Mathematical demography is the centerpiece of quantitative social science. The founding works of this field from Roman times to the late Twentieth Century are collected here, in a new edition of a classic work by David R. Smith and Nathan Keyfitz. Commentaries by Smith and Keyfitz have been brought up to date and extended by Kenneth Wachter and Hervé Le Bras, giving a synoptic picture of the leading achievements in formal population studies. Like the original collection, this new edition constitutes an indispensable source for students and scientists alike, and illustrates the deep roots and continuing vitality of mathematical demography.
The third edition of this classic text maintains its focus on applications of demographic models, while extending its scope to matrix models for stage-classified populations. The authors first introduce the life table to describe age-specific mortality, and then use it to develop theory for stable populations and the rate of population increase. This theory is then revisited in the context of matrix models, for stage-classified as well as age-classified populations. Reproductive value and the stable equivalent population are introduced in both contexts, and Markov chain methods are presented to describe the movement of individuals through the life cycle. Applications of mathematical demography to population projection and forecasting, kinship, microdemography, heterogeneity, and multi-state models are considered. The new edition maintains and extends the book’s focus on the consequences of changes in the vital rates. Methods are presented for calculating the sensitivity and elasticity of population growth rate, life expectancy, stable stage distribution, and reproductive value, and for applying those results in comparative studies. Stage-classified models are important in both human demography and population ecology, and this edition features examples from both human and non-human populations. In short, this third edition enlarges considerably the scope and power of demography. It will be an essential resource for students and researchers in demography and in animal and plant population ecology. Nathan Keyfitz is Professor Emeritus of Sociology at Harvard University. After holding positions at Canada’s Dominion Bureau of Statistics, the University of Chicago, and the University of California at Berkeley, he became Andelot Professor of Sociology and Demography at Harvard in 1972. After retiring from Harvard, he became Director of the Population Program at the International Institute for Applied Systems Analysis (IIASA) in Vienna from 1983 to 1993. Keyfitz is a member of the U.S. National Academy of Sciences and the Royal Society of Canada, and a Fellow of the American Academy of Arts and Sciences. He has received the Mindel Sheps Award of the Population Association of America and the Lazarsfeld Award of the American Sociological Association, and was the 1997 Laureate of the International Union for the Scientific Study of Population. He has written 12 books, including Introduction to the Mathematics of Population (1968) and, with Fr. Wilhelm Flieger, SVD, World Population Growth and Aging: Demographic Trends in the Late Twentieth Century (1990). Hal Caswell is a Senior Scientist in the Biology Department of the Woods Hole Oceanographic Institution, where he holds the Robert W. Morse Chair for Excellence in Oceanography. He is a Fellow of the American Academy of Arts and Sciences. He has held a Maclaurin Fellowship from the New Zealand Institute of Mathematics and its Applications and a John Simon Guggenheim Memorial Fellowship. His research focuses on mathematical population ecology with applications in conservation biology. He is the author of Matrix Population Models: Construction, Analysis, and Interpretation (2001).
What follows is a new edition of the second in a series of three books providing an account of the mathematical development of demography. The first, Introduction to the Mathematics of Population (Addison-Wesley, 1968), gave the mathematical background. The second, the original of the present volume, was concerned with demography itself. The third in the sequence, Mathematics Through Problems (with John Beekman; Springer Verlag, 1982), supplemented the first two with an ordered sequence of problems and answers. Readers interested in the mathematics may consult the earlier book, republished with revisions by Addison-Wesley in 1977 and still in print. There is no overlap in subject matter between Applied Mathematical Demography and the Introduction to the Mathematics of Population. Three new chapters have been added, dealing with matters that have come recently into the demographic limelight: multi-state calculations, family demogra phy, and heterogeneity. vii PREFACE This book is concerned with commonsense questions about, for instance, the effect of a lowered death rate on the proportion of old people or the effect of abortions on the birth rate. The answers that it reaches are not always commonsense, and we will meet instances in which intuition has to be adjusted to accord with what the mathematics shows to be the case.
Gender-Structured Population Modeling gives a unified presentation of and mathematical framework for modeling population growth by couple formation. It provides an overview of both past and present modeling results. The authors focus on pair formation (marriage) and two-sex models with different forms of the marriage function -- the basis of couple formation -- and discuss which of these forms might make a better choice for a particular population (the United States). The book also provides results on model analysis, gives an up-to-date review of mathematical demography, discusses numerical methods, and puts deterministic modeling of human populations into historical perspective.
This open access book shows how to use sensitivity analysis in demography. It presents new methods for individuals, cohorts, and populations, with applications to humans, other animals, and plants. The analyses are based on matrix formulations of age-classified, stage-classified, and multistate population models. Methods are presented for linear and nonlinear, deterministic and stochastic, and time-invariant and time-varying cases. Readers will discover results on the sensitivity of statistics of longevity, life disparity, occupancy times, the net reproductive rate, and statistics of Markov chain models in demography. They will also see applications of sensitivity analysis to population growth rates, stable population structures, reproductive value, equilibria under immigration and nonlinearity, and population cycles. Individual stochasticity is a theme throughout, with a focus that goes beyond expected values to include variances in demographic outcomes. The calculations are easily and accurately implemented in matrix-oriented programming languages such as Matlab or R. Sensitivity analysis will help readers create models to predict the effect of future changes, to evaluate policy effects, and to identify possible evolutionary responses to the environment. Complete with many examples of the application, the book will be of interest to researchers and graduate students in human demography and population biology. The material will also appeal to those in mathematical biology and applied mathematics.
This volume contains pedagogical and elementary introductions to genetics for mathematicians and physicists as well as to mathematical models and techniques of population dynamics. It also offers a physicist''s perspective on modeling biological processes. Each chapter starts with an overview followed by the recent results obtained by authors. Lectures are self-contained and are devoted to various phenomena such as the evolution of the genetic code and genomes, age-structured populations, demography, sympatric speciation, the Penna model, Lotka-Volterra and other predator-prey models, evolutionary models of ecosystems, extinctions of species, and the origin and development of language. Authors analyze their models from the computational and mathematical points of view.
This book provides new theories, applications and quantitative methods in demography, population studies and statistics. It presents and applies data analysis, statistics and stochastic modeling techniques focusing on demography, population aging, mortality and health sciences. The book describes diverse stochastic processes as well as Markov and semi-Markov models in demography and population studies, along with chapters on statistical models and methods in biostatistics and epidemiology. As such the book will be a valuable source to demographers, health scientists, statisticians, economists and sociologists.
The practice of modeling is best learned by those armed with fundamental methodologies and exposed to a wide variety of modeling experience. Ideally, this experience could be obtained by working on actual modeling problems. But time constraints often make this difficult. Applied Mathematical Modeling provides a collection of models illustrating the power and richness of the mathematical sciences in supplying insight into the operation of important real-world systems. It fills a gap within modeling texts, focusing on applications across a broad range of disciplines. The first part of the book discusses the general components of the modeling process and highlights the potential of modeling in practice. These chapters discuss the general components of the modeling process, and the evolutionary nature of successful model building. The second part provides a rich compendium of case studies, each one complete with examples, exercises, and projects. In keeping with the multidimensional nature of the models presented, the chapters in the second part are listed in alphabetical order by the contributor's last name. Unlike most mathematical books, in which you must master the concepts of early chapters to prepare for subsequent material, you may start with any chapter. Begin with cryptology, if that catches your fancy, or go directly to bursty traffic if that is your cup of tea. Applied Mathematical Modeling serves as a handbook of in-depth case studies that span the mathematical sciences, building upon a modest mathematical background. Readers in other applied disciplines will benefit from seeing how selected mathematical modeling philosophies and techniques can be brought to bear on problems in their disciplines. The models address actual situations studied in chemistry, physics, demography, economics, civil engineering, environmental engineering, industrial engineering, telecommunications, and other areas.
The Second Autumn Course on Mathematical Ecology was held at the Intern ational Centre for Theoretical Physics in Trieste, Italy in November and December of 1986. During the four year period that had elapsed since the First Autumn Course on Mathematical Ecology, sufficient progress had been made in applied mathemat ical ecology to merit tilting the balance maintained between theoretical aspects and applications in the 1982 Course toward applications. The course format, while similar to that of the first Autumn Course on Mathematical Ecology, consequently focused upon applications of mathematical ecology. Current areas of application are almost as diverse as the spectrum covered by ecology. The topiys of this book reflect this diversity and were chosen because of perceived interest and utility to developing countries. Topical lectures began with foundational material mostly derived from Math ematical Ecology: An Introduction (a compilation of the lectures of the 1982 course published by Springer-Verlag in this series, Volume 17) and, when possible, progressed to the frontiers of research. In addition to the course lectures, workshops were arranged for small groups to supplement and enhance the learning experience. Other perspectives were provided through presentations by course participants and speakers at the associated Research Conference. Many of the research papers are in a companion volume, Mathematical Ecology: Proceedings Trieste 1986, published by World Scientific Press in 1988. This book is structured primarily by application area. Part II provides an introduction to mathematical and statistical applications in resource management.
