Detecting Multivariate Changes in Biological Assemblages ...



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, Zero-adjusted 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 pair-wise 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: 557-562

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

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