Mathematical theories of populations have appeared both implicitly and explicitly in many important studies of populations, human populations as well as populations of animals, cells and viruses. They provide a systematic way for studying a population's underlying structure. A basic model in population age structure is studied and then applied, extended and modified, to several population phenomena such as stable age distributions, self-limiting effects, and two-sex populations. Population genetics are studied with special attention to derivation and analysis of a model for a one-locus, two-allele trait in a large randomly mating population. The dynamics of contagious phenomena in a population are studied in the context of epidemic diseases.

As Eugene Wigner stressed, mathematics has proven unreasonably effective in the physical sciences and their technological applications. The role of mathematics in the biological, medical and social sciences has been much more modest but has recently grown thanks to the simulation capacity offered by modern computers. This book traces the history of population dynamics---a theoretical subject closely connected to genetics, ecology, epidemiology and demography---where mathematics has brought significant insights. It presents an overview of the genesis of several important themes: exponential growth, from Euler and Malthus to the Chinese one-child policy; the development of stochastic models, from Mendel's laws and the question of extinction of family names to percolation theory for the spread of epidemics, and chaotic populations, where determinism and randomness intertwine. The reader of this book will see, from a different perspective, the problems that scientists face when governments ask for reliable predictions to help control epidemics (AIDS, SARS, swine flu), manage renewable resources (fishing quotas, spread of genetically modified organisms) or anticipate demographic evolutions such as aging.

This is the first of a planned two-volume work discussing the mathematical aspects of population genetics with an emphasis on evolutionary theory. This volume draws heavily from the author’s 1979 classic, but it has been revised and expanded to include recent topics which follow naturally from the treatment in the earlier edition, such as the theory of molecular population genetics.

The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions on population biology. Part I focusses on single species simple models including those which have been used to predict the growth of human and animal population in the past. Single population models are, in some sense, the building blocks of more realistic models -- the subject of Part II. Their role is fundamental to the study of ecological and demographic processes including the role of population structure and spatial heterogeneity -- the subject of Part III. This book, which will include both examples and exercises, is of use to practitioners, graduate students, and scientists working in the field.

"It is close to being a masterpiece...could well be the classic presentation of the area." Warren J. Ewens, University of Pennsylvania, USA Population genetics is concerned with the study of the genetic, ecological, and evolutionary factors that influence and change the genetic composition of populations. The emphasis here is on models that have a direct bearing on evolutionary quantitative genetics. Applications concerning the maintenance of genetic variation in quantitative traits and their dynamics under selection are treated in detail. * Provides a unified, self-contained and in-depth study of the theory of multilocus systems * Introduces the basic population-genetic models * Explores the dynamical and equilibrium properties of the distribution of quantitative traits under selection * Summarizes important results from more demanding sections in a comprehensible way * Employs a clear and logical presentation style Following an introduction to elementary population genetics and discussion of the general theory of selection at two or more loci, the author considers a number of mutation-selection models, and derives the dynamical equations for polygenic traits under general selective regimes. The final chapters are concerned with the maintenance of quantitative-genetic variation, the response to directional selection, the evolutionary role of deleterious mutations, and other topics. Graduate students and researchers in population genetics, evolutionary theory, and biomathematics will benefit from the in-depth coverage. This text will make an excellent reference volume for the fields of quantitative genetics, population and theoretical biology.

The formulation, analysis, and re-evaluation of mathematical models in population biology has become a valuable source of insight to mathematicians and biologists alike. This book presents an overview and selected sample of these results and ideas, organized by biological theme rather than mathematical concept, with an emphasis on helping the reader develop appropriate modeling skills through use of well-chosen and varied examples. Part I starts with unstructured single species population models, particularly in the framework of continuous time models, then adding the most rudimentary stage structure with variable stage duration. The theme of stage structure in an age-dependent context is developed in Part II, covering demographic concepts, such as life expectation and variance of life length, and their dynamic consequences. In Part III, the author considers the dynamic interplay of host and parasite populations, i.e., the epidemics and endemics of infectious diseases. The theme of stage structure continues here in the analysis of different stages of infection and of age-structure that is instrumental in optimizing vaccination strategies. Each section concludes with exercises, some with solutions, and suggestions for further study. The level of mathematics is relatively modest; a "toolbox" provides a summary of required results in differential equations, integration, and integral equations. In addition, a selection of Maple worksheets is provided. The book provides an authoritative tour through a dazzling ensemble of topics and is both an ideal introduction to the subject and reference for researchers.

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.