The focus of this monograph is on generalizing the notion of variation in a set of numbers to variation in a set of probability distributions. The authors collect some known ways of comparing stochastic matrices in the context of information theory, statistics, economics, and population sciences. They then generalize these comparisons, introduce new comparisons, and establish the relations of implication or equivalence among sixteen of these comparisons. Some of the possible implications among these comparisons remain open questions. The results in this book establish a new field of investigation for both mathematicians and scientific users interested in the variations among multiple probability distributions. The work is divided into two parts. The first deals with finite stochastic matrices, which may be interpreted as collections of discrete probability distributions. The first part is presented in a fairly elementary mathematical setting. The introduction provides sketches of applications of concepts and methods to discrete memory-less channels in information theory, to the design and comparison of experiments in statistics, to the measurement of inequality in economics, and to various analytical problems in population genetics, ecology, and demography. Part two is more general and entails more difficult analysis involving Markov kernels. Here, many results of the first part are placed in a more general setting, as required in more sophisticated applications. A great strength of this text is the resulting connections among ideas from diverse fields: mathematics, statistics, economics, and population biology. In providing this array of new tools and concepts, the work will appeal to the practitioner. At the same time, it will serve as an excellent resource for self-study of for a graduate seminar course, as well as a stimulus to further research.

This volume presents a rigorous account of statistical forecasting efforts that led to the successful resolution of the Johns-Manville asbestos litigation. This case, taking 12 years to reach settlement, is expected to generate nearly 500,000 claims at a total nominal value of over $34 billion. The forecasting task, to project the number, timing, and nature of claims for asbestos-related injuries from a set of exposed persons of unknown size, is a general problem: the models in this volume can be adapted to forecast industry-wide asbestos liability. More generally, because the models are not overly dependent on the U.S. legal system and the role of asbestos as a dangerous/defective product, this volume will be of interest in other product liability cases, as well as similar forecasting situations for a range of insurable or compensable events. The volume stresses the iterative nature of model building and the uncertainty generated by lack of complete knowledge of the injury process. This uncertainty is balanced against the Court's need for a definitive settlement, and the volume addresses how these opposing principles can be reconciled. The volume is written for a broad audience of actuaries, biostatisticians, demographers, economists, epidemiologists, environmental health scientists, financial analysts, industrial-risk analysts, occumpational health analysts, product liability analysts, and statisticians. The modest prerequisites include basic concepts of statistics, calculus, and matrix algebra. Care is taken that readers without specialized knowledge in these areas can understand the rationale for specific applications of advanced methods. As a consequence, this volume will be an indispensable reference for all whose work involves these topics. Eric Stallard, A.S.A., M.A.A.A., is Research Professor and Associate Director of the Center for Demographic Studies at Duke University. He is a Member of the American Academy of Actuaries and an Associate of the Society of Actuaries. He serves on the American Academy of Actuaries Committees on Long Term Care and Social Insurance. He also serves on the society of Actuaries' Long Term Care Experience Committee. His research interests include modelling and forecasting for medical demography and health actuarial practice. He was the 1996 winner of the National Institute on Aging's James A. Shannon Director's Award. Kenneth G. Manton, Ph.D., is Research Professor, Research Director, and Director of the Center for Demographic Studies at Duke University and Medical Research Professor at Duke University Medical Center's Department of Community and Family Medicine. Dr. Manton is also a Senior Fellow of the Duke University Medical Center's Center for the Study of Aging and Human Development. His research interests include mathematical models of human aging, mortality, and chronic disease. He was the 1990 recipient of the Mindel C. Sheps Award in Mathematical Demography presented by the Population Association of America; and in 1991 he received the Allied-Signal Inc. Achievement Award in Aging administred by the Johns Hopkins Center on Aging. Joel E. Cohen, Ph.D., Dr. P.H., is Professor of Populations, and Head of the Laboratory of Populations, Rockefeller University. He also is Professor of Populations at Columbia University. His research interests include the demography, ecology, epidemiology, and social organization of human and non-human populations, and related mathematical concepts. In 1981, he was elected Fellow of the MacArthur and Guggenheim Foundations. He was the 1992 recipient of the Mindel C. Sheps Award in Mathematical Demography presented by the Population Association of America; and in 1994, he received the Distinguished Statistical Ecologist Award at the Sixth International Congress of Ecology.

Although universal schooling has been adopted as a goal by international organizations, bilateral aid agencies, national governments, and non-profit organizations, little sustained international attention has been devoted to the purposes or goals of universal education. What is universal primary and secondary education intended to accomplish? This book, which grew out of a project of the American Academy of Arts & Sciences, offers views from Asia, Africa, Europe, North America and South America on the purposes of universal education while considering diverse cultures, religions, and professions. It is the first book in which renowned authors from around the world have proposed, considered, and debated goals of basic and secondary education, engaging in a constructive dialogue on one of the most pressing issues facing education today.

Food webs hold a central place in ecology. They describe which organisms feed on which others in natural habitats. This book describes recently discovered empirical regularities in real food webs: it proposes a novel theory unifying many of these regularities, as well as extensive empirical data. After a general introduction, reviewing the empirical and theoretical discoveries about food webs, the second portion of the book shows that community food webs obey several striking phenomenological regularities. Some of these unify, regardless of habitat. Others differentiate, showing that habitat significantly influences structure. The third portion of the book presents a theoretical analysis of some of the unifying empirical regularities. The fourth portion of the book presents 13 community food webs. Collected from scattered sources and carefully edited, they are the empirical basis for the results in the volume. The largest available set of data on community food webs provides a valuable foundation for future studies of community food webs. The book is intended for graduate students, teachers and researchers primarily in ecology. The theoretical portions of the book provide materials useful to teachers of applied combinatorics, in particular, random graphs. Researchers in random graphs will find here unsolved mathematical problems.

This selection of papers encompasses recent methodological advances in several important areas, such as multivariate failure time data and interval censored data, as well as innovative applications of the existing theory and methods. Using a rigorous account of statistical forecasting efforts that led to the successful resolution of the John-Manville asbestos litigation, the models in this volume can be adapted to forecast industry-wide asbestos liability. More generally, because the models are not overly dependent on the U.S. legal system and the role of asbestos, this volume will be of interest in other product liability cases, as well as similar forecasting situations for a range of insurable or compensational events. Throughout the text, the emphasis is on the iterative nature of model building and the uncertainty generated by lack of complete knowledge of the injury process. This uncertainty is balanced against the court's need for a definitive settlement, and how these opposing principles can be reconciled. A valuable reference for researchers and practitioners in the field of survival analysis.

Universal schooling has been adopted as a goal by international organizations, bilateral aid agencies, national governments, and non-profit organizations. Yet little sustained international attention has been devoted to the purposes or goals of universal education. What is universal primary and secondary education intended to accomplish? This book, which grew out of a project of the American Academy of Arts & Sciences, offers diverse views from Asia, Africa, Europe, North America and South America and from diverse cultures, religions, and professions, on the purposes of universal education. It is the first book in which renowned authors from around the world have confronted one another in proposing goals of basic and secondary education, and in considering and responding to the differing views of others on one of the most pressing issues facing education today.

What is the minimum dimension of a niche space necessary to represent the overlaps among observed niches? This book presents a new technique for obtaining a partial answer to this elementary question about niche space. The author bases his technique on a relation between the combinatorial structure of food webs and the mathematical theory of interval graphs.

Professor Cohen collects more than thirty food webs from the ecological literature and analyzes their statistical and combinatorial properties in detail. As a result, he is able to generalize: within habitats of a certain limited physical and temporal heterogeneity, the overlaps among niches, along their trophic (feeding) dimensions, can be represented in a one-dimensional niche space far more often than would be expected by chance alone and perhaps always. This compatibility has not previously been noticed. It indicates that real food webs fall in a small subset of the mathematically possible food webs.

Professor Cohen discusses other apparently new features of real food webs, including the constant ratio of the number of kinds of prey to the number of kinds of predators in food webs that describe a community. In conclusion he discusses possible extensions and limitations of his results and suggests directions for future research.

A compelling new analysis of world population issues and what the numbers tell us. . . . "A gem of a book."--New York Times Book Review

With the world population now at 5.7 billion, and increasing by about 90 million per year, we have clearly entered a zone where we can see, and may well encounter, limits on the human carrying capacity of the Earth. In this penetrating analysis of one of the most crucial questions of our time, a leading scholar in the field reviews the history of world population growth and appraises what can be known about its future.

"The definitive work on the global population problem. Cohen, one of the foremost theoretical biologists in the world, has brought extraordinary analytic powers and humanitarian learning to the topic, and those who care about the human future will do well to read his conclusions."--Edward O. Wilson, Harvard University

"It would be hard to conceive of a better book for those interested in a scholarly and nonideological review and analysis of population issues. . . . Fascinating and lucid. . . . A gem of a book."--William D. Nordhaus, Yale University, in the New York Times Book Review

"A probing, scholarly analysis of the population issue in all its complexity. . . . An enduring resource book."--Thomas E. Lovejoy, Smithsonian Institution

Joel E. Cohen is head of the Laboratory of Populations at the Rockefeller University. He lives in New York City.