Distance matrix methods calculate a measure of distance between each pair of species, then find a...

Distance matrix methodscalculate a measure of distance between each pair of species, then find a tree that predicts the observed set of distances.

Branch lengths and times in distance matrix methods, branch lengths reflect the expected amount of evolution in different branches of the tree.

branch length = ri • ti

rate of evolution

elapsed time

The least squares method

A B C D E

A 0 Dab Dac Dad Dae

B Dab 0 Dbc Dbd Dbe

C Dac Dbc 0 Dcd Dce

D Dad Dbd Dcd 0 Dde

E Dae Dbe Dce Dde 0

Observed matrix

minimise the difference between the observed matrix of distances and the matrix of distances predicted by the tree.


A B C D E

A 0 dab dac dad dae

B dab 0 dbc dbd dbe

C dac dbc 0 dcd dce

D dad dbd dcd 0 dde

E dae dbe dce dde 0

Expected matrix c

e

ab

d

0.08

0.05

0.10

0.07

0.06

0.05

0.03


c

e

ab

d

0.08

0.05

0.10

0.07

0.06

0.05

A B C D E

A 0

B 0

C 0

D 0

E 0

0.03

Expected matrix


c

e

ab

d

0.08

0.05

0.10

0.07

0.06

0.05

A B C D E

A 0 0.23

B 0

C 0

D 0

E 0

0.08+0.05+0.10

0.03

Expected matrix


c

e

ab

d

0.08

0.05

0.10

0.07

0.06

0.05

A B C D E

A 0 0.23 0.16 0.20 0.17

B 0.23 0 0.23 0.17 0.24

C 0.16 0.23 0 0.15 0.11

D 0.20 0.17 0.15 0 0.21

E 0.17 0.24 0.11 0.21 0

0.03

Expected matrix


Q = S S wij (Dij – dij)2 i=1 j=1

n n

observed distancebetween species i and j

expected distancebetween species i and j

Q is a measure for the discrepancy between the observed and the expected matrix.



n n

weight(1, 1/D2, 1/D)

distances can be weighed or not.


c

e

ab

d

v1

v7

v2

v4

v5

v3

v6

xij,k= 1 if branch k is on the path between species j and k

= 0 if branch k is not on the path between species j and k

Xij, k is a handy variable


c

e

ab

d

v1

v7

v2

v4

v5

v3

v6

Xa-b,1= 1


c

e

ab

d

v1

v7

v2

v4

v5

v3

v6

Xa-b,1= 1Xa-b,7= 1


c

e

ab

d

v1

v7

v2

v4

v5

v3

v6

Xa-b,1= 1Xa-b,7= 1Xa-b,3= 0



n n

dij = S xij,k vkk

rewrite dij, the expected values


Q = S S wij (Dij – Sxij,k vk)2 i=1 j=1

n n

k


Q = S S wij (Dij – Sxij,k vk)2 i=1 j=1

n n

k

= -2 S S wij xij, k (Dij – Sxij,k vk) i=1 j=1

n ndQdvk

k

differentiate Q and equate the derivative to zero


= -2 S S xij, k (Dij – Sxij,k vk) = 0i=1 j=1

n ndQdvk

k

for the unweighted case


= -2 S S xij, 1 (Dij – Sxij,k vk) = 0i=1 j:j≠1

n ndQdv1

k

xAB,1 (DAB-SxAB,kvk) + xAC,1 (DAC-SxAC, kvk) + xAD,1 (DAD-SxAD, kvk) + xAB,1 (DAE-SxAE, kvk)

+ xBC,1 (DBC-SxBC, kvk) + xBD,1 (DBD-SxBD, kvk)+ xBE,1 (DBE-SxBE, kvk)

+ xCD,1 (DCD-SxCD, kvk) + xCE,1 (DCE-SxCE, kvk)

+ xDE,1 (DDE-SxDE, kvk) = 0

i=1

i=2

i=3

i=4

j=2 j=3 j=4 j=5

j=3 j=4 j=5

j=4 j=5

j=5

written in full


c

e

ab

d

v1

v7

v2

v4

v5

v3

v6

Xij,1 A B C D E

A - 1 1 1 1

B - 0 0 0

C - 0 0

D - 0

E -


= -2 S S xij, 1 (Dij – Sxij,k vk) = 0i=1 j=1

n ndQdv1

k

1 (DAB-SxAB,kvk) + 1 (DAC-SxAC, kvk)+ 1 (DAD-SxAD, kvk)+ 1 (DAE-SxAE, kvk)

+ 0 (DBC-SxBC, kvk) + 0 (DBD-SxBD, kvk)+ 0 (DBE-SxBE, kvk)

+ 0 (DCD-SxCD, kvk) + 0 (DCE-SxCE, kvk)

+ 0 (DDE-SxDE, kvk) = 0

Xij,1 A B C D E

A - 1 1 1 1

B - 0 0 0

C - 0 0

D - 0

E -

many terms are zero



n ndQdv1

k

(DAB-SxAB,kvk) + (DAC-SxAC, kvk) + (DAD-SxAD, kvk) + (DAE-SxAE, kvk) = 0

c

e

ab

d

v1

v7

v2

v4

v5

v3

v6

=1•v1 + 1•v2 + 0•v3 + 0•v4 + 0*v5 + 0•v6 + 1*v7

non-zero terms expanded



n ndQdv1

k

(DAB-SxAB, kvk) + (DAC-SxAC, kvk) + (DAD-SxAD, kvk) + (DAE-SxAE, kvk) = 0

c

e

ab

d

v1

v7

v2

v4

v5

v3

v6

=1•v1 + 0•v2 + 1•v3 + 0•v4 + 0*v5 + 1•v6 + 0*v7



n ndQdv1

k


DAB + DAC + DAD + DAE – 4v1 – v2 – v3 – v4 – v5 – 2v6 – 2v7 = 0

DAB + DAC + DAD + DAE = 4v1 + v2 + v3 + v4 + v5 + 2v6 + 2v7

rearranging to



n ndQdv1

k


DAB + DAC + DAD + DAE – 4v1 – v2 – v3 – v4 – v5 – 2v6 – 2v7 = 0

DAB + DAC + DAD + DAE = 4v1 + v2 + v3 + v4 + v5 + 2v6 + 2v7 equation for v1



DAB + DBC + DBD + DBE = v1 + 4v2 + v3 + v4 + v5 + 2v6 + 3v7

equation for v1equation for v2

mutatis mutandis for v2



DAB + DBC + DBD + DBE = v1 + 4v2 + v3 + v4 + v5 + 2v6 + 3v7

DAC + DBC + DCD + DDE = v1 + v2 + 4v3 + v4 + v5 + 3v6 + 2v7

DAD + DBD + DCD + DDE = v1 + v2 + v3 + 4v4 + v5 + 2v6 + 3v7

DAE + DBE + DCE + DDE = v1 + v2 + v3 + v4 + 4v5 + 3v6 + 2v7

DAC + DAE + DCE + DBE + DCD + DDE = 2v1 + 2v2 + 3v3 + 2v4 + 3v5 + 6v6 + 4v7

DAB + DAD + DBC + DCD + DBE + DDE = 2v1 + 3v2 + 2v3 + 3v4 + 2v5 + 4v6 + 6v7

equation for v1equation for v2

v3

v4

v5

v6

v7

and all other branches

The least squares method solving linear equations with matrices

x + 2y = 4

3x - 5y = 1

1 2

3 -5

4

1A = = B

A-1 =-5 -2

-3 1

1

| A |=

1

1*(-5)- 3*2

-5 -2

-3 1 = -

-5 -2

-3 1

1

11

X = A-1 B = --5 -2

-3 1

1

11

4

1= -

1

11

-22

-11

2

1=

Clustering algorithms clustering methods have no criterion but apply algorithms to come up with trees

Clustering algorithms: UPGMA

an ultrametric tree

UPGMA assumes that evolutionary rates are the same in all lineages

UnweightedPairGroupMethod withArithmetic mean

Clustering algorithms: UPGMAdog bear raccoon weasel seal sea lion cat monkey

dog 0 32 48 51 50 48 98 148

bear 32 0 26 34 29 33 84 136

raccoon 48 26 0 42 44 44 92 152

weasel 51 34 42 0 44 38 86 142

seal 50 29 44 44 0 24 89 142

sea lion 48 33 44 38 24 0 90 142

cat 98 84 92 86 89 90 0 148

monkey 148 136 152 142 142 142 148 0

1. Find species i and j with the smallest distance .

2. Calculate branch length between i and j.




sea

lion

seal

12


dog 0 32 48 51 50 48 98 148

bear 32 0 26 34 29 33 84 136

raccoon 48 26 0 42 44 44 92 152

weasel 51 34 42 0 44 38 86 142

seal 50 29 44 44 0 24 89 142

sea lion 48 33 44 38 24 0 90 142

cat 98 84 92 86 89 90 0 148

monkey 148 136 152 142 142 142 148 0



3. Lump i and j into a new group.

dog bear raccoon weasel SS cat monkey

dog 0 32 48 51 98 148

bear 32 0 26 34 84 136

raccoon 48 26 0 42 92 152

weasel 51 34 42 0 86 142

SS 0

cat 98 84 92 86 0 148

monkey 148 136 152 142 148 0


dog 0 32 48 51 50 48 98 148

bear 32 0 26 34 29 33 84 136

raccoon 48 26 0 42 44 44 92 152

weasel 51 34 42 0 44 38 86 142

seal 50 29 44 44 0 24 89 142

sea lion 48 33 44 38 24 0 90 142

cat 98 84 92 86 89 90 0 148

monkey 148 136 152 142 142 142 148 0


2. Calculate branch length between i and.


4. Compute distance between new group and all other groups (weigh for number of species in groups).


dog 0 32 48 51 98 148

bear 32 0 26 34 84 136

raccoon 48 26 0 42 92 152

weasel 51 34 42 0 86 142

SS 0

cat 98 84 92 86 0 148

monkey 148 136 152 142 148 0


dog 0 32 48 51 50 48 98 148

bear 32 0 26 34 29 33 84 136

raccoon 48 26 0 42 44 44 92 152

weasel 51 34 42 0 44 38 86 142

seal 50 29 44 44 0 24 89 142

sea lion 48 33 44 38 24 0 90 142

cat 98 84 92 86 89 90 0 148

monkey 148 136 152 142 142 142 148 0


dog 0 32 48 51 49 98 148

bear 32 0 26 34 84 136

raccoon 48 26 0 42 92 152

weasel 51 34 42 0 86 142

SS 0

cat 98 84 92 86 0 148

monkey 148 136 152 142 148 0






dog 0 32 48 51 50 48 98 148

bear 32 0 26 34 29 33 84 136

raccoon 48 26 0 42 44 44 92 152

weasel 51 34 42 0 44 38 86 142

seal 50 29 44 44 0 24 89 142

sea lion 48 33 44 38 24 0 90 142

cat 98 84 92 86 89 90 0 148

monkey 148 136 152 142 142 142 148 0


dog 0 32 48 51 49 98 148

bear 32 0 26 34 31 84 136

raccoon 48 26 0 42 92 152

weasel 51 34 42 0 86 142

SS 0

cat 98 84 92 86 0 148

monkey 148 136 152 142 148 0






dog 0 32 48 51 50 48 98 148

bear 32 0 26 34 29 33 84 136

raccoon 48 26 0 42 44 44 92 152

weasel 51 34 42 0 44 38 86 142

seal 50 29 44 44 0 24 89 142

sea lion 48 33 44 38 24 0 90 142

cat 98 84 92 86 89 90 0 148

monkey 148 136 152 142 142 142 148 0


dog 0 32 48 51 49 98 148

bear 32 0 26 34 31 84 136

raccoon 48 26 0 42 44 92 152

weasel 51 34 42 0 41 86 142

SS 49 31 44 41 0 89.5 142

cat 98 84 92 86 89.5 0 148

monkey 148 136 152 142 142 148 0









dog 0 32 48 51 49 98 148

bear 32 0 26 34 31 84 136

raccoon 48 26 0 42 44 92 152

weasel 51 34 42 0 41 86 142

SS 49 31 44 41 0 89.5 142

cat 98 84 92 86 89.5 0 148

monkey 148 136 152 142 142 148 0




sea

lion

seal

12

racc

oon

bear

13

Clustering algorithms: UPGMAdog bear raccoon weasel SS cat monkey

dog 0 32 48 51 49 98 148

bear 32 0 26 34 31 84 136

raccoon 48 26 0 42 44 92 152

weasel 51 34 42 0 41 86 142

SS 49 31 44 41 0 89.5 142

cat 98 84 92 86 89.5 0 148

monkey 148 136 152 142 142 148 0

dog BR weasel SS cat monkey

dog 0 40 51 49 98 148

BR 40 0 38 37.5 88 144

weasel 51 38 0 41 86 142

SS 49 37.5 41 0 89.5 142

cat 98 88 86 89.5 0 148

monkey 148 144 142 142 148 0








dog BR weasel SS cat monkey

dog 0 40 51 49 98 148

BR 40 0 38 37.5 88 144

weasel 51 38 0 41 86 142

SS 49 37.5 41 0 89.5 142

cat 98 88 86 89.5 0 148

monkey 148 144 142 142 148 0




sea

lion

seal

12

racc

oon

bear

1318.756.755.75

Clustering algorithms: UPGMAdog BR weasel SS cat monkey

dog 0 40 51 49 98 148

BR 40 0 38 37.5 88 144

weasel 51 38 0 41 86 142

SS 49 37.5 41 0 89.5 142

cat 98 88 86 89.5 0 148

monkey 148 144 142 142 148 0

dog BRSS weasel cat monkey

dog 0 44.5 51 98 148

BRSS 44.5 0 39.5 88.75 143

weasel 51 39.5 0 86 142

cat 98 88.75 86 0 148

monkey 148 143 142 148 0









dog 0 44.5 51 98 148

BRSS 44.5 0 39.5 88.75 143

weasel 51 39.5 0 86 142

cat 98 88.75 86 0 148

monkey 148 143 142 148 0




sea

lion

seal

12

racc

oon

bear

13 19.756.755.75

wea

sel



2. Calculate branch length between i and j. Lump i and j into a new group.




dog 0 44.5 51 98 148

BRSS 44.5 0 39.5 88.75 143

weasel 51 39.5 0 86 142

cat 98 88.75 86 0 148

monkey 148 143 142 148 0

dog BRSSW cat monkey

dog 0 98 148

BRSSW 0

cat 98 0 148

monkey 148 148 0

= (4*44.5 + 1*51)/5

4 species in BRSS

1 species in weasel







dog 0 44.5 51 98 148

BRSS 44.5 0 39.5 88.75 143

weasel 51 39.5 0 86 142

cat 98 88.75 86 0 148

monkey 148 143 142 148 0


dog 0 45.8 98 148

BRSSW 45.8 0

cat 98 0 148

monkey 148 148 0

= (4*44.5 + 1*51)/5

4 species in BRSS

1 species in weasel







dog 0 44.5 51 98 148

BRSS 44.5 0 39.5 88.75 143

weasel 51 39.5 0 86 142

cat 98 88.75 86 0 148

monkey 148 143 142 148 0


dog 0 45.8 98 148

BRSSW 45.8 0 88.2 142.8

cat 98 88.2 0 148

monkey 148 142.8 148 0





dog 0 45.8 98 148

BRSSW 45.8 0 88.2 142.8

cat 98 88.2 0 148

monkey 148 142.8 148 0




sea

lion

seal

12

racc

oon

bear

13 19.756.755.75

wea

sel

dog

22.9







dog 0 45.8 98 148

BRSSW 45.8 0 88.2 142.8

cat 98 88.2 0 148

monkey 148 142.8 148 0

BRSSWD cat monkey

BRSSWD 0

cat 0 148

monkey 148 0

= (5*88.2 + 1*98)/6

1 species in dog

5 species in BRSSW







dog 0 45.8 98 148

BRSSW 45.8 0 88.2 142.8

cat 98 88.2 0 148

monkey 148 142.8 148 0

BRSSWD cat monkey

BRSSWD 0 89.833

cat 89.833 0 148

monkey 148 0

= (5*88.2 + 1*98)/6

1 species in dog

5 species in BRSSW







dog 0 45.8 98 148

BRSSW 45.8 0 88.2 142.8

cat 98 88.2 0 148

monkey 148 142.8 148 0

BRSSWD cat monkey

BRSSWD 0 89.833 143.66

cat 89.833 0 148

monkey 143.66 148 0

= (5*88.2 + 1*98)/6

1 species in dog

5 species in BRSSW




BRSSWD cat monkey

BRSSWD 0 89.833 143.66

cat 89.833 0 148

monkey 143.66 148 0




sea

lion

seal

12

racc

oon

bear

13 19.756.755.75

wea

sel

dog

22.9

cat

44.916622.0166






BRSSWD cat monkey

BRSSWD 0 89.833 143.66

cat 89.833 0 148

monkey 143.66 148 0

BRSSWD monkey

BRSSWD 0

monkey 0= (6*143.66 + 1*148)/7

1 species in cat

6 species in BRSSWD






BRSSWD cat monkey

BRSSWD 0 89.833 143.66

cat 89.833 0 148

monkey 143.66 148 0

BRSSWD monkey

BRSSWD 0 144.2857

monkey 144.2857 0= (6*143.66 + 1*148)/7

1 species in cat

6 species in BRSSWD




sea

lion

seal

12

racc

oon

bear

13 19.756.755.75

wea

sel

dog

22.9

cat

44.916622.0166

mon

key

72.142827.22619

Clustering algorithms: Neighbour-joining

1. Calculate Sx = (SDx)/(n-2)dog bear raccoon weasel seal sea lion cat monkey

dog 0 32 48 51 50 48 98 148

bear 32 0 26 34 29 33 84 136

raccoon 48 26 0 42 44 44 92 152

weasel 51 34 42 0 44 38 86 142

seal 50 29 44 44 0 24 89 142

sea lion 48 33 44 38 24 0 90 142

cat 98 84 92 86 89 90 0 148

monkey 148 136 152 142 142 142 148 0

79.2

62.3

74.7

72.8

70.3

69.8

114.5

168.3

79.2 62.3 74.7 72.8 70.3 69.8 114.5 168.3


1. Calculate Sx = (SDx)/(n-2)2. Calculate Mij = Dij-Si-Sj and

select pair with smallest Mij

dog bear raccoon weasel seal sea lion cat monkey

dog 0 32 48 51 50 48 98 148

bear 32 0 26 34 29 33 84 136

raccoon 48 26 0 42 44 44 92 152

weasel 51 34 42 0 44 38 86 142

seal 50 29 44 44 0 24 89 142

sea lion 48 33 44 38 24 0 90 142

cat 98 84 92 86 89 90 0 148

monkey 148 136 152 142 142 142 148 0

79.2

62.3

74.7

72.8

70.3

69.8

114.5

168.3

79.2 62.3 74.7 72.8 70.3 69.8 114.5 168.3


dog -109.50

bear

raccoon

weasel

seal

sea lion

cat

monkey

32 - 79.2 - 62.3 =

-109.5





dog 0 32 48 51 50 48 98 148

bear 32 0 26 34 29 33 84 136

raccoon 48 26 0 42 44 44 92 152

weasel 51 34 42 0 44 38 86 142

seal 50 29 44 44 0 24 89 142

sea lion 48 33 44 38 24 0 90 142

cat 98 84 92 86 89 90 0 148

monkey 148 136 152 142 142 142 148 0

79.2

62.3

74.7

72.8

70.3

69.8

114.5

168.3

79.2 62.3 74.7 72.8 70.3 69.8 114.5 168.3


dog -109.50 -105.83 -101.00 -99.50 -101.00 -95.67 -99.50

bear -109.50 -111.00 -101.17 -103.67 -99.17 -92.83 -94.67

raccoon -105.83 -111.00 -105.50 -101.00 -100.50 -97.17 -91.00

weasel -101.00 -101.17 -105.50 -99.17 -104.67 -101.33 -99.17

seal -99.50 -103.67 -101.00 -99.17 -116.17 -95.83 -96.67

sea lion -101.00 -99.17 -100.50 -104.67 -116.17 -94.33 -96.17

cat -95.67 -92.83 -97.17 -101.33 -95.83 -94.33 -134.83

monkey -99.50 -94.67 -91.00 -99.17 -96.67 -96.17 -134.83




3. Create a node that joins this pair and calculate branch lengths as (Dij/2)+(Si-Sj)/2


dog 0 32 48 51 50 48 98 148

bear 32 0 26 34 29 33 84 136

raccoon 48 26 0 42 44 44 92 152

weasel 51 34 42 0 44 38 86 142

seal 50 29 44 44 0 24 89 142

sea lion 48 33 44 38 24 0 90 142

cat 98 84 92 86 89 90 0 148

monkey 148 136 152 142 142 142 148 0

79.2

62.3

74.7

72.8

70.3

69.8

114.5

168.3

79.2 62.3 74.7 72.8 70.3 69.8 114.5 168.3

branch length cat-cm = 148/2 + (114.5-168.5)/2 = 47.08






dog 0 32 48 51 50 48 98 148

bear 32 0 26 34 29 33 84 136

raccoon 48 26 0 42 44 44 92 152

weasel 51 34 42 0 44 38 86 142

seal 50 29 44 44 0 24 89 142

sea lion 48 33 44 38 24 0 90 142

cat 98 84 92 86 89 90 0 148

monkey 148 136 152 142 142 142 148 0

79.2

62.3

74.7

72.8

70.3

69.8

114.5

168.3

79.2 62.3 74.7 72.8 70.3 69.8 114.5 168.3

branch length cat-cm = 148/2 + (114.5-168.5)/2 = 47.08

branch length monkey-cm = 148/2 + (168.5-114.5)/2 = 110.92


catsea lion

seal

monkey

weasel

bear raccoon

dog1. Calculate Sx = (SDx)/(n-2)2. Calculate Mij = Dij-Si-Sj and



4. Join the two species and make all other taxa in form of a star.


cat

sea lion

seal

monkey

weasel

bear raccoon

dog

cm 47.08

100.92





Clustering algorithms: Neighbour-joiningdog bear raccoon weasel seal sea lion cat monkey

dog 0 32 48 51 50 48 98 148

bear 32 0 26 34 29 33 84 136

raccoon 48 26 0 42 44 44 92 152

weasel 51 34 42 0 44 38 86 142

seal 50 29 44 44 0 24 89 142

sea lion 48 33 44 38 24 0 90 142

cat 98 84 92 86 89 90 0 148

monkey 148 136 152 142 142 142 148 0

dog bear raccoon weasel seal sea lion cm

dog 0 32 48 51 50 48 49

bear 32 0 26 34 29 33

raccoon 48 26 0 42 44 44

weasel 51 34 42 0 44 38

seal 50 29 44 44 0 24

sea lion 48 33 44 38 24 0

cm





5. Create a new matrix. Calculate the distances between the new node and other taxa as Dxij=(Dix+Djx-Dij)/2

(98+148-148)/2 =

49

Clustering algorithms: Neighbour-joiningdog bear raccoon weasel seal sea lion cat monkey

dog 0 32 48 51 50 48 98 148

bear 32 0 26 34 29 33 84 136

raccoon 48 26 0 42 44 44 92 152

weasel 51 34 42 0 44 38 86 142

seal 50 29 44 44 0 24 89 142

sea lion 48 33 44 38 24 0 90 142

cat 98 84 92 86 89 90 0 148

monkey 148 136 152 142 142 142 148 0


dog 0 32 48 51 50 48 49

bear 32 0 26 34 29 33 36

raccoon 48 26 0 42 44 44 48

weasel 51 34 42 0 44 38 40

seal 50 29 44 44 0 24 41.5

sea lion 48 33 44 38 24 0 42

cm 49 36 48 40 41.5 42 0






(98+148-148)/2 =

49

Clustering algorithms: Neighbour-joiningdog bear raccoon weasel seal sea lion cm

dog 0 32 48 51 50 48 49bear 32 0 26 34 29 33 36raccoon 48 26 0 42 44 44 48weasel 51 34 42 0 44 38 40seal 50 29 44 44 0 24 41.5sea lion 48 33 44 38 24 0 42cm 49 36 48 40 41.5 42 0

55.6

38

50.4

49.8

46.5

45.8

51.3

55.6 38 50.4 49.8 46.5 45.8 51.3

1. Calculate Sx = (SDx)/(n-2)


dog 0 32 48 51 50 48 49bear 32 0 26 34 29 33 36

raccoon 48 26 0 42 44 44 48

weasel 51 34 42 0 44 38 40

seal 50 29 44 44 0 24 41.5

sea lion 48 33 44 38 24 0 42

cm 49 36 48 40 41.5 42 0

55.6

38

50.4

49.8

46.5

45.8

51.3

55.6 38 50.4 49.8 46.5 45.8 51.3




dog -61.60 -58.00 -54.40 -52.10 -53.40 -57.90

bear -61.60 -62.40 -53.80 -55.50 -50.80 -53.30

raccoon -58.00 -62.40 -58.20 -52.90 -52.20 -53.70

weasel -54.40 -53.80 -58.20 -52.30 -57.60 -61.10

seal -52.10 -55.50 -52.90 -52.30 -68.30 -56.30

sea lion -53.40 -50.80 -52.20 -57.60 -68.30 -55.10

cm -57.90 -53.30 -53.70 -61.10 -56.30 -55.10


dog 0 32 48 51 50 48 49bear 32 0 26 34 29 33 36

raccoon 48 26 0 42 44 44 48

weasel 51 34 42 0 44 38 40

seal 50 29 44 44 0 24 41.5

sea lion 48 33 44 38 24 0 42

cm 49 36 48 40 41.5 42 0

55.6

38

50.4

49.8

46.5

45.8

51.3

55.6 38 50.4 49.8 46.5 45.8 51.3




branch length seal-ss = 24/2 + (46.5-45.8)/2 = 12.35

branch length sealion-ss = 24/2 + (45.8-46.5)/2 = 11.65


cat

sea lion

seal

monkey

weasel

bear raccoon

dog

cm 47.08

100.92

ss






dog 0 32 48 51 50 48 49bear 32 0 26 34 29 33 36

raccoon 48 26 0 42 44 44 48

weasel 51 34 42 0 44 38 40

seal 50 29 44 44 0 24 41.5

sea lion 48 33 44 38 24 0 42

cm 49 36 48 40 41.5 42 0






dog bear raccoon weasel ss cm

dog 0 32 48 51 37 49

bear 32 0 26 34 19 36

raccoon 48 26 0 42 32 48

weasel 51 34 42 0 29 40

ss 37 19 32 29 0 29.75

cm 49 36 48 40 29.75 0


cat

sea lion

seal

monkey

weasel

bear

raccoon

dog

cm 47.08

100.92

ss

br

Round 3bear+raccoon


cat

sea lion

seal

monkey

weasel

bear

raccoondog

cm 47.08

100.92

ss

brbrd

Round 4(bear+raccoon)+dog


catsea lion

seal

monkey

weasel

bear

raccoondog

cm 47.08

100.92

ss

brbrd

cmw

Round 5(cat+monkey)+weasel


catsea lion

seal

monkey

weasel

bear

raccoondog

cm 47.08

100.92

ss

brbdr

cmwbdrss

Round 6(seal+sealion)+(bear+raccoon+dog)


catsea lion

seal

monkey

weasel

bear

raccoondog

cm 47.08

100.92

ss

brbdr

cmwbdrss


cat

sea

lion

seal

mon

key

wea

sel

bear

racc

oon

dog

sea

lion

seal

racc

oon

bear

wea

sel

dog

cat

mon

keyUPGMA

Distance matrix methods calculate a measure of distance between each pair of species, then find a...

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Transcript of Distance matrix methods calculate a measure of distance between each pair of species, then find a...