Jason Matthiopoulos

How to be a Quantitative Ecologist (eBook, ePUB)

The 'A to R' of Green Mathematics and Statistics

• Format: ePub

Produktbeschreibung

Ecological research is becoming increasingly quantitative, yet students often opt out of courses in mathematics and statistics, unwittingly limiting their ability to carry out research in the future. This textbook provides a practical introduction to quantitative ecology for students and practitioners who have realised that they need this opportunity. The text is addressed to readers who haven't used mathematics since school, who were perhaps more confused than enlightened by their undergraduate lectures in statistics and who have never used a computer for much more than word processing and data entry. From this starting point, it slowly but surely instils an understanding of mathematics, statistics and programming, sufficient for initiating research in ecology. The book's practical value is enhanced by extensive use of biological examples and the computer language R for graphics, programming and data analysis. Key Features: * Provides a complete introduction to mathematics statistics and computing for ecologists. * Presents a wealth of ecological examples demonstrating the applied relevance of abstract mathematical concepts, showing how a little technique can go a long way in answering interesting ecological questions. * Covers elementary topics, including the rules of algebra, logarithms, geometry, calculus, descriptive statistics, probability, hypothesis testing and linear regression. * Explores more advanced topics including fractals, non-linear dynamical systems, likelihood and Bayesian estimation, generalised linear, mixed and additive models, and multivariate statistics. * R boxes provide step-by-step recipes for implementing the graphical and numerical techniques outlined in each section. How to be a Quantitative Ecologist provides a comprehensive introduction to mathematics, statistics and computing and is the ideal textbook for late undergraduate and postgraduate courses in environmental biology. "With a book like this, there is no excuse for people to be afraid of maths, and to be ignorant of what it can do." --Professor Tim Benton, Faculty of Biological Sciences, University of Leeds, UK

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 496
• Erscheinungstermin: 12. April 2011
• Englisch
• ISBN-13: 9781119991724
• Artikelnr.: 38261619

Autorenporträt

Jason Matthiopoulos, Lecturer in biology (University of St Andrews). He is a senior researcher in the Sea Mammal Research Unit and member of the Centre for Ecological and Environmental Modelling.

Inhaltsangabe

How I chose to write this book, and why you might choose to read it.
Preface. 0. How to start a meaningful relationship with your computer.
Introduction to R. 0.1 What is R? 0.2 Why use R for this book? 0.3
Computing with a scientific package like R. 0.4 Installing and interacting
with R. 0.5 Style conventions. 0.6 Valuable R accessories. 0.7 Getting
help. 0.8 Basic R usage. 0.9 Importing data from a spreadsheet. 0.10
Storing data in data frames. 0.11 Exporting data from R. 0.12 Quitting R.
1. How to make mathematical statements. Numbers, equations and functions.
1.1 Qualitative and quantitative scales. 1.2 Numbers. 1.3 Symbols. 1.4
Logical operations. 1.5 Algebraic operations. 1.6 Manipulating numbers. 1.7
Manipulating units. 1.8 Manipulating expressions. 1.9 Polynomials. 1.10
Equations. 1.11 First order polynomial equations. 1.12 Proportionality and
scaling: a special kind of first order polynomial equation. 1.13 Second and
higher order polynomial equations. 1.14 Systems of polynomial equations.
1.15 Inequalities. 1.16 Coordinate systems. 1.17 Complex numbers. 1.18
Relations and functions. 1.19 The graph of a function. 1.20 First order
polynomial functions. 1.21 Higher order polynomial functions. 1.22 The
relationship between equations and functions. 1.23 Other useful functions.
1.24 Inverse functions. 1.25 Functions of more than one variable. 2. How to
describe regular shapes and patterns. Geometry and trigonometry. 2.1
Primitive elements. 2.2 Axioms of Euclidean geometry. 2.3 Propositions. 2.4
Distance between two points. 2.5 Areas and volumes. 2.6 Measuring angles.
2.7 The trigonometric circle. 2.8 Trigonometric functions. 2.9 Polar
coordinates. 2.10 Graphs of trigonometric functions. 2.11 Trigonometric
identities. 2.12 Inverses of trigonometric functions. 2.13 Trigonometric
equations. 2.14 Modifying the basic trigonometric graphs. 2.15
Superimposing trigonometric functions. 2.16 Spectral analysis. 2.17 Fractal
geometry. 3. How to change things, one step at a time. Sequences,
difference equations and logarithms. 3.1 Sequences. 3.2 Difference
equations. 3.3 Higher order difference equations. 3.4 Initial conditions
and parameters. 3.5 Solutions of a difference equation. 3.6 Equilibrium
solutions. 3.7 Stable and unstable equilibria. 3.8 Investigating stability.
3.9 Chaos. 3.10 Exponential function. 3.11 Logarithmic function. 3.12
Logarithmic equations. 4. How to change things, continuously. Derivatives
and their applications. 4.1 Average rate of change. 4.2 Instantaneous rate
of change. 4.3 Limits. 4.4 The derivative of a function. 4.5
Differentiating polynomials. 4.6 Differentiating other functions. 4.7 The
chain rule. 4.8 Higher order derivatives. 4.9 Derivatives of functions of
many variables. 4.10 Optimisation. 4.11 Local stability for difference
equations. 4.12 Series expansions. 5. How to work with accumulated change.
Integrals and their applications. 5.1 Antiderivatives. 5.2 Indefinite
integrals. 5.3 Three analytical methods of integration. 5.4 Summation. 5.5
Area under a curve. 5.6 Definite integrals. 5.7 Some properties of definite
integrals. 5.8 Improper integrals. 5.9 Differential equations. 5.10 Solving
differential equations. 5.11 Stability analysis for differential equations.
6. How to keep stuff organised in tables. Matrices and their applications.
6.1 Matrices. 6.2 Matrix operations. 6.3 Geometric interpretation of
vectors and square matrices. 6.4 Solving systems of equations with
matrices. 6.5 Markov chains. 6.6 Eigenvalues and eigenvectors. 6.7 Leslie
matrix models. 6.8 Analysis of linear dynamical systems. 6.9 Analysis of
nonlinear dynamical systems. 7. How to visualise and summarise data.
Descriptive statistics. 7.1 Overview of statistics. 7.2 Statistical
variables. 7.3 Populations and samples. 7.4 Single-variable samples. 7.5
Frequency distributions. 7.6 Measures of centrality. 7.7 Measures of
spread. 7.8 Skewness and kurtosis. 7.9 Graphical summaries. 7.10 Data sets
with more than one variable. 7.11 Association between qualitative
variables. 7.12 Association between quantitative variables. 7.13 Joint
frequency distributions. 8. How to put a value on uncertainty. Probability.
8.1 Random experiments and event spaces. 8.2 Events. 8.3 Frequentist
probability. 8.4 Equally likely events. 8.5 The union of events. 8.6
Conditional probability. 8.7 Independent events. 8.8 Total probability. 8.9
Bayesian probability. 9. How to identify different kinds of randomness.
Probability distributions. 9.1 Probability distributions. 9.2 Discrete
probability distributions. 9.3 Continuous probability distributions. 9.4
Expectation. 9.5 Named distributions. 9.6 Equally likely events: the
uniform distribution. 9.7 Hit or miss: the Bernoulli distribution. 9.8
Count of occurrences in a given number of trials: the binomial
distribution. 9.9 Counting different types of occurrences: the multinomial
distribution. 9.10 Number of occurrences in a unit of time or space: the
Poisson distribution. 9.11 The gentle art of waiting: geometric, negative
binomial, exponential and gamma distributions. 9.12 Assigning probabilities
to probabilities: the beta and Dirichlet distributions. 9.13 Perfect
symmetry: the normal distribution. 9.14 Because it looks right: using
probability distributions empirically. 9.15 Mixtures, outliers and the
t-distribution. 9.16 Joint, conditional and marginal probability
distributions. 9.17 The bivariate normal distribution. 9.18 Sums of random
variables: the central limit theorem. 9.19 Products of random variables:
the log-normal distribution. 9.20 Modelling residuals: the chi-square
distribution. 9.21 Stochastic simulation. 10. How to see the forest from
the trees. Estimation and testing. 10.1 Estimators and their properties.
10.2 Normal theory. 10.3 Estimating the population mean. 10.4 Estimating
the variance of a normal population. 10.5 Confidence intervals. 10.6
Inference by bootstrapping. 10.7 More general estimation methods. 10.8
Estimation by least squares. 10.9 Estimation by maximum likelihood. 10.10
Bayesian estimation. 10.11 Link between maximum likelihood and Bayesian
estimation. 10.12 Hypothesis testing: rationale. 10.13 Tests for the
population mean. 10.14 Tests comparing two different means. 10.15
Hypotheses about qualitative data. 10.16 Hypothesis testing debunked. 11.
How to separate the signal from the noise. Statistical modelling. 11.1
Comparing the means of several populations. 11.2 Simple linear regression.
11.3 Prediction. 11.4 How good is the best-fit line? 11.5 Multiple linear
regression. 11.6 Model selection. 11.7 Generalised linear models. 11.8
Evaluation, diagnostics and model selection for GLMs. 11.9 Modelling
dispersion. 11.10 Fitting more complicated models to data: polynomials,
interactions, nonlinear regression. 11.11 Letting the data suggest more
complicated models: smoothing. 11.12 Partitioning variation: mixed effects
models. 12. How to measure similarity. Multivariate methods 12.1 The
problem with multivariate data. 12.2 Ordination in general. 12.3 Principal
components analysis. 12.4 Clustering in general. 12.5 Agglomerative
hierarchical clustering. 12.6 Nonhierarchical clustering: k means analysis.
12.7 Classification in general. 12.8 Logistic regression: two classes. 12.9
Logistic regression: many classes. Further reading. References. Appendix:
Formulae. R Index. Index.

Rezensionen

"For those looking through R books for something a bit more technical, this book will be an essential accomplice to mastering R." (British Ecological Society, 1 April 2013)

"The book is written in a style that is easy to read and for which one quickly forgets that the examples are essentially mathematical in nature. If you are an ecologist who has shied away from quantitative ecology in the past then this may be the text to convince you that there is much to be learnt from quantitative ecology. I thoroughly recommend this book and trust that you enjoy reading it as much as I did." (International Statistical Review, 2012) "After a course of one or two semesters using this textbook, he says, students should have the absolute minimum of knowledge about quantitative research that ecologists need, but can provide a foundation for students who want to move further in that direction." (Book News, 1 August 2011)