Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities

Rebecca Sanft , Anne Walter 지음

elsevier 2020년 04월 14일 출간

작품소개

책소개

Exploring Mathematical Modeling in Biology through Case Studies and Experimental Activities provides supporting materials for courses taken by students majoring in mathematics, computer science or in the life sciences. The book's cases and lab exercises focus on hypothesis testing and model development in the context of real data. The supporting mathematical, coding and biological background permit readers to explore a problem, understand assumptions, and the meaning of their results. The experiential components provide hands-on learning both in the lab and on the computer. As a beginning text in modeling, readers will learn to value the approach and apply competencies in other settings. Included case studies focus on building a model to solve a particular biological problem from concept and translation into a mathematical form, to validating the parameters, testing the quality of the model and finally interpreting the outcome in biological terms. The book also shows how particular mathematical approaches are adapted to a variety of problems at multiple biological scales. Finally, the labs bring the biological problems and the practical issues of collecting data to actually test the model and/or adapting the mathematics to the data that can be collected.Presents a single volume on mathematics and biological examples, with data and wet lab experiences suitable for non-expertsContains three real-world biological case studies and one wet lab for application of the mathematical modelsIncludes R code templates throughout the text, which are also available through an online repository, along with the necessary data files to complete all projects and labs

목차

Unit 1 Introduction to Modeling using Difference Equations 1.1? Discrete-Time Models 1.1.1? Solutions to First-Order Difference Equations 1.1.2? Using Linear Regression to Estimate Parameters 1.2? Putting it all together: The Whooping Crane 1.3? CaseStudy1: Island Biogeography 1.3.1? Background 1.3.2? Model Formulation 1.3.3? Rakata Story 1.3.4? Modern Approach:? Lineage Data 1.3.5? Back to MacArthur and Wilson: Effects of Distance and Area 1.4? CaseStudy2: Pharmacokinetics Model 1.4.1? Background 1.4.2? Formulating the model 1.4.3? Understanding the Model 1.4.4? Parameter Estimation 1.4.5? Model Evaluation/Analysis 1.4.6? Further Exploration 1.5? CaseStudy3: Invasive Plant Species 1.5.1? Background 1.5.2? Model Formulation 1.5.3? Parameter Estimation 1.5.4? Model Predictions 1.5.5? Management Strategies 1.6? Wet Lab: Logistic Growth Model of Bacterial Population Dynamics 1.6.1? Introduction 1.6.2? Modeling populations 1.6.3? The Experiment 1.6.4? Model Calibration and Analysis 1.6.5? Experiment Part2:? Effect of changing Media Unit 2 Differential Equations: Model Formulation, Nonlinear Regression, and Model Selection 2.1? Biological Background 2.2? Mathematical and R Background 2.2.1? Differential Equation Based Model Formulation 2.2.2? Solutions to Ordinary Differential Equations 2.2.3? Investigating Parameter Space 2.2.4? Nonlinear Fitting 2.3? Model Selection 2.4? Case Study 1: How Leaf Decomposition Rates Vary with Anthropogenic Nitrogen Deposition 2.4.1 Background 2.4.2 The Data 2.4.3 Model Formulation 2.4.4 Parameter Estimation 2.4.5 Model Evaluation 2.5? Case Study 2: Exploring Models to Describe Tumor Growth Rates 2.5.1 Background 2.5.2 The Data 2.5.3 Model Formulation 2.5.4 Parameter Estimation 2.5.5 Model Evaluation:? Descriptive Power 2.5.6 Model Evaluation:? Predictive Power 2.6? Case Study 3: Predator Responses to Prey Density Vary with Temperature 2.6.1 Background 2.6.2 Analy

작가정보

저자(글) Rebecca Sanft

저자(글) Anne Walter