Mantel Test

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.

• Mantels 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
wijxij
n
i 1 j1 ij ji
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
16
(No Transcript)
17
(No Transcript)
18
Results