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Multivariate analysis of community structure data Colin Bates UBC Bamfield Marine Sciences Centre

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Goals 1)To understand the ideas behind multivariate community structure analysis. 2)To understand how to perform these analyses in PRIMER. 3)To be prepared to analyse and interpret your class data later today.

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What are multivariate statistics? Statistics that allow us to look at how multiple variables change together

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What are multivariate statistics? Statistics that allow us to look at how multiple variables change together: EG: How do 50 species in a community react to an environmental perturbation?

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What are multivariate statistics? Statistics that allow us to look at how multiple variables change together: EG: How do 50 species in a community react to an environmental perturbation? 50 ANOVAs?

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What are multivariate statistics? Statistics that allow us to look at how multiple variables change together: EG: How do 50 species in a community react to an environmental perturbation? 50 ANOVAs? No… Multivariate stats allow us to “condense” information for simplicity

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When might I use this type of analysis? For a multi-species community, you may wish to: - pull order from complex systems - visualize these patterns - comparisons over time and space - test hypotheses

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The vehicle:

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Example: Seaweed Communities at Cape Beale - Is flora different at two close sites, each exposed to different wave intensity?

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Data collection:

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2. Data Analysis Step 1: Entering your data into PRIMER

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How to analyze this type of data? 1. Diversity indices

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How to analyze this type of data? 1. Diversity indices Yet, most diversity indices do not consider species identity…

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How to analyze this type of data? 1. Diversity indices Yet, most diversity indices do not consider species identity… Multivariate community structure analyses

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Analysis flow samples species sample similarities a a a b b b c c c ordination a a a b b b c c c are sites different? How?

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Analysis flow samples species sample similarities a a a b b b c c c ordination Calculate Bray – Curtis Similarity gives a triangular similarity matrix

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within between

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Analysis flow samples species sample similarities a a a b b b c c c ordination a a a b b b c c c are sites different? How?

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Visualizing similarities Ordination “maps” similarity relationships between samples a a a b b b c c c ordination

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nMDS ordination example

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Distance between points reflects relative similarity!

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Nonmetric multidimensional scaling (nMDS) Nonmetric: no axes Multidimensional: represents relationships between multiple variables in two or three dimensions Scaling: the ratio between reality and representation “the future of ordination is in nonmetric multidimensional scaling” – McCune & Grace, 2002

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How does nMDS work? nMDS uses the RANK ORDER of similarity relationships between samples: Sample % similarity rank A1A299%1 A1A396%2 A2A395%3 A1 is closer to A2 than it is to A3

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How does nMDS work? Then, nMDS tries to place points in 2 (or 3) dimensional space to represent this ranked order: A1 A2 A3 A1 is closer to A2 than it is to A3

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How does nMDS work? Then, nMDS tries to place points in 2 (or 3) dimensional space to represent this ranked order: A1 A2 A3 A1 is closer to A2 than it is to A3

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How accurate is the nMDS map? - Sometimes the nMDS can’t represent all relationship accurately - this is reflected by a high STRESS value

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- Sometimes the nMDS can’t represent all relationship accurately - this is reflected by a high STRESS value distance on nMDS similarity in sim. matrix If Stress Value = 0.0 : perfect map 0.1 : decent map 0.2 : ok map 0.3 : don’t bother How accurate is the nMDS map?

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- Ordination is a way to visualize how similar your samples are - nMDS tries to represent visually the rank order within the underlying similarity matrix - all that matters is the relative distance between points. - stress value allows you to estimate ‘quality’ of the nMDS’ Main points about ordination! sample similarities a a a b b b c c c ordination

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Obviously distinct groups

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Less obvious! Are they really different?

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Analysis flow samples species sample similarities a a a b b b c c c ordination a a a b b b c c c are sites different?

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Analysis flow samples species sample similarities a a a b b b c c c ordination a a a b b b c c c are sites different? How?

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Analysis of Similarities – a statistical approach Are groups different? exposed sheltered

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Analysis of Similarities – a statistical approach Are groups different? H o = sites the same H a = sites are different exposed sheltered

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If H o (sites the same) = true Similarity within = Similarity between

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If H a (sites different) = true Similarity within > Similarity between

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Analysis of Similarities – a statistical approach Are groups different? (r between - r within ) R = standardizing factor

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Analysis of Similarities – a statistical approach Are groups different? (r between - r within ) R = ~1

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If H o (sites the same) = true Similarity within = Similarity between ~ 0 (r between - r within ) R = ~1

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If H a (sites different) = true Similarity within > Similarity between ~ 1 (r between - r within ) R = ~1

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To simulate null distribution

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Similarity within = Similarity between

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To simulate null distribution Similarity within = Similarity between Calculate R

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To simulate null distribution Similarity within = Similarity between Calculate R

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.477

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1 999 P== 0.001

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Analysis flow samples species sample similarities a a a b b b c c c ordination a a a b b b c c c are sites different? How?

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Sites are different – why? We will use the SIMPER routine: - Similarity Percentages Basically indicates which species are responsible for the patterns that we see.

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Data analysis summary samples species sample similarities a a a b b b c c c nMDS a a a b b b c c c are sites different? How? SIMPER ANOSIM

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