Biodiversity Conservation and Phylogenetic Systematics

161

q^ =

2

Relative

abundances

Phylo-Morisita-Horn^1

11

• 
  


• 
  


• 
  

  ()

  
  


• 
  

  ()
  QQNT

  
  

Q

ga

a

/

Phylo-regional-overlap^1

1

• 
  


• 
  


• 
  

  ()

  
  


• 
  

  ()
  QQ
  NT

  
  

Q

ga

g

Absolute abundances

1

1

2

1

2

• 
  


• 
  

  ()

  
  


• 
  

  Î>()

  
  

Î=

åå

åå

i

imk

N

im

ik

i

N ik

ik

T

T

Lz

z

NL

z

B

B

1

1

2

2

• 
  


• 
  

  ()

  
  


• 
  

  Î>()

  
  

Î

+

åå

å

i

N imk

im

ik

i

ii

T

T

Lz

z

NL

z

B

B

1.

zik

: species abundance (or any species importance measure) descended from branch

i in the

kth assemblage,

zz

zz

i

N k

ik

k

S i

ik

+

=

+

=

==

åå

11

,

(assemblage size of the

kth assemblage in the present-day assemblage with species richness

S), and

zz

S i

N k

ik

++

==

=

åå

11

(the total abundance in the present-day pooled assemblage).

B

: the T

set of all branches in the time interval [−

T, 0],

Li

: length of branch

i

2.

q^ =

0.

Lγ

(T

) and

Lα

(T

):

gamma

and

alpha

total

branch

length

(i.e.,

Faith’s

PD)

3.

q^ =

1.

H

P,γ

and

H

P,α

: gamma and alpha phylogenetic entropy

4.

q^ =

2.

Q

and γ

Q

: gamma and alpha quadratic entropyα

Phylogenetic Diversity Measures and Their Decomposition: A Framework Based...