Shandelle M. Henson – författare

Mathematical Modeling in Biology: A Research Methods Approach is a textbook written primarily for advanced mathematics and science undergraduate students and graduate-level biology students. Although the applications center on ecology, the expertise of the authors, the methodology can be imported to any other science, including social science and economics. The aim of the book, beyond being a useful aid to teaching and learning the core modeling skills needed for mathematical biology, is to encourage students to think deeply and clearly about the meaning of mathematics in science and to learn significant research methods. Most importantly, it is hoped that students will experience some of the excitement of doing research.

Features

Mathematical Modeling in Biology: A Research Methods Approach is a textbook written primarily for advanced mathematics and science undergraduate students and graduate-level biology students. Although the applications center on ecology, the expertise of the authors, the methodology can be imported to any other science, including social science and economics. The aim of the book, beyond being a useful aid to teaching and learning the core modeling skills needed for mathematical biology, is to encourage students to think deeply and clearly about the meaning of mathematics in science and to learn significant research methods. Most importantly, it is hoped that students will experience some of the excitement of doing research.

Features

Complex Population Dynamics: Theory and Data brings together over two decades of research and reflection on experimental nonlinear population dynamics. The broad theme of the book is the interface of population data and mathematical models. The authors establish a cornerstone example of a low-dimensional mathematical population model for which quantitative predictions, often unexpected, were borne out in controlled and replicated experiments. Central messages include the importance of low-dimensional, mechanistic models that serve as testable hypotheses; the importance of model validation on independent data; the prediction of novel outcomes in response to parameter manipulation; the interaction of nonlinearity and stochasticity—and how stochasticity illuminates, rather than obscures, deterministic forces; abrupt transitions in dynamic regimes in response to interventions; and how chaotic dynamics are expressed in discrete-state, noisy population systems. The book explores nonlinear phenomena in experimental data, including equilibria, cycles, bifurcations, invariant loops, multiple attractors, resonance and attenuance, saddles, stable and unstable manifolds, basins of attraction, basin boundaries, and chaos, and shows how these dynamics manifest in real data in both time series and state space plots.

The book offers an invaluable resource to professional ecologists and applied mathematicians. Although primarily a reference text, it is written to be accessible and engaging to a student audience and could be used as supplementary reading in an advanced ecological modeling class.

Features

Complex Population Dynamics: Theory and Data brings together over two decades of research and reflection on experimental nonlinear population dynamics. The broad theme of the book is the interface of population data and mathematical models. The authors establish a cornerstone example of a low-dimensional mathematical population model for which quantitative predictions, often unexpected, were borne out in controlled and replicated experiments. Central messages include the importance of low-dimensional, mechanistic models that serve as testable hypotheses; the importance of model validation on independent data; the prediction of novel outcomes in response to parameter manipulation; the interaction of nonlinearity and stochasticity—and how stochasticity illuminates, rather than obscures, deterministic forces; abrupt transitions in dynamic regimes in response to interventions; and how chaotic dynamics are expressed in discrete-state, noisy population systems. The book explores nonlinear phenomena in experimental data, including equilibria, cycles, bifurcations, invariant loops, multiple attractors, resonance and attenuance, saddles, stable and unstable manifolds, basins of attraction, basin boundaries, and chaos, and shows how these dynamics manifest in real data in both time series and state space plots.

The book offers an invaluable resource to professional ecologists and applied mathematicians. Although primarily a reference text, it is written to be accessible and engaging to a student audience and could be used as supplementary reading in an advanced ecological modeling class.

Features

This monograph summarizes several decades of collaborations between ecologists and mathematicians, presenting novel applications in biological modeling. The authors are among the first researchers to pioneer the use of dynamical systems models to successfully describe and predict animal behavior in relation to environmental changes. The text highlights the biological and mathematical techniques used in the research, including three main components: 1) large data sets on natural populations in the field; 2) mathematical models rigorously tied to data, which describe, explain, and predict behavioral dynamics in relation to environmental variables; and 3) simplified, proof-of-concept models to probe dynamic mechanisms, suggest testable hypotheses, and allow study of the consequences of environmental change and evolving traits. It is a suitable text for field ecologists interested in the modeling procedures and conclusions addressed therein, as well as mathematicians interested inapplications to population, ecological, and evolutionary dynamics.