Multivariate community analysis

Similarity ANOSIM Cluster analysis Ordination

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

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

Similarity: distance Site 1 Site 2 Site 1-Site 2 (absolute) A 12 10 2 8 C 4 D 6 E 5 1 Total 38 31 13 Bray-Curtis= sum of absolute differences = 13 total abundances (38+31)

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

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!

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

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.

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)

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 0.264. 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 2450448 possible ways to divide the dataset into 5,7,5 “groups”. Randomly select 999 of these, calculate R.

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

Global Test Sample statistic (Global R): 0.264 Significance level of sample statistic: 1.3% Number of permutations: 999 (Random sample from 2450448) 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 0.175 9.7 792 792 77 A, C 0.592 0.8 126 126 1 B, C 0.147 11.5 792 792 91

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

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

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

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

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

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

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