How to be a quantitative ecologist : the 'A to R' of green mathematics and statistics / Jason Matthiopoulos.

Format:

Book

Author/Creator:

Matthiopoulos, Jason.

Language:

English

Subjects (All):

Ecology--Mathematics.

Ecology.

Ecology--Research.

Ecology--Vocational guidance.

Mathematics--Vocational guidance.

Mathematics.

Quantitative analysts.

Quantitative research.

Physical Description:

1 online resource (491 pages)

Edition:

1st ed.

Place of Publication:

Chichester, West Sussex, U.K. : Wiley, 2011.

Language Note:

English

Summary:

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

Contents:

Intro

How to be a Quantitative Ecologist

The A to Rof green mathematics &amp

statistics

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

Further reading

References

1. How to make mathematical statements Numbers, equations and functions

1.1 Qualitative and quantitative scales

Habitat classifications

1.2 Numbers

Observations of spatial abundance

1.3 Symbols

Population size and carrying capacity

1.4 Logical operations

1.5 Algebraic operations

Size matters in male garter snakes

1.6 Manipulating numbers

1.7 Manipulating units

1.8 Manipulating expressions

Energy acquisition in voles

1.9 Polynomials

The law of mass action in epidemiology

1.10 Equations

1.11 First order polynomial equations

Population size and composition

1.12 Proportionality and scaling: a special kind of first order polynomial equation

Simple mark-recapture

Converting density to population size

1.13 Second and higher order polynomial equations

Estimating the number of infected animals from the rate of infection

1.14 Systems of polynomial equations

Deriving population structure from data on population size

1.15 Inequalities

Minimum energetic requirements in voles

1.16 Coordinate systems

Non-Cartesian map projections

1.17 Complex numbers

1.18 Relations and functions

Food webs.

Mating systems in animals

1.19 The graph of a function

Two aspects of vole energetics

1.20 First order polynomial functions

Population stability in a time series

Population stability and population change

Visualising goodness-of-fit

1.21 Higher order polynomial functions

1.22 The relationship between equations and functions

Extent of an epidemic when the transmission rate exceeds a critical value

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

Suicidal lemmings, parsimony, evidence and proof

2.3 Propositions

Radio-tracking of terrestrial animals

2.4 Distance between two points

Spatial autocorrelation in ecological variables

2.5 Areas and volumes

Hexagonal territories

2.6 Measuring angles

The bearing of a moving animal

2.7 The trigonometric circle

The position of a seed following dispersal

2.8 Trigonometric functions

2.9 Polar coordinates

Random walks

2.10 Graphs of trigonometric functions

2.11 Trigonometric identities

A two-step random walk

2.12 Inverses of trigonometric functions

Displacement during a random walk

2.13 Trigonometric equations

VHF tracking for terrestrial animals

2.14 Modifying the basic trigonometric graphs

Nocturnal flowering in dry climates

2.15 Superimposing trigonometric functions

More realistic model of nocturnal flowering

2.16 Spectral analysis

Dominant frequencies in density fluctuations of Norwegian lemming populations

Spectral analysis of oceanographic covariates

2.17 Fractal geometry.

Availability of coastal habitat

Fractal dimension of the Koch curve

3. How to change things, one step at a time Sequences, difference equations and logarithms

3.1 Sequences

Reproductive output in social wasps

Unrestricted population growth

3.2 Difference equations

More realistic models of population growth

3.3 Higher order difference equations

Delay-difference equations in a biennial plant

3.4 Initial conditions and parameters

3.5 Solutions of a difference equation

3.6 Equilibrium solutions

Harvesting an unconstrained population

Visualising the equilibria

3.7 Stable and unstable equilibria

Parameter sensitivity and ineffective fishing quotas

Stable and unstable equilibria in a density-dependent population

3.8 Investigating stability

Cobweb plot for an unconstrained, harvested population

Conditions for stability under unrestricted growth

3.9 Chaos

Chaos in a model with density dependence

3.10 Exponential function

Modelling bacterial loads in continuous time

A negative blue tit? Using exponential functions to constrain models

3.11 Logarithmic function

Log-transforming population time series

3.12 Logarithmic equations

4. How to change things, continuously Derivatives and their applications

4.1 Average rate of change

Seasonal tree growth

Tree growth

4.2 Instantaneous rate of change

4.3 Limits

Methane concentration around termite mounds

4.4 The derivative of a function

Plotting change in tree biomass

Linear tree growth

4.5 Differentiating polynomials

Spatial gradients

4.6 Differentiating other functions

Consumption rates of specialist predators

4.7 The chain rule.

Diurnal rate of change in the attendance of insect pollinators

4.8 Higher order derivatives

4.9 Derivatives of functions of many variables

The slope of the sea-floor

4.10 Optimisation

Maximum rate of disease transmission

The marginal value theorem

4.11 Local stability for difference equations

Unconstrained population growth

Density dependence and proportional harvesting

4.12 Series expansions

5. How to work with accumulated change Integrals and their applications

5.1 Antiderivatives

Invasion fronts

Diving in seals

5.2 Indefinite integrals

Allometry

5.3 Three analytical methods of integration

Stopping invasion fronts

5.4 Summation

Metapopulations

5.5 Area under a curve

Swimming speed in seals

5.6 Definite integrals

5.7 Some properties of definite integrals

Total reproductive output in social wasps

Net change in number of birds at migratory stop-over

Total number of arrivals and departures at migratory stop-over

5.8 Improper integrals

Failing to stop invasion fronts

5.9 Differential equations

A differential equation for a plant invasion front

5.10 Solving differential equations

Exponential population growth in continuous time

Constrained growth in continuous time

5.11 Stability analysis for differential equations

The Levins model for metapopulations

6. How to keep stuff organised in tables Matrices and their applications

6.1 Matrices

Plant community composition

Inferring diet from fatty acid analysis

6.2 Matrix operations

Movement in metapopulations

6.3 Geometric interpretation of vectors and square matrices.

Random walks as sequences of vectors

6.4 Solving systems of equations with matrices

6.5 Markov chains

Redistribution between population patches

6.6 Eigenvalues and eigenvectors

Growth in patchy populations

Metapopulation growth

6.7 Leslie matrix models

Stage-structured seal populations

Equilibrium of linear Leslie model

Stability in a linear Leslie model

Stable age structure in a linear Leslie model

6.8 Analysis of linear dynamical systems

A fragmented population in continuous time

Phase-space for a two-patch metapopulation

Stability analysis of a two-patch metapopulation

6.9 Analysis of nonlinear dynamical systems

The Lotka-Volterra, predator-prey model

Stability analysis of the Lotka-Volerra model

7 How to visualise and summarise data Descriptive statistics

7.1 Overview of statistics

7.2 Statistical variables

Activity budgets in honey bees

7.3 Populations and samples

Production of gannet chicks

7.4 Single-variable samples

7.5 Frequency distributions

Activity budgets from different studies

Visualising activity budgets

Height of tree ferns

Gannets on Bass rock

7.6 Measures of centrality

Chick rearing in red grouse

Swimming speed in grey seals

Median of chicks reared by red grouse

7.7 Measures of spread

Gannet foraging

7.8 Skewness and kurtosis

7.9 Graphical summaries

7.10 Data sets with more than one variable

7.11 Association between qualitative variables

Community recovery in abandoned fields

7.12 Association between quantitative variables

Height and root depth of tree ferns

7.13 Joint frequency distributions

Mosaics of abandoned fields.

Joint distribution of tree height and root depth.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and indexes.

ISBN:

9786613405357

9781283405355

1283405350

9781119991724

1119991722

9781119991588

1119991587

9781119991595

1119991595