This 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.

Chaos in Ecology is a convincing demonstration of chaos in a biological population. The book synthesizes an ecologically focused interdisciplinary blend of non-linear dynamics theory, statistics, and experimentation yielding results of uncommon clarity and rigor. Topics include fundamental issues that are of general and widespread importance to population biology and ecology. Detailed descriptions are included of the mathematical, statistical, and experimental steps they used to explore nonlinear dynamics in ecology. Beginning with a brief overview of chaos theory and its implications for ecology. The book continues by deriving and rigorously testing a mathematical model that is closely wedded to biological mechanisms of their research organism. Therefrom were generated a variety of predictions that are fundamental to chaos theory and experiments were designed and analyzed to test those predictions. Discussion of patterns in chaos and how they can be investigated using real data follows and book ends with a discussion of the salient lessons learned from this research program Book jacket.

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 textbook offers a rigorous mathematical introduction to cellular automata (CA). Numerous colorful graphics illustrate the many intriguing phenomena, inviting undergraduates to step into the rich field of symbolic dynamics. Beginning with a brief history, the first half of the book establishes the mathematical foundations of cellular automata. After recapping the essentials from advanced calculus, the chapters that follow introduce symbolic spaces, equicontinuity, and attractors. More advanced topics include the Garden of Eden theorem and Conway's Game of Life, and a chapter on stochastic CA showcases a model of virus spread. Exercises and labs end each chapter, covering a range of applications, both mathematical and physical. Designed for undergraduates studying mathematics and related areas, the text provides ample opportunities for end-of-semester projects or further study. Computer use for the labs is largely optional, providing flexibility for different preferences and resources. Knowledge of advanced calculus and linear algebra is essential, while a course in real analysis would be ideal.

Updated to include two new chapters, a modified Part II structure, more recent empirical examples, and online spreadsheet simulations.

Introduces readers to key case studies that illustrate how theory and data can be integrated to understand wildlife disease ecology.

Demography relates observable facts about individuals to the dynamics of populations. If the dynamics are linear and do not change over time, the classical theory of Lotka (1907) and Leslie (1945) is the central tool of demography. This book addresses the situation when the assumption of constancy is dropped. In many practical situations, a population will display unpredictable variation over time in its vital rates, which must then be described in statistical terms. Most of this book is concerned with the theory of populations which are subject to random temporal changes in their vital rates, although other kinds of variation (e. g. , cyclical) are also dealt with. The central questions are: how does temporal variation work its way into a population's future, and how does it affect our interpretation of a population's past. The results here are directed at demographers of humans and at popula tion biologists. The uneven mathematical level is dictated by the material, but the book should be accessible to readers interested in population the ory. (Readers looking for background or prerequisites will find much of it in Hal Caswell's Matrix population models: construction, analysis, and in terpretation (Sinauer 1989) ). This book is in essence a progress report and is deliberately brief; I hope that it is not mystifying. I have not attempted to be complete about either the history or the subject, although most sig nificant results and methods are presented.

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.

Understanding the symbiosis between plants and pathogenic microbes is at the core of effective disease management for crops and managed forests. At the same time, plant-pathogen interactions comprise a wonderfully diverse set of ecological relationships that are powerful and yet so commonplace that they often go unnoticed. Ecologists and evolutionary biologists are increasingly exploring the terrain of plant disease ecology, investigating topics such as how pathogens shape diversity in plant communities, how features of plant-microbe interactions including host range and mutualism/antagonism evolve, and how biological invasions, climate change, and other agents of global change can drive disease emergence. Traditional training in ecology and evolutionary biology seldom provides structured exposure to plant pathology or microbiology, and training in plant pathology rarely offers depth in the theoretical frameworks of evolutionary ecology or includes examples from complex wild ecosystems. This novel textbook seeks to unite the research communities of plant disease ecology and plant pathology by bridging this gap.

Molecular epidemiology has recently broaden its focuses due to the development of molecular tools but also by incorporating advances of other fields such as mathematical epidemiology, molecular ecology, population genetics and evolution. Facing new risks of emerging and re-emerging infectious diseases that are threats for humans and their livestock, the objectives of molecular epidemiology include: - the development of molecular tools, genotyping and gene expression - the incorporation of concepts and results of population genetics of infectious diseases - the integration of recent advances in theoretical epidemiology and evolutionary ecology of diseases - a better understanding of transmission for the development of risk factors analyses. This book will demonstrate how the latest developments in molecular tools and in epidemiology can be integrated with studies of host-pathogen interactions. Besides a strong theoretical component, there will also be an emphasis on applications in the fields of epidemiology, public health, veterinary medicine, and health ecology. Students and researchers in the fields of epidemiology, animal and human health, evolutionary ecology, parasitology are the main potential readers of the book, as well as a broader audience from veterinary medicine and conservation.