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The Mathematics of Darwin’s Legacy

Author: Fabio A. C. C. Chalub

Publisher: Springer Science & Business Media

Published: 2011-06-24

Total Pages: 298

ISBN-13: 303480122X

The book presents a general overview of mathematical models in the context of evolution. It covers a wide range of topics such as population genetics, population dynamics, speciation, adaptive dynamics, game theory, kin selection, and stochastic processes. Written by leading scientists working at the interface between evolutionary biology and mathematics the book is the outcome of a conference commemorating Charles Darwin's 200th birthday, and the 150th anniversary of the first publication of his book "On the origin of species". Its chapters vary in format between general introductory and state-of-the-art research texts in biomathematics, in this way addressing both students and researchers in mathematics, biology and related fields. Mathematicians looking for new problems as well as biologists looking for rigorous description of population dynamics will find this book fundamental.

Chaos, Information Processing And Paradoxical Games: The Legacy Of John S Nicolis

Author: Gregoire Nicolis

Publisher: World Scientific

Published: 2014-12-30

Total Pages: 474

ISBN-13: 9814602140

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This volume provides a self-contained survey of the mechanisms presiding information processing and communication. The main thesis is that chaos and complexity are the basic ingredients allowing systems composed of interesting subunits to generate and process information and communicate in a meaningful way. Emphasis is placed on communication in the form of games and on the related issue of decision making under conditions of uncertainty. Biological, cognitive, physical, engineering and societal systems are approached from a unifying point of view, both analytically and by numerical simulation, using the methods of nonlinear dynamics and probability theory. Epistemological issues in connection with incompleteness and self-reference are also addressed.

Proving Darwin

Author: Gregory Chaitin

Publisher: Vintage

Published: 2013-02-26

Total Pages: 146

ISBN-13: 1400077982

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Groundbreaking mathematician Gregory Chaitin gives us the first book to posit that we can prove how Darwin’s theory of evolution works on a mathematical level. For years it has been received wisdom among most scientists that, just as Darwin claimed, all of the Earth’s life-forms evolved by blind chance. But does Darwin’s theory function on a purely mathematical level? Has there been enough time for evolution to produce the remarkable biological diversity we see around us? It’s a question no one has yet answered—in fact, no one has attempted to answer it until now. In this illuminating and provocative book, Gregory Chaitin elucidates the mathematical scheme he’s developed that can explain life itself, and examines the works of mathematical pioneers John von Neumann and Alan Turing through the lens of biology. Fascinating and thought-provoking, Proving Darwin makes clear how biology may have found its greatest ally in mathematics.

Encyclopedia of Theoretical Ecology

Author: Dr. Alan Hastings

Publisher: Univ of California Press

Published: 2012-05-31

Total Pages: 1877

ISBN-13: 0520951786

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This major reference is an overview of the current state of theoretical ecology through a series of topical entries centered on both ecological and statistical themes. Coverage ranges across scales—from the physiological, to populations, landscapes, and ecosystems. Entries provide an introduction to broad fields such as Applied Ecology, Behavioral Ecology, Computational Ecology, Ecosystem Ecology, Epidemiology and Epidemic Modeling, Population Ecology, Spatial Ecology and Statistics in Ecology. Others provide greater specificity and depth, including discussions on the Allee effect, ordinary differential equations, and ecosystem services. Descriptions of modern statistical and modeling approaches and how they contributed to advances in theoretical ecology are also included. Succinct, uncompromising, and authoritative—a "must have" for those interested in the use of theory in the ecological sciences.

Parabolic Equations in Biology

Author: Benoît Perthame

Publisher: Springer

Published: 2015-09-09

Total Pages: 204

ISBN-13: 331919500X

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This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.

Theory-based Ecology

Author: Liz Pásztor

Publisher: Oxford University Press

Published: 2016

Total Pages: 337

ISBN-13: 0199577854

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The first text to adopt a Darwinian approach to develop a universal, coherent and robust theory of ecology and provide a unified treatment of ecology and evolution.

Nonlinear Dynamics and Complexity

Author: Valentin Afraimovich

Publisher: Springer Science & Business Media

Published: 2013-11-22

Total Pages: 297

ISBN-13: 3319023535

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This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.

Matrix Inequalities for Iterative Systems

Author: Hanjo Taubig

Publisher: CRC Press

Published: 2017-02-03

Total Pages: 144

ISBN-13: 1351679090

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The book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.

Contributions to the Theory of Zeta-Functions

Author: Shigeru Kanemitsu

Publisher: World Scientific

Published: 2014-12-15

Total Pages: 316

ISBN-13: 9814449628

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This volume provides a systematic survey of almost all the equivalent assertions to the functional equations - zeta symmetry - which zeta-functions satisfy, thus streamlining previously published results on zeta-functions. The equivalent relations are given in the form of modular relations in Fox H-function series, which at present include all that have been considered as candidates for ingredients of a series. The results are presented in a clear and simple manner for readers to readily apply without much knowledge of zeta-functions. This volume aims to keep a record of the 150-year-old heritage starting from Riemann on zeta-functions, which are ubiquitous in all mathematical sciences, wherever there is a notion of the norm. It provides almost all possible equivalent relations to the zeta-functions without requiring a reader's deep knowledge on their definitions. This can be an ideal reference book for those studying zeta-functions.

The Philosophy of Social Evolution

Author: Jonathan Birch

Publisher: Oxford University Press

Published: 2017-10-13

Total Pages: 281

ISBN-13: 0191047368

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From mitochondria to meerkats, the natural world is full of spectacular examples of social behaviour. In the early 1960s Bill Hamilton changed the way we think about how such behaviour evolves. He introduced three key innovations - now known as Hamilton's rule, kin selection, and inclusive fitness - which have been enormously influential, but which remain the subject of fierce controversy. Hamilton's pioneering work kick-started a research program now known as social evolution theory. This is a book about the philosophical foundations and future prospects of that program. Part I, "Foundations", is a careful exposition and defence of Hamilton's ideas, with a few modifications along the way. In Part II, "Extensions", Jonathan Birch shows how these ideas can be applied to phenomena including cooperation in micro-organisms, cooperation among the cells of a multicellular organism, and culturally evolved cooperation in the earliest human societies. Birch argues that real progress can be made in understanding microbial evolution, evolutionary transitions, and human evolution by viewing them through the lens of social evolution theory, provided the theory is interpreted with care and adapted where necessary. The Philosophy of Social Evolution places social evolution theory on a firm philosophical footing and sets out exciting new directions for further work.