Individual Based Models And Their Limits

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Individual Based Models And Their Limits

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Author : Ryszard Rudnicki
language : en
Publisher: Springer Nature
Release Date : 2024-11-01

Individual Based Models And Their Limits written by Ryszard Rudnicki and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-01 with Mathematics categories.

Individual-based models (IBM) describe a population as a collection of different organisms whose local interactions determine the behaviour of the entire population. The individual description is convenient for computer simulations and the determination of various model parameters, and appropriate limit passages lead to the transport equations used in classical population dynamics models. The aim of this book is to provide a brief mathematical introduction to IBMs and their application to selected biological topics. The book is divided into seven chapters. In the first chapter we give a general description of IBMs and we present examples of models to illustrate their possible applications. Examples of applications include age, size and phenotype models, coagulation-fragmentation process, and models of genome evolution. The second chapter contains some theoretical results concerning limit passages from IBMs to phenotype and age-structured models. The rate of this convergence formulated as functional central limit theorems is presented in Chapter 3. As a result of the limit passage can be a superprocess, i.e., a stochastic process with values in a space of measures. Chapter 4 presented examples of such passages: from the branching Brownian motion to the Dawson--Watanabe superprocess and from the Moran's model of genetic drift with mutations to the Fleming--Viot superprocess. The next three chapters are devoted to models, in which we directly participated in the study. In Chapter 5 we study IBMs phenotype models and their limit passages. We show that random mating stabilises the distribution of traits, while assortative mating can lead to a polymorphic population. Formation of aggregates of phytoplankton and their movement is studied in Chapter 6. We present two types of models based on: fragmentation-coagulation processes; and diffusion with chemical signals leading to advanced superprocesses. Chapter 7 is devoted to rather advanced models with chemotaxis used to description of retinal angiogenesis and cell proliferations. The book is complemented by two appendices in which we have collected information about stochastic processes and various spaces we have used. The book is dedicated both to mathematicians and biologists. The first group will find here new biological models which leads to interesting and often new mathematical questions. Biologists can observe how to include seemingly different biological processes into a unified mathematical theory and deduce from this theory interesting biological conclusions. Apart from the sections on superprocesses, where quite advanced mathematical issues arise, such as stochastic partial equations, we try to keep the required mathematical and biological background to a minimum so that the topics are accessible to students.

Individual Based Models And Approaches In Ecology

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Author : D. L. DeAngelis
language : en
Publisher: CRC Press
Release Date : 2018-01-18

Individual Based Models And Approaches In Ecology written by D. L. DeAngelis and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-18 with Mathematics categories.

Until fairly recently, populations were handled as homogenized averages, which made modeling feasible but which ignored the essential fact that in any population there is a great variety of individuals of different ages, sizes, and degrees of fitness. Recently, because of the increased availability of affordable computer power, approaches have been developed which are able to recognize individual differences. Individual-based models are of great use in the areas of aquatic ecology, terrestrial ecology, landscape or physiological ecology, terrestrial ecology, landscape or physiological ecology, and agriculture. This book discusses which biological problems individual-based models can solve, as well as the models' inherent limitations. It explores likely future directions of theoretical development in these models, as well as currently feasible management applications and the best mathematical approaches and computer languages to use. The book also details specific applications to theory and management.

Individual Based Modeling And Ecology

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Author : Volker Grimm
language : en
Publisher: Princeton University Press
Release Date : 2013-11-28

Individual Based Modeling And Ecology written by Volker Grimm and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-28 with Science categories.

Individual-based models are an exciting and widely used new tool for ecology. These computational models allow scientists to explore the mechanisms through which population and ecosystem ecology arises from how individuals interact with each other and their environment. This book provides the first in-depth treatment of individual-based modeling and its use to develop theoretical understanding of how ecological systems work, an approach the authors call "individual-based ecology.? Grimm and Railsback start with a general primer on modeling: how to design models that are as simple as possible while still allowing specific problems to be solved, and how to move efficiently through a cycle of pattern-oriented model design, implementation, and analysis. Next, they address the problems of theory and conceptual framework for individual-based ecology: What is "theory"? That is, how do we develop reusable models of how system dynamics arise from characteristics of individuals? What conceptual framework do we use when the classical differential equation framework no longer applies? An extensive review illustrates the ecological problems that have been addressed with individual-based models. The authors then identify how the mechanics of building and using individual-based models differ from those of traditional science, and provide guidance on formulating, programming, and analyzing models. This book will be helpful to ecologists interested in modeling, and to other scientists interested in agent-based modeling.

Agent Based And Individual Based Modeling

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Author : Steven F. Railsback
language : en
Publisher: Princeton University Press
Release Date : 2025-06-03

Agent Based And Individual Based Modeling written by Steven F. Railsback and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-03 with Science categories.

The essential textbook on agent-based modeling—now fully updated and expanded Agent-Based and Individual-Based Modeling has become the standard textbook on the subject for classroom use and self-instruction. Drawing on the latest version of NetLogo and fully updated with new examples, exercises, and an enhanced text for easier comprehension, this is the essential resource for anyone seeking to understand how the dynamics of biological, social, and other complex systems arise from the characteristics of the agents that make up these systems. Steven Railsback and Volker Grimm lead students stepwise through the processes of designing, programming, documenting, and doing scientific research with agent-based models, focusing on the adaptive behaviors that make these models necessary. They cover the fundamentals of modeling and model analysis, introduce key modeling concepts, and demonstrate how to implement them using NetLogo. They also address pattern-oriented modeling, an invaluable strategy for modeling real-world problems and developing theory. This accessible and authoritative book focuses on modeling as a tool for understanding real complex systems. It explains how to pose a specific question, use observations from actual systems to design models, write and test software, and more. A hands-on introduction that guides students from conceptual design to computer implementation to analysis Filled with new examples and exercises and compatible with the latest version of NetLogo Ideal for students and researchers across the natural and social sciences Written by two leading practitioners Supported by extensive instructional materials at www.railsback-grimm-abm-book.com

Models And Theories

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Author : Roman Frigg
language : en
Publisher: Taylor & Francis
Release Date : 2022-06-28

Models And Theories written by Roman Frigg and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-28 with Philosophy categories.

Models and theories are of central importance in science, and scientists spend substantial amounts of time building, testing, comparing and revising models and theories. It is therefore not surprising that the nature of scientific models and theories has been a widely debated topic within the philosophy of science for many years. The product of two decades of research, this book provides an accessible yet critical introduction to the debates about models and theories within analytical philosophy of science since the 1920s. Roman Frigg surveys and discusses key topics and questions, including: What are theories? What are models? And how do models and theories relate to each other? The linguistic view of theories (also known as the syntactic view of theories), covering different articulations of the view, its use of models, the theory-observation divide and the theory-ladenness of observation, and the meaning of theoretical terms. The model-theoretical view of theories (also known as the semantic view of theories), covering its analysis of the model-world relationship, the internal structure of a theory, and the ontology of models. Scientific representation, discussing analogy, idealisation and different accounts of representation. Modelling in scientific practice, examining how models relate to theories and what models are, classifying different kinds of models, and investigating how robustness analysis, perspectivism, and approaches committed to uncertainty-management deal with multi-model situations. Models and Theories is the first comprehensive book-length treatment of the topic, making it essential reading for advanced undergraduates, researchers, and professional philosophers working in philosophy of science and philosophy of technology. It will also be of interest to philosophically minded readers working in physics, computer sciences and STEM fields more broadly.

Hyperbolic And Kinetic Models For Self Organised Biological Aggregations

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Author : Raluca Eftimie
language : en
Publisher: Springer
Release Date : 2019-01-07

Hyperbolic And Kinetic Models For Self Organised Biological Aggregations written by Raluca Eftimie and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-07 with Mathematics categories.

This book focuses on the spatio-temporal patterns generated by two classes of mathematical models (of hyperbolic and kinetic types) that have been increasingly used in the past several years to describe various biological and ecological communities. Here we combine an overview of various modelling approaches for collective behaviours displayed by individuals/cells/bacteria that interact locally and non-locally, with analytical and numerical mathematical techniques that can be used to investigate the spatio-temporal patterns produced by said individuals/cells/bacteria. Richly illustrated, the book offers a valuable guide for researchers new to the field, and is also suitable as a textbook for senior undergraduate or graduate students in mathematics or related disciplines.

Some Mathematical Models From Population Genetics

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Author : Alison Etheridge
language : en
Publisher: Springer
Release Date : 2011-01-05

Some Mathematical Models From Population Genetics written by Alison Etheridge and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-05 with Mathematics categories.

This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour summer school in probability. It provides a rapid introduction to a range of mathematical models that have their origins in theoretical population genetics. The models fall into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time (coalescent) models that trace out the genealogical relationships between individuals in a sample from the population. Some, like the classical Wright-Fisher model, date right back to the origins of the subject. Others, like the multiple merger coalescents or the spatial Lambda-Fleming-Viot process are much more recent. All share a rich mathematical structure. Biological terms are explained, the models are carefully motivated and tools for their study are presented systematically.

Quantitative Analyses In Wildlife Science

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Author : Leonard A. Brennan
language : en
Publisher: Johns Hopkins University Press
Release Date : 2019-09-10

Quantitative Analyses In Wildlife Science written by Leonard A. Brennan and has been published by Johns Hopkins University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-10 with Science categories.

An authoritative guide to quantitative methods that will help wildlife scientists improve analysis and decision-making. Over the past fifty years, wildlife science has become increasingly quantitative. But to wildlife scientists, many of whom have not been formally trained as biometricians, computer modelers, or mathematicians, the wide array of available techniques for analyzing wildlife populations and habitats can be overwhelming. This practical book aims to help students and professionals alike understand how to use quantitative methods to inform their work in the field. Covering the most widely used contemporary approaches to the analysis of wildlife populations and habitats, Quantitative Analyses in Wildlife Science is divided into five broad areas: • general statistical methods • demographic estimation • dynamic process modeling • analysis of spatially based data on animals and resources • numerical methods Addressing a variety of topics, from population estimation and growth trend predictions to the study of migration patterns, this book presents fresh data on such pressing issues as sustainable take, control of invasives, and species reintroduction. Authored by leading researchers in wildlife science, each chapter considers the structure of data in relation to a particular analytical technique, as well as the structure of variation in those data. Providing conceptual and quantitative overviews of modern analytical methods, the techniques covered in this book also apply to conservation research and wildlife policy. Whether a quick refresher or a comprehensive introduction is called for, Quantitative Analyses in Wildlife Science is an indispensable addition to every wildlife professional's bookshelf. Contributors: William M. Block, Leonard A. Brennan, Stephen T. Buckland, Christopher C. Chizinski, Evan C. Cooch, Raymond J. Davis, Stephen J. DeMaso, Randy W. DeYoung, Jane Elith, Joseph J. Fontane, Julie A. Heinrichs, Mevin B. Hooten, Julianna M. A. Jenkins, Zachary S. Laden, Damon B. Lesmeister, Daniel Linden, Jeffrey J. Lusk, Bruce G. Marcot, David L. Miller, Michael L. Morrison, Eric Rexstad, Jamie S. Sanderlin, Joseph P. Sands, Erica F. Stuber, Chris Sutherland, Andrew N. Tri, David B. Wester, Gary C. White, Christopher K. Williams, Damon L. Williford

The Mathematics Behind Biological Invasions

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Author : Mark A. Lewis
language : en
Publisher: Springer
Release Date : 2016-05-05

The Mathematics Behind Biological Invasions written by Mark A. Lewis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-05 with Mathematics categories.

This book investigates the mathematical analysis of biological invasions. Unlike purely qualitative treatments of ecology, it draws on mathematical theory and methods, equipping the reader with sharp tools and rigorous methodology. Subjects include invasion dynamics, species interactions, population spread, long-distance dispersal, stochastic effects, risk analysis, and optimal responses to invaders. While based on the theory of dynamical systems, including partial differential equations and integrodifference equations, the book also draws on information theory, machine learning, Monte Carlo methods, optimal control, statistics, and stochastic processes. Applications to real biological invasions are included throughout. Ultimately, the book imparts a powerful principle: that by bringing ecology and mathematics together, researchers can uncover new understanding of, and effective response strategies to, biological invasions. It is suitable for graduate students and established researchers in mathematical ecology.

The Geographic Spread Of Infectious Diseases

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Author : Lisa Sattenspiel
language : en
Publisher: Princeton University Press
Release Date : 2009-07-06

The Geographic Spread Of Infectious Diseases written by Lisa Sattenspiel and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-06 with Medical categories.

The 1918-19 influenza epidemic killed more than fifty million people worldwide. The SARS epidemic of 2002-3, by comparison, killed fewer than a thousand. The success in containing the spread of SARS was due largely to the rapid global response of public health authorities, which was aided by insights resulting from mathematical models. Models enabled authorities to better understand how the disease spread and to assess the relative effectiveness of different control strategies. In this book, Lisa Sattenspiel and Alun Lloyd provide a comprehensive introduction to mathematical models in epidemiology and show how they can be used to predict and control the geographic spread of major infectious diseases. Key concepts in infectious disease modeling are explained, readers are guided from simple mathematical models to more complex ones, and the strengths and weaknesses of these models are explored. The book highlights the breadth of techniques available to modelers today, such as population-based and individual-based models, and covers specific applications as well. Sattenspiel and Lloyd examine the powerful mathematical models that health authorities have developed to understand the spatial distribution and geographic spread of influenza, measles, foot-and-mouth disease, and SARS. Analytic methods geographers use to study human infectious diseases and the dynamics of epidemics are also discussed. A must-read for students, researchers, and practitioners, no other book provides such an accessible introduction to this exciting and fast-evolving field.