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

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

Detalles Bibliográficos
Autor principal: Matthiopoulos, Jason (-)
Formato: Libro electrónico
Idioma:Inglés
Publicado: Chichester, West Sussex, U.K. : Wiley 2011.
Edición:1st ed
Materias:
Ecology > Mathematics.
Ecology > Research.
Ecology > Vocational guidance.
Mathematics > Vocational guidance.
Quantitative analysts.
Quantitative research.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009664730606719
Tabla de Contenidos:
  • 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
  • Two aspects of vole energetics
  • Further reading
  • 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
  • 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
  • Further reading
  • 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 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
  • Further reading
  • References
  • 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
  • Spatial gradients
  • 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
  • Further reading
  • 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
  • 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
  • Constrained growth in continuous time
  • The Levins model for metapopulations
  • Further reading
  • References
  • 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
  • Plant community composition
  • 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
  • Further reading
  • References
  • 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 in honey bees
  • 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.

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