
34 Pedodiversity
functions may be applicable to any set of classes of events C(O) for which
the weight can be made relative to the total weight, i.e., p
i
= w
i
=
Q
i
/ΣQ
i
,
with Σp
i
=1.
4.1 Crispy diversity measures
These measures correspond to the formulas of entropies (H) of Rényi
(1961), Patil and Taillie (1976) and of Hill (1973) that are respectively
known as alpha-diversity, beta-diversity and N-diversity.
The fi rst is:
α
α
α
−
Σ
==
1
ln
)(
ii
p
HOD
α
α
α
1)
The second is:
β
β
β
)1(
)(
1+
Σ−
==
ii
p
HOD
β
β
β
2)
The third is:
()
1
1
()
i
a
a
ai
DO N p
−
==Σ
(
(
3)
The parameters α, β and a defi ne an infi nite number of possible “point
measures” of diversity for the corresponding formulas, ...