How to be a quantitative ecologist : the A to R of green mathematics and statistics Machine generated contents note: 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 Further reading 0.13 References 1. How to make mathematical statements Numbers equations and functions 1.1 Quantitative and qualitative 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 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 Linking population size to population composition 1.12 Proportionality and scaling 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 Modelling saturation 1.24 Inverse functions 1.25 Functions of more than one variables 1.26 Further reading 1.27 References 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 in dry climates 2.16 Spectral analysis Dominant frequencies in Norwegian lemming populations Spectral analysis of oceanographic covariates 2.17 Fractal geometry Availability of coastal habitat  Fractal dimension of the Koch curve 2.18 Further reading 2.19 References 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 herb 3.4 Initial conditions and parameters 3.5 Solutions of a difference equation 3.6 Equilibrium solutions Unrestricted population growth with harvesting 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 unconstrained harvested population Conditions for stability under unrestricted growth 3.9 Chaos Deterministic 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 3.13 Further reading 3.14 References 4. How to change things continuously Derivatives and their applications 4.1 Average rate of change Seasonal tree growth 4.2 Instantaneous rate of change 4.3 Limits  Pheromone 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 Spatial gradients and foraging in beaked whales 4.9 Derivatives for 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 4.13 Further reading 4.14 References 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 Swimming speed in seals The book will comprise two equal parts on mathematics and statistics with emphasis on quantitative skills