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

Detalles Bibliográficos
Autor principal: Matthiopoulos, Jason (autor)
Formato: Libro
Lenguaje:English
Publicado: Chichester, West Sussex, U.K. : John Wiley and Sons, 2011.
Edición:First published.
Materias:
Ecología > Matemáticas.
Ecología > Orientación vocacional
Ecología > Investigación
Tabla de Contenidos:
  • 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

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