00000cmm a22000003i 4500 UP-1685594773862075693 Buklod 20170323085447.0 g||| | || || ta 170323s2011 enk u eng d 9781119991595 (eBook) 9781119991588 (eBook) (iLib)UPBAG-00023619760 DLC DML BAG rda eng ML-ebook Matthiopoulos, Jason author. How to be a quantitative ecologist [electronic resource] the 'A to R' of green mathematics and statistics Jason Matthiopoulos. Chichester, West Sussex, U.K. John Wiley & Sons Inc. 2011. 1 online resource (xix, 467 pages) illustrations text txt rdacontent computer rdamedia online resource cr rdacarrier 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 -- IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. "The book will comprise two equal parts on mathematics and statistics with emphasis on quantitative skills"--Provided by publisher. Electronic reproduction. Wiley Wiley & Sons, Inc. 2011. Available via World Wide Web through Wiley Online Library. Ecology Mathematics. Ecology Vocational guidance. Ecology Research. Quantitative analysts. Quantitative research. Mathematics Vocational guidance. Wiley Online Library. Available for University of the Philippines Baguio via Wiley Online Library. Click here to access http://dx.doi.org/10.1002/9781119991595 (viewed 17 September 2022) FO Monograph UPBAG UPBAG-MAIN ML-ebook Electronic Resource