Detecting Multivariate Changes in Biological Assemblages: Experimental Design and Data Analysis
Faculty of Natural and Agricultural Sciences, University of Western Australia, 15th – 26th November 2010
Lectures will be in the Agriculture lecture theatre, with computer sessions in the adjacent lab.
Analysis of assemblage data using PRIMER v6 (Bob Clarke & Ray Gorley)
Monday, 15 November
08:45-09:15
Introduction and house keeping
09:15-11:00
Lecture: Measures of resemblance (similarity/dissimilarity/distance) in multivariate structure for
assemblage & environmental data, including pre-treatment options (standardisation,
transformation, normalisation) and the effects of different coefficient choices
11:00-11:15
Coffee break
11:15-12:30
Lecture: Hierarchical clustering of samples (CLUSTER), including a global test for the presence of
multivariate structure in a priori unstructured biotic or environmental samples, using similarity
profiles (the SIMPROF test)
12:30-13:00
Demo: Introduction to PRIMER v6 routines
13:00-14:15
Lunch break
14:15-15:00
Lab session on similarity options, CLUSTER and SIMPROF
15:00-15:45
Lecture: Ordination (of environmental data) by Principal Components Analysis (PCA)
15:45-16:00
Coffee break
16:00-18:00
Lab session on ordination by PCA and own data
Tuesday, 16 November
09:00-10:00
Lecture: Ordination (of assemblage data) by non-metric Multi-Dimensional Scaling (MDS)
10:00-11:00
Lab session on MDS
11:00-11:15
Coffee break
11:15-13:00
Lecture: Multivariate testing for differences between groups of samples (1- and 2-way crossed and
nested ANOSIM)
13:00-14:15
Lunch break
14:15-15:45
Lab session on 1- and 2-way ANOSIM
15:45-16:00
Coffee break
16:00-16:30
Lecture: Determining variables which discriminate groups of samples (1- and 2-way similarity
percentages, SIMPER)
16:30-18:00
Lab session on SIMPER and own data
Wednesday,17 November
09:00-10:00
Lecture: Comparison of multivariate patterns 1: Linking potential environmental drivers to an
observed assemblage pattern, via the matching of multivariate structures (the BEST procedure)
10:00-11:00
Lab session on draftsman plots, PCA and BEST
11:00-11:15
Coffee break
11:15-11:45
Lecture: Linkage trees – a further technique for ‘explaining’ assemblage patterns by environmental
variables (LINKTREE, a non-parametric ‘classification and regression tree’ approach)
11:45-12:15
Lab session on LINKTREE
12:15-13:00
Lecture: Comparison of multivariate patterns 2: Global hypothesis tests of no agreement between
two resemblance matrices (RELATE, a non-parametric Mantel test), comparing assemblage (or
environmental) structure with linear or cyclic models in space and time
13:00-14:15
Lunch
14:15-15:45
Lab session on RELATE and model matrices
15:45-16:00
Coffee break
16:00-17:00
Lecture: Comparison of multivariate patterns 3&4: Test of no evidence for a biota-environment
link, allowing for the selection effects in finding an optimum match (the global BEST test);
stepwise form of the BEST routine, e.g. for species subsets determining overall assemblage pattern
17:00-18:00
Lab session on the global BEST test and BEST for species selection
Thursday, 18 November
09:00-10:00
Lecture: Diversity measures (DIVERSE) and comments on sampling properties and multivariate
treatment of multiple indices. Dominance plots and tests for differences between sets of curves
(DOMDIS), particle-size distributions etc
10:00-11:00
Lab session on DIVERSE, dominance plots and testing sets of curves (DOMDIS)
11:00-11:15
Coffee break
11:15-12:15
Lecture: Taxonomic (or phylogenetic) diversity and distinctness for quantitative data, or simple
species lists, as valid biodiversity measures (DIVERSE) over broad spatial and temporal scales;
sampling properties and testing structures (TAXDTEST)
12:15-13:00
Lab session on DIVERSE and TAXDTEST
13:00-14:15
Lunch
14:15-18:00
First all-afternoon lab session analysing own data using PRIMER v6
Throughout, participants will be given real data sets to analyse in the lab sessions, to exemplify the
main points. However, it is anticipated that they will wish to bring some of their own data to the
workshop, to analyse during this session (and similar ones next week), whilst the lecturer is on
hand to give advice. Data should be in numeric, rectangular arrays, with variables (e.g. species) as
rows, samples as columns, or vice-versa, in Excel or a text file. Non-numeric sets of information
(factors) on each sample are placed below (or to the side of) this table, separated by a blank row
(or blank column). There is also a 3-column format (sample label, variable label, non-zero entry)
suitable for very large arrays
18:15-19:45
Light refreshments in the UWA staff club
Friday, 19 November
09:00-09:45
Lecture: Comparison of multivariate patterns 5: Second-stage analysis (2STAGE) to compare
taxonomic levels and transformation or coefficient choices; also for a possible testing framework
in some repeated measures designs
09:45-11:00
Lab session on 2STAGE
11:00:11:15
Coffee break
11:15-12:15
Lecture: Further options in PRIMER v6 (EM algorithm for estimating missing environmental data;
direct SIMPROF tests; modifying Bray-Curtis for denuded samples; dispersion weighting to
downweight counts from clumped species; dissimilarity measures based on taxonomic distinctness)
12:15-13:00
Lab session on further tests & resemblance measures (SIMPROF, Dispersion weighting, Zeroadjusted Bray-Curtis, 2STAGE for similarities)
13:00-14:15
Lunch
14:15-18:00
Second all-afternoon lab session analysing own data using PRIMER v6
Multivariate analysis of complex experimental designs and the PERMANOVA+ add-on to PRIMER v6
(Marti Anderson & Ray Gorley)
Monday, 22 November
09:00-11:00
Lecture: The nature of multivariate data and its properties; MANOVA, ANOSIM and extending
distance-based approaches to more complex experimental designs; Permutational multivariate
analysis of variance (PERMANOVA); some changes to underlying assumptions but retaining
flexibility and robustness; testing interaction terms for multivariate data; logical choices for pairwise comparisons.
11:00-11:15
Coffee break
11:15-12:00
Lecture: Principal coordinate analysis (PCO) as another ordination technique to accompany direct
analyses of dissimilarity matrices, its uses and its relationship with PCA and non-metric MDS.
12:00-13:00
Practical: Introduction to the new add-on package to PRIMERv6: PERMANOVA, PCO and
interpreting multivariate interactions.
13:00-14:00
Lunch
14:00-15:45
Lecture: Permutational tests of homogeneity of multivariate dispersions (PERMDISP). Tests to
accompany and help interpret the PERMANOVA tests for differences in location. Tests to examine
dispersion issues in their own right, including beta diversity. Considerations regarding the use of
different dissimilarity measures when analysing relative within-group dispersions among different
groups.
15:45-16:00
Coffee break
16:00-18:00
Practical: The use of PERMANOVA, PERMDISP and PCO together for interpreting differences
among groups in dispersion and/or location, including tests for differences in beta diversity.
Tuesday, 23 November
09:00-11:00
Lecture: Complex multi-factorial ANOVA experimental designs; fixed vs random factors; nested
vs crossed relationships among factors; consequences for the hypothesis being tested and the extent
of the inference; consequences for the expected mean squares and construction of appropriate
pseudo-F ratios; estimating components of variation; multivariate analogues in PERMANOVA
follow the univariate results; permutation tests for complex designs; exchangeable units; Monte
Carlo P-values.
11:00-11:15
Coffee break
11:15-13:00
Practical: Complex experimental designs using PERMANOVA; getting the model right to begin
with matters a lot! Choosing appropriate pair-wise comparisons to do after fitting and analysing the
full model; choice of relevant ordination graphics to accompany and interpret analyses.
13:00-14:00
Lunch
14:00-15:00
Lecture: Unbalanced designs and designs that include covariates; non-independence of terms in the
model and Types of Sums of Squares; consequences for expectations of mean squares; linear
combinations of mean squares; tests, interpretations and inferences.
15:00-15:45
Practical: Real examples and practice in the analysis and interpretation of results for unbalanced
designs and designs with covariates..
15:45-16:00
Coffee break
16:00-17:00
Lecture: Designs for detecting environmental impact; BACI and Beyond BACI; contrasts and
asymmetrical designs; designs that lack replication, such as randomized blocks and repeated
measures; pooling or removing terms from a model.
17:00-18:00
Practical: Real examples and practice in analysing designs that lack replication and Beyond BACI
asymmetrical designs.
Wednesday, 24 November
09:00-11:00
Lecture: Analysing the relationship between species assemblage data and environmental variables;
multivariate multiple regression; the distance-based linear model (DISTLM); procedures for model
fitting (forward selection, backward elimination, step-wise fitting and a ‘best’ procedure); model
selection criteria (R2, adjusted R2, Mallow’s Cp, AIC and BIC); marginal and conditional tests.
11:00-11:15
Coffee break
11:15-13:00
Practical: Fitting multivariate regression models and model selection using DISTLM.
13:00-14:00
Lunch
14:00-15:45
Lecture: Visualising regression models in a constrained ordination; distance-based redundancy
analysis (dbRDA); the meaning and interpretation of the dbRDA axes; the use of biplot vectors and
their interpretation; comparison with PCO.
15:45-16:00
Coffee break
16:00-18:00
Practical: DISTLM and dbRDA.
Thursday, 25 November
09:00-11:00
Lecture: Constrained and unconstrained ordination; canonical analysis of principal coordinates
(CAP); generalised discriminant analysis based on distances; finding axes through the cloud of
points that best discriminate among groups; leave-one-out allocation success
11:00-11:15
Coffee break
11:15-13:00
Practical: Constrained and unconstrained ordinations (CAP and PCO) for data with a priori
groupings, understanding the diagnostics and the results of the analysis
13:00-14:00
Lunch
14:00-15:45
Lecture: Canonical correlation analysis using CAP; obtaining models of community change along
environmental gradients; models of ‘ecosystem health’; interpretation and uses; placement of new
points into existing models; predictions; interpretation of biplot vectors; distinguishing the
difference between CAP and dbRDA and when to use which one
15:45-16:00
Coffee break
16:00-18:00
Practical: Practice in the analysis of community data along environmental gradients and
interpretation
18:15-19:45
Light refreshments in the UWA staff club.
Friday, 26 November
09:00-18:00
Practical: All day lab session and analysis of ‘own data’ using PERMANOVA+ and PRIMER v6
Some methodological papers on PRIMER and PERMANOVA+
PRIMER
Clarke KR (1990) Comparisons of dominance curves. J Exp Mar Biol Ecol 138: 143-157
Clarke KR (1993) Non-parametric multivariate analyses of changes in community structure. Aust J Ecol 18: 117-143
Clarke KR (1999) Non-metric multivariate analysis in community-level ecotoxicology. Environ Toxicol Chem 18: 118-127
Clarke KR, Ainsworth M (1993) A method of linking multivariate community structure to environmental variables. Mar Ecol
Progr Ser 92: 205-219
Clarke KR, Chapman MG, Somerfield PJ, Needham HR (2006) Dispersion-based weighting of species counts in assemblage
analyses. Mar Ecol Progr Ser 320: 11-27
Clarke KR, Gorley RN (2006) PRIMER v6: User Manual/Tutorial. PRIMER-E, Plymouth, UK, 192 pp.
Clarke KR, Green RH (1988) Statistical design and analysis for a 'biological effects' study. Mar Ecol Progr Ser 46: 213-226
Clarke KR, Somerfield PJ, Airoldi L, Warwick RM (2006) Exploring interactions by second-stage community analyses. J Exp
Mar Biol Ecol 338: 179-192
Clarke KR, Somerfield PJ, Chapman MG (2006) On resemblance measures for ecological studies, including taxonomic
dissimil-arities and a zero-adjusted Bray-Curtis coefficient for denuded assemblages. J Exp Mar Biol Ecol 330: 55-80
Clarke KR, Somerfield PJ, Gorley RN (2008). Exploratory null hypothesis testing for community data: similarity profiles and
biota-environment linkage. J Exp Mar Biol Ecol 366: 56-69
Clarke KR, Warwick RM, Brown BE (1993) An index showing breakdown of seriation, related to disturbance, in a coral-reef
assemblage. Mar Ecol Prog Ser 102: 153-160
Clarke KR, Warwick RM (1994) Similarity-based testing for community pattern: the 2-way layout with no replication. Mar
Biol 118: 167-176
Clarke KR, Warwick RM (1998) Quantifying structural redundancy in ecological communities. Oecologia 113: 278-289
Clarke KR, Warwick RM (1998) A taxonomic distinctness index and its statistical properties. J Appl Ecol 35: 523-531
Clarke KR, Warwick RM (1999) The taxonomic distinctness measure of biodiversity: weighting of step lengths between
hierarchical levels. Mar Ecol Prog Ser 184: 21-29
Clarke KR, Warwick RM (2001) A further biodiversity index applicable to species lists: variation in taxonomic distinctness.
Mar Ecol Progr Ser 216: 265-278
Clarke KR, Warwick RM (2001) Change in Marine Communities: An Approach to Statistical Analysis and Interpretation, 2nd
ed. PRIMER-E: Plymouth, UK, 172 pp.
Field JG, Clarke KR, Warwick RM (1982) A practical strategy for analysing multispecies distribution patterns. Mar Ecol
Progr Ser 8: 37-52
Gray JS, Clarke KR, Warwick RM, Hobbs G (1990) Detection of initial effects of pollutants on marine benthos: an example
from the Ekofisk and Eldfisk oilfields, N Sea. Mar Ecol Prog Ser 66: 285-299
Olsgard F, Somerfield PJ, Carr MR (1997) Relationships between taxonomic resolution and data transformations in analyses
of a macrobenthic community along an established pollution gradient. Mar Ecol Progr Ser 149: 173-181
Somerfield PJ, Clarke KR (1995) Taxonomic levels, in marine community studies, revisited. Mar Ecol Progr Ser 127: 113-119
Somerfield PJ, Clarke KR, Olsgard F (2002) A comparison of the power of categorical and correlational tests applied to
community ecology data from gradient studies. J Anim Ecol 71: 581-593
Somerfield PJ, Clarke KR, Warwick RM, Dulvy NK (2008) Average functional distinctness as a measure of the composition
of assemblages. ICES J Mar Sci 65: 1462-1468
Warwick RM (1986) A new method for detecting pollution effects on marine macrobenthic communities. Mar Biol 92: 557562
Warwick RM, Clarke KR, Gee JM (1990) The effect of disturbance by soldier crabs, Mictyris platycheles H Milne Edwards,
on meiobenthic community structure. J exp mar Biol Ecol 135: 19-33
Warwick RM, Clarke KR (1991) A comparison of some methods for analysing changes in benthic community structure. J Mar
Biol Ass UK 71: 225-244
Warwick RM, Clarke KR (1993) Increased variability as a symptom of stress in marine communities. J Exp Mar Biol Ecol
172: 215-226
Warwick RM, Clarke KR (1995) New ‘biodiversity’ measures reveal a decrease in taxonomic distinctness with increasing
stress. Mar Ecol Progr Ser 129: 301-305
Warwick RM, Clarke KR (2001) Practical measures of marine biodiversity based on relatedness of species. Oceanog Mar Biol
Annu Rev 39: 207-231
PERMANOVA+
Anderson MJ (2001) A new method for non-parametric multivariate analysis of variance. Austral Ecol 26: 32-46
Anderson MJ (2001) Permutation tests for univariate or multivariate analysis of variance and regression. Can J Fish Aquat Sci
58: 626-639
Anderson MJ (2006) Distance-based tests for homogeneity of multivariate dispersions. Biometrics 62: 245-253
Anderson MJ (2008) Animal-sediment relationships revisited: characterising species’ distributions along an environmental
gradient using canonical analysis and quantile regression splines. J Exp Mar Biol Ecol 366: 16-27
Anderson MJ, Connell SD, Gillanders BM, Diebel CE, Blom WM, Landers TJ, Saunders JE (2005) Relationships between
taxonomic resolution and spatial scales of multivariate variation in kelp holdfast assemblages. J Anim Ecol 74: 636-646
Anderson MJ, Diebel CE, Blom WM, Landers TJ (2005) Consistency and variation in kelp holdfast assemblages: spatial
patterns of biodiversity for the major phyla at different taxonomic resolutions. J Exp Mar Biol Ecol 320: 35-56
Anderson MJ, Ellingsen KE, McArdle BH (2006) Multivariate dispersion as a measure of beta diversity. Ecol Lett 9: 683-693
Anderson MJ, Ford RB, Feary DA, Honeywill C (2004) Quantitative measures of sedimentation in an estuarine system and its
relationship with intertidal soft-sediment infauna. Mar Ecol Progr Ser 272: 33-48
Anderson MJ, Gorley RN, Clarke KR (2008) PERMANOVA+ for PRIMER: Guide to Software and Statistical Methods.
PRIMER-E: Plymouth, UK, 214 pp.
Anderson MJ, Gribble NA (1998) Partitioning the variation among spatial, temporal and environmental components in a
multivariate data set. Aust J Ecol 23: 158-167
Anderson MJ, Legendre P (1999) An empirical comparison of permutation methods for tests of partial regression coefficients
in a linear model. J Statist Comput Sim 62: 271-303
Anderson MJ, Millar RB (2004) Spatial variation and effects of habitat on temperate reef fish assemblages in northeastern
New Zealand. J Exp Mar Biol Ecol 305(2): 191-221
Anderson MJ, Robinson J (2003) Generalized discriminant analysis based on distances. Aust NZ J Stat 45: 301-318
Anderson MJ, Robinson J (2001) Permutation tests for linear models. Aust NZ J Stat 43: 75-88
Anderson MJ, ter Braak CJF (2003) Permutation tests for multi-factorial analysis of variance. J Statist Comput Sim 73: 85-113
Anderson MJ, WillisTJ (2003) Canonical analysis of principal coordinates: a useful method of constrained ordination for
ecology. Ecology 84: 511-525
Legendre P, Anderson MJ (1999) Distance-based redundancy analysis: testing multispecies responses in multifactorial
ecological experiments. Ecol Monogr 69: 1-24
McArdle BH, Anderson MJ (2001) Fitting multivariate models to community data: a comment on distance-based redundancy
analysis. Ecology 82: 290-297