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

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

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=

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

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

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

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

Reference Rosemary Scrub Semi-improved Pasture Disturbed Scrub Vegetation Types

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

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

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

Results Semi-improved pasture variablesmantel-rp-valuepval2pval3llim.2.5%ulim.97.5% veg vs. sb veg vs. xy sb vs. xy partial Disturbed Scrub variablesmantel-rp-valuepval2pval3llim.2.5%ulim.97.5% veg vs. sb veg vs. xy sb vs. xy partial Rosemary Scrub variablesmantel-rp-valuepval2pval3llim.2.5%ulim.97.5% veg vs. sb veg vs. xy sb vs. xy partial

Pasture

Disturbed Scrub

Rosemary Scrub

Results Vegetation Typemantel-rp-valuepval2pval3llim.2.5%ulim.97.5% Pasture Disturbed Scrub Rosemary Scrub Disturbed Scrub variablesmantel-rp-valuepval2pval3llim.2.5%ulim.97.5% veg vs. sb veg vs. xy sb vs. xy partial Rosemary Scrub variablesmantel-rp-valuepval2pval3llim.2.5%ulim.97.5% veg vs. sb veg vs. xy sb vs. xy partial