Search

A computer-assisted mathematical modeling method that emphasizes the interaction between analysts and computers is presented. It combines algebraic and graph-theoretic approaches to extract a trade-off between human mental models and models based on the use of data collected from the system under study. The method is oriented to the modeling of the so-called "gray box" systems which often involve human behavioral aspects and also knowledge of the experts in relevant fields. By recursive dialogues with the computer, the modeler finds a system model which can be nonlinear with respect to descriptive variables. The structure of the computer program packages is also presented.

Given the central importance of diversity in ecology and the life sciences more generally, it is not surprising that a variety of methods and measures have been developed to describe and summarize diversity. In the two previous parts of this series of papers, comparisons were drawn between concentration curves and frequency distributions, the most widely used graphical display of variation, and between concentration curves and dominance-diversity curves. This final part of the three paper series compares various statistics that might be used to summarize diversity, with a focus on the usefulness of have-statistics as a supplement to more traditional measures. The first section of our discussion lays out some reasonable criteria and principles that good measures of diversity should satisfy: some traditional measures violate at least one of the criteria; the have-statistics pass the hurdles and have some desirable properties in addition. We then illustrate the use of different measures by way of examples drawn from Howard's studies of bullfrogs (discussed in Part I), the study of species diversity among diatoms (discussed in Part II), an analysis of mating systems of various birds, and a survey of human fertility in 41 countries.

The LEXIS computer program, which was developed at the International Institute for Applied Systems Analysis (IIASA) and Duke University, is intended to aid demographers in the analysis of large arrays of data. Its application as a supplement t o other methods of graphic display is demonstrated in Thousands of Data at a GLance: Shaded Contour Maps of PopuLation Surfaces (Vaupel. Gambill, and Yashin, forthcoming) and will not be discussed here. This paper provides instructions on the use of the program, gives some hints concerning the art and craft of using the program in a creative way, and briefly describes the algorithm used in designing the program. A diskette containing a copy of the LEXIS program is enclosed. The program is copyrighted but the diskette is not protected against copying: please feel free to make and distribute copies. By making the program available to demographers and others interested in mapping the contours of surfaces, we hope to encourage the development of this method of data analysis. We would, of course, sincerely appreciate it if we and the International Institute for Applied Systems Analysis were acknowledged when the program or some modified version of it is used to produce maps for presentation or publication. Comments and suggestions are welcome!

Concentration curves and a set of summary statistics called have-statistics are useful in ecological analyses of dominance and evenness among individuals in reproductive success. This approach complements, but does not replace, approaches based on frequency distributions and standard summary statistics. Examples are drawn from studies of bullfrogs, red deer, elephant seals, sculpins, fruit flies, and rice weevils, as well as from some theoretical models similar to the Wright-Fisher model of evolutionary genetics.

Important recent research by Samuel Preston and Ansley Coale (1982) extends the Lotka system of stable population equations (Lotka 1939) to any population. Here we present an alternative general system and describe its duality with the Preston-Coale system: We derive these results by considering the calculus of change on the surface of population density defined over age and time. We show that analysis of this Lexis surface leads to all the known fundamental relationships of the dynamics of single-region human populations, as well as some interesting new relationships.

Patterns of marriage and fertility in China have changed rapidly over the last three decades. Fertility has dramatically declined, especially before age 20 and after age 30. Marriage remains virtually' universal, but the age of first marriage, previously concentrated between ages 16 and 20, has shifted upward to between ages 20 and 25. These trends were sharply punctuated by marriage and fertility booms and slumps associated with the disturbances of the Great Leap Forward and the Cultural Revolution. Thus, strong age, period, and cohort fluctuations, some transient and others persistent, interact to produce a complex mosaic of turbulent demographic change. Coale masterfully analyzed these patterns of change. Here we supplement Coale's analysis by presenting and discussing some shaded contour maps of various surfaces of Chinese marriage and fertility rates. As discussed in detail elsewhere, such maps permit visualization of population surfaces defined over age and time and offer a panoramic view of the interaction of age, period, and cohort variations. Because the use of shaded maps of population surfaces is implicit in one of Lexis' original diagrams, and because the term Lexis surface is increasing being used to refer to surfaces of demographic rates defined over age and time, the shaded contour maps presented here might be called Lexis maps. An early instance of the use of contour maps (without shading) may be found in Delaporte's pioneering comparison of trends in age-specific mortality rates in various European countries. The data used to construct the Lexis maps are from China's one-per-thousand fertility survey conducted in 1982; the total sample size was a bit more than one million. The principle information gathered in the survey, which covered all of China except Tibet, Hong Kong, and Taiwan, comprised detailed marriage and fertility histories of more than 300 thousand women aged 15 to 67, gathered through face-to-face interviews. This information was then used to reconstruct the pattern of age-specific fertility rates in China from 1940 through 1981 and the pattern of age-specific first-marriage rates from 1950 through 1981. For both fertility and first-marriage rates, an urban vs. rural breakdown was also published for 1950 through 1981. Coale and several other analysts have scrutinized the quality of the data and conclude that the data are reasonably reliable and give a generally accurate representation of the evolving age-specific patterns of Chinese marriage and fertility. Coale used the survey data to construct a set of estimates of age-specific proportions of women ever married. We use these estimates, but otherwise the maps we present are based directly on the original data....

Individuals at the same age in the same population differ along numerous risk factors that affect their chances of various causes of death. The frail and susceptible tend to die first. This differential selection may partially account for some of the puzzles in cancer epidemiology, including the lack of apparent progress in reducing cancer incidence and mortality rates over time.

Contour maps are useful for displaying demographic surfaces, including surfaces of population levels and fertility, marriage, and mortality rates. Most often the surfaces are defined over age and time, but such other dimensions can be used as life expectancy or population growth rate. This paper presents a bouquet of contour maps to suggest the broad potential of their use in demographic studies. The maps presented range from maps of Italian mortality, French population levels, and U.S. birth rates, to maps of Coale and Demeny's and Brass's model life tables. The value of the maps lies in their substantive import: by giving demographers visual access to population surfaces, the maps can help demographers uncover and understand population patterns. The text of the paper adumbrates some of these patterns and discusses the use of contour maps in exploratory data analyses and model building, including the use of maps of residuals in fitting models to data.

At current mortality rates, life expectancy is most responsive to change in mortality rates at older ages. Mathematical formulas that describe the linkage between change in age-specific mortality rates and change in life expectancy reveal why. These formulas also shed light on how past progress against mortality has been translated into increases in life expectancy--and on the impact that future progress is likely to have. Furthermore, the mathematics can be adapted to study the effect of mortality change in heterogeneous populations in which those who die at some age would, if saved, have a different life expectancy than those who live.

Heterogeneity is sometimes used as a synonym for variability or diversity; here it has a narrower meaning of variability with respect to mortality (or with respect to attributes of individuals that affect their mortality). This concept of heterogeneity is closely linked with the concept of selection: a heterogeneous population is one in which there is differential mortality and hence one in which selection is occurring. Because of the effects of selection, the patterns of mortality (or exit) in a heterogeneous population can differ qualitatively from the patterns of mortality in the constituent sub-populations. These qualitative differences can be surprising; unsuspecting researchers who are not wary of heterogeneity's ruses may fallaciously assume that observed patterns for the population as a whole also hold on the sub-population or individual level. Such incorrect inferences may produce erroneous policy recommendations, because the effect of an intervention usually depends on the behavior and response of individuals. In addition, because rates for homogeneous groups often follow simpler patterns than composite population rates, both theoretical and empirical research may be unnecessarily complicated by failure to recognize the effects of heterogeneity. The multiplicity of heterogeneity's ruses can be neatly illustrated in the simplest example of a heterogeneous population -- namely, a composite population that consists of two homogeneous sub-populations. It is not difficult to develop models of heterogeneous sub-populations that consist of a very large or infinite number of sub-populations. The ruses illustrated here could have been described in the context of such a model, but for purposes of simplicity and clarity, a focus on the most elementary kind of heterogeneous population seems appropriate. Moreover, it turns out that almost all the distinctive features of heterogeneous populations become apparent as soon as the transition is made from a homogeneous population to a mixed population with two major sub-populations.

Udgivelsesdato: 2008-Feb To investigate the genetic contribution to familial similarity in longevity, we set up a novel experimental design where cousin-pairs born from siblings who were concordant or discordant for the longevity trait were analyzed. To check this design, two chromosomal regions already known to encompass longevity-related genes were examined: 6p21.3 (genes TNFalpha, TNFbeta, HSP70.1) and 11p15.5 (genes SIRT3, HRAS1, IGF2, INS, TH). Population pools of 1.6, 2.3 and 2.0 million inhabitants were screened, respectively, in Denmark, France and Italy to identify families matching the design requirements. A total of 234 trios composed by one centenarian, his/her child and a child of his/her concordant or discordant sib were collected. By using population-specific allele frequencies, we reconstructed haplotype phase and estimated the likelihood of Identical By Descent (IBD) haplotype sharing in cousin-pairs born from concordant and discordant siblings. In addition, we analyzed haplotype transmission from centenarians to offspring, and a statistically significant Transmission Ratio Distortion (TRD) was observed for both chromosomal regions in the discordant families (P=0.007 for 6p21.3 and P=0.015 for 11p15.5). In concordant families, a marginally significant TRD was observed at 6p21.3 only (P=0.06). Although no significant difference emerged between the two groups of cousin-pairs, our study gave new insights on the hindrances to recruiting a suitable sample to obtain significant IBD data on longevity-related chromosomal regions. This will allow to dimension future sampling campaigns to study-genetic basis of human longevity.European Journal of Human Genetics (2008) 16, 236-242; doi:10.1038/sj.ejhg.5201950; published online 7 November 2007.

This paper aims to discuss the validation and family determinants affecting the longevity of Sardinian centenarians, using a genealogical approach. This preliminary study presents the first results of a genealogical tree reconstruction of selected centenarians aged 105 and over, from certain areas. These are mostly situated in the province of Nuoro, an area with the highest rate of centenarians and where the female-to-male sex ratio tends to be male-biased. An accurate centenarian age validation was performed that required a meticulous examination of numerous civil status records and parish registers. An important finding was that longevity occurs among the ascendants of a particular branch of the family. The data used are still provisional but, should it apply to other validated cases, it would provide empirical evidence of a genetic component in longevity. A more thorough examination of the data available may yield deeper insights into the role played by endogamy and consanguinity.

In 2004, the integrated European project GEHA (Genetics of Healthy Ageing) was initiated with the aim of identifying genes involved in healthy ageing and longevity. The first step in the project was the recruitment of more than 2500 pairs of siblings aged 90years or more together with one younger control person from 15 areas in 11 European countries through a coordinated and standardised effort. A biological sample, preferably a blood sample, was collected from each participant, and basic physical and cognitive measures were obtained together with information about health, life style, and family composition. From 2004 to 2008 a total of 2535 families comprising 5319 nonagenarian siblings were identified and included in the project. In addition, 2548 younger control persons aged 50-75years were recruited. A total of 2249 complete trios with blood samples from at least two old siblings and the younger control were formed and are available for genetic analyses (e.g. linkage studies and genome-wide association studies). Mortality follow-up improves the possibility of identifying families with the most extreme longevity phenotypes. With a mean follow-up time of 3.7years the number of families with all participating siblings aged 95years or more has increased by a factor of 5 to 750 families compared to when interviews were conducted. Thus, the GEHA project represents a unique source in the search for genes related to healthy ageing and longevity. In 2004, the integrated European project GEHA (Genetics of Healthy Ageing) was initiated with the aim of identifying genes involved in healthy ageing and longevity. The first step in the project was the recruitment of more than 2500 pairs of siblings aged 90years or more together with one younger control person from 15 areas in 11 European countries through a coordinated and standardised effort. A biological sample, preferably a blood sample, was collected from each participant, and basic physical and cognitive measures were obtained together with information about health, life style, and family composition. From 2004 to 2008 a total of 2535 families comprising 5319 nonagenarian siblings were identified and included in the project. In addition, 2548 younger control persons aged 50-75years were recruited. A total of 2249 complete trios with blood samples from at least two old siblings and the younger control were formed and are available for genetic analyses (e.g. linkage studies and genome-wide association studies). Mortality follow-up improves the possibility of identifying families with the most extreme longevity phenotypes. With a mean follow-up time of 3.7years the number of families with all participating siblings aged 95years or more has increased by a factor of 5 to 750 families compared to when interviews were conducted. Thus, the GEHA project represents a unique source in the search for genes related to healthy ageing and longevity.

Udgivelsesdato: 2007-Apr The aim of the 5-year European Union (EU)-Integrated Project GEnetics of Healthy Aging (GEHA), constituted by 25 partners (24 from Europe plus the Beijing Genomics Institute from China), is to identify genes involved in healthy aging and longevity, which allow individuals to survive to advanced old age in good cognitive and physical function and in the absence of major age-related diseases. To achieve this aim a coherent, tightly integrated program of research that unites demographers, geriatricians, geneticists, genetic epidemiologists, molecular biologists, bioinfomaticians, and statisticians has been set up. The working plan is to: (a) collect DNA and information on the health status from an unprecedented number of long-lived 90+ sibpairs (n = 2650) and of younger ethnically matched controls (n = 2650) from 11 European countries; (b) perform a genome-wide linkage scannning in all the sibpairs (a total of 5300 individuals); this investigation will be followed by linkage disequilibrium mapping (LD mapping) of the candidate chromosomal regions; (c) study in cases (i.e., the 2650 probands of the sibpairs) and controls (2650 younger people), genomic regions (chromosome 4, D4S1564, chromosome 11, 11.p15.5) which were identified in previous studies as possible candidates to harbor longevity genes; (d) genotype all recruited subjects for apoE polymorphisms; and (e) genotype all recruited subjects for inherited as well as epigenetic variability of the mitochondrial DNA (mtDNA). The genetic analysis will be performed by 9 high-throughput platforms, within the framework of centralized databases for phenotypic, genetic, and mtDNA data. Additional advanced approaches (bioinformatics, advanced statistics, mathematical modeling, functional genomics and proteomics, molecular biology, molecular genetics) are envisaged to identify the gene variant(s) of interest. The experimental design will also allow (a) to identify gender-specific genes involved in healthy aging and longevity in women and men stratified for ethnic and geographic origin and apoE genotype; (b) to perform a longitudinal survival study to assess the impact of the identified genetic loci on 90+ people mortality; and (c) to develop mathematical and statistical models capable of combining genetic data with demographic characteristics, health status, socioeconomic factors, lifestyle habits.