Geoscience Reference
In-Depth Information
As noted earlier, much of the available geolocated specimen data is typically analysed in aggre-
gated form. Most commonly one is working with lists of taxa that occur within the bounds of a
geographic cell, with that cell typically being square. Having such a collection of taxa (or labels
to be more general) makes standard spatial analyses difficult to apply. One might perhaps consider
separating the data into individual layers for analysis, but there are many other approaches that
could potentially be used to analyse the collection of species, not only according to their internal
structure but also in terms of how they relate to geographic neighbours. It is exactly to address this
sort of diversity analysis problem that tools such as Biodiverse (Laffan et al., 2010; Laffan, 2011)
have been developed.
Given that one is analysing a set of labels within some spatial unit, diversity analyses have appli-
cation to many non-biological phenomena. The methods are essentially functions of sets so, as noted
previously, are generic in terms of their application domain. One recent GC example amenable to
such analyses is surnames (Longley et al., 2011; Cheshire and Longley, 2012), which themselves
have a link to human genetics (Winney et al., 2012). If one has data on an interval or ratio scale,
then methods related to the semivariance of geostatistics can also be used (Di Virgilio et al., 2012).
In their simplest form, diversity analyses assess the set of species and their abundances within
a neighbourhood, possibly in relation to the data set as a whole. Of these, the simplest analysis is
species richness (SR; Equation 6.1), which is merely the count of taxa that occur at a location. Such
analyses have a long history of application in biology (Mayr, 1944; Legendre and Legendre, 2000).
∑
1
SR
i
=
(6.1)
tT
i
∈
where
t
is a taxon in the set of taxa
T
i
at a location
i
.
A key advantage of having geolocated data is that one can begin to include the geographic
properties of the species distributions in an analysis. An important example is analyses of range
restriction (relative endemism). The range of a species is the full geographic distribution over which
it is found. A species is endemic to a region when its range is entirely bounded by that region. This
clearly has issues with boundary definitions and is therefore subject to the modifiable areal unit
problem (MAUP; Openshaw, 1983). A more effective approach is to calculate the relative proportion
of the species range that is found within an analysis window (Crisp
et al., 2001; Laffan and Crisp,
2003; Gonzales-Orozco
et al., 2011). This results in a value ranging between 0 and 1 for each spe-
cies, with widespread species having low values and range-restricted species having high values.
The sum of these values results in a measure of weighted endemism (WE; Equation 6.2), which is
analogous to a range-weighted richness score. This can then be divided by the SR to obtain an aver-
age range restriction of species in that neighbourhood (referred to as the corrected weighted ende-
mism [CWE; Equation 6.3]). Depending on the aims of the study, one can focus on those areas that
have concentrations of range-restricted species, or the inverse. By varying the window sizes (and
shapes), one can explore the rate of change of the range restriction and begin to identify the extent
of spatial regions (Laffan and Crisp, 2003). The extension of such an approach to analysing rarity is
achieved simply, as one need only replace the species ranges with their abundances.
r
R
∑
t
WE
i
=
(6.2)
t
tT
∈
i
WE
SR
CWE
i
=
(6.3)
where
R
t
is the full geographic range of taxon
t
in the set of taxa
T
i
in neighbourhood
i
r
t
is the local range of taxon
t
restricted to neighbourhood
i
