1. Mantel Test Evaluates correlation between distance, similarity, correlation or dissimilarity matrices Null: no relationship between matrices Pearson correlation (r) can be used to measure strength of relationship r ranges from -1 to 1

2. Test for Significance • Evaluates the results from repeated randomizations • If randomizations frequently produce a correlation stronger or as strong as the original data little evidence that correlation differs from zero. • Order of randomization is important - order of row and columns are shuffled for one matrix

3. Randomization cont. • Mantel’s Z statistic is computed after each permutations and a distribution is created • Z statistic from nonrandomized data is compared to the distribution of the shuffled matrix. • If null is true, Mantel statistic will fall near the middle of the reference distribution • 10,000 randomizations is recommended • wij = connectivity or Euclidean distance matrix and xij = dissimilarity or distance matrix n Z= n wijxij i =1 j=1 i=j j=i

4. What is really computed? • Is the relationship between distance measures not the raw data

5. When to use Examples: • Two groups of organisms form same set of sample units • Community structure before and after disturbance • Genetic distance and geographic distance • Ecological distance and geographic distance

6. Partial Mantel Test • Quantifies the relationship between two matrices while controlling for the effects of a third one.

7. Problem with Mantel • Relationship is a global outcome for all variables • Can pick out which variables have the most influence • Solution: Use ordination: CCA and RDA

8. Vegetation Types • Reference Rosemary Scrub Semi-improved Pasture Disturbed Scrub

9. Sampling Design Macroplot Subplot Quadrat 16 X 16 m 2 x 2 m 40 x 40 cm

10. Data Matrices Seed Bank Horn-Morisita Percent Cover Bray-Curtis X-Y Coordinates Euclidean

11. Mantel Test in R • ecodist and vegan package • Both matrix must be identical and contain x and y coordinates • Must choose an appropriate distance measure: • Bray-Curtis - Manhattan • Euclidean • Morisita • Horn-Morisita

12. Results

13. Pasture

14. Disturbed Scrub

15. Rosemary Scrub

18. Results