How to be a quantitative ecologist: the 'A to R' of green mathematics and statistics
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| Format: | Book |
| Language: | English |
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Chichester
Wiley
2011
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| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | http://catalogimages.wiley.com/images/db/jimages/9780470699782.jpg Inhaltsverzeichnis |
| Physical Description: | XIX, 467 S. Ill., graph. Darst. |
| ISBN: | 9780470699782 9780470699799 9781119991595 |
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| adam_text | How TO BE A QUANTITATIVE
ECOLOGIST
THE A TO R OF GREEN MATHEMATICS AND STATISTICS
Jason Matthiopoulos
University of St Andrews, Scotland, UK
)WILEY
A John Wiley amp; Sons, Ltd , Publication
How to be a
Quantitative Ecologist
The A to R of green
mathematics amp;
statistics
How I chose to write this book, and why you might choose to
read it xvii
Preface
0 How to start a meaningful relationship with your computer 1
Introduction to R
0 1 What is R?
0 3 Computing with a scientific package like R
pinstaljingandinteractingwith-R^~:; v,
0,5 Style conventions
Je^Jcfessories-—— —
0 7 Getting help
108 Basic R usage
209 Importing data from a spreadsheet
0 10 Storing data in data frames
p MExporting data from R
6 Further reading
7 References
VIII CONTENTS
1; How to make mathematical statements 15
1 u
:/l1 Qualitative and quantitative scales
• Habitat classifications, - „
1 2 Numbers / /
• Observations of spatial abundance
1 3 Symbols
• Population size and carrying
capac i ty
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 act ion
in epidemiology
1 10 Equations
1 11 First order polynomial equations
• Population size and composit ion
1 12 Proportionality and scaling: a special kind
of first order polynomial equation
• Simple mark-recapture
• Converting density to populat ion 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
Numbers, equations and functions
16 • Deriving population structure from data
on population size
;••*- • - J
17 115 Inequalities
v
• - • Minimum energetic requirements in
{/* voles
1 U Coordinate systems
• Non-Cartesian map projections
21 1 17 Complex numbers
21 1 18 Relations and functions
• Food webs
• Mat ing systems in animals
1 19 The graph of a function
26 • Two aspects of vole energetics
26 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 55
1 22 The relationship between equations and
functions 57
• Extent of a n ep idem ic when the
transmission rate exceeds a cr i t ical va lue
341 23 Other useful functions 58
1 24 Inverse functions 60
1 25 Functions of more than one variable 62
36 • Two aspects of vole energet ics
Further reading 64
38 References 65
CONTENTS
2 How to describe regular shapes and patterns 67
2 1 Primitive elements
2 2 Axioms of Euclidean geometry
• Suicidal lemmings, parsimony,
evidence and proof t
2 3 Propositions
• Radio- t racking of terrestrial anirpdls •
2 4 Distance between two points )
• Spatial autocorrelationWecoiogical
variables
^ ^G^epmetry^gnd triggppmetry
2 11 Trigonometric identities fsff1 : ,
;• A two-s tep rando);n,wdll«,, -
,2 12 Inye rses of trigonometric functions^,
v , •^DispiqGeijhentjduring a r andom w a
2fV3Trigonometricequations - ;
— • VHF tracking for terrestrial animals
2 5 Areas and volumes 78
• Hexagona l territories
2 6 Measuring angles 80
• The bear ing of a mov ing an imal
2 7 The trigonometric circle 82
• The position of a seed fol lowing
dispersal
2 8 Trigonometric functions 83
2 9 Polar coordinates 85
• Random walks
2 10 Graphs of trigonometric functions 8 6
2:14 Modifying the basic trigonometfic graphs
• • Nocturnal flowering in dry climates
v2J5 Superimposing trigonometric functions
•More realistic mode l of nocturnal
f lowering
2 16 Spectral analysis
• Dominant frequencies in density
fluctuations of Norwegian lemming
populations
• Spectral analysis of oceanographic
covariates
2 17 Fractal geometry 102
• Availability of coastal habitat
• Fractal dimension of the Koch curve
Further reading 105
References 106
3 How to change things, one step at a time 107
Sequences, difference equations and logarithms
3 1 Sequences
• Reproductive output in social wasps
• Unrestricted population growth
108 3 4 Initial conditions and parameters
3 5 Solutions of a difference equation
3 2 Difference equations 111
• More realistic models of popu la t ion
growth
JiJqujlibrium solutions
3 3 Higher order difference equations
• Delay-difference equations in a
biennial plant
• i ! ,
Harvestihg-an unconstrained
population „
• Visualising the equilibria ° i
/ -, 114 y, / )U
)
A V /
CONTENTS
3 7 Stable and unstable equilibria 119
• Parameter sensitivity and ineffect ive
fishing quotas
• Stable and unstable equilibria in a
densi ty-dependent popu la t ion
3 8 Investigating stability 122
• 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 130
• Modelling bacterial loads in continuous
time
• A negative blue tit? Using exponential
functions to constrain models
3 11 Logarithmic function 132
• Log-transforming popu la t ion t ime
series
3 12 Logarithmic equations 135
Further reading 136
References 136
4 How to change things, continuously 137
Derivatives and thehqpplications
4 1 Average rate of change 138
• Seasonal tree growth
• Tree growth
4 2 Instantaneous rate of change 141
4 3 Limits 142
• Methane concentrat ion around termite
mounds
4 4 The derivative of a function
• Plotting c hange in tree biomass
• Linear tree growth
4 5 Differentiating polynomials
• Spatial gradients
4 6 Differentiating other functions
• Consumpt ion rates of specialist
predators
4 7 The chain rule
• Diurnal rate of chdngejn the arte~hdance
of insect pollinators
4 8 Higher order derivatives
• Spatial gradients
4 9 Derivatives of functions of many variables
• The slope of the sea-flooo-^^1
4 10 Optimisation x k
• Maximum rate of disease transrnission
• The marginal value theorem
4 11 Local stability for difference equations , /
• Unconstrained population growth
• Density dependence and proportional
harvesting
152 4 12 Series expansions
Further reading
155 References
CONTENTS
5 How to work with accumulated change 177
Integrals and their applications
5 1 Anfiderivatives
• Invasion fronts
• Diving in seals
5 2 Indefinite integrals
• Allometry
5 3 Three analytical methods of integration
• Stopping invasion fronts
5 4 Summation
• Metapopulat ions
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 reproduct ive ou tpu t in social
wasps
• Net change in number of birds a t
migratory stop-over
178 • Total numberof arrivals and departures at
migratory stop-over
/
5 8 Improper integrals 198
181 • Failing to stop invasion fronts Is
5 9 Differential equations 202 3?
182 • A differential equation for a plant ,-,^
invasion front /-: « ; !••
187 5 10 Solving differential equations • 203
• Exponential population growth in
continuous time
190 • Constrained growth in continuous time
5 11 Stability analysis for differential equations 209
193 • Constrained growth in cont inuous t ime
• The Levins mode l for metapopu la t ions
195 Further reading 212
References 212
6 How to keep stuff organised in tables 213
Matrices and their applications
6 1 Matrices
• Plant community composition
• Inferring diet from fatty acid analysis
214 6 6 Eigenvalues and^eigenyectors^/ 230 /
• • Growth in patchy pppulations • /
• Metapopulation growth : /
6 2 Matrix operations
• Movement in metapopulations
6 3 Geometric interpretation of vectors and
square matrices 221
• Random walks as sequences of vectors
217 6 7 Leslie matrix models
• Stage-structured seal populations
• Equilibrium of linear Leslie model
• Stability in a linear Leslie model • -y
• Stable age structure in a linear Leslie
model
6 4 Solving systems of equations with matrices
• Plant community composition
6 5 Markov chains
• Redistribution between population
patches
223 $-8 Analysis of linear dynamical systems 2 3 7
• A fragmented population in continuous
time
• Phase-space for a two-patch
227 metapopulation
• Stability analysis of a two-patch
• metapopulation
XII CONTENTS
6 9 Analysis of nonlinear dynamical systems
• The Lotka-Volterra, predator-prey
model
• Stability analysis of the Lotka-Volerra
model
243 Further reading
References
7 How to visualise and summarise data 251
Descriptive statistics^
7 1 Overview of statistics 252
7 2 Statistical variables 253
• Activity budgets in honey bees
7 3 Populations and samples 255
• Production of ganne t chicks
7 4 Single-variable samples 255
7 5 Frequency distributions 256
• Activity budgets in honey bees
• Activity budgets from different studies
• Visualising act ivi ty budgets
• Height of tree ferns
• Gannets on Bass rock
7 6 Measures of centrality 260
• Chick rearing in red grouse
• Swimming speed in grey seals
• Med ian of chicks reared by red grouse
7 7 Measures of spread 263
• Ganne t foraging
7 8 Skewness and kurtosis
7 9 Graphical summaries
sj 266
/ x - 3J 267 Y_
7 10 Data sets with more than oneVariable ^ } |j 268^ f
7 11 Association between qualitative variables % M amp;J-
• Community recovery in abanaSneoP
fields f ^J£(— •
7 12 Association between quantitative ^- p^ /,
variables Vi--t f ^
• Height and root depth of tree ferns: /
7 13 Joint frequency distributions
y
y
273
• Mosaics of abandgne d fields X*
• Joint distribution of tree he i gh t and root
depth ^y
» Joint and marginal distributions of tree
size
Further reading
References
8 How to put a value on uncertainty
8 1 Random experiments and event spaces 280
• Assumptions of r andom experiments
8 2 Events 281
• Plant occu r rence in survey quadra ts
• Over lapp ing events
• Mutual ly exclusive events
8 3 Frequentist probability 284
• Fluctuating f requency of newborn
male wi ldebeest
Probability ii
8 4 Equally likely events
• Something is certain to occur
(even if it is nothing)
• Undirected movement
/ • -
8 5 The union of events
• Seed germinatioj! on a gridded
landscape / •• • ;
• Coexisting sparrows
8 6 Conditional probability ~ v 288
• Territoriality and survival in red grouse
!
CONTENTS xm
8 7 Independent events
• Sex of successive calves
8 8 Total probability 292
• Seed germination in a heterogeneous
environment
291 • Null and alternative hypotheses for
wildebeest sex ratio
• Bayesian updat ing for wildebeest sex
ratio
8 9 Bayesian probability
• Does the sex ratio at birth deviate
from 1:1?
Further reading
293 References
9 How to identify different kinds of randomness 299
Probability distribptidns
9 1 Probability distributions
• Probability distribution of nominal
variables
9 2 Discrete probability distributions
• Beetle eggs per cluster: a coun t
• PMF for egg cluster size
• CDF for egg cluster size
9 3 Continuous probability distributions
• Are all fern heights equal ly likely?
• CDF for tree fern heights
• PDF for tree fern heights
9 4 Expectation
• Mean egg cluster size
• Expected tree fern heights
9 5 Named distributions
300 9 10 Numberof occurrence^ in a unit of time or
space: the Poisson distribution
/ • Data on p lant abundance
, „ - 9 11 The gentle art of waiting: geometric, [
/ negative binomial, exponential and gamma
:*• %J ^distributions /
(;
ix - ; ^Catastrophic events and sp ecies
extinctions - :••„•
( - • ({{ • •
304 9 12 Assigning probabilities to probabilities: the
; - beta and Dirichlet distributions i
9 13 Perfect symmetry: the normal distribution
30^ « v!/ eiglnt:distribution in voles
9 14 Because it looks right: using probability
distributions empirically 326
• A be ta prior for w i ldebeest sex at-bir th
-•319
-322
y
9 6 Equally likely events: the uniform distribution
• River ot ter home ranges
9 7 Hit or miss: the Bernoulli distribution
• Bernoulli births
9 8 Count of occurrences in a given number of
trials: the binomial distribution
• Wi ldebeest r ep roduc t i ve histories
• Wildebeest reproduct ive ou tpu t
9 9 Counting dierent types of occurrences:
the multinomial distribution
• Metapopulat ion transitions
310 9 15 Mixtures, outliers and the t-distribution
• Bimodal weight distribution in voles
9 16 Joint, conditional and marginal probability
312 distributions 329
• Feeding site fidelity in kittiwakes
313 9 17 The bivariate normal distribution 333
• Height and root d ep t h of tree ferns
9 18 Sums of random variables: the central limit
theorem
316 • Food provisioning in starlings
• Mixed-diet provisioning in starlings
CONTENTS
9 19 Products of random variables: the
log-normal distribution 337
• Stochastic exponent ia l g rowth
9 20 Modelling residuals: the chi-square
distribution 340
• Position of limpets relative to wa te r
9 21 Stochastic simulation
• Populat ion viability analysis
Further reading
References
10 How to see the forest from the trees 345
Estimation and testing
10 1 Estimators and their properties
• Sampling ganne tegg weights
10 2 Normal theory
10 3 Estimating the population mean
10 4 Estimating the variance of a normal
population
10 5 Confidence intervals
• Maximum likelihood estimator for
wildebeest sex ratio
10 10 Bayesianestimation , 364
• Bayesian-estimator for wildebeest sex
ratio i • •!
10 11 Link between maximum likelihood and , , ^
Bayesianestimation 368
• Compar ing ML and Bayes estimates of sex
ratio a t birth~~ / •
• Estimating the unknown parameters of the
gannet egg weight distribution )
10 6 Inference by bootstrapping 354 ;
• Bootstrap inference for gannet age -_, /
distribution •• -A -
/ i
10 12 Hypothesis testing: rationale
10 13 Tests for the population mean
10 7 More general estimation methods
• Estimating parameters for animal
movement
10 8 Estimation by least squares 358
• Weight distribution in voles of different
ages
• Mean weight in a cohor t of voles
10 9 Estimation by maximum likelihood 359
• Maximum likelihood estimation of mean
and var iance of vole weight distribution
10 15 Hypotheses about qualitative data
• Tree selection in Peruvian ants
• Niche part i t ioning in Peruvian ants
-10 14Tests comparing two different means ^-y 373
• Paired samples of gannet condition
• How to rank observations
10 16 Hypothesis testing debunked
Further reading
References
CONTENTS xv
11 How to separate the signal from the noise 381
Statistical modelling
11 1 Comparing the means of several
populations 382
• Samples of gannet condition
• Estimates of multiple population
averages r~
• Seeing the linear model as a special case
of the GLM V
• Likelihood for a log-linear-GLM
• Modejiog senescence in turtles
Estimating survival as a function of age
11 2 Simple linear regression
• Density dependence of gannet
condition
• Modelling density dependence of gannet
condition
11 3 Prediction 390
• Predicting dens i ty -dependent changes in
gannet condi t ion
11 4 How good is the best-fit line? 391
• Diagnostics for the density dependence
model
11 5 Multiple linear regression 394
• Comb ined effects of density and the
environment
11 6 Model selection 396
• Should the beat ing of a butterfly s wings
be used to explain ganne t condi t ion?
• Model selection by adjusted r2 and AIC
• Collinearity in covariates of ganne t
condit ion
gg ^ 11 8 Evaluation, diagnostics dnixmodel
selection for GLMs
11 9 Modelling dispersion
11 7 Generalised linear models
• Many response variables are
constrained
• Log-transforming fecundity data
• Modelling count data
11 10 Fitting more complicated models to 7 /
data: polynomials, interactions, nonlinear
regression 410
• Density dependenceand polynomial
terms
• Predation, immigrat ion and interact ion
terms
11 11 Letting the data suggest more
complicated models: smoothing 415
• Distribution a long a linear habi ta t
• Otter density estimation by kernel
smoothing
• Otter density estimation by G A M
11 12 Partitioning variation: mixed effects
models 419
• Samples of ganne t condi t ion
• Model l ing individual and colony
variat ion
• Why not use colony as a factor?
Further reading 422
References 4 2 3
12 How to measure similarity / 425
Multivariate methods
12 1 The problem with multivariate data 426 12 3 Principal components analysis 4 2 8
• Characterising environmental similarity • Collinearities between four
• Characterising patterns of occurrence environmental variables
• PCA for four environmental variables
12 2 Ordination in general 427
• Correlations represent r edundancy 2-4 Clustering in general 432
XVI CONTENTS
, Identifying functional groups in ecological 12 8 Logistic regression: two classes
communities
• Clustering data frame for Antarctic
species
12 5 Agglomerative hierarchical clustering 433
• Dend rog ram for An ta rc tic species
12 6 Nonhierarchical clustering: k means
analysis 434
12 7 Classification in general 435
Characterising fern habitat
Further reading
References
12 9 Logistic regression: many classes 438
• Classif ication of wha l e vocal isat ions
Appendix: Formulae
R Index
Index
|
| any_adam_object | 1 |
| author | Matthiopoulos, Jason |
| author_facet | Matthiopoulos, Jason |
| author_role | aut |
| author_sort | Matthiopoulos, Jason |
| author_variant | j m jm |
| building | Verbundindex |
| bvnumber | BV039529033 |
| classification_rvk | QT 000 WC 7000 |
| classification_tum | BIO 107f MAT 620f UMW 002f BIO 105f |
| ctrlnum | (OCoLC)732358560 (DE-599)HEB23184963X |
| dewey-full | 577.1 570.28 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 577 - Ecology 570 - Biology |
| dewey-raw | 577.1 570.28 |
| dewey-search | 577.1 570.28 |
| dewey-sort | 3577.1 |
| dewey-tens | 570 - Biology |
| discipline | Biologie Mathematik Wirtschaftswissenschaften Umwelt |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV039529033 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:05:35Z |
| institution | BVB |
| isbn | 9780470699782 9780470699799 9781119991595 |
| language | English |
| lccn | 2010051191 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024381356 |
| oclc_num | 732358560 |
| open_access_boolean | |
| owner | DE-188 DE-M49 DE-BY-TUM DE-20 DE-384 DE-Grf2 DE-703 |
| owner_facet | DE-188 DE-M49 DE-BY-TUM DE-20 DE-384 DE-Grf2 DE-703 |
| physical | XIX, 467 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Wiley |
| record_format | marc |
| spelling | Matthiopoulos, Jason Verfasser aut How to be a quantitative ecologist the 'A to R' of green mathematics and statistics Jason Matthiopoulos 1. publ. Chichester Wiley 2011 XIX, 467 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ökologie (DE-588)4043207-5 gnd rswk-swf Biostatistik (DE-588)4729990-3 gnd rswk-swf Biomathematik (DE-588)4139408-2 gnd rswk-swf Ökologie (DE-588)4043207-5 s Biomathematik (DE-588)4139408-2 s Biostatistik (DE-588)4729990-3 s DE-188 Erscheint auch als Online-Ausgabe, EPUB 978-1-119-99172-4 Erscheint auch als Online-Ausgabe, PDF 978-1-119-99158-8 http://catalogimages.wiley.com/images/db/jimages/9780470699782.jpg HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024381356&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Matthiopoulos, Jason How to be a quantitative ecologist the 'A to R' of green mathematics and statistics Ökologie (DE-588)4043207-5 gnd Biostatistik (DE-588)4729990-3 gnd Biomathematik (DE-588)4139408-2 gnd |
| subject_GND | (DE-588)4043207-5 (DE-588)4729990-3 (DE-588)4139408-2 |
| title | How to be a quantitative ecologist the 'A to R' of green mathematics and statistics |
| title_auth | How to be a quantitative ecologist the 'A to R' of green mathematics and statistics |
| title_exact_search | How to be a quantitative ecologist the 'A to R' of green mathematics and statistics |
| title_full | How to be a quantitative ecologist the 'A to R' of green mathematics and statistics Jason Matthiopoulos |
| title_fullStr | How to be a quantitative ecologist the 'A to R' of green mathematics and statistics Jason Matthiopoulos |
| title_full_unstemmed | How to be a quantitative ecologist the 'A to R' of green mathematics and statistics Jason Matthiopoulos |
| title_short | How to be a quantitative ecologist |
| title_sort | how to be a quantitative ecologist the a to r of green mathematics and statistics |
| title_sub | the 'A to R' of green mathematics and statistics |
| topic | Ökologie (DE-588)4043207-5 gnd Biostatistik (DE-588)4729990-3 gnd Biomathematik (DE-588)4139408-2 gnd |
| topic_facet | Ökologie Biostatistik Biomathematik |
| url | http://catalogimages.wiley.com/images/db/jimages/9780470699782.jpg http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024381356&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT matthiopoulosjason howtobeaquantitativeecologisttheatorofgreenmathematicsandstatistics |