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
n
Z=
n
i =1 j=1
i=j
j=i
wijxij
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
Vegetation Types
Reference Rosemary Scrub
Semi-improved Pasture
Disturbed Scrub
Sampling Design
Macroplot
1
2
4
8
3
5
9
13
17
10
18
25
7
12
15
19
22
26
29
6
14
21
4
16
23
27
30
Subplot
20
24
1
4
28
31
2
32
6
5
7
9
16 X 16 m
11
3
8
Quadrat
10
12
13
2x2m
40 x 40 cm
Data Matrices
Seed Bank
Horn-Morisita
1
2
4
X-Y Coordinates
Euclidean
8
3
5
9
13
17
10
18
25
15
22
16
20
23
27
30
7
12
19
26
29
6
14
21
4
24
28
31
32
Percent Cover
Bray-Curtis
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
variables
mantel-r
p-value
pval2
pval3
llim.2.5%
ulim.97.5%
veg vs. sb
0.069081
0.001
1
0.001
0.056771
0.0839679
veg vs. xy
0.156158
0.001
1
0.001
0.144083
0.1701316
sb vs. xy
-0.01436
0.812
0.189
0.364
-0.02715
-0.001866
partial
0.072217
0.001
1
0.001
0.059767
0.0865884
Disturbed Scrub
variables
mantel-r
p-value
pval2
pval3
llim.2.5%
ulim.97.5%
veg vs. sb
0.025741
0.069
0.932
0.119
0.015409
0.0383087
veg vs. xy
0.386585
0.001
1
0.001
0.37253
0.4001216
0.0403
0.001
1
0.001
0.030128
0.0521906
0.011028
0.23
0.771
0.483
-0.00018
0.022464
sb vs. xy
partial
Rosemary Scrub
variables
mantel-r
p-value
pval2
pval3
llim.2.5%
ulim.97.5%
veg vs. sb
0.012174
0.077
0.924
0.137
0.005401
0.0182065
veg vs. xy
0.098474
0.001
1
0.001
0.088841
0.107974
sb vs. xy
0.012598
0.143
0.858
0.284
0.003271
0.0220178
partial
0.010987
0.095
0.906
0.174
0.004906
0.0177172
-0.015
-0.05
0.05
0
500
1500
Distance
-0.005
0.005
seed bank mantel r
0.00
vegetation mantel r
0.015
0.10
Pasture
0
500
1500
Distance
-0.01
-0.10
0.00
0.05
0
500
1500
Distance
0.00
0.01
seed bank mantel r
-0.05
vegetation mantel r
0.02
0.10
0.03
0.15
Disturbed Scrub
0
500
1500
Distance
-0.005
0.00
0
500
1500
Distance
0.000
0.005
seed bank mantel r
0.05
vegetation mantel r
0.010
0.10
Rosemary Scrub
0
500
1500
Distance
Results
Vegetation Type
mantel-r
p-value
pval2
pval3
llim.2.5%
ulim.97.5%
Pasture
0.069081
0.001
1
0.001
0.056771
0.0839679
Disturbed Scrub
0.025741
0.069
1
0.001
0.144083
0.1701316
Rosemary Scrub
0.012174
0.077
0.189
0.364
-0.02715
-0.001866
Disturbed Scrub
variables
mantel-r
p-value
pval2
pval3
llim.2.5%
ulim.97.5%
veg vs. sb
0.025741
0.069
0.932
0.119
0.015409
0.0383087
veg vs. xy
0.386585
0.001
1
0.001
0.37253
0.4001216
0.0403
0.001
1
0.001
0.030128
0.0521906
0.011028
0.23
0.771
0.483
-0.00018
0.022464
sb vs. xy
partial
Rosemary Scrub
variables
mantel-r
p-value
pval2
pval3
llim.2.5%
ulim.97.5%
veg vs. sb
0.012174
0.077
0.924
0.137
0.005401
0.0182065
veg vs. xy
0.098474
0.001
1
0.001
0.088841
0.107974
sb vs. xy
0.012598
0.143
0.858
0.284
0.003271
0.0220178
partial
0.010987
0.095
0.906
0.174
0.004906
0.0177172