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Multivariate analysis of community structure data

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Presentation on theme: "Multivariate analysis of community structure data"— Presentation transcript:

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

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

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

4 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?

5 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?

6 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

7 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

8 The vehicle:

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

10 Data collection:

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

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

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

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

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

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

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23 within within between

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

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

26 nMDS ordination example

27 nMDS ordination example
Distance between points reflects relative similarity!

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

29 A1 is closer to A2 than it is to A3
How does nMDS work? nMDS uses the RANK ORDER of similarity relationships between samples: Sample % similarity rank A1 A2 99% 1 A3 96% 2 95% 3 A1 is closer to A2 than it is to A3

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

31 A1 is closer to A2 than it is to A3
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

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

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

34 Main points about ordination!
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’ a b c sample similarities ordination

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42 Obviously distinct groups

43 Less obvious! Are they really different?

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

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

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

47 Analysis of Similarities – a statistical approach
Are groups different? Analysis of Similarities – a statistical approach Ho = sites the same Ha = sites are different exposed sheltered

48 If Ho (sites the same) = true
Similarity within = Similarity between

49 If Ha (sites different) = true
Similarity within > Similarity between

50 Analysis of Similarities – a statistical approach
Are groups different? Analysis of Similarities – a statistical approach (rbetween - rwithin ) R = standardizing factor

51 Analysis of Similarities – a statistical approach
Are groups different? Analysis of Similarities – a statistical approach (rbetween - rwithin ) R = ~1

52 If Ho (sites the same) = true
Similarity within = Similarity between (rbetween - rwithin ) R = ~1 ~ 0

53 If Ha (sites different) = true
Similarity within > Similarity between (rbetween - rwithin ) R = ~1 ~ 1

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57 To simulate null distribution

58 To simulate null distribution
Similarity within = Similarity between

59 Calculate R To simulate null distribution
Similarity within = Similarity between Calculate R

60 Calculate R To simulate null distribution
Similarity within = Similarity between Calculate R

61 .477

62 1 P= = 0.001 999 .477

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

64 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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71 Data analysis summary How? SIMPER ANOSIM samples species
b c species sample similarities nMDS are sites different? a b c How? SIMPER ANOSIM


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