How to be a quantitative ecologist
Subtitle: the 'A to R' of green mathematics and statistics
By: Jason Matthiopoulos
Publisher: Wiley
Published: 2011
Place of publication: Chichester, West Sussex, U.K
Language: eng
Number of pages: 467
ISBN-13: 9780470699782; 9780470699799
Subjects: Ecology; Vocational guidance; Mathematics; Quantitative research; Research; Quantitative analysts
Description: "The book will comprise two equal parts on mathematics and statistics with emphasis on quantitative skills"--
Notes: Includes bibliographical references and indexes.
Table of contents: title: Machine generated contents note: 0. How to start a meaningful relationship with your computer Introduction to R; title: 0.1 What is R?; title: 0.2 Why use R for this book?; title: 0.3 Computing with a scientific package like R; title: 0.4 Installing and interacting with R; title: 0.5 Style conventions; title: 0.6 Valuable R accessories; title: 0.7 Getting help; title: 0.8 Basic R usage; title: 0.9 Importing data from a spreadsheet; title: 0.10 Storing data in data frames; title: 0.11 Exporting data from R; title: 0.12 Further reading; title: 0.13 References; title: 1. How to make mathematical statements Numbers, equations and functions 1.1 Quantitative and qualitative scales? Habitat classifications; title: 1.2 Numbers? Observations of spatial abundance; title: 1.3 Symbols? Population size and carrying capacity; title: 1.4 Logical operations; title: 1.5 Algebraic operations? Size matters in garter snakes; title: 1.6 Manipulating numbers; title: 1.7 Manipulating units; title: 1.8 Manipulating expressions? Energy acquisition in voles; title: 1.9 Polynomials? The law of mass action in epidemiology; title: 1.10 Equations; title: 1.11 First order polynomial equations? Linking population size to population composition; title: 1.12 Proportionality and scaling? Simple mark-recapture? Converting density to population size; title: 1.13 Second and higher-order polynomial equations? Estimating the number of infected animals from the rate of infection; title: 1.14 Systems of polynomial equations? Deriving population structure from data on population size; title: 1.15 Inequalities? Minimum energetic requirements in voles; title: 1.16 Coordinate systems? Non-cartesian map projections; title: 1.17 Complex numbers; title: 1.18 Relations and functions? Food webs? Mating systems in animals; title: 1.19 The graph of a function? Two aspects of vole energetics; title: 1.20 First order polynomial functions? Population stability in a time series? Population stability and population change? Visualising goodness-of-fit; title: 1.21 Higher-order polynomial functions; title: 1.22 The relationship between equations and functions? Extent of an epidemic when the transmission rate exceeds a critical value; title: 1.23 Other useful functions? Modelling saturation; title: 1.24 Inverse functions; title: 1.25 Functions of more than one variables; title: 1.26 Further reading; title: 1.27 References; title: 2. How to describe regular shapes and patterns Geometry and trigonometry; title: 2.1 Primitive elements; title: 2.2 Axioms of Euclidean geometry? Suicidal lemmings, parsimony, evidence and proof; title: 2.3 Propositions? Radio-tracking of terrestrial animals; title: 2.4 Distance between two points? Spatial autocorrelation in ecological variables; title: 2.5 Areas and volumes? Hexagonal territories; title: 2.6 Measuring angles? The bearing of a moving animal; title: 2.7 The trigonometric circle? The position of a seed following dispersal; title: 2.8 Trigonometric functions; title: 2.9 Polar coordinates? Random walks; title: 2.10 Graphs of trigonometric functions; title: 2.11 Trigonometric identities? A two-step random walk; title: 2.12 Inverses of trigonometric functions? Displacement during a random walk; title: 2.13 Trigonometric equations? VHF tracking for terrestrial animals; title: 2.14 Modifying the basic trigonometric graphs? Nocturnal flowering in dry climates; title: 2.15 Superimposing trigonometric functions? More realistic model of nocturnal flowering in dry climates; title: 2.16 Spectral analysis? Dominant frequencies in Norwegian lemming populations? Spectral analysis of oceanographic covariates; title: 2.17 Fractal geometry? Availability of coastal habitat ? Fractal dimension of the Koch curve; title: 2.18 Further reading; title: 2.19 References; title: 3. How to change things, one step at a time Sequences, difference equations and logarithms; title: 3.1 Sequences? Reproductive output in social wasps? Unrestricted population growth; title: 3.2 Difference equations? More realistic models of population growth; title: 3.3 Higher-order difference equations? Delay-difference equations in a biennial herb; title: 3.4 Initial conditions and parameters; title: 3.5 Solutions of a difference equation; title: 3.6 Equilibrium solutions? Unrestricted population growth with harvesting? Visualising the equilibria; title: 3.7 Stable and unstable equilibria? Parameter sensitivity and ineffective fishing quotas? Stable and unstable equilibria in a density-dependent population; title: 3.8 Investigating stability? Cobweb plot for unconstrained, harvested population? Conditions for stability under unrestricted growth; title: 3.9 Chaos? Deterministic chaos in a model with density-dependence; title: 3.10 Exponential function? Modelling bacterial loads in continuous time? A negative blue tit? Using exponential functions to constrain models; title: 3.11 Logarithmic function? Log-transforming population time series; title: 3.12 Logarithmic equations; title: 3.13 Further reading; title: 3.14 References; title: 4. How to change things, continuously Derivatives and their applications; title: 4.1 Average rate of change? Seasonal tree growth; title: 4.2 Instantaneous rate of change; title: 4.3 Limits ? Pheromone concentration around termite mounds; title: 4.4 The derivative of a function? Plotting change in tree biomass? Linear tree growth; title: 4.5 Differentiating polynomials? Spatial gradients; title: 4.6 Differentiating other functions? Consumption rates of specialist predators; title: 4.7 The chain rule? Diurnal rate of change in the attendance of insect pollinators; title: 4.8 Higher-order derivatives? Spatial gradients and foraging in beaked whales; title: 4.9 Derivatives for functions of many variables? The slope of the sea floor; title: 4.10 Optimisation? Maximum rate of disease transmission? The marginal value theorem; title: 4.11 Local stability for difference equations? Unconstrained population growth? Density dependence and proportional harvesting; title: 4.12 Series expansions; title: 4.13 Further reading; title: 4.14 References; title: 5. How to work with accumulated change Integrals and their applications; title: 5.1 Antiderivatives? Invasion fronts? Diving in seals; title: 5.2 Indefinite integrals? Allometry; title: 5.3 Three analytical methods of integration? Stopping invasion fronts; title: 5.4 Summation? Metapopulations; title: 5.5 Area under a curve? Swimming speed in seals; title: 5.6 Definite integrals? Swimming speed in seals