Mathematical Models of Plant-Herbivore Interactions PDF Download

Author: Zhilan Feng
Publisher: CRC Press
ISBN: 1498769187
Category : Mathematics
Languages : en
Pages : 240

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Book Description
Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.

Author: Zhilan Feng
Publisher:
ISBN: 9781315154138
Category : NATURE
Languages : en
Pages : 219

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Book Description
"Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology."--Provided by publisher.

Author: Zhilan Feng
Publisher: CRC Press
ISBN: 1351650173
Category : Mathematics
Languages : en
Pages : 425

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Book Description
Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.

Author: Sultanah Hadi Masmali
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Book Description
The Nicholas-Bailey model was designed to study population dynamics of host-parasite systems. The model was first developed by Nicholson and Bailey (1935) and applied to parasites (Encarsia Formosa) and hosts (Trialeurodes vaporariorum). These types of models are presented by discrete-time equations for biological systems that involve two species, e.g. a parasite population and its hosts. In this dissertation, we develop and then investigate a revised version of Nicholson-Bailey's discrete host-parasite model. Additionally, we incorporate and analyze the Allee effect dynamics in this newly constructed model. In Chapter one of this dissertation, we outline some background and literature. Second, we provide basic definitions of ordinary differential equations. We define several core concepts of dynamical systems including stability and instability analysis, manifold analysis, stable and unstable manifold, invariant manifold, center manifold, bifurcation, and the Lambert W function. Then we provide some known results and theorems that are useful in this research investigation. Third, we study the dynamics behavior of the newly developed system of a host-parasite model with four positive parameters in the first closed quadrant. A re-scaling procedure will be then applied to reduce the model to a two-parameter model that reproduces the entire dynamics of the original model. The model always possesses two boundary steady states and a third interior steady state may exist for particular conditions imposed on the parameters. Moreover, by applying the linearized stability function, we find thresholds for which the system is stable or unstable. We then study locally the long-term stability of steady states and center manifold theory based on the separating boundary curves for non-hyperbolic steady states, that is analyzing steady states when crossing from stable to unstable regions. We then analyze the stability for one or two parameter bifurcation (co-dimension one or two) depending on a different range of parameters, by considering the linearization of the model about each of the steady states. We show a period-doubling bifurcation occurs once the eigenvalue crosses these thresholds, leading to chaos. Numerical simulations support the results and conclusions. Fourth, we introduce the density dependence of the Allee effect and population dynamics into the model by adding a parameter to the modified system of the Nicholson-Bailey model. We then study the local stability of its steady states. Multiple bifurcation analyses of the system, including the period-doubling behavior and Neimark-Sacker bifurcation, will be analyzed. We then identify regions where the Allee effect system ultimately leads to chaos. Finally, the modified systems of the Nicholson-Bailey model and the Allee effect model are compared by analyzing different short-term and long-term dynamical behaviors and results acquired from the two systems.

Author: Leah Edelstein-Keshet
Publisher: SIAM
ISBN: 9780898719147
Category : Mathematics
Languages : en
Pages : 629

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Book Description
Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.

Author: Mike Gillman
Publisher: John Wiley & Sons
ISBN: 1405194898
Category : Science
Languages : en
Pages : 165

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Book Description
Students often find it difficult to grasp fundamental ecological and evolutionary concepts because of their inherently mathematical nature. Likewise, the application of ecological and evolutionary theory often requires a high degree of mathematical competence. This book is a first step to addressing these difficulties, providing a broad introduction to the key methods and underlying concepts of mathematical models in ecology and evolution. The book is intended to serve the needs of undergraduate and postgraduate ecology and evolution students who need to access the mathematical and statistical modelling literature essential to their subjects. The book assumes minimal mathematics and statistics knowledge whilst covering a wide variety of methods, many of which are at the fore-front of ecological and evolutionary research. The book also highlights the applications of modelling to practical problems such as sustainable harvesting and biological control. Key features: Written clearly and succinctly, requiring minimal in-depth knowledge of mathematics Introduces students to the use of computer models in both fields of ecology and evolutionary biology Market - senior undergraduate students and beginning postgraduates in ecology and evolutionary biology

Author: Richard J. Morris
Publisher: Springer
ISBN: 3319990705
Category : Science
Languages : en
Pages : 230

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Book Description
Progress in plant biology relies on the quantification, analysis and mathematical modeling of data over different time and length scales. This book describes common mathematical and computational approaches as well as some carefully chosen case studies that demonstrate the use of these techniques to solve problems at the forefront of plant biology. Each chapter is written by an expert in field with the goal of conveying concepts whilst at the same time providing sufficient background and links to available software for readers to rapidly build their own models and run their own simulations. This book is aimed at postgraduate students and researchers working the field of plant systems biology and synthetic biology, but will also be a useful reference for anyone wanting to get into quantitative plant biology.

Author: Mike Gillman
Publisher: John Wiley & Sons
ISBN: 1444312073
Category : Science
Languages : en
Pages : 168

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Book Description
Students often find it difficult to grasp fundamental ecologicaland evolutionary concepts because of their inherently mathematicalnature. Likewise, the application of ecological and evolutionarytheory often requires a high degree of mathematical competence. This book is a first step to addressing these difficulties,providing a broad introduction to the key methods and underlyingconcepts of mathematical models in ecology and evolution. The bookis intended to serve the needs of undergraduate and postgraduateecology and evolution students who need to access the mathematicaland statistical modelling literature essential to theirsubjects. The book assumes minimal mathematics and statistics knowledgewhilst covering a wide variety of methods, many of which are at thefore-front of ecological and evolutionary research. The book alsohighlights the applications of modelling to practical problems suchas sustainable harvesting and biological control. Key features: Written clearly and succinctly, requiring minimal in-depthknowledge of mathematics Introduces students to the use of computer models in bothfields of ecology and evolutionary biology Market - senior undergraduate students and beginningpostgraduates in ecology and evolutionary biology

Author: Leah Edelstein-Keshet
Publisher:
ISBN:
Category : Insect-plant relationships
Languages : en
Pages : 54

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Book Description

Author: Anthony G. Pakes
Publisher: Cambridge University Press
ISBN: 9780521373883
Category : Mathematics
Languages : en
Pages : 216

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Book Description
Presented in this document is a class of deterministic models describing the dynamics of two plant species whose characteristics are common to the majority of annual plants that have a seedbank. Formulated in terms of elementary dynamical systems, these models were developed in response to four major questions on the long-term outcomes of binary mixtures of plant species: Is ultimate coexistence possible? If not, which strain will win? Does the mixture approach an equilibrium? If so, how long does the mixture take to attain it? The book gives a detailed account of model construction, analysis and application to field data obtained from long-term trials. In the particular case study modelled, the species involved are two pastural strains whose dynamics have critical agricultural and economic implications for the areas in which they are found, including North America, the Mediterranean region and Australia. This study will be valuable to researchers and students in mathematical biology and to agronomists and botanists interested in population dynamics.