Introduction

This Task View contains information about using R to analyse ecological and environmental data.

The base version of R ships with a wide range of functions for use within the field of environmetrics. This functionality is complemented by a plethora of packages available via CRAN, which provide specialist methods such as ordination & cluster analysis techniques. A brief overview of the available packages is provided in this Task View, grouped by topic or type of analysis. As a testament to the popularity of R for the analysis of environmental and ecological data, a special volume of the Journal of Statistical Software was produced in 2007.

Those useRs interested in environmetrics should consult the Spatial view. Complementary information is also available in the Multivariate and Cluster task views.

If you have any comments or suggestions for additions or improvements, then please contact the maintainer .

A list of available packages and functions is presented below, grouped by analysis type.

Modelling species responses and other data

Analysing species response curves or modeling other data often involves the fitting of standard statistical models to ecological data and includes simple (multiple) regression, Generalised Linear Models (GLM), extended regression (e.g. Generalised Least Squares [GLS]), Generalised Additive Models (GAM), and mixed effects models, amongst others.

• The base installation of R provides lm() and glm() for fitting linear and generalised linear models, respectively.
• Generalised least squares and linear and non-linear mixed effects models extend the simple regression model to account for clustering, heterogeneity and correlations within the sample of observations. Package nlme provides functions for fitting these models. The package is supported by Pinheiro & Bates (2000) Mixed-effects Models in S and S-PLUS , Springer, New York. An updated approach to mixed effects models, which also fits Generalised Linear Mixed Models (GLMM) and Generalised non-Linear Mixed Models (GNLMM) is provided by the lme4 package, though this is currently beta software and does not yet allow correlations within the error structure.
• Recommended package mgcv fits GAMs and Generalised Additive Mixed Models (GAMM) with automatic smoothness selection via generalised cross-validation. The author of mgcv has also written a companion monograph, Wood (2006) Generalized Additive Models; An Introduction with R Chapman Hall/CRC, which has an accompanying package gamair.
• Alternatively, package gam provides an implementation of the S-PLUS function gam() that includes LOESS smooths.
• Proportional odds models for ordinal responses can be fitted using polr() in the MASS package, of Bill Venables and Brian Ripley.
• A negative binomial family for GLMs to model over-dispersion in count data is available in MASS.
• Models for overdispersed counts and proportions
  • Package pscl also contains several functions for dealing with over-dispersed count data. Poisson or negative binomial distributions are provided for both zero-inflated and hurdle models.
  • aod provides a suite of functions to analyse overdispersed counts or proportions, plus utility functions to calculate e.g. AIC, AICc, Akaike weights.
• Detecting change points and structural changes in parametric models is well catered for in the segmented package and the strucchange package respectively. segmented has recently been the subject of an R News article ( R News, volume 8 issue 1 ).

Tree-based models

Tree-based models are being increasingly used in ecology, particularly for their ability to fit flexible models to complex data sets and the simple, intuitive output of the tree structure. Ensemble methods such as bagging, boosting and random forests are advocated for improving predictions from tree-based models and to provide information on uncertainty in regression models or classifiers.

Tree-structured models for regression, classification and survival analysis, following the ideas in the CART book, are implemented in

• recommended package rpart
• party provides an implementation of conditional inference trees which embed tree-structured regression models into a well defined theory of conditional inference procedures

Multivariate trees are available in

• package mvpart, which provides an adaptation of rpart for multivariate responses.
• package party can also handle multivariate responses.

Ensemble techniques for trees:

• The Random Forest method of Breiman and Cutler is implemented in randomForest, providing classification and regression based on a forest of trees using random inputs
• Package ipred provides functions for improved predictive models for classification, regression and survival problems.

Graphical tools for the visualization of trees are available in packages maptree and pinktoe.

Packages mda and earth implement Multivariate Adaptive Regression Splines (MARS), a technique which provides a more flexible, tree-based approach to regression than the piecewise constant functions used in regression trees.

Ordination

R and add-on packages provide a wide range of ordination methods, many of which are specialised techniques particularly suited to the analysis of species data. The two main packages are ade4 and vegan. ade4 derives from the traditions of the French school of Analyse des Donnees and is based on the use of the duality diagram. vegan follows the approach of Mark Hill, Cajo ter Braak and others, though the implementation owes more to that presented in Legendre & Legendre (1988) Numerical Ecology, 2 ^nd English Edition , Elsevier. Where the two packages provide duplicate functionality, the user should choose whichever framework that best suits their background.

• Principal Components (PCA) is available via the prcomp() function. rda() (in package vegan), pca() (in package labdsv) and dudi.pca() (in package ade4), provide more ecologically-orientated implementations. A form of PCA used in the climate and climate change fields is Empirical Orthogonal Function (EOF) analysis and is implemented in EOF() in package clim.pact.
• Redundancy Analysis (RDA) is available via rda() in vegan and pcaiv() in ade4.
• Canonical Correspondence Analysis (CCA) is implemented in cca() in both vegan and ade4.
• Detrended Correspondence Analysis (DCA) is implemented in decorana() in vegan.
• Principal coordinates analysis (PCO) is implemented in dudi.pco() in ade4, pco() in labdsv, pco() in ecodist, and cmdscale() in package MASS.
• Non-Metric multi-Dimensional Scaling (NMDS) is provided by isoMDS() in package MASS and nmds() in ecodist. nmds(), a wrapper function for isoMDS(), is also provided by package labdsv. vegan provides helper function metaMDS() for isoMDS(), implementing random starts of the algorithm and standardised scaling of the NMDS results. The approach adopted by vegan with metaMDS() is the recommended approach for ecological data.
• Coinertia analysis is available via coinertia() and mcoa(), both in ade4.
• Co-correspondence analysis to relate two ecological species data matrices is available in cocorresp.
• Canonical Correlation Analysis (CCoA - not to be confused with CCA, above) is available in cancor() in standard package stats.
• Procrustes rotation is available in procrustes() in vegan and procuste() in ade4, with both vegan and ade4 providing functions to test the significance of the association between ordination configurations (as assessed by Procrustes rotation) using permutation/randomisation and Monte Carlo methods.
• Constrained Analysis of Principal Coordinates (CAP), implemented in capscale() in vegan, fits constrained ordination models similar to RDA and CCA but with any any dissimilarity coefficient.
• Constrained Quadratic Ordination (CQO; formerly known as Canonical Gaussian Ordination (CGO)) is a maximum likelihood estimation alternative to CCA fit by Quadratic Reduced Rank Vector GLMs. Constrained Additive Ordination (CAO) is a flexible alternative to CQO which uses Quadratic Reduced Rank Vector GAMs. These methods and more are provided in Thomas Yee's VGAM package.
• Fuzzy set ordination (FSO), an alternative to CCA/RDA and CAP, is available in package fso. fso complements a recent paper on fuzzy sets in the journal Ecology by Dave Roberts (2008, Statistical analysis of multidimensional fuzzy set ordinations. Ecology 89(5) , 1246-1260).
• See also the Multivariate task view for complementary information.

Dissimilarity coefficients

Much ecological analysis proceeds from a matrix of dissimilarities between samples. A large amount of effort has been expended formulating a wide range of dissimilarity coefficients suitable for ecological data. A selection of the more useful coefficients are available in R and various contributed packages.

Standard functions that produce, square, symmetric matrices of pair-wise dissimilarities include:

• dist() in standard package stats
• daisy() in recommended package cluster
• vegdist() in vegan
• dsvdis() in labdsv
• Dist() in amap
• distance() in ecodist
• a suite of functions in ade4

Function distance() in package analogue can be used to calculate dissimilarity between samples of one matrix and those of a second matrix. The same function can be used to produce pair-wise dissimilarity matrices, though the other functions listed above are faster. distance() can also be used to generate matrices based on Gower's coefficient for mixed data (mixtures of binary, ordinal/nominal and continuous variables). Function daisy() in package cluster provides a faster implementation of Gower's coefficient for mixed-mode data than distance() if a standard dissimilarity matrix is required.

Cluster analysis

Cluster analysis aims to identify groups of samples within multivariate data sets. A large range of approaches to this problem have been suggested, but the main techniques are hierarchical cluster analysis, partitioning methods, such as k -means, and finite mixture models or model-based clustering. In the machine learning literature, cluster analysis is an unsupervised learning problem.

The Cluster task view provides a more detailed discussion of available cluster analysis methods and appropriate R functions and packages.

Hierarchical cluster analysis:

• hclust() in standard package stats
• Recommended package cluster provides functions for cluster analysis following the methods described in Kaufman and Rousseeuw (1990) Finding Groups in data: an introduction to cluster analysis , Wiley, New York
• hcluster() in amap
• pvclust is a package for assessing the uncertainty in hierarchical cluster analysis. It provides approximately unbiased p -values as well as bootstrap p -values.

Partitioning methods:

• kmeans() in stats provides k -means clustering
• cmeans() in e1071 implements a fuzzy version of the k -means algorithm
• Recommended package cluster also provides functions for various partitioning methodologies.

Mixture models and model-based cluster analysis:

• mclust and flexmix provide implementations of model-based cluster analysis.
• prabclus clusters a species presence-absence matrix object by calculating an MDS from the distances, and applying maximum likelihood Gaussian mixtures clustering to the MDS points. The maintainer's, Christian Hennig, web site contains several publications in ecological contexts that use prabclus, especially Hausdorf & Hennig (2007; Oikos 116 (2007), 818-828 ).

Ecological theory

There is a growing number of packages and books that focus on the use of R for theoretical ecological models.

• vegan provides a wide range of functions related to ecological theory, such as diversity indices (including the so-called Hill's numbers [e.g. Hill's N ² ] and rarefaction), ranked abundance diagrams, Fisher's log series, Broken Stick model, Hubbell's abundance model, amongst others.
• The vegetarian provides the diversity measures suggested by Jost ( 2006, Oikos 113(2), 363-375 ; 2007, Ecology 88(10), 2427-2439 ).
• untb provides a collection of utilities for biodiversity data, including the simulation ecological drift under Hubbell's Unified Neutral Theory of Biodiversity, and the calculation of various diagnostics such as Preston curves.
• primer is a support software for Stevens ( 2009, A Primer of Ecology with R , Springer ). The package provides a variety of functions for modeling ecological data and basic theoretical ecology, including functions related to demographic matrix models, metapopulation and source-sink models, host-parasitoid and disease models, multiple basins of attraction, the storage effect, neutral theory, and diversity partitioning.
• Package BiodiversityR provides a GUI for biodiversity and community ecology analysis.
• Function betadiver() in vegan implements all of the diversity indices reviewed in Koleff et al (2003; Journal of Animal Ecology 72(3), 367-382 ). betadiver() also provides a plot method to produce the co-occurrence frequency triangle plots of the type found in Koleff et al (2003).
• Function betadisper(), also in vegan, implements Marti Anderson's distance-based test for homogeneity of multivariate dispersions (PERMDISP, PERMDISP2), a multivariate analogue of Levene's test (Anderson 2006; Biometrics 62, 245-253 ). Anderson et al (2006; Ecology Letters 9(6), 683-693 ) demonstrate the use of this approach for measuring beta diversity.

Population dynamics

Estimating vital rates (i.e., growth, survival, and reproduction), especially in monitoring studies of tagged individuals over time:

• age-specific survival and reproduction using life tables in demogR,
• stage-specific vital rates using transition frequency tables in popbio,
• mark and recapture methods in mra and Rcapture when tagged individuals cannot be consistently detected identified.

Modeling population growth rates:

• Packages demogR and popbio can be used to construct and analyse age- or stage-specific matrix population models

Environmental time series

• Time series objects in R are created using the ts() function, though see tseries, zoo and its below for alternatives.
• Classical time series functionality is provided by the ar(), and arima() functions in standard package stats for autoregressive (AR), moving average (MA), autoregressive moving average (ARMA) and integrated ARMA (ARIMA) models.
• The dse package provide a variety of more advanced estimation methods and multivariate time series analysis.
• Packages tseries and zoo provide general handling and analysis of time series data.
• Irregular time series can be handled using packages zoo and its, as well as by irts() in package tseries.
• pastecs provides functions specifically tailored for the analysis of space-time ecological series.
• strucchange allows for testing, dating and monitoring of structural change in linear regression relationships.
• Detecting change points in time series data --- see segmented above .
• The surveillance package implements statistical methods for the modeling of and change-point detection in time series of counts, proportions and categorical data. Focus is on outbreak detection in count data time series.
• Package dynlm provides a convenient interface to fitting time series regressions via ordinary least squares
• Package dyn provides a different approach to that of dynlm, which allows time series data to be used with any regression function written in the style of lm such as lm(), glm(), loess(), rlm() and lqs() from MASS, randomForest() (package randomForest), rq() (package quantreg) amongst others, whilst preserving the time series information.

Spatial data analysis

See the Spatial CRAN Task View for an overview of spatial analysis in R.

Extreme values

ismev provides functions for models for extreme value statistics and is support software for Coles (2001) An Introduction to Statistical Modelling of Extreme Values , Springer, New York. Other packages for extreme value theory include:

• evir
• evd
• evdbayes, which provides a Bayesian approach to extreme value theory
• extRemes
• POT, which provides functions for the Generalized Pareto Distribution and the Peaks Over Threshold method
• The SpatialExtremes provides several approaches for modelling spatial extreme events.

Phylogenetics and evolution

Packages specifically tailored for the analysis of phylogenetic and evolutionary data include:

• ape
• ouch
• PHYLOGR

UseRs may also be interested in Paradis (2006) Analysis of Phylogenetics and Evolution with R , Springer, New York, a book in the new UseR series from Springer.

Other packages

Several other relevant contributed packages for R are available that do not fit under nice headings.

• adehabitat complements ade4 and provides a collection of tools for the analysis of habitat selection by animals.
• Andrew Robinson's equivalence package provides some statistical tests and graphics for assessing tests of equivalence. Such tests have similarity as the alternative hypothesis instead of the null. The package contains functions to perform two one-sided t-tests (TOST) and paired t-tests of equivalence.
• Thomas Petzoldt's simecol package provides an object oriented framework and tools to simulate ecological (and other) dynamic systems within R. See the simecol website and a R News article on the package for further information.
• Functions for circular statistics are found in CircStats and circular.
• Package eco fits Bayesian models of ecological inference to 2 x 2 contingency tables.
• Package e1071 provides functions for latent class analysis, short time Fourier transform, fuzzy clustering, support vector machines, shortest path computation, bagged clustering, naive Bayes classifier, and more...
• Package seacarb provides functions for calculating parameters of the seawater carbonate system.
• Package NADA contains methods described by Dennis R. Helsel in his book Nondetects And Data Analysis: Statistics for Censored Environmental Data .
• Package pcurve fits a principal curve to a numeric multivariate dataset in arbitrary dimensions. Produces diagnostic plots.
• Package clim.pact contains R functions for retrieving data, making climate analysis and downscaling of monthly mean and daily mean global climate scenarios.
• Package SoPhy provides soil physics tools in R including water flow by SWMS_2D.
• Package pgirmess provides a suite of miscellaneous functions for data analysis in ecology.
• mefa provides functions for handling and reporting on multivariate count data in ecology and biogeography.
• analogue fits Modern Analogue Technique and Weighted Averaging transfer function models for calibration (aka bioindication), for prediction of environmental data from species data
• Stephen Sefick's StreamMetabolism package contains function for calculating stream metabolism characteristics, such as GPP, NDM, and R, from single station diurnal Oxygen curves.