Analysis of refugial potential

The potential of a given location (grid cell) to serve as a refugium, for a given biological group under a given climate scenario, was estimated using predictions from the fitted GDM model for that group. This model predicts the level of compositional dissimilarity d_ij , and conversely similarity s_ij = 1– d_ij , expected between two locations i and j knowing only the values of relevant environmental variables at these locations.

Predicted similarities can range between zero (where two locations are predicted to have no species in common) and one (where the locations are predicted to be identical in terms of species composition).

When predicting compositional similarity between location i and j under present environmental conditions, we can denote this as:

𝑠

60 Climate change refugia for terrestrial biodiversity

Invoking space-for-time substitution, a fitted GDM model can also be used to predict the compositional similarity between a given location i in the present and this same location in the future under a given climate scenario:

𝑠

This provides an indication of the amount of change in species composition expected at this location, and has been used extensively in previous GDM-based studies mapping potential levels of compositional turnover (vs. compositional stability) under climate change across the Australian continent (Dunlop et al. 2012, Prober et al. 2012, Williams et al. 2012b) and across North America (Fitzpatrick et al. 2011, Blois et al. in revision).

Three further types of compositional similarity can be readily estimated using this same approach:

𝑠

(the compositional similarity expected between location i under present environmental conditions, and a different location j in the future under a given climate scenario);

𝑠

(the compositional similarity expected between location i in the future under a given climate scenario, and location j under present conditions); and

𝑠

(the compositional similarity expected between locations i and j in the future under a given climate scenario).

These different types of predicted similarity can be combined in various ways to produce a wide range of biotically scaled measures of climate stability, the velocity of climate change, and novel and disappearing climates. Refer to Dunlop et al. (2012) and Williams et al. (2012b) for GDM-based examples of such applications for the Australian continent and Queensland respectively.

For the current project we developed a new measure, tailored specifically to the challenge of identifying potential refugia under climate change. This calculates the refugial potential r of grid-cell i under a given climate scenario as:

𝑟

= ∑

𝑠

�∑

𝑠

�

The set of n grid-cells with which cell i is compared in these calculations is drawn from within a specified spatial radius around the cell of interest (Figure 33). To assess the effect that variation in dispersal capacity between different organisms is likely to have on refugial potential, each analysis (for a given combination of biological group and climate scenario) was repeated using three different sets of surrounding grid-cells:

• all cells within a 1 km radius of cell i

Climate change refugia for terrestrial biodiversity 61

• a sample of 20 000 cells within a radius of 100 km of cell i with these cells selected randomly according to a half-Cauchy distribution (Shaw 1995) with a mean dispersal distance of 10 km

• as for the previous sample but with a mean dispersal distance of 50 km.

Figure 36: The two types of predicted compositional similarities used to

calculate refugial potential for a given grid-cell i under a given climate scenario:

in red, predicted similarities, in the future, between cell i and each of n cells within a surrounding radius; and in blue, predicted similarities between cell i under future environmental conditions and each of the same n cells under present conditions.

This particular measure of refugial potential assesses the extent to which a given location is predicted to exhibit an environment in the future (i.e. under a given climate scenario) that is likely to have undergone a marked proportional reduction in extent, and will be relatively rare throughout the surrounding landscape as a result of climate change (note that the squared denominator in the above formula results from dividing the proportional reduction in extent by the extent remaining in the future). This general concept is illustrated in Figure 34 in which, for ease of explanation, both geographical space and environmental space have been simplified to a single dimension each (the geographical dimension can be thought of as a straight-line transect across a

landscape, whereas the environmental dimension can be thought of as a biotically-scaled temperature gradient). The concentric ellipses centred on each of the labelled locations depict decreasing levels of compositional similarity with increasing distance from a location in biotically scaled environmental space, and decreasing likelihood of dispersal with increasing distance in geographical space.

A visual impression of the refugial potential of each of the labelled locations (A to E) can be obtained by comparing the extent to which the concentric ellipses, centred on the future environment of that location, overlap with current environments in the surrounding landscape versus the extent of overlap with future environments in the same landscape. For example, the future environment at location B (think of this as situated on a flat plain surrounded by an expanse of similar elevation, and therefore temperature) is expected to be much more extensive in the surrounding landscape under climate change than it is at present, and this location therefore has very low refugial potential. In contrast, the future environment of location E (a mountain peak) is

62 Climate change refugia for terrestrial biodiversity

expected to be considerably less extensive in the surrounding landscape than it is a present, indicating good potential for this location to serve as a refugium for biota associated with this particular environment. Applying the same logic to the other labelled locations, location A (a relatively high outcrop, or sheltered topographic

position in the middle of a flat plain) and location D (at mid-elevation in highly dissected terrain) exhibit moderate levels of refugial potential (but less than location E), whereas location C has relatively low refugial potential (but more than location B).

Figure 37: Diagrammatic representation of the shifting relationship between geographical space and biotically scaled environmental space under climate change. For ease of explanation, both geographical space and environmental space have been simplified to a single dimension each. The geographical dimension can be thought of as a straight-line transect across a landscape, and the environmental dimension can be thought of as a biotically scaled

temperature gradient. The labelled locations (A to E) are discussed in the text.

The concentric ellipses centred on each of these locations depict decreasing levels of compositional similarity with increasing distance from a location in biotically scaled environmental space, and decreasing likelihood of dispersal with increasing distance in geographical space.

The calculation of refugial potential was carried out using the MPI/ OpenMP hybrid implementation of the Muru GDM model, developed by Tom Harwood and Maciej Golebiewski at CSIRO. Utilising 120 to 160 parallel processes, the required CPU time of 344 hours (for each combination of biological group, climate scenario, and dispersal distance, across the entire continent at 250 m resolution) was reduced to a more manageable 3.6 hours, subject to availability of the required number of nodes on the CSIRO High Performance Computing cluster.

4.4 Results and outputs