Introduction To Population Modeling

The text of this monograph represents the author's lecture notes from a course taught in the Department of Applied Mathematics and Statistics at the State University of New York at Stony Brook in the Spring of 1977. On account of its origin as lecture notes, some sections of the text are telegraphic in style while other portions are overly detailed. This stylistic foible has not been modified as it does not appear to detract seriously from the readability and it does help to indicate which topics were stressed. The audience for the course at Stony Brook was composed almost entirely of fourth year undergraduates majoring in the mathematical sciences. All of these students had studied at least four semesters of calculus and one of probability; few had any prior experience with either differential equations or ecology. It seems prudent to point out that the author's background is in engineering and applied mathematics and not in the biological sciences. It is hoped that this is not painfully obvious. -vii- The focus of the monograph is on the formulation and solution of mathematical models; it makes no pretense of being a text in ecology. The idea of a population is employed mainly as a pedagogic tool, providing unity and intuitive appeal to the varied mathematical ideas introduced. If the biological setting is stripped away, what remains can be interpreted as topics on the qualitative behavior of differential and difference equations.

Integrated Population Models: Theory and Ecological Applications with R and JAGS is the first book on integrated population models, which constitute a powerful framework for combining multiple data sets from the population and the individual levels to estimate demographic parameters, and population size and trends. These models identify drivers of population dynamics and forecast the composition and trajectory of a population. Written by two population ecologists with expertise on integrated population modeling, this book provides a comprehensive synthesis of the relevant theory of integrated population models with an extensive overview of practical applications, using Bayesian methods by means of case studies. The book contains fully-documented, complete code for fitting all models in the free software, R and JAGS. It also includes all required code for pre- and post-model-fitting analysis. Integrated Population Models is an invaluable reference for researchers and practitioners involved in population analysis, and for graduate-level students in ecology, conservation biology, wildlife management, and related fields. The text is ideal for self-study and advanced graduate-level courses. Offers practical and accessible ecological applications of IPMs (integrated population models) Provides full documentation of analyzed code in the Bayesian framework Written and structured for an easy approach to the subject, especially for non-statisticians

This book provides a complete treatment of matrix population models and their applications in ecology and demography. It is written for graduate students and researchers in ecology, population biology, conservation biology and human demography.

This monograph introduces the theory of structured population dynamics and its applications, focusing on the asymptotic dynamics of deterministic models.

This book provides a user-friendly, hands-on introduction to the Nonlinear Mixed Effects Modeling (NONMEM) system, the most powerful tool for pharmacokinetic / pharmacodynamic analysis. • Introduces requisite background to using Nonlinear Mixed Effects Modeling (NONMEM), covering data requirements, model building and evaluation, and quality control aspects • Provides examples of nonlinear modeling concepts and estimation basics with discussion on the model building process and applications of empirical Bayesian estimates in the drug development environment • Includes detailed chapters on data set structure, developing control streams for modeling and simulation, model applications, interpretation of NONMEM output and results, and quality control • Has datasets, programming code, and practice exercises with solutions, available on a supplementary website

In the summer of 1993, twenty-six graduate and postdoctoral stu dents and fourteen lecturers converged on Cornell University for a summer school devoted to structured-population models. This school was one of a series to address concepts cutting across the traditional boundaries separating terrestrial, marine, and freshwa ter ecology. Earlier schools resulted in the books Patch Dynamics (S. A. Levin, T. M. Powell & J. H. Steele, eds., Springer-Verlag, Berlin, 1993) and Ecological Time Series (T. M. Powell & J. H. Steele, eds., Chapman and Hall, New York, 1995); a book on food webs is in preparation. Models of population structure (differences among individuals due to age, size, developmental stage, spatial location, or genotype) have an important place in studies of all three kinds of ecosystem. In choosing the participants and lecturers for the school, we se lected for diversity-biologists who knew some mathematics and mathematicians who knew some biology, field biologists sobered by encounters with messy data and theoreticians intoxicated by the elegance of the underlying mathematics, people concerned with long-term evolutionary problems and people concerned with the acute crises of conservation biology. For four weeks, these perspec tives swirled in discussions that started in the lecture hall and carried on into the sweltering Ithaca night. Diversity mayor may not increase stability, but it surely makes things interesting.

This book provides an introduction to age-structured population modeling which emphasizes the connection between mathematical theory and underlying biological assumptions. Through the rigorous development of the linear theory and the nonlinear theory alongside numerics, the authors explore classical equations that describe the dynamics of certain ecological systems. Modeling aspects are discussed to show how relevant problems in the fields of demography, ecology and epidemiology can be formulated and treated within the theory. In particular, the book presents extensions of age-structured modeling to the spread of diseases and epidemics while also addressing the issue of regularity of solutions, the asymptotic behavior of solutions, and numerical approximation. With sections on transmission models, non-autonomous models and global dynamics, this book fills a gap in the literature on theoretical population dynamics. The Basic Approach to Age-Structured Population Dynamics will appeal to graduate students and researchers in mathematical biology, epidemiology and demography who are interested in the systematic presentation of relevant models and mathematical methods.

This book is an introduction to mathematical biology for students with no experience in biology, but who have some mathematical background. The work is focused on population dynamics and ecology, following a tradition that goes back to Lotka and Volterra, and includes a part devoted to the spread of infectious diseases, a field where mathematical modeling is extremely popular. These themes are used as the area where to understand different types of mathematical modeling and the possible meaning of qualitative agreement of modeling with data. The book also includes a collections of problems designed to approach more advanced questions. This material has been used in the courses at the University of Trento, directed at students in their fourth year of studies in Mathematics. It can also be used as a reference as it provides up-to-date developments in several areas.

Population biology has been investigated quantitatively for many decades, resulting in a rich body of scientific literature. Ecologists often avoid this literature, put off by its apparently formidable mathematics. This textbook provides an introduction to the biology and ecology of populations by emphasizing the roles of simple mathematical models in explaining the growth and behavior of populations. The author only assumes acquaintance with elementary calculus, and provides tutorial explanations where needed to develop mathematical concepts. Examples, problems, extensive marginal notes and numerous graphs enhance the book's value to students in classes ranging from population biology and population ecology to mathematical biology and mathematical ecology. The book will also be useful as a supplement to introductory courses in ecology.

A beginner’s guide to stochastic growth modeling The chief advantage of stochastic growth models over deterministic models is that they combine both deterministic and stochastic elements of dynamic behaviors, such as weather, natural disasters, market fluctuations, and epidemics. This makes stochastic modeling a powerful tool in the hands of practitioners in fields for which population growth is a critical determinant of outcomes. However, the background requirements for studying SDEs can be daunting for those who lack the rigorous course of study received by math majors. Designed to be accessible to readers who have had only a few courses in calculus and statistics, this book offers a comprehensive review of the mathematical essentials needed to understand and apply stochastic growth models. In addition, the book describes deterministic and stochastic applications of population growth models including logistic, generalized logistic, Gompertz, negative exponential, and linear. Ideal for students and professionals in an array of fields including economics, population studies, environmental sciences, epidemiology, engineering, finance, and the biological sciences, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling: • Provides precise definitions of many important terms and concepts and provides many solved example problems • Highlights the interpretation of results and does not rely on a theorem-proof approach • Features comprehensive chapters addressing any background deficiencies readers may have and offers a comprehensive review for those who need a mathematics refresher • Emphasizes solution techniques for SDEs and their practical application to the development of stochastic population models An indispensable resource for students and practitioners with limited exposure to mathematics and statistics, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling is an excellent fit for advanced undergraduates and beginning graduate students, as well as practitioners who need a gentle introduction to SDEs. Michael J. Panik, PhD, is Professor in the Department of Economics, Barney School of Business and Public Administration at the University of Hartford in Connecticut. He received his PhD in Economics from Boston College and is a member of the American Mathematical Society, The American Statistical Association, and The Econometric Society.