The Theory of Island Biogeography
Author: Robert H. MacArthur
Publisher: Princeton University Press
Published: 2001
Total Pages: 226
ISBN-13: 9780691088365
DOWNLOAD EBOOKPopulation theory.
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An Introduction to Structured Population Dynamics
Author: J. M. Cushing
Publisher: SIAM
Published: 1998-01-01
Total Pages: 106
ISBN-13: 9781611970005
DOWNLOAD EBOOKInterest in the temporal fluctuations of biological populations can be traced to the dawn of civilization. How can mathematics be used to gain an understanding of population dynamics? This monograph introduces the theory of structured population dynamics and its applications, focusing on the asymptotic dynamics of deterministic models. This theory bridges the gap between the characteristics of individual organisms in a population and the dynamics of the total population as a whole. In this monograph, many applications that illustrate both the theory and a wide variety of biological issues are given, along with an interdisciplinary case study that illustrates the connection of models with the data and the experimental documentation of model predictions. The author also discusses the use of discrete and continuous models and presents a general modeling theory for structured population dynamics. Cushing begins with an obvious point: individuals in biological populations differ with regard to their physical and behavioral characteristics and therefore in the way they interact with their environment. Studying this point effectively requires the use of structured models. Specific examples cited throughout support the valuable use of structured models. Included among these are important applications chosen to illustrate both the mathematical theories and biological problems that have received attention in recent literature.
The Mass-Extinction Debates
Author: William Glen
Publisher: Stanford University Press
Published: 1994
Total Pages: 387
ISBN-13: 0804722862
DOWNLOAD EBOOKThis book examines the arguments and behavior of the scientists who have been locked in conflict over two competing theories to explain why, 65 million years ago, most life on earth—including the dinosaurs—perished.
Progress on Difference Equations and Discrete Dynamical Systems
Author: Steve Baigent
Publisher: Springer Nature
Published: 2021-01-04
Total Pages: 440
ISBN-13: 3030601072
DOWNLOAD EBOOKThis book comprises selected papers of the 25th International Conference on Difference Equations and Applications, ICDEA 2019, held at UCL, London, UK, in June 2019. The volume details the latest research on difference equations and discrete dynamical systems, and their application to areas such as biology, economics, and the social sciences. Some chapters have a tutorial style and cover the history and more recent developments for a particular topic, such as chaos, bifurcation theory, monotone dynamics, and global stability. Other chapters cover the latest personal research contributions of the author(s) in their particular area of expertise and range from the more technical articles on abstract systems to those that discuss the application of difference equations to real-world problems. The book is of interest to both Ph.D. students and researchers alike who wish to keep abreast of the latest developments in difference equations and discrete dynamical systems.
The Theory of Island Biogeography Revisited
Author: Jonathan B. Losos
Publisher: Princeton University Press
Published: 2009-10-19
Total Pages: 988
ISBN-13: 140083192X
DOWNLOAD EBOOKRobert H. MacArthur and Edward O. Wilson's The Theory of Island Biogeography, first published by Princeton in 1967, is one of the most influential books on ecology and evolution to appear in the past half century. By developing a general mathematical theory to explain a crucial ecological problem--the regulation of species diversity in island populations--the book transformed the science of biogeography and ecology as a whole. In The Theory of Island Biogeography Revisited, some of today's most prominent biologists assess the continuing impact of MacArthur and Wilson's book four decades after its publication. Following an opening chapter in which Wilson reflects on island biogeography in the 1960s, fifteen chapters evaluate and demonstrate how the field has extended and confirmed--as well as challenged and modified--MacArthur and Wilson's original ideas. Providing a broad picture of the fundamental ways in which the science of island biogeography has been shaped by MacArthur and Wilson's landmark work, The Theory of Island Biogeography Revisited also points the way toward exciting future research.
Modeling and Dynamics of Infectious Diseases
Author: Zhien Ma
Publisher: World Scientific
Published: 2009
Total Pages: 355
ISBN-13: 9814261254
DOWNLOAD EBOOKThis book provides a systematic introduction to the fundamental methods and techniques and the frontiers of ? along with many new ideas and results on ? infectious disease modeling, parameter estimation and transmission dynamics. It provides complementary approaches, from deterministic to statistical to network modeling; and it seeks viewpoints of the same issues from different angles, from mathematical modeling to statistical analysis to computer simulations and finally to concrete applications.
Dynamics, Games and Science
Author: Jean-Pierre Bourguignon
Publisher: Springer
Published: 2015-07-24
Total Pages: 766
ISBN-13: 3319161180
DOWNLOAD EBOOKThe focus of this volume is research carried out as part of the program Mathematics of Planet Earth, which provides a platform to showcase the essential role of mathematics in addressing problems of an economic and social nature and creating a context for mathematicians and applied scientists to foster mathematical and interdisciplinary developments that will be necessary to tackle a myriad of issues and meet future global economic and social challenges. Earth is a planet with dynamic processes in its mantle, oceans and atmosphere creating climate, causing natural disasters and influencing fundamental aspects of life and life-supporting systems. In addition to these natural processes, human activity has developed highly complex systems, including economic and financial systems; the World Wide Web; frameworks for resource management, transportation, energy production and utilization; health care delivery, and social organizations. This development has increased to the point where it impacts the stability and equilibrium in human societies. Issues such as financial and economic crisis, sustainability, management of resources, risk analysis, and global integration have come to the fore. Written by some of the world’s leading specialists, this book presents the proceedings of the International Conference and Advanced School Planet Earth, Dynamics, Games and Science II, held in Lisbon, Portugal, 28 August -6 September 2013, which was organized by the International Center of Mathematics (CIM) as a partner institution of the international program Mathematics of Planet Earth 2013. The book describes the state of the art in advanced research and ultimate techniques in modeling natural, economic and social phenomena. It constitutes a tool and a framework for researchers and graduate students, both in mathematics and applied sciences, focusing mainly on dynamical systems, game theory and applied sciences.
Matrix Models for Population, Disease, and Evolutionary Dynamics
Author: J. M. Cushing
Publisher: American Mathematical Society
Published: 2024-02-29
Total Pages: 293
ISBN-13: 1470473348
DOWNLOAD EBOOKThis book offers an introduction to the use of matrix theory and linear algebra in modeling the dynamics of biological populations. Matrix algebra has been used in population biology since the 1940s and continues to play a major role in theoretical and applied dynamics for populations structured by age, body size or weight, disease states, physiological and behavioral characteristics, life cycle stages, or any of many other possible classification schemes. With a focus on matrix models, the book requires only first courses in multivariable calculus and matrix theory or linear algebra as prerequisites. The reader will learn the basics of modeling methodology (i.e., how to set up a matrix model from biological underpinnings) and the fundamentals of the analysis of discrete time dynamical systems (equilibria, stability, bifurcations, etc.). A recurrent theme in all chapters concerns the problem of extinction versus survival of a population. In addition to numerous examples that illustrate these fundamentals, several applications appear at the end of each chapter that illustrate the full cycle of model setup, mathematical analysis, and interpretation. The author has used the material over many decades in a variety of teaching and mentoring settings, including special topics courses and seminars in mathematical modeling, mathematical biology, and dynamical systems.
Applied Analysis in Biological and Physical Sciences
Author: Jim M. Cushing
Publisher: Springer
Published: 2016-12-01
Total Pages: 432
ISBN-13: 8132236408
DOWNLOAD EBOOKThe book contains recent developments and contemporary research in mathematical analysis and in its application to problems arising from the biological and physical sciences. The book is of interest to readers who wish to learn of new research in such topics as linear and nonlinear analysis, mathematical biology and ecology, dynamical systems, graph theory, variational analysis and inequalities, functional analysis, differential and difference equations, partial differential equations, approximation theory, and chaos. All papers were prepared by participants at the International Conference on Recent Advances in Mathematical Biology, Analysis and Applications (ICMBAA-2015) held during 4–6 June 2015 in Aligarh, India. A focal theme of the conference was the application of mathematics to the biological sciences and on current research in areas of theoretical mathematical analysis that can be used as sophisticated tools for the study of scientific problems. The conference provided researchers, academicians and engineers with a platform that encouraged them to exchange their innovative ideas in mathematical analysis and its applications as well as to form interdisciplinary collaborations. The content of the book is divided into three parts: Part I contains contributions from participants whose topics are related to nonlinear dynamics and its applications in biological sciences. Part II has contributions which concern topics on nonlinear analysis and its applications to a variety of problems in science, engineering and industry. Part III consists of contributions dealing with some problems in applied analysis.
Understanding Complex Biological Systems with Mathematics
Author: Ami Radunskaya
Publisher: Springer
Published: 2018-10-24
Total Pages: 207
ISBN-13: 3319980831
DOWNLOAD EBOOKThis volume examines a variety of biological and medical problems using mathematical models to understand complex system dynamics. Featured topics include autism spectrum disorder, ectoparasites and allogrooming, argasid ticks dynamics, super-fast nematocyst firing, cancer-immune population dynamics, and the spread of disease through populations. Applications are investigated with mathematical models using a variety of techniques in ordinary and partial differential equations, difference equations, Markov-chain models, Monte-Carlo simulations, network theory, image analysis, and immersed boundary method. Each article offers a thorough explanation of the methodologies used and numerous tables and color illustrations to explain key results. This volume is suitable for graduate students and researchers interested in current applications of mathematical models in the biosciences. The research featured in this volume began among newly-formed collaborative groups at the 2017 Women Advancing Mathematical Biology Workshop that took place at the Mathematical Biosciences Institute in Columbus, Ohio. The groups spent one intensive week working at MBI and continued their collaborations after the workshop, resulting in the work presented in this volume.
