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 w ij x ij n n i =1 j=1 i=j j=i Z=

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

9. 1234 4567 891012 13141516 17181920 21222324 25262728 29303132 123 45 678 910 111213 16 X 16 m 2 x 2 m Macroplot Subplot Quadrat 40 x 40 cm Sampling Design

10. Data Matrices Seed Bank Horn-Morisita Percent Cover Bray-Curtis X-Y Coordinates Euclidean 1234 4567 891012 13141516 17181920 21222324 25262728 29303132

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 Semi-improved pasture variablesmantel-rp-valuepval2pval3llim.2.5%ulim.97.5% veg vs. sb0.0690810.0011 0.0567710.0839679 veg vs. xy0.1561580.0011 0.1440830.1701316 sb vs. xy-0.014360.8120.1890.364-0.02715-0.001866 partial0.0722170.0011 0.0597670.0865884 Disturbed Scrub variablesmantel-rp-valuepval2pval3llim.2.5%ulim.97.5% veg vs. sb0.0257410.0690.9320.1190.0154090.0383087 veg vs. xy0.3865850.0011 0.372530.4001216 sb vs. xy0.04030.0011 0.0301280.0521906 partial0.0110280.230.7710.483-0.000180.022464 Rosemary Scrub variablesmantel-rp-valuepval2pval3llim.2.5%ulim.97.5% veg vs. sb0.0121740.0770.9240.1370.0054010.0182065 veg vs. xy0.0984740.0011 0.0888410.107974 sb vs. xy0.0125980.1430.8580.2840.0032710.0220178 partial0.0109870.0950.9060.1740.0049060.0177172

13. Pasture

14. Disturbed Scrub

15. Rosemary Scrub

18. Results Vegetation Typemantel-rp-valuepval2pval3llim.2.5%ulim.97.5% Pasture0.0690810.0011 0.0567710.0839679 Disturbed Scrub0.0257410.06910.0010.1440830.1701316 Rosemary Scrub0.0121740.0770.1890.364-0.02715-0.001866 Disturbed Scrub variablesmantel-rp-valuepval2pval3llim.2.5%ulim.97.5% veg vs. sb0.0257410.0690.9320.1190.0154090.0383087 veg vs. xy0.3865850.0011 0.372530.4001216 sb vs. xy0.04030.0011 0.0301280.0521906 partial0.0110280.230.7710.483-0.000180.022464 Rosemary Scrub variablesmantel-rp-valuepval2pval3llim.2.5%ulim.97.5% veg vs. sb0.0121740.0770.9240.1370.0054010.0182065 veg vs. xy0.0984740.0011 0.0888410.107974 sb vs. xy0.0125980.1430.8580.2840.0032710.0220178 partial0.0109870.0950.9060.1740.0049060.0177172