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of species as a function of environmental change and with geographic distance. For unsampled loca-
tions, this allows one to predict, if not the actual species, at least how many there are likely to be.
This is a computationally involved process requiring a combination of approaches with application
to, or parallels in, GC.
Biodiversity itself can be partitioned into three interdependent components referred to as α-,
β- and γ-diversity (Whittaker, 1960). Each component operates at different scales (see Tuomisto,
2010), with γ-diversity being the total effective number of species in a study area. This can then be
partitioned into α-diversity, the mean effective number of species per subunit (mean SR; Equation
6.1), and β-diversity, the rate of change of diversity between spatial units. β-diversity is more gener-
ally referred to as compositional turnover, as many of the indices devised to measure it do not fol-
low the strict definition (Tuomisto, 2010). Such compositional turnover is typically measured along
geographic gradients but can also be assessed for environmental gradients.
One can potentially derive species composition across regions using species distribution models
applied to multiple species, with α, β and γ calculated from these surfaces. However, the fact that
the observation data are typically sparsely distributed geographically, and frequently biased, makes
such models difficult to calibrate for individual species across the entire regions (Newbold, 2010).
Predictive modelling of SR has proven effective (e.g. Bickford and Laffan, 2006), but rates of turn-
over cannot be estimated from these predictions. For example, two locations might have the same
predicted number of species, but one cannot infer how many species are common to both locations.
One recent approach is to model the turnover component of diversity patterns (Ferrier et al.,
2007) by assessing the relationship between biological and environmental turnover, an approach
termed GDM. In this approach, one does not obtain an estimate of which species are occurring
where. Instead one obtains an estimate of the rate of change of species between any pair of locations
as a function of the environmental change occurring (Figure 6.3).
GDM is essentially a combination of generalised linear models, non-linear matrix regressions
and generalised additive models with monotone regression splines (Ferrier et al., 2007). In the
GDM approach, one constructs a site-by-site matrix of turnover scores as dissimilarities. This turn-
over is then compared with the relative turnover of environmental conditions for the same site-pair
locations. This environmental turnover is a function of the absolute difference of the environmental
values between each site pair, but where the original environmental layers have been first trans-
formed using an I-spline basis function (Ferrier et al., 2007).
The choice of turnover metric can be an important consideration in a GDM, with a plethora of
indices available (see Tuomisto, 2010). Most GDM research to date has applied species-based turn-
over metrics. However, these have the potential issue that the differences between locations can rap-
idly become saturated, losing the ability to differentiate between certain types of biome (Rosauer
et al., 2014). For example, a rainforest site (site 1) might have no species in common with a second
rainforest site some distance away (site 2). Equally, it will have no species in common with a desert
site (site 3). There will be complete species turnover from site 1 to each of sites 2 and 3, a difference
that could be important in model calibration and particularly interpretation. In such cases, one can
begin to explore indices of phylogenetic turnover (e.g. Rosauer et al., 2014). A tree-based turnover
measure is simply a function of the branch lengths shared between two sites, such that sites 1 and
2 of the previous example will share some phylogenetic material, while very little will be shared
with site 3.
GDM is a method with considerable potential but also with many open research questions. Three
examples related to GC are considered here.
First, in most investigations, the available environmental layers are available at a finer resolution
than that used for the analyses. In these cases, the values are aggregated to the analysis resolution
by taking the mean of observations within the coarser resolution. As with any aggregation process,
details can be lost about the statistical spread of the data values. There is some potential in analysing
the turnover of quantiles of these aggregated values, analogous to the quantile regression process
(Cade and Noon, 2003).
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