The Mathematical Theory of the Dynamics of Biological Populations PDF Download
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Author: Institute of Mathematics and Its Applications
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 360
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Book Description
Author: Institute of Mathematics and Its Applications
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 360
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Book Description
Author: R. W. Hiorns
Publisher:
ISBN:
Category : Animal populations
Languages : en
Pages : 348
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Book Description
Author: Nicolas Bacaër
Publisher: Springer Science & Business Media
ISBN: 0857291157
Category : Mathematics
Languages : en
Pages : 160
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Book Description
As Eugene Wigner stressed, mathematics has proven unreasonably effective in the physical sciences and their technological applications. The role of mathematics in the biological, medical and social sciences has been much more modest but has recently grown thanks to the simulation capacity offered by modern computers. This book traces the history of population dynamics---a theoretical subject closely connected to genetics, ecology, epidemiology and demography---where mathematics has brought significant insights. It presents an overview of the genesis of several important themes: exponential growth, from Euler and Malthus to the Chinese one-child policy; the development of stochastic models, from Mendel's laws and the question of extinction of family names to percolation theory for the spread of epidemics, and chaotic populations, where determinism and randomness intertwine. The reader of this book will see, from a different perspective, the problems that scientists face when governments ask for reliable predictions to help control epidemics (AIDS, SARS, swine flu), manage renewable resources (fishing quotas, spread of genetically modified organisms) or anticipate demographic evolutions such as aging.
Author: Peter Turchin
Publisher: Princeton University Press
ISBN: 0691090211
Category : Science
Languages : en
Pages : 470
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Book Description
Why do organisms become extremely abundant one year and then seem to disappear a few years later? Why do population outbreaks in particular species happen more or less regularly in certain locations, but only irregularly (or never at all) in other locations? Complex population dynamics have fascinated biologists for decades. By bringing together mathematical models, statistical analyses, and field experiments, this book offers a comprehensive new synthesis of the theory of population oscillations. Peter Turchin first reviews the conceptual tools that ecologists use to investigate population oscillations, introducing population modeling and the statistical analysis of time series data. He then provides an in-depth discussion of several case studies--including the larch budmoth, southern pine beetle, red grouse, voles and lemmings, snowshoe hare, and ungulates--to develop a new analysis of the mechanisms that drive population oscillations in nature. Through such work, the author argues, ecologists can develop general laws of population dynamics that will help turn ecology into a truly quantitative and predictive science. Complex Population Dynamics integrates theoretical and empirical studies into a major new synthesis of current knowledge about population dynamics. It is also a pioneering work that sets the course for ecology's future as a predictive science.
Author: Xiao-Qiang Zhao
Publisher: Springer Science & Business Media
ISBN: 0387217614
Category : Mathematics
Languages : en
Pages : 285
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Book Description
Population dynamics is an important subject in mathematical biology. A cen tral problem is to study the long-term behavior of modeling systems. Most of these systems are governed by various evolutionary equations such as difference, ordinary, functional, and partial differential equations (see, e. g. , [165, 142, 218, 119, 55]). As we know, interactive populations often live in a fluctuating environment. For example, physical environmental conditions such as temperature and humidity and the availability of food, water, and other resources usually vary in time with seasonal or daily variations. Therefore, more realistic models should be nonautonomous systems. In particular, if the data in a model are periodic functions of time with commensurate period, a periodic system arises; if these periodic functions have different (minimal) periods, we get an almost periodic system. The existing reference books, from the dynamical systems point of view, mainly focus on autonomous biological systems. The book of Hess [106J is an excellent reference for periodic parabolic boundary value problems with applications to population dynamics. Since the publication of this book there have been extensive investigations on periodic, asymptotically periodic, almost periodic, and even general nonautonomous biological systems, which in turn have motivated further development of the theory of dynamical systems. In order to explain the dynamical systems approach to periodic population problems, let us consider, as an illustration, two species periodic competitive systems dUI dt = !I(t,Ul,U2), (0.
Author: J. M. Cushing
Publisher: Elsevier
ISBN: 9780121988760
Category : Mathematics
Languages : en
Pages : 248
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Book Description
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.
Author: Mimmo Iannelli
Publisher: Springer
ISBN: 9402411461
Category : Mathematics
Languages : en
Pages : 357
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Book Description
This book provides an introduction to age-structured population modeling which emphasizes the connection between mathematical theory and underlying biological assumptions. Through the rigorous development of the linear theory and the nonlinear theory alongside numerics, the authors explore classical equations that describe the dynamics of certain ecological systems. Modeling aspects are discussed to show how relevant problems in the fields of demography, ecology and epidemiology can be formulated and treated within the theory. In particular, the book presents extensions of age-structured modeling to the spread of diseases and epidemics while also addressing the issue of regularity of solutions, the asymptotic behavior of solutions, and numerical approximation. With sections on transmission models, non-autonomous models and global dynamics, this book fills a gap in the literature on theoretical population dynamics. The Basic Approach to Age-Structured Population Dynamics will appeal to graduate students and researchers in mathematical biology, epidemiology and demography who are interested in the systematic presentation of relevant models and mathematical methods.
Author: Eric Renshaw
Publisher: Cambridge University Press
ISBN: 9780521448550
Category : Mathematics
Languages : en
Pages : 428
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Book Description
This volume develops a unifying approach to population studies, emphasising the interplay between modelling and experimentation. Throughout, mathematicians and biologists are provided with a framework within which population dynamics can be fully explored and understood. Aspects of population dynamics covered include birth-death and logistic processes, competition and predator-prey relationships, chaos, reaction time-delays, fluctuating environments, spatial systems, velocities of spread, epidemics, and spatial branching structures. Both deterministic and stochastic models are considered. Whilst the more theoretically orientated sections will appeal to mathematical biologists, the material is presented so that readers with little mathematical expertise can bypass these without losing the main flow of the text.
Author: Mimmo Iannelli
Publisher: Springer
ISBN: 3319030264
Category : Mathematics
Languages : en
Pages : 351
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Book Description
This book is an introduction to mathematical biology for students with no experience in biology, but who have some mathematical background. The work is focused on population dynamics and ecology, following a tradition that goes back to Lotka and Volterra, and includes a part devoted to the spread of infectious diseases, a field where mathematical modeling is extremely popular. These themes are used as the area where to understand different types of mathematical modeling and the possible meaning of qualitative agreement of modeling with data. The book also includes a collections of problems designed to approach more advanced questions. This material has been used in the courses at the University of Trento, directed at students in their fourth year of studies in Mathematics. It can also be used as a reference as it provides up-to-date developments in several areas.
Author: Alfred J. Lotka
Publisher: Springer Science & Business Media
ISBN: 1475791763
Category : Social Science
Languages : en
Pages : 266
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Book Description
In the 50 years that have passed since Alfred Latka's death in 1949 his position as the father of mathematical demography has been secure. With his first demographic papers in 1907 and 1911 (the latter co authored with F. R. Sharpe) he laid the foundations for stable population theory, and over the next decades both largely completed it and found convenient mathematical approximations that gave it practical applica tions. Since his time, the field has moved in several directions he did not foresee, but in the main it is still his. Despite Latka's stature, however, the reader still needs to hunt through the old journals to locate his principal works. As yet no exten sive collections of his papers are in print, and for his part he never as sembled his contributions into a single volume in English. He did so in French, in the two part Theorie Analytique des Associations Biologiques (1934, 1939). Drawing on his Elements of Physical Biology (1925) and most of his mathematical papers, Latka offered French readers insights into his biological thought and a concise and mathematically accessible summary of what he called recent contributions in demographic analy sis. We would be accurate in also calling it Latka's contributions in demographic analysis.
