Biodiversity Conservation and Phylogenetic Systematics

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generalizations (section “Phylogeneticgeneralizedentropies”) for an assemblage.
Then we focus on the framework of Hill numbers (section “Hill numbers and the
replication principle”), phylogenetic Hill numbers (section “PhylogeneticHillnum-
bers and related measures”) and related phylogenetic diversity measures. We also
discuss the replication principle and its phylogenetic generalization (section
“Replicationprincipleforphylogeneticdiversitymeasures”). For multiple assem-
blages, we review the diversity decomposition based on phylogenetic diversity mea-
sures (section “Decomposition of phylogenetic diversity measures”). The associated
phylogenetic similarity and differentiation measures are then presented (section
“Normalized phylogenetic similarity measures”). We use a real example for illustra-
tion (section “An example”). Our practical recommendations are provided in sec-
tion “Conclusion”.

Classic Measures and Their Phylogenetic Generalizations

Generalized Entropies

The species richness of an assemblage is a simple count of the number of species
present. It is the most intuitive and frequently used measure of biodiversity, and is a
key metric in conservation biology (MacArthur and Wilson 1967 ; Hubbell 2001 ;
Magurran 2004 ). However, it does not incorporate any information about the abun-
dances of species, and it is a very hard number to estimate accurately from small
samples (Colwell and Coddington 1994 ; Chao 2005 ; Gotelli and Colwell 2011 ).
Shannon entropy is a popular classical abundance-based diversity index and has
been used in many disciplines. Shannon entropy is

HpSh p

i

S

=- ii

=

å

1

log,

(1a)

where S is the number of species in the assemblage, and the ith species has relative
abundance pi. Shannon entropy gives the uncertainty in the species identity of a
randomly chosen individual in the assemblage. Another popular measure is the
Gini-Simpson index,

HpGS

i

S

=- i

=

(^1) å
1
(^2) ,
(1b)
which gives the probability that two randomly chosen individuals belong to differ-
ent species. These two abundance-sensitive measures, along with species richness,
can be united into a single family of generalized entropy:
q
i
S
i
Hp=-æ q q
è
ç
ö
ø

÷ ()-

=

(^11) å
1

/.

(1c)

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