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Stage-based demographic methods, such as matrix population models (MPMs), are powerful tools used to address a broad range of fundamental questions in ecology, evolutionary biology and conservation science. Accordingly, MPMs now exist for over 3000 species worldwide. These data are being digitised as an ongoing process and periodically released into two large open-access online repositories: the COMPADRE Plant Matrix Database and the COMADRE Animal Matrix Database. During the last decade, data archiving and curation of COMPADRE and COMADRE, and subsequent comparative research, have revealed pronounced variation in how MPMs are parameterized and reported.Here, we summarise current issues related to the parameterisation and reporting of MPMs that arise most frequently and outline how they affect MPM construction, analysis, and interpretation. To quantify variation in how MPMs are reported, we present results from a survey identifying key aspects of MPMs that are frequently unreported in manuscripts. We then screen COMPADRE and COMADRE to quantify how often key pieces of information are omitted from manuscripts using MPMs.Over 80% of surveyed researchers (n = 60) state a clear benefit to adopting more standardised methodologies for reporting MPMs. Furthermore, over 85% of the 300 MPMs assessed from COMPADRE and COMADRE omitted one or more elements that are key to their accurate interpretation. Based on these insights, we identify fundamental issues that can arise from MPM construction and communication and provide suggestions to improve clarity, reproducibility and future research utilising MPMs and their required metadata. To fortify reproducibility and empower researchers to take full advantage of their demographic data, we introduce a standardised protocol to present MPMs in publications. This standard is linked to www.compadre-db.org, so that authors wishing to archive their MPMs can do so prior to submission of publications, following examples from other open-acce

Contains fulltext : 149074.pdf (Publisher’s version ) (Open Access)

Contains fulltext : 149074.pdf (Publisher’s version ) (Open Access)

Much research aimed at discovering the genetic bases of longevity focuses on the budding yeast Saccharomyces cerevisiae. Unfortunately, yeast researchers use a definition of longevity not applied to other species. We propose here a method that makes it possible to estimate for yeast the same measures of longevity calculated for other species. We also show that the conventional method (equating longevity with the number of offspring) is only an approximate measure of true chronological lifespan. Our method will allow results for yeast to be compared more correctly with those for other species.

Much research aimed at discovering the genetic bases of longevity focuses on the budding yeast Saccharomyces cerevisiae. Unfortunately, yeast researchers use a definition of longevity not applied to other species. We propose here a method that makes it possible to estimate for yeast the same measures of longevity calculated for other species. We also show that the conventional method (equating longevity with the number of offspring) is only an approximate measure of true chronological lifespan. Our method will allow results for yeast to be compared more correctly with those for other species.

Much research aimed at discovering the genetic bases of longevity focuses on the budding yeast Saccharomyces cerevisiae. Unfortunately, yeast researchers use a definition of longevity not applied to other species. We propose here a method that makes it possible to estimate for yeast the same measures of longevity calculated for other species. We also show that the conventional method (equating longevity with the number of offspring) is only an approximate measure of true chronological lifespan. Our method will allow results for yeast to be compared more correctly with those for other species.

Three major groups call on demographers to produce medium- and long-term population forecasts at the national, regional, or global levels - or produce them themselves. They are: other scientists, government and international agencies, and the general public, including private industry. What these consumers of forecasts demand of demographers, or what demographers think that they should demand, has been changing. The types of forecasts demanded are changing, the relevant dimension of forecasts is expanding, and users are increasingly requiring that forecasts include an indication of the degree of uncertainty of the forecast. Because the demands placed on demographers for population forecasts have been changing, it is an appropriate time to rethink some of their basic aspects. In this volume we address what we see as key issues in population forecasting: in what dimensions and at what levels of disaggregation should forecasts be provided? (And, in particular, are the traditional dimensions of age and sex sufficient?) Should population forecasts take note of limits to population or interactions between population and other variables? And how should uncertainty be treated? We believe that, at least in part, these issues are driven by changes in what users of forecasts want from population forecasters. The reader will note that we have used the term "forecasts" rather than the more common "projections." Demographers claim to produce population "projections," which are correctly computed numerical outcomes of a specified algorithm whose form, initial values, and controlling parameters or transition values are specified by the analyst. By definition, a projection must be correct unless arithmetical or other errors are made. However, users of population projections require population "forecasts." Forecasts are what Donald Pittenger (1980) called a "population projection selected as a likely outcome." Thus although a demographer makes a "projection," the user employs it as a

Any breakdown of the total population (i.e., the number of living individuals staying within a well-defined area) for analytical purposes follows a certain implicit or explicit logic. In demography it has become standard practice to sort the total population along the dimensions of age and sex. Although this practice is usually taken for granted and not explicitly justified, it may be useful to recall the good reasons that have lead to this practice. This appraisal of age and sex helps to evaluate the importance one should assign to explicit consideration of such other possible dimensions as marital status, ethnicity, labor force participation, region of origin, and educational status. Three criteria should govern the determination to explicitly consider a particular dimension (breakdown) in demographic analysis in general and in population projections in particular: Criterion 1. To the users the dimension is interesting in its own right and therefore desirable as an explicit output parameter. Criterion 2. The dimension is a relevant source of demographic heterogeneity with an impact on the dynamics of the whole system and therefore on the resulting population size. Criterion 3. It is feasible (in terms of data and methodology) to consider the dimension explicitly. Age meets these criteria....

To improve population forecasting in the future, demographers should conduct more thorough assessments of the accuracy of past projections. Research should also focus on making greater use of: (1) models that include marriage, divorce, cohabitation, morbidity, and other demographic events that influence fertility, mortality, and migration as well as models that break populations down by educational achievement, employment status, and other variables; (2) models that take account of economic, social, and environmental dynamics, including integrated structural models and models with constraints; and (3) forecasting approaches that systematically quantify uncertainty. A further area that requires rethinking is the appropriate use of expert judgment in population projections. Finally, new ways need to be developed for distributing software for making population forecasts and for disseminating the results of alternative forecasts.

Most users of population projections are interested in one likely path of future population trends based on the best existing knowledge. Whether it is called the medium variant, central scenario, or median of an uncertainty distribution, this projected path will be taken as a forecast on which further considerations can be based. For many users such a best guess will suffice. It can be taken as an exogenous input into their own models for school planning, social security considerations, energy outlook, and the like. For this reason a medium projection is an indispensable component of any set of published projections intended for practical use.

Most users of demographic data in government and industry require population forecasts-soundly based information on future population trends at the local, national, or global level. In the eyes of the public this is a principal justification for the discipline of demography And increasingly, sophisticated users expect not a single "best guess" of a population trajectory - perhaps straddled by "high" and "low" variants - but a range of demographic futures with associated indications of uncertainty, or even formal confidence intervals. Or they may want full-fledged scenarios of the development of the demographic system in different economic or environmental circumstances. Many population agencies, on the other hand, continue to generate population "projections" by methods that have been virtually unchanged for decades, with no assessment of probability and often claiming no ambition to predict. It is time to reexamine the procedures of population forecasting and to respond to these emerging demands by users. The nine chapters in this volume take on this task. The key issues they address include: What population characteristics beyond the standard variables of age and sex should routinely enter population forecasts? When should forecasts take account of economic or environmental feedbacks? How is forecasting accuracy to be assessed and what is the past record? What is the state of the art of stochastic time series modeling of population change? How can users cope with probability distributions? What scope is there for application of methods to incorporate expert opinion into population forecasting? Recent years have seen substantial advances in forecasting methods. These are beginning to be applied in population. For end users of forecasts who are familiar mainly with UN or similar population projection series and for the many professional demographers whose knowledge of projections has not progressed much since graduate, school, this volume opens a window on significa

Three major groups call on demographers to produce medium- and long-term population forecasts at the national, regional, or global levels - or produce them themselves. They are: other scientists, government and international agencies, and the general public, including private industry. What these consumers of forecasts demand of demographers, or what demographers think that they should demand, has been changing. The types of forecasts demanded are changing, the relevant dimension of forecasts is expanding, and users are increasingly requiring that forecasts include an indication of the degree of uncertainty of the forecast. Because the demands placed on demographers for population forecasts have been changing, it is an appropriate time to rethink some of their basic aspects. In this volume we address what we see as key issues in population forecasting: in what dimensions and at what levels of disaggregation should forecasts be provided? (And, in particular, are the traditional dimensions of age and sex sufficient?) Should population forecasts take note of limits to population or interactions between population and other variables? And how should uncertainty be treated? We believe that, at least in part, these issues are driven by changes in what users of forecasts want from population forecasters. The reader will note that we have used the term "forecasts" rather than the more common "projections." Demographers claim to produce population "projections," which are correctly computed numerical outcomes of a specified algorithm whose form, initial values, and controlling parameters or transition values are specified by the analyst. By definition, a projection must be correct unless arithmetical or other errors are made. However, users of population projections require population "forecasts." Forecasts are what Donald Pittenger (1980) called a "population projection selected as a likely outcome." Thus although a demographer makes a "projection," the user employs it as a

Any breakdown of the total population (i.e., the number of living individuals staying within a well-defined area) for analytical purposes follows a certain implicit or explicit logic. In demography it has become standard practice to sort the total population along the dimensions of age and sex. Although this practice is usually taken for granted and not explicitly justified, it may be useful to recall the good reasons that have lead to this practice. This appraisal of age and sex helps to evaluate the importance one should assign to explicit consideration of such other possible dimensions as marital status, ethnicity, labor force participation, region of origin, and educational status. Three criteria should govern the determination to explicitly consider a particular dimension (breakdown) in demographic analysis in general and in population projections in particular: Criterion 1. To the users the dimension is interesting in its own right and therefore desirable as an explicit output parameter. Criterion 2. The dimension is a relevant source of demographic heterogeneity with an impact on the dynamics of the whole system and therefore on the resulting population size. Criterion 3. It is feasible (in terms of data and methodology) to consider the dimension explicitly. Age meets these criteria....

To improve population forecasting in the future, demographers should conduct more thorough assessments of the accuracy of past projections. Research should also focus on making greater use of: (1) models that include marriage, divorce, cohabitation, morbidity, and other demographic events that influence fertility, mortality, and migration as well as models that break populations down by educational achievement, employment status, and other variables; (2) models that take account of economic, social, and environmental dynamics, including integrated structural models and models with constraints; and (3) forecasting approaches that systematically quantify uncertainty. A further area that requires rethinking is the appropriate use of expert judgment in population projections. Finally, new ways need to be developed for distributing software for making population forecasts and for disseminating the results of alternative forecasts.

Most users of population projections are interested in one likely path of future population trends based on the best existing knowledge. Whether it is called the medium variant, central scenario, or median of an uncertainty distribution, this projected path will be taken as a forecast on which further considerations can be based. For many users such a best guess will suffice. It can be taken as an exogenous input into their own models for school planning, social security considerations, energy outlook, and the like. For this reason a medium projection is an indispensable component of any set of published projections intended for practical use.

Most users of demographic data in government and industry require population forecasts-soundly based information on future population trends at the local, national, or global level. In the eyes of the public this is a principal justification for the discipline of demography And increasingly, sophisticated users expect not a single "best guess" of a population trajectory - perhaps straddled by "high" and "low" variants - but a range of demographic futures with associated indications of uncertainty, or even formal confidence intervals. Or they may want full-fledged scenarios of the development of the demographic system in different economic or environmental circumstances. Many population agencies, on the other hand, continue to generate population "projections" by methods that have been virtually unchanged for decades, with no assessment of probability and often claiming no ambition to predict. It is time to reexamine the procedures of population forecasting and to respond to these emerging demands by users. The nine chapters in this volume take on this task. The key issues they address include: What population characteristics beyond the standard variables of age and sex should routinely enter population forecasts? When should forecasts take account of economic or environmental feedbacks? How is forecasting accuracy to be assessed and what is the past record? What is the state of the art of stochastic time series modeling of population change? How can users cope with probability distributions? What scope is there for application of methods to incorporate expert opinion into population forecasting? Recent years have seen substantial advances in forecasting methods. These are beginning to be applied in population. For end users of forecasts who are familiar mainly with UN or similar population projection series and for the many professional demographers whose knowledge of projections has not progressed much since graduate, school, this volume opens a window on significa

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.

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 other dimensions can be used such as life expectancy or population growth rate. This research report 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 US 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 research report 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.

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!

Suppose progress continues to be made in reducing mortality rates at all ages. What impact would this progress have on the size and age composition of the U.S. population? The supposition that mortality rates will continue to fall is admittedly questionable. The view popularized by James F. Fries is that "the median natural human life span is set at a maximum of 85 years with a standard error of less than one year" (Fries and Crapo, 1981). Paul Demeny, in making long-term population forecasts for the World Bank, assumes that even by the year 2100 there will be no country with a life expectancy above 82.5 years. Demeny notes that in some countries life expectancy seems to be slowly decreasing. The possibility of a general decline in life expectancy cannot be ruled out. On the other hand, as Demeny points out, "the upper limit to life expectancy" of 82.5 years "may yield to technological changes in medicine and to changes in life styles, perhaps even within the next few decades" (Demeny, 1984). As documented by Crimmins (1981), remarkably rapid progress in reducing mortality rates was made in the United States from 1968 to 1977. This progress has continued and even accelerated from 1977 to 1983. At most ages, including older ages, mortality rates over the last decade have been declining at a rate of one or two percent per year. Hope that this progress might continue is butressed by recent advances in the biological, medical, and gerontological sciences. The life sciences appear to be poised at roughly the point the physical sciences were a century ago and breakthroughs comparable to electricity, automobiles, television, and computers may be forthcoming in the areas of genetic engineering, prevention and treatment of such diseases as atherosclerosis, cancer, and diabetes, and perhaps understanding and control of the process of aging itself (see, e.g. Walford (1983), Bulkley (1983), and Rosenfeld (1976)). In this note, we explore three possibilities: no change in mortal

How does saving lives affect the force of mortality and lifetable statistics? How can the progress being made in reducing the force of mortality be interpreted in terms of lifesaving? How many times can a person expect to have his or her life saved as a result of this progress? We develop a model to answer these questions and illustrate the results using U.S. mortality rates for 1900 and 1980 and as projected for 2050.

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.

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.

An important part of the activity of IIASA's Population Program is related to the development of data visualization techniques. The paper is devoted to the analysis of cause specific mortality data for Japan using the shaded contour map approach which was recently developed in the program by an international team of scientists.

An important part of the activity of IIASA's Population Program is related to the development of data visualization techniques. The paper is devoted to the analysis of cause specific mortality data for Japan using the shaded contour map approach which was recently developed in the program by an international team of scientists.

This paper presents a bouquet of contour maps to suggest the broad potential of their use in demographic studies. Every picture presented could serve as the basis for a thousand words or more of explanation and analysis, but here we merely serve up the maps as illustrations of the method. For an example of how such maps can be used in demographic analysis, see Caselli, Vaupel, and Yashin (1985): Mortality in Italy--Contours of a Century of Evolution (CP-85-24, International Institute for Applied Systems Analysis, Laxenburg, Austria).

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.

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.

A stochastic differential equation model is developed to clarify the interaction of debilitation, recuperation, selection and aging. The model yields various insights about lingering mortality consequences of disasters such as wars, famines and epidemics that may weaken the survivors. A key result is that debilitation and selection are interdependent: debilitation that increases population heterogeneity will result in subsequent selection; selection, by altering the distribution of population heterogeneity, will influence the impact of debilitating events.

A stochastic differential equation model is developed to clarify the interaction of debilitation, recuperation, selection and aging. The model yields various insights about lingering mortality consequences of disasters such as wars, famines and epidemics that may weaken the survivors. A key result is that debilitation and selection are interdependent: debilitation that increases population heterogeneity will result in subsequent selection; selection, by altering the distribution of population heterogeneity, will influence the impact of debilitating events.

Risk analysis and policy analysis can play important roles in facilitating the siting of potentially hazardous facilities if one recognizes the descriptive features of the decision process. The case of siting a liquified natural gas (LNG) facility in California illustrates the multi-party sequential nature of the process and the role that widely differing risk estimates play in fueling conflicts between stakeholders. Risk analysis does have a useful function in clarifying the nature of the potential losses, particularly if rules of evidence are instituted for evaluating different studies. Policy analysis can facilitate the negotiation process by the use of compensation to redistribute gains and losses between the different parties. Examples from case studies are presented to illustrate the challenges for risk analysis and policy analysis in the siting process.

This article uses Swedish life tables to examine saving years of life at different ages in order to gain a deeper demographic understanding of the link between age-specific mortality and life expectancy. Before 1900 most of the potential for saving years of life was concentrated in the 1st 5 childhood years; today developed countries concentrate on old age. As life expectancy increases reducing age-specific mortality means less and less increase of life expectancy. The author uses a simple model to examine whether continued progress in mortality reduction will mean a continued increase in life expectancy and finds that the absolute increase in life expectancy remains constant--perhaps a decade of life expectancy per century. Considerations contained within the article include 1) the possible uniqueness of the Swedish data 2) the limitations of using only life table data 3) the reduced quality of life at older ages and 4) the greater ease in averting deaths at younger ages. Since it is also desirable to avert death at any age and to have a society diverse in its age composition many questions of value policy and cost come into play.

Life expectancy in a heterogeneous population can be increased by lowering mortality rates or by averting deaths at different ages, from different causes, or for different groups, as well as by changing the proportions of individuals in various risk groups, perhaps by altering the transition rates between groups. Understanding how such changes in population structure affect life expectancy is useful in evaluating alternative lifesaving policies.

Various multivariate stochastic process models have been developed to represent human physiological aging and mortality. These efforts are extended by considering the effects of observed and unobserved state variables on the age trajectory of physiological parameters. This is done by deriving the Kolmogorov-Fokker-Planck equations describing the distribution of the unobserved state variables conditional on the history of the observed state variables. Given some assumptions, it is proved that the distribution is Gaussian. Strategies for estimating the parameters of the distribution are suggested based on an extension of the theory of Kalman filters to include systematic mortality selection. Various empirical applications of the model to studies of human aging and mortality as well as to other types of “failure” processes in heterogeneous populations are discussed.

As a cohort of people, animals, or machines ages, the individuals at highest risk tend to die or exit first. This differential selection can produce patterns of mortality for the population as a whole that are surprisingly different from the patterns for subpopulations or individuals. Naive acceptance of observed population patterns may lead to erroneous policy recommendations if an intervention depends on the response of individuals. Furthermore, because patterns at the individual level may be simpler than composite population patterns, both theoretical and empirical research may be unnecessarily complicated by failure to recognize the effects of heterogeneity.

This article uses Swedish life tables to examine saving years of life at different ages in order to gain a deeper demographic understanding of the link between age-specific mortality and life expectancy. Before 1900 most of the potential for saving years of life was concentrated in the 1st 5 childhood years; today developed countries concentrate on old age. As life expectancy increases reducing age-specific mortality means less and less increase of life expectancy. The author uses a simple model to examine whether continued progress in mortality reduction will mean a continued increase in life expectancy and finds that the absolute increase in life expectancy remains constant--perhaps a decade of life expectancy per century. Considerations contained within the article include 1) the possible uniqueness of the Swedish data 2) the limitations of using only life table data 3) the reduced quality of life at older ages and 4) the greater ease in averting deaths at younger ages. Since it is also desirable to avert death at any age and to have a society diverse in its age composition many questions of value policy and cost come into play.

Risk analysis and policy analysis can play important roles in facilitating the siting of potentially hazardous facilities if one recognizes the descriptive features of the decision process. The case of siting a liquified natural gas (LNG) facility in California illustrates the multi-party sequential nature of the process and the role that widely differing risk estimates play in fueling conflicts between stakeholders. Risk analysis does have a useful function in clarifying the nature of the potential losses, particularly if rules of evidence are instituted for evaluating different studies. Policy analysis can facilitate the negotiation process by the use of compensation to redistribute gains and losses between the different parties. Examples from case studies are presented to illustrate the challenges for risk analysis and policy analysis in the siting process.

A stochastic differential equation model is developed to clarify the interaction of debilitation, recuperation, selection and aging. The model yields various insights about lingering mortality consequences of disasters such as wars, famines and epidemics that may weaken the survivors. A key result is that debilitation and selection are interdependent: debilitation that increases population heterogeneity will result in subsequent selection; selection, by altering the distribution of population heterogeneity, will influence the impact of debilitating events.

Life expectancy in a heterogeneous population can be increased by lowering mortality rates or by averting deaths at different ages, from different causes, or for different groups, as well as by changing the proportions of individuals in various risk groups, perhaps by altering the transition rates between groups. Understanding how such changes in population structure affect life expectancy is useful in evaluating alternative lifesaving policies.

A stochastic differential equation model is developed to clarify the interaction of debilitation, recuperation, selection and aging. The model yields various insights about lingering mortality consequences of disasters such as wars, famines and epidemics that may weaken the survivors. A key result is that debilitation and selection are interdependent: debilitation that increases population heterogeneity will result in subsequent selection; selection, by altering the distribution of population heterogeneity, will influence the impact of debilitating events.

Various multivariate stochastic process models have been developed to represent human physiological aging and mortality. These efforts are extended by considering the effects of observed and unobserved state variables on the age trajectory of physiological parameters. This is done by deriving the Kolmogorov-Fokker-Planck equations describing the distribution of the unobserved state variables conditional on the history of the observed state variables. Given some assumptions, it is proved that the distribution is Gaussian. Strategies for estimating the parameters of the distribution are suggested based on an extension of the theory of Kalman filters to include systematic mortality selection. Various empirical applications of the model to studies of human aging and mortality as well as to other types of “failure” processes in heterogeneous populations are discussed.

The paper is devoted to the analysis of stochastic process models of mortality which can explain both selection and debilitation processes in the evolution of cohort mortality. The relative importance of each process is analyzed. The examples of various regimes of mortality evolution are demonstrated.

An important part of the activity of IIASA's Population Program is related to the development of data visualization techniques. The paper is devoted to the analysis of cause specific mortality data for Japan using the shaded contour map approach which was recently developed in the program by an international team of scientists.

This paper presents a bouquet of contour maps to suggest the broad potential of their use in demographic studies. Every picture presented could serve as the basis for a thousand words or more of explanation and analysis, but here we merely serve up the maps as illustrations of the method. For an example of how such maps can be used in demographic analysis, see Caselli, Vaupel, and Yashin (1985): Mortality in Italy--Contours of a Century of Evolution (CP-85-24, International Institute for Applied Systems Analysis, Laxenburg, Austria).

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.

Contour maps of Italian male and female mortality rates from age 0 to 79 and from 1870 to 1979 graphically display persistent global and prominent local patterns of mortality, simultaneously over age, by period, and for cohorts. The maps give demographers visual access to previously recognized features of the evolution of Italian mortality as well as focusing attention on some neglected features. Use of contour maps to display various kinds of mortality data, including mortality comparisons, may help demographers better understand the social and biological determinants of mortality.

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.

As a cohort of people, animals, or machines ages, the individuals at highest risk tend to die or exit first. This differential selection can produce patterns of mortality for the population as a whole that are surprisingly different from the patterns for subpopulations or individuals. Naive acceptance of observed population patterns may lead to erroneous policy recommendations if an intervention depends on the response of individuals. Furthermore, because patterns at the individual level may be simpler than composite population patterns, both theoretical and empirical research may be unnecessarily complicated by failure to recognize the effects of heterogeneity.