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This monograph presents new tools for modeling multiscale biological processes. Natural processes are usually driven by mechanisms widely differing from each other in the time or space scale at which they operate and thus should be described by appropriate multiscale models. However, looking at all such scales simultaneously is often infeasible, costly, and provides information that is redundant for a particular application. Hence, there has been a growing interest in providing a more focused description of multiscale processes by aggregating variables in a way that is relevant and preserves the salient features of the dynamics. The aim of this book is to present a systematic way of deriving the so-called limit equations for such aggregated variables and ensuring that the coefficients of these equations encapsulate the relevant information from the discarded levels of description. Since any approximation is only valid if an estimate of the incurred error is available, the tools described allow for proving that the solutions to the original multiscale family of equations converge to the solution of the limit equation if the relevant parameter converges to its critical value.   The chapters are arranged according to the mathematical complexity of the analysis, from systems of ordinary linear differential equations, through nonlinear ordinary differential equations, to linear and nonlinear partial differential equations. Many chapters begin with a survey of mathematical techniques needed for the analysis. All problems discussed in this book belong to the class of singularly perturbed problems; that is, problems in which the structure of the limit equation is significantly different from that of the multiscale model. Such problems appear in all areas of science and can be attacked using many techniques.   Methods of Small Parameter in Mathematical Biology will appeal to senior undergraduate and  graduate students in appled and biomathematics, as well as researchers specializing in differential equations and asymptotic analysis.

Differential equations. --- Genetics --- Mathematics. --- Math --- Science --- 517.91 Differential equations --- Differential equations --- Biology --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Differential Equations. --- Ordinary Differential Equations. --- Mathematical and Computational Biology. --- Genetics and Population Dynamics. --- Biomathematics. --- Mathematics

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This volume not only offers an intellectual biography of one of the most important biologists and social thinkers of the twentieth century but also illuminates the development of evolutionary studies in Russia and in the West. Theodosius Dobzhansky (1900-1975), a creator of the "evolutionary synthesis" and the author of its first modern statement, Genetics and the Origin of Species (1937), founded modern Western population genetics and wrote many popular books on such topics as human evolution, race and racism, equality, and human destiny. In this, the first book devoted to an analysis of the historical, scientific, and cultural dimensions of Dobzhansky's life and thought, an international group of historians, biologists, and philosophers addresses the full span of his career in Russia and the United States.Beginning with the reminiscences of his daughter, Sophia Dobzhansky Coe, these essays cover Dobzhansky's Russian roots (Nikolai L. Krementsov, Daniel A. Alexandrov, Mikhail B. Konashev), the Morgan Lab (Garland E. Allen, William B. Provine, Robert E. Kohler, Richard M. Burian), his scientific legacy (Scott F. Gilbert, Bruce Wallace, Charles E. Taylor), and his social, political, philosophical, and religious thought (Costas B. Krimbas, John Beatty, Diane B. Paul, Michael Ruse).Originally published in 1994.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Evolution (Biology) --- Genetics --- SCIENCE / History. --- Biology --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Animal evolution --- Animals --- Biological evolution --- Darwinism --- Evolutionary biology --- Evolutionary science --- Origin of species --- Evolution --- Biological fitness --- Homoplasy --- Natural selection --- Phylogeny --- History --- Dobzhansky, Theodosius, --- Political and social views

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This monograph is concerned with the mathematical analysis of patterns which are encountered in biological systems. It summarises, expands and relates results obtained in the field during the last fifteen years. It also links the results to biological applications and highlights their relevance to phenomena in nature. Of particular concern are large-amplitude patterns far from equilibrium in biologically relevant models. The approach adopted in the monograph is based on the following paradigms: • Examine the existence of spiky steady states in reaction-diffusion systems and select as observable patterns only the stable ones • Begin by exploring spatially homogeneous two-component activator-inhibitor systems in one or two space dimensions • Extend the studies by considering extra effects or related systems, each motivated by their specific roles in developmental biology, such as spatial inhomogeneities, large reaction rates, altered boundary conditions, saturation terms, convection, many-component systems. Mathematical Aspects of Pattern Formation in Biological Systems will be of interest to graduate students and researchers who are active in reaction-diffusion systems, pattern formation and mathematical biology.

Pattern formation (Biology) --- Reaction-diffusion equations. --- Diffusion-reaction equations --- Equations, Reaction-diffusion --- Biological pattern formation --- Mathematics. --- Partial differential equations. --- Biomathematics. --- Partial Differential Equations. --- Mathematical and Computational Biology. --- Genetics and Population Dynamics. --- Physiological, Cellular and Medical Topics. --- Biology --- Mathematics --- Partial differential equations --- Math --- Science --- Differential equations, Parabolic --- Developmental biology --- Differential equations, partial. --- Genetics --- Physiology --- Animal physiology --- Animals --- Anatomy --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Biological systems --- Mathematical models.

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This book presents the fundamental theory for non-standard diffusion problems in movement ecology. Lévy processes and anomalous diffusion have shown to be both powerful and useful tools for qualitatively and quantitatively describing a wide variety of spatial population ecological phenomena and dynamics, such as invasion fronts and search strategies. Adopting a self-contained, textbook-style approach, the authors provide the elements of statistical physics and stochastic processes on which the modeling of movement ecology is based and systematically introduce the physical characterization of ecological processes at the microscopic, mesoscopic and macroscopic levels. The explicit definition of these levels and their interrelations is particularly suitable to coping with the broad spectrum of space and time scales involved in bio-ecological problems.   Including numerous exercises (with solutions), this text is aimed at graduate students and newcomers in this field at the interface of theoretical ecology, mathematical biology and physics.

Animal ecology. --- Spatial behavior in animals. --- Animals --- Zoology --- Ecology --- Physics. --- Ecology. --- System theory. --- Biomathematics. --- Sociophysics. --- Econophysics. --- Complexity, Computational. --- Socio- and Econophysics, Population and Evolutionary Models. --- Theoretical Ecology/Statistics. --- Genetics and Population Dynamics. --- Complexity. --- Complex Systems. --- Animal behavior --- Genetics --- Engineering. --- Data-driven Science, Modeling and Theory Building. --- Mathematics. --- Construction --- Industrial arts --- Technology --- Biology --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Balance of nature --- Bionomics --- Ecological processes --- Ecological science --- Ecological sciences --- Environment --- Environmental biology --- Oecology --- Environmental sciences --- Population biology --- Ecology . --- Computational complexity. --- Systems, Theory of --- Systems science --- Science --- Complexity, Computational --- Electronic data processing --- Machine theory --- Mathematics --- Economics --- Statistical physics --- Mathematical sociology --- Philosophy --- Statistical methods

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This volume contains the proceedings of the 19th International Conference on Difference Equations and Applications, held at Sultan Qaboos University, Muscat, Oman in May 2013. The conference brought together experts and novices in the theory and applications of difference equations and discrete dynamical systems. The volume features papers in difference equations and discrete time dynamical systems with applications to mathematical sciences and, in particular, mathematical biology, ecology, and epidemiology. It includes four invited papers and eight contributed papers. Topics covered include: competitive exclusion through discrete time models, Benford solutions of linear difference equations, chaos and wild chaos in Lorenz-type systems, advances in periodic difference equations, the periodic decomposition problem, dynamic selection systems and replicator equations, and asymptotic equivalence of difference equations in Banach Space. This book will appeal to researchers, scientists, and educators who work in the fields of difference equations, discrete time dynamical systems and their applications.  .

Equations --- Equations. --- Mathematics. --- Math --- Science --- Algebra --- Mathematics --- Graphic methods --- Functional equations. --- Differentiable dynamical systems. --- Genetics --- Difference and Functional Equations. --- Dynamical Systems and Ergodic Theory. --- Genetics and Population Dynamics. --- Applications of Mathematics. --- Mathematical Modeling and Industrial Mathematics. --- Biology --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Equations, Functional --- Functional analysis --- Difference equations. --- Dynamics. --- Ergodic theory. --- Biomathematics. --- Applied mathematics. --- Engineering mathematics. --- Mathematical models. --- Models, Mathematical --- Simulation methods --- Engineering --- Engineering analysis --- Mathematical analysis --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Calculus of differences --- Differences, Calculus of --- Equations, Difference