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

wijxij

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

1 2 3 4

4 5 6 7

8 9 10 12

13 14 15 16

17 18 19 20

21 22 23 24

25 26 27 28

29 30 31 32

1 2 3

4 5

6 7 8

9 10

11 12 1316 X 16 m

2 x 2 m

Macroplot

Subplot

Quadrat

40 x 40 cm

Sampling Design

Data Matrices

Seed BankHorn-Morisita

Percent CoverBray-Curtis

X-Y CoordinatesEuclidean

1 2 3 4

4 5 6 7

8 9 10 12

13 14 15 16

17 18 19 20

21 22 23 24

25 26 27 28

29 30 31 32

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

ResultsSemi-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

sb vs. xy 0.0403 0.001 1 0.001 0.030128 0.0521906

partial 0.011028 0.23 0.771 0.483 -0.00018 0.022464

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

Pasture

0 500 1500

-0.0

50

.00

0.0

50

.10

Distance

veg

eta

tion

ma

nte

l r

0 500 1500

-0.0

15

-0.0

05

0.0

05

0.0

15

Distance

see

d b

an

k m

an

tel r

Disturbed Scrub

0 500 1500

-0.1

0-0

.05

0.0

00

.05

0.1

00

.15

Distance

veg

eta

tion

ma

nte

l r

0 500 1500

-0.0

10

.00

0.0

10

.02

0.0

3

Distance

see

d b

an

k m

an

tel r

Rosemary Scrub

0 500 1500

0.0

00

.05

0.1

0

Distance

veg

eta

tion

ma

nte

l r

0 500 1500

-0.0

05

0.0

00

0.0

05

0.0

10

Distance

see

d b

an

k m

an

tel r

ResultsVegetation 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

sb vs. xy 0.0403 0.001 1 0.001 0.030128 0.0521906

partial 0.011028 0.23 0.771 0.483 -0.00018 0.022464

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