Download or read book Evolution Dynamics of Some Population Models in Heterogeneous Environments written by Ruiwen Wu and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Spatial and/or temporal evolutions are very important topics in epidemiology and ecology. This thesis is devoted to the study of the global dynamics of some population models incorporating with environmental heterogeneities. Vector-borne diseases such as West Nile virus and malaria, pose a threat to public health worldwide. Both vector life cycle and parasite development are highly sensitive to climate factors. To understand the role of seasonality on disease spread, we start with a periodic West Nile virus transmission model with time-varying incubation periods. Apart from seasonal variations, another important feature of our environment is the spatial heterogeneity. Hence, we incorporate the movement of both vectors and hosts, temperature-dependent incubation periods, seasonal fluctuations and spatial heterogeneity into a general reaction-diffusion vector-borne disease model. By using the theory of basic reproduction number, R0, and the theory of infinite dimensional dynamical systems, we derive R0 and establish a threshold-type result for the global dynamics in terms of R0 for each model. As biological invasions have significant impacts on ecology and human society, how the growth and spatial spread of invasive species interact with environment becomes an important and challenging problem. We first propose an impulsive integro-differential model to describe a single invading species with a birth pulse in the reproductive stage and a nonlocal dispersal stage. Next, we study the propagation dynamics for a class of integro-difference two-species competition models in a spatially periodic habitat.
Download or read book Integro differential Models for Evolutionary Dynamics of Populations in Time heterogeneous Environments written by Susely Figueroa Iglesias and published by . This book was released on 2019 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis focuses on the qualitative study of several parabolic equations of the Lotka-Volterra type from evolutionary biology and ecology taking into account a time-periodic growth rate and a non-local competition term. In the initial part we first study the dynamics of phenotypically structured populations under the effect of mutations and selection in environments that vary periodically in time and then the impact of a climate change on such population considering environmental conditions which vary according to a linear trend, but in an oscillatory manner. In both problems we first study the long-time behaviour of the solutions. Then we use an approach based on Hamilton-Jacobi equations to study these long-time solutions asymptotically when the effect of mutations is small. We prove that when the effect of mutations vanishes, the phenotypic density of the population is concentrated on a single trait (which varies linearly over time in the second model), while the population size oscillates periodically. For the climate change model we also provide an asymptotic expansion of the mean population size and of the critical speed leading to the extinction of the population, which is closely related to the derivation of an asymptotic expansion of the Floquet eigenvalue in terms of the diffusion rate. In the second part we study some particular examples of growth rates by providing explicit and semi-explicit solutions to the problem and present some numerical illustrations for the periodic model. In addition, being motivated by a biological experiment, we compare two populations evolved in different environments (constant or periodic). In addition, we present a numerical comparison between stochastic and deterministic models modelling the horizontal gene transfer phenomenon. In a Hamilton-Jacobi context, we are able to numerically reproduce the evolutionary rescue of a small population that we observe in the stochastic model.
Download or read book Global Dynamics of Some Spatially Heterogeneous Population Models written by Fang Zhang and published by . This book was released on 2006 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modeling Evolution of Heterogeneous Populations written by Irina Kareva and published by Academic Press. This book was released on 2019-10-16 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling Evolution of Heterogeneous Populations: Theory and Applications describes, develops and provides applications of a method that allows incorporating population heterogeneity into systems of ordinary and discrete differential equations without significantly increasing system dimensionality. The method additionally allows making use of results of bifurcation analysis performed on simplified homogeneous systems, thereby building on the existing body of tools and knowledge and expanding applicability and predictive power of many mathematical models. Introduces Hidden Keystone Variable (HKV) method, which allows modeling evolution of heterogenous populations, while reducing multi-dimensional selection systems to low-dimensional systems of differential equations Demonstrates that replicator dynamics is governed by the principle of maximal relative entropy that can be derived from the dynamics of selection systems instead of being postulated Discusses mechanisms behind models of both Darwinian and non-Darwinian selection Provides examples of applications to various fields, including cancer growth, global demography, population extinction, tragedy of the commons and resource sustainability, among others Helps inform differences in underlying mechanisms of population growth from experimental observations, taking one from experiment to theory and back
Download or read book Evolution in Changing Environments written by Richard Levins and published by Princeton University Press. This book was released on 1968-08-21 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Levins, one of the leading explorers in the field of integrated population biology, considers the mutual interpenetration and joint evolution of organism and environment, occurring on several levels at once. Physiological and behavioral adaptations to short-term fluctuations of the environment condition the responses of populations to long-term changes and geographic gradients. These in turn affect the way species divide the environments among themselves in communities, and, therefore, the numbers of species which can coexist. Environment is treated here abstractly as pattern: patchiness, variability, range, etc. Populations are studied in their patterns: local heterogeneity, geographic variability, faunistic diversity, etc.
Download or read book Nonlinear Dynamics and Evolution Equations written by Hermann Brunner and published by American Mathematical Soc.. This book was released on 2006 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume reflect a broad spectrum of current research activities on the theory and applications of nonlinear dynamics and evolution equations. They are based on lectures given during the International Conference on Nonlinear Dynamics and Evolution Equations at Memorial University of Newfoundland, St. John's, NL, Canada, July 6-10, 2004. This volume contains thirteen invited and refereed papers. Nine of these are survey papers, introducing the reader to, anddescribing the current state of the art in major areas of dynamical systems, ordinary, functional and partial differential equations, and applications of such equations in the mathematical modelling of various biological and physical phenomena. These papers are complemented by four research papers thatexamine particular problems in the theory and applications of dynamical systems. Information for our distributors: Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Download or read book Modeling Populations of Adaptive Individuals written by Steven F. Railsback and published by Princeton University Press. This book was released on 2020-05-19 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ecologists now recognize that the dynamics of populations, communities, and ecosystems are strongly affected by adaptive individual behaviors. Yet until now, we have lacked effective and flexible methods for modeling such dynamics. Traditional ecological models become impractical with the inclusion of behavior, and the optimization approaches of behavioral ecology cannot be used when future conditions are unpredictable due to feedbacks from the behavior of other individuals. This book provides a comprehensive introduction to state- and prediction-based theory, or SPT, a powerful new approach to modeling trade-off behaviors in contexts such as individual-based population models where feedbacks and variability make optimization impossible. Modeling Populations of Adaptive Individuals features a wealth of examples that range from highly simplified behavior models to complex population models in which individuals make adaptive trade-off decisions about habitat and activity selection in highly heterogeneous environments. Steven Railsback and Bret Harvey explain how SPT builds on key concepts from the state-based dynamic modeling theory of behavioral ecology, and how it combines explicit predictions of future conditions with approximations of a fitness measure to represent how individuals make good—not optimal—decisions that they revise as conditions change. The resulting models are realistic, testable, adaptable, and invaluable for answering fundamental questions in ecology and forecasting ecological outcomes of real-world scenarios.
Download or read book Population Dynamics written by Bertram G. Jr. Murray and published by Elsevier. This book was released on 2013-07-22 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Population Dynamics: Alternative Models provides a theoretical framework of population dynamics. This book contains seven chapters that discuss the controversies surrounding discussions on the explicit view of the subject. Chapters 1 and 2 present a general introduction to the terminology, the mathematical background, and the philosophical approach that lie behind the theoretical development. Chapter 3 contains a series of models accounting for variations in population growth rates, sizes, and fluctuations, while Chapter 4 examines a model accounting for the evolution of life history patterns. A more detailed examination of the effects of predation on prey populations, especially with respect to determining a prey population's maximum sustainable yield, is explored in Chapter 5. Chapter 6 highlights the interspecific competition theory in terms of the population dynamics models presented in a previous chapter. Chapter 7 summarizes the developments in the population dynamics research studies. This work will be of great value to ecologists, biologists, and population dynamics researchers.
Download or read book Global Dynamics of Some Population Models with Spatial Dispersal written by Yuxiang Zhang and published by . This book was released on 2012 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantitative Ecology and Evolutionary Biology written by Otso Ovaskainen and published by Oxford University Press. This book was released on 2016-09-01 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This novel, interdisciplinary text achieves an integration of empirical data and theory with the aid of mathematical models and statistical methods. The emphasis throughout is on spatial ecology and evolution, especially on the interplay between environmental heterogeneity and biological processes. The book provides a coherent theme by interlinking the modelling approaches used for different subfields of spatial ecology: movement ecology, population ecology, community ecology, and genetics and evolutionary ecology (each being represented by a separate chapter). Each chapter starts by describing the concept of each modelling approach in its biological context, goes on to present the relevant mathematical models and statistical methods, and ends with a discussion of the benefits and limitations of each approach. The concepts and techniques discussed throughout the book are illustrated throughout with the help of empirical examples. This is an advanced text suitable for any biologist interested in the integration of empirical data and theory in spatial ecology/evolution through the use of quantitative/statistical methods and mathematical models. The book will also be of relevance and use as a textbook for graduate-level courses in spatial ecology, ecological modelling, theoretical ecology, and statistical ecology.
Download or read book Spatiotemporal Models of Population and Community Dynamics written by T. Czaran and published by Springer Science & Business Media. This book was released on 1998 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive typology and a comprehensible description of spatiotemporal models used in population dynamics. The main types included are: reaction-diffusion systems, patch models, matapopulation approaches, host parasitoid models, cellular automata (interacting particle systems), tessellations and distance models. The models are introduced through examples and with informative verbal explanations to help understanding. Some of the cellular automation examples are models not yet published elsewhere. Possible extensions of certain model types are suggested.
Download or read book Quantitative Ecology and Evolutionary Biology written by Otso Ovaskainen and published by Oxford University Press. This book was released on 2016-09-01 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This novel, interdisciplinary text achieves an integration of empirical data and theory with the aid of mathematical models and statistical methods. The emphasis throughout is on spatial ecology and evolution, especially on the interplay between environmental heterogeneity and biological processes. The book provides a coherent theme by interlinking the modelling approaches used for different subfields of spatial ecology: movement ecology, population ecology, community ecology, and genetics and evolutionary ecology (each being represented by a separate chapter). Each chapter starts by describing the concept of each modelling approach in its biological context, goes on to present the relevant mathematical models and statistical methods, and ends with a discussion of the benefits and limitations of each approach. The concepts and techniques discussed throughout the book are illustrated throughout with the help of empirical examples. This is an advanced text suitable for any biologist interested in the integration of empirical data and theory in spatial ecology/evolution through the use of quantitative/statistical methods and mathematical models. The book will also be of relevance and use as a textbook for graduate-level courses in spatial ecology, ecological modelling, theoretical ecology, and statistical ecology.
Download or read book Evolution Equations with Applications to Population Dynamics written by Elisa Affili and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the role of heterogeneity in equations and interactions in coupled systems. In this direction, we investigate three separate problems. The first problem addresses the evolution of a single population living in a periodic medium with a fast diffusion line; this corresponds to the study of a reaction-diffusion system with equations in different dimensions. Result on asymptotic behaviour are derived through the study of some generalised principal eigenvalues. We find that the presence of the road has no impact on the survival chances of the population, despite the deleterious effect expected from fragmentation. The second study regards a model describing the competition between two populations in a situation of asymmetrically aggressive interactions; this consists in a system of two ODEs. The evolution progresses through two possible scenarios, where only one population survives. The interpretation of one of the parameters as the aggressiveness of the attacker naturally raises questions of controllability. We characterise the set of initial conditions leading to the victory of the attacker through a suitable (possibly time-dependant) strategy. The third part of this thesis analyses the time decay of some evolution equations with classical and fractional time derivatives. Depending on the type of derivative and some degree of non-degeneracy of the spatial operator, quantitative polynomial or exponential estimates are entailed.
Download or read book Mathematical Ecology written by Thomas G. Hallam and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: There isprobably no more appropriate location to hold a course on mathematical ecology than Italy, the countryofVito Volterra, a founding father ofthe subject. The Trieste 1982Autumn Course on Mathematical Ecology consisted of four weeksofvery concentrated scholasticism and aestheticism. The first weeks were devoted to fundamentals and principles ofmathematicalecology. A nucleusofthe material from the lectures presented during this period constitutes this book. The final week and a half of the Course was apportioned to the Trieste Research Conference on Mathematical Ecology whose proceedings have been published as Volume 54, Lecture Notes in Biomathematics, Springer-Verlag. The objectivesofthe first portionofthe course wereambitious and, probably, unattainable. Basic principles of the areas of physiological, population, com munitY, and ecosystem ecology that have solid ecological and mathematical foundations were to be presented. Classical terminology was to be introduced, important fundamental topics were to be developed, some past and some current problems of interest were to be presented, and directions for possible research were to be provided. Due to time constraints, the coverage could not be encyclopedic;many areas covered already have merited treatises of book length. Consequently, preliminary foundation material was covered in some detail, but subject overviewsand area syntheseswerepresented when research frontiers were being discussed. These lecture notes reflect this course philosophy.
Download or read book Population Dynamics Based on Individual Stochasticity written by Ryo Oizumi and published by Springer Nature. This book was released on 2022-09-17 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates that population structure and dynamics can be reconstructed by stochastic analysis. Population projection is usually based on age-structured population models. These models consist of age-dependent fertility and mortality, whereas birth and death processes generally arise from states of individuals. For example, a number of seeds are proportional to tree size, and amount of income and savings are the basis of decision making for birth behavior in human beings. Thus, even though individuals belong to an identical cohort, they have different fertility and mortality. To treat this kind of individual heterogeneity, stochastic state transitions are reasonable rather than the deterministic states. This book extends deterministic systems to stochastic systems specifically, constructing a state transition model represented by stochastic differential equations. The diffusion process generated by stochastic differential equations provides statistics determining population dynamics, i.e., heterogeneity is incorporated in population dynamics as its statistics. Applying this perspective to demography and evolutionary biology, we can consider the role of heterogeneity in life history or evolution. These concepts are provided to readers with explanations of stochastic analysis.
Download or read book The Dynamics of Biological Systems written by Arianna Bianchi and published by Springer Nature. This book was released on 2019-10-02 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents nine mini-courses from a summer school, Dynamics of Biological Systems, held at the University of Alberta in 2016, as part of the prestigious seminar series: Séminaire de Mathématiques Supérieures (SMS). It includes new and significant contributions in the field of Dynamical Systems and their applications in Biology, Ecology, and Medicine. The chapters of this book cover a wide range of mathematical methods and biological applications. They - explain the process of mathematical modelling of biological systems with many examples, - introduce advanced methods from dynamical systems theory, - present many examples of the use of mathematical modelling to gain biological insight - discuss innovative methods for the analysis of biological processes, - contain extensive lists of references, which allow interested readers to continue the research on their own. Integrating the theory of dynamical systems with biological modelling, the book will appeal to researchers and graduate students in Applied Mathematics and Life Sciences.
Download or read book General Technical Report RM written by and published by . This book was released on 1988 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt:
