of on an individual level. The time-use information of all members of the household provides much more insight in research fields that until now largely used data gathered at the individual level. One of these research fields is the study of quality of life, based on the (quality) time partners within a household spend together which in turn is often linked to studying the associations between the amount of time spent together and relationship satisfaction. The amount of face-to-face spousal interaction is considered to be critically important for marital quality and is assumed to be violated within dual-earner couples, especially those with women working long hours. In this contribution we analyze the time-use of couples in the Belgian Time Use Surveys of 1999 and 2005. We identify which activities couples do together and which they do apart, and what household characteristics predict couples’ together time. Working times in general seem the most decisive factor influencing the amount of together time. The increased labor market participation of women, on the other hand, seems not to be so much a threat for the time a couple spends together.     

Women in community radio: a framework of gendered participation

Women’s participation in community radio is examined through a case study of Ireland, with data gathered by survey, interviews and a focus group. Key findings note that women are under-represented as participants in community radio, but there is little activity within the sector to address this imbalance. Similarly, women’s voices are absent from community airwaves but this is framed through a limited understanding women lacking on-air confidence. Solutions to the problem were limited to individual stations rather than approached in a collective manner. There was no sense of women’s voices on air being a priority issue for stations, for the sector, nor for the national regulatory body. With regard to content, stations largely tended to produce “islands” of specialist women’s programmes but there was a sense that women produced content in ways that were not normative and were explicitly linked to gender. Gendered social structures, as well as organisational structures within community radio, constituted further barriers to women’s equal participation in community radio in Ireland. Finally, the presence of women as role models, sponsors, and managers, who were relational in their approach, was key gendered benefits that women derived from their participation in community radio.     

Survival of related individuals: an extension of some fundamental results of heterogeneity analysis

"Many ideas in the analysis of heterogeneous mortality are based on the relationship between individual and observed hazard rates. This connection is established with the help of conditional averaging procedure: The observed risk of death at age x is calculated among those who survive this age. The analogy of this result for bivariate survival model with correlated individual hazards is derived. In the case of correlated frailty model the parametric specification of the mean, variance and correlation coefficient of the bivariate frailty distribution among survivors is obtained. The relationship between local association measure and the characteristics of the bivariate frailty distribution among survivors is established." (SUMMARY IN FRE)     

A fixed-effects multilevel analysis of how community family structure affects individual mortality in Norway

By using register data for the entire Norwegian population aged 50-89 in the period 1980-1999, during which there were about 720,000 deaths, I estimate how the proportions of persons who were divorced or never married in the municipality affected all-cause mortality, net of individual marital status. The data include individual histories of changes in marital status and places of residence, providing a rare opportunity to enter municipality fixed effects into the model, thereby capturing the time-invariant unobserved factors at that level. The positive health externality of marriage that is suggested in the literature is supported by some of the estimates for women. Other estimates--especially those for men--point in the opposite direction. One possible interpretation of these findings is that social cohesion is perhaps not as beneficial for people's health as often claimed, at least not for both sexes. Alternatively, the results may reflect that marriage perhaps undermines rather than strengthens social cohesion, or that other mechanisms are involved-for example, those that are related to people 's perceptions of their health relative to the health of others. Estimates from models without such municipality fixed effects are markedly different, but these also shed doubt on the notion that a high proportion of unmarried persons generally increases individual mortality.     

Incomplete reporting of men’s fertility in the united states and britain: A research note

We evaluate men's retrospective fertility histories from the British Household Panel Survey and the U.S. Panel Study of Income Dynamics (PSID). Further, we analyze the PSID men's panel-updated fertility histories for their possible superiority over retrospective collection. One third to one half of men's nonmarital births and births within previous marriages are missed in estimates from retrospective histories. Differential survey underrepresentation of previously married men compared with previously married women accounts for a substantial proportion of the deficits in previous-marriage fertility. More recent retrospective histories and panel-updated fertility histories improve reporting completeness, primarily by reducing the proportion of marital births from unions that are no longer intact at the survey date.     

Reconstruction of Birth Histories from Census and Household Survey Data

In this paper a new procedure for reconstructing birth histories from census or household survey data is developed. Given the number of children ever born, the number of deceased children, and the ‘own children’ birth history of each woman, it is possible to ‘fill in’ probabilistically the missing births of her deceased children and of children not present in the household. Thus, the procedure generates complete birth histories from which such measures as age-specific fertility rates, parity progression ratios, and birth interval measures may be estimated. For purposes of illustration and validation, the method is applied to the household survey data of the 1974 Korean National Fertility Survey, both to the entire sample of households, and to households with women from whom individual birth histories were collected. Age-specific fertility rates and parity progression measures estimated from the reconstructed birth histories are compared with those estimated by applying the ‘own children’ method, for the period 1960–74.     

Union Transitions Following the Birth of a Child to Cohabiting Parents

Despite a growing interest in the family trajectories of unmarried women, there has been limited research on union transitions among cohabiting parents. Using data from the 2002 National Survey of Family Growth, we examined how family complexity (including relationship and fertility histories), as well as characteristics of the union and birth, were associated with transitions to marriage or to separation among 1,105 women who had a birth in a cohabiting relationship. Cohabiting parents had complex relationship and fertility histories, which were tied to union transitions. Having a previous nonmarital birth was associated with a lower relative risk of marriage and a greater risk of separation. In contrast, a prior marriage or marital birth was linked to union stability (getting married or remaining cohabiting). Characteristics of the union and birth were also important. Important racial/ethnic differences emerged in the analyses. Black parents had the most complex family histories and the lowest relative risk of transitioning to marriage. Stable cohabitations were more common among Hispanic mothers, and measures of family complexity were particularly important to their relative risk of marriage. White mothers who began cohabiting after conception were the most likely to marry, suggesting that “shot-gun cohabitations” serve as a stepping-stone to marriage.     

Health and quality of life of older people,a replication after six years

Replicating a survey of 875 people 55 years old or more undertaken in September 1999 throughout the former Northern Interior Health Region (NIHR) of British Columbia, in September 2005 a sample of 656 people completed a 22-page questionnaire. The average age of the respondents was 68, with a range running from 55 to 96 years, and 64% were women. Responses to the SF-36 questionnaire indicated that for male respondents aged 55–64, the mean score for the 8 dimensions was 76.1. This mean was a bit higher than the 74.4 mean of 1999. For male respondents aged 65 and older the mean was 69.0, which was also higher than the 68.3 mean of 1999. For females aged 55–64, the mean score for 8 dimensions was 73.1, versus 73.0 in 1999. For female respondents aged 65 and older, the mean score was 67.0, versus 65.4 in 1999. Based on these mean scores for the 8 dimensions, then, it is fair to say that the overall health status of males and females aged 55 years and older in the region in 2005 was at least as good as (i.e., the same as or better than) that in 1999. Comparing 28 average figures for the 2005 respondents on satisfaction with specific domains of life (e.g., financial security, health, sense of meaning) and three global indicators (satisfaction with life as a whole and with the overall quality of life, and happiness) with those of the 1999 respondents, we found that the scores for the 2005 sample were at least as high as those of the other sample. Thus, it seems fair to say that the perceived quality of life of older people in the former NIHR so far as it is revealed in domain and global satisfaction and happiness scores, is at least as good as the perceived quality of life of a similar sample in 1999. Although a large majority perceived increases in crime in the 2 year periods prior to both surveys, smaller percentages of the 2005 sample than of the 1999 sample thought that crime had increased over the past two years, avoided going out at night, feared for their safety, had crime-related worries, engaged in crime-related defensive behaviours and were actually the victims of any crimes. Therefore, it seems fair to say that, so far as crime-related issues are concerned for the two samples of seniors responding to our surveys, there is more evidence of improvement than of deterioration. Applying stepwise multiple regression, each of the eight dependent variables was explained on the basis of four clusters of predictors separately and then a final regression was run using only the statistically significant predictors from the four clusters. Broadly speaking, 7 SF-36 health status scales explained from 28% to 45% of the variance in the 8 dependent variables, running from satisfaction with the overall quality of life (28%) to the single item measure of general health (45%). The seven predictors in the Social Relations cluster explained from 7% of the variance in the SF-36 General Health scale scores to 57% of the variance in the Life Satisfaction scores. The four predictors in the Problems cluster explained from 10% of the variance in the SF-36 General Health scale scores to 24% of the variance in the SWLS scores. The 11 predictors in the Domain Satisfaction cluster explained from 14% of the variance in the SF-36 General Health scale scores to 64% of the variance in the SWB scores. Putting all the significant predictors together for each dependent variable, in the weakest case, 4 of 11 potential predictors explained 33% of the variance in the SF-36 General Health scale scores and in the strongest case, 9 of 15 potential predictors explained 70% of the variance in Life Satisfaction scores. Among other things, these results clearly show that respondents’ ideas about a generally healthy life are different from, but not independent of, their ideas about a happy, satisfying or contented life, or about the perceived quality of their lives or their subjective wellbeing. Finally, the 7 core discrepancy predictors of MDT plus incomes were used to explain the eight dependent variables. From 13% of the variance in the SF-36 General Health scale scores to 57% of the variance in SWLS scores was explained using those predictors. Based on an examination of the Total Effects scores for the predictors of the 8 dependent variables, the most influential predictors were Self-Wants, followed by Self-Others and then Self-Best. In other words, the most influential discrepancy predictors of respondents’ overall life assessments were those between what respondents have versus what they want, followed by what they have versus what others of the same age and sex have, and then by what they have versus the best they ever had in the past. We would like to thank the Social Sciences and Humanities Research Council of Canada for support of this research with funds granted to Alex C. Michalos through the Gold Medal Award in 2004.