Evolution Dynamics of Some Population Models in Heterogeneous Environments
Evolution Dynamics of Some Population Models in Heterogeneous Environments

Author: Ruiwen Wu

Publisher:

Published: 2019

Total Pages:

ISBN-13:

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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.

Integro-differential Models for Evolutionary Dynamics of Populations in Time-heterogeneous Environments
Integro-differential Models for Evolutionary Dynamics of Populations in Time-heterogeneous Environments

Author: Susely Figueroa Iglesias

Publisher:

Published: 2019

Total Pages: 142

ISBN-13:

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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.

Modeling Evolution of Heterogeneous Populations
Modeling Evolution of Heterogeneous Populations

Author: Irina Kareva

Publisher: Academic Press

Published: 2019-10-16

Total Pages: 354

ISBN-13: 0128144327

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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

Nonlinear Dynamics and Evolution Equations
Nonlinear Dynamics and Evolution Equations

Author: Hermann Brunner

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 322

ISBN-13: 0821837214

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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).

Evolution in Changing Environments
Evolution in Changing Environments

Author: Richard Levins

Publisher: Princeton University Press

Published: 1968-08-21

Total Pages: 136

ISBN-13: 9780691080628

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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.

Modeling Populations of Adaptive Individuals
Modeling Populations of Adaptive Individuals

Author: Steven F. Railsback

Publisher: Princeton University Press

Published: 2020-05-19

Total Pages: 195

ISBN-13: 0691195374

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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.

Population Dynamics
Population Dynamics

Author: Bertram G. Jr. Murray

Publisher: Elsevier

Published: 2013-07-22

Total Pages: 223

ISBN-13: 0323159850

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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.

Quantitative Ecology and Evolutionary Biology
Quantitative Ecology and Evolutionary Biology

Author: Otso Ovaskainen

Publisher: Oxford University Press

Published: 2016-09-01

Total Pages: 301

ISBN-13: 0191024228

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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.