1. Multivariate community analysis

2. Similarity
ANOSIM
Cluster analysis
Ordination

3. Similarity Site 1 Site 2 A 12 10 B 8 C 4 D 6 E 5 Presence/absenceD 6 E 5
Presence/absence
Distance coefficients

4. Similarity: presence/absence
Site 1
Site 2 A 1 B C D E
Jaccard = number of species in both = 80%
total number of species

5. Similarity: distance Site 1 Site 2 Site 1-Site 2 (absolute) A 12 10 28 C 4 D 6 E 5 1
Total 38 31 13
Bray-Curtis= sum of absolute differences = 13
total abundances (38+31)

6. Similarity matrix A B C D
0.78
0.67
0.54
0.18
0.21
0.44
All pairwise combinations, excluding repeats and diagonal

7. ANOSIM (Analysis of similarity)
1. Rank all pairwise combinations of species by their similarity. Therefore rank 1 means the most similar.
2. Divide the pairwise combinations into two types: between groups and within groups.
3. Calculate the mean rank for each type. The smaller the rank, the more similar!

8. ANOSIM (Analysis of similarity)
mean rank between groups - mean rank within groups
correction factor for number of combinations

9. ANOSIM (Analysis of similarity)
Same!
R =
mean rank between groups - mean rank within groups
correction factor for number of combinations
If no effect of groups expect R=0.

10. ANOSIM (Analysis of similarity)
mean rank between groups - mean rank within groups
correction factor for number of combinations
If no effect of groups expect R=0.
If within groups are more similar than between groups, expect R>0.
Big (dissimilar)
Small (similar)

11. ANOSIM (Analysis of similarity)
How to test for significance? Randomisation test!
In the following data, three groups were composed of 5, 7, and 5 samples and gave an R of
What is the likelihood of obtaining this R by chance division of the dataset into three “groups” of 5,7 and 5 samples?
There are possible ways to divide the dataset into 5,7,5 “groups”. Randomly select 999 of these, calculate R.

12. Null “groups” R Real group R (0.26)
12 out of 999 permutations (1.3%) are greater than 0.26

13. Global Test
Sample statistic (Global R): 0.264
Significance level of sample statistic: 1.3%
Number of permutations: 999 (Random sample from )
Number of permuted statistics greater than or equal to Global R: 12
Pairwise Tests
R Significance Possible Actual Number >=
Groups Statistic Level % Permutations Permutations Observed
A, B
A, C
B, C

14. Cluster analysis -nearest neighbour
Similarity matrix A B C D
0.78
0.67
0.54
0.18
0.21
0.44
0.67
Distances are 1- similarity
Site A
Site C
0.44
0.78
0.54
0.18
Site B
0.21
Site D

15. Cluster analysis -nearest neighbour
Similarity matrix A B C D
0.78
0.67
0.54
0.18
0.21
0.44
Similarity
0.78 1 A B
0.67
Distances are 1- similarity
Site A
Site C
0.44
0.78
0.54
0.18
Site B
0.21
Site D

16. Cluster analysis -nearest neighbour
Similarity matrix A B C D
0.78
0.67
0.54
0.18
0.21
0.44
Similarity
0.67 1 A B C
0.67
Distances are 1- similarity
Site A
Site C
0.44
0.78
0.54
0.18
Site B
0.21
Site D

17. Cluster analysis -nearest neighbour
Similarity matrix A B C D
0.78
0.67
0.54
0.18
0.21
0.44
0.44
Similarity 1 A B C D
0.67
Distances are 1- similarity
Site A
Site C
0.44
0.78
0.54
0.18
Site B
0.21
Site D

18. Cluster analysis-furthest neighbour
Similarity matrix A B C D
0.78
0.67
0.54
0.18
0.21
0.44
0.54
Similarity 1 A B C
0.67
Distances are 1- similarity
Site A
Site C
0.44
0.78
0.54
0.18
Site B
0.21
Site D

19. Cluster analysis - average linkage
Similarity matrix A B C D
0.78
0.67
0.54
0.18
0.21
0.44
Similarity
0.61
0.61
0.195 1 A B C
Distances are 1- similarity
Site A
Site C
0.61
0.44
0.78
Site B
0.195
Site D

20. Ordination
Site A
Site C
Site B
Site D
Plot the most similar sites closest to each other - can be multidimensional