Mathematical Methods in Biology
Wiley Series in Pure and Applied Mathematics
1. Auflage September 2009
436 Seiten, Softcover
Wiley & Sons Ltd
Kurzbeschreibung
Mathematical Methods in Biology uniquely covers both deterministic and probabilistic models, including algorithms in the MATLAB platform. The book focuses mostly in one area of the life sciences, focusing mainly on theoretical ecology. This resource provides an introduction to ecological modeling, population dynamics for single species, structure and interacting populations, interactions in continuous time, concepts of probability, statistical inference, and stochastic processes. This valuable reference explains quantifiable theories in relation to population growth, animal behavior, life histories, and environmental influences for environmental professionals.
Mathematik trifft Biologie: Dieser Band lotet ein spannendes Grenzgebiet aus. Er informiert nicht nur über Grundlagen, sondern auch über moderne Spezialthemen wie Populationsdynamik, Fütterungstheorie und Theorie der Lebensgeschichte und enthält Material, dass Sie ansonsten kaum in der Literatur finden. Zunächst vermitteln die Autoren das notwendige mathematische Rüstzeug (biologische Modellierung, Infinitesimalrechnung, Differenzialgleichungen, dimensionslose Variable, deskriptive Statistik). Anschließend untersuchen sie diskrete und kontinuierliche Standardmodelle (Matrizenalgebra ebenso wie Differenzen- und Differenzialgleichungen). Im letzten Teil geht es um Wahrscheinlichkeitsrechnung, Statistik, stochastische Methoden, Bootstrapping und stochastische Differenzialgleichungen.
1. Introduction To Ecological Modeling.
1.1 Mathematical Models.
1.2 Rates of Change.
1.3 Balance Laws.
1.4 Temperature in the Environment.
1.5 Dimensionless Variables.
1.6 Descriptive Statistics.
1.7 Regression and Curve Fitting.
1.8 Reference Notes.
2. Population Dynamics for Single Species.
2.1 Laws of Population Dynamics.
2.2 Continuous Time Models.
2.3 Qualitative Analysis of Population Models.
2.4 Dynamics of Predation.
2.5 Discrete Time Models.
2.6 Equilibria, Stability, and Chaos.
2.7 Reference Notes.
3. Structure and Interacting Populations.
3.1 Structure--Juveniles and Adults.
3.2 Structured Linear Models.
3.3 Nonlinear Interactions.
3.4 Appendix--Matrices.
3.5 Reference Notes.
4. Interactions in Continuous Time.
4.1 Interacting Populations.
4.2 Phase Plane Analysis.
4.3 Linear Systems.
4.4 Nonlinear Systems.
4.5 Bifurcation.
4.6 Reference Notes.
5. Concepts of Probability.
5.1 Introductory Examples and Definitions.
5.2 The Hardy-Weinberg Law.
5.3 Continuous Random Variables.
5.4 Discrete Random Variables.
5.5 Joint Probability Distributions.
5.6 Covariance and Correlation.
5.7 Reference Notes.
6. Statistical Inference.
6.1 Introduction.
6.2 Interval Analysis.
6.3 Estimating Proportions.
6.4 The Chi-Squared Test.
6.5 Hypothesis Testing.
6.6 Bootstrap Methods.
6.7 Reference Notes.
7. Stochastic Processes.
7.1 Introduction.
7.2 Randomizing Discrete Dynamics.
7.3 Random Walk.
7.4 Birth Processes.
7.5 Stochastic Differential Equations.
7.6 SDEs from Markov Models.
7.7 Solving SDEs.
7.8 The Fokker-Planck Equation.
7.9 Reference Notes.
A. Hints and Solutions to Exercises
