Matrix Models for Population, Disease, and Evolutionary Dynamics

Matrix Models for Population, Disease, and Evolutionary Dynamics
Author: J. M. Cushing
Publisher: American Mathematical Society
Total Pages: 293
Release: 2024-02-29
Genre: Mathematics
ISBN: 1470473348

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

Chaos in Ecology
Author: J. M. Cushing
Publisher: Elsevier
Total Pages: 248
Release: 2003
Genre: Mathematics
ISBN: 9780121988760

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.

Sensitivity Analysis: Matrix Methods in Demography and Ecology

Sensitivity Analysis: Matrix Methods in Demography and Ecology
Author: Hal Caswell
Publisher: Springer
Total Pages: 308
Release: 2019-04-02
Genre: Social Science
ISBN: 3030105342

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.

Complex Population Dynamics

Complex Population Dynamics
Author: Bernd Blasius
Publisher: World Scientific
Total Pages: 257
Release: 2007
Genre: Science
ISBN: 9812771573

This collection of review articles is devoted to the modeling of ecological, epidemiological and evolutionary systems. Theoretical mathematical models are perhaps one of the most powerful approaches available for increasing our understanding of the complex population dynamics in these natural systems. Exciting new techniques are currently being developed to meet this challenge, such as generalized or structural modeling, adaptive dynamics or multiplicative processes. Many of these new techniques stem from the field of nonlinear dynamics and chaos theory, where even the simplest mathematical rule can generate a rich variety of dynamical behaviors that bear a strong analogy to biological populations.

The Mathematics of Cellular Automata

The Mathematics of Cellular Automata
Author: Jane Hawkins
Publisher: American Mathematical Society
Total Pages: 247
Release: 2024-03-21
Genre: Mathematics
ISBN: 1470475375

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.

Introduction to Population Biology

Introduction to Population Biology
Author: Dick Neal
Publisher: Cambridge University Press
Total Pages: 461
Release: 2019
Genre: Science
ISBN: 1107605121

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

Wildlife Disease Ecology

Wildlife Disease Ecology
Author: Kenneth Wilson
Publisher: Cambridge University Press
Total Pages: 693
Release: 2019-11-14
Genre: Language Arts & Disciplines
ISBN: 1107136563

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

The Evolutionary Ecology of Plant Disease

The Evolutionary Ecology of Plant Disease
Author: Gregory Gilbert
Publisher: Oxford University Press
Total Pages: 337
Release: 2023-06-19
Genre: Science
ISBN: 0192518763

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.

Structured-Population Models in Marine, Terrestrial, and Freshwater Systems

Structured-Population Models in Marine, Terrestrial, and Freshwater Systems
Author: Shripad Tuljapurkar
Publisher: Springer Science & Business Media
Total Pages: 644
Release: 2012-12-06
Genre: Science
ISBN: 1461559731

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.