fHill {OnomasticDiversity} | R Documentation |
Calculate the Hill's diversity numbers
Description
This function obtains the Hill's diversity numbers introduced by M. O. Hill. It is a method for quantifying species biodiversity that can be adapted to the context of onomastic.
Usage
fHill(x, k, n, location, lambda)
Arguments
x |
dataframe of the data values for each species. |
k |
name of a variable which represents absolute frequency for each species. |
n |
name of a variable which represents total number of individuals. |
location |
represents the grouping element. |
lambda |
free parameter. |
Details
For a community , the Hill's diversity numbers are defined by the expression
with the restriction
where
represents the relative frequency of species
and
are all species at the community, species richness, and
is a free parameter. (This is equivalent to the exponential of Renyi's generalised entropy). The Renyi entropy of order
, where
and
, is defined as
Here,
is a discrete random variable with possible outcomes in the set
and corresponding probabilities
for
. The logarithm is conventionally taken to be base 2, especially in the context of information theory where bits are used. If the probabilities are
for all
, then all the Renyi entropies of the distribution are equal:
. In general, for all discrete random variables
is a non-increasing function in
..
Particular cases of values:
, it corresponds species richness;
, it corresponds the exponential of Shannon's entropy; and
, it corresponds the 'inverse' Simpson index.
In onomastic context, denotes the relative frequency of surname
in region (
community diversity context)
and
are all surnames in region
.
Value
A dataframe containing the following components:
location |
represents the grouping element, for example the communities / regions. |
hill |
the value of the Hill's diversity index. |
Author(s)
Maria Jose Ginzo Villamayor
References
Hill, M. O. (1973). Diversity and Evenness: a unifying notation and its consequences. Ecology, 54, 427–32.
See Also
Examples
data(surnamesgal14)
result = fHill (x= surnamesgal14, k="number", n="population",
location = "muni", lambda= 0)
result
data(namesmengal16)
result = fHill (x= namesmengal16, k="number", n="population",
location = "muni", lambda= 0)
result
data(nameswomengal16)
result = fHill (x= nameswomengal16, k="number", n="population",
location = "muni", lambda= 0)
result