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Up- and downscaling methods

“Scaling” means transforming a quantity measured at one scale so that it applies to a narrower or finer scale (downscaling) or a broader or coarser one (upscaling). The SCALES project produced several scaling tools, which are summarised here.

Scaling tools from SCALES

Scaling

Some properties scale linearly with space or time, being proportional to extent. These typically include population size, total carbon stock and water runoff, in a homogeneous system - or at spatial extents large enough with respect to the grain of heterogeneity. Other properties need not vary at all when the extent varies, because they are averages or ratios with respect to extent. These typically include population density (per unit space), productivity (per unit time and space) and rainfall (per unit time) - again, in a homogeneous system. A third class of properties vary with extent but are not generally proportional to it. These may include the richness of species or alleles in a region: properties that are scale-specific. Such properties raise the most challenging questions of scaling. Perhaps a transformation of axes will provide a linear relationship with extent, but often the problem is better solved when we have an understanding of underlying ecological processes.

Scaling includes upscaling and downscaling. Upscaling is often a form of extrapolation to a larger extent or coverage (Fig. 1a), while downscaling is often a form of extrapolation or projection to an increased resolution (Fig. 1b). One of the earliest SCALES reports concluded that there are important non-linearities between drivers of biodiversity change as measured at different spatial scales and, because general methods for downscaling these drivers do not exist, recommended that policy tools incorporate information from local scales. However, in some cases, especially where physical and ecological processes are concerned, downscaling and upscaling are possible, and the SCALES project produced some tools to do this.

Tools

Downscaling species' occupancy
The Thomas-model occupancy downscaling method predicts the proportion of grid cells that a species would occupy at an arbitrary resolution, based on observed spatial patterns of occupancy at a number of coarser resolutions. In the published example (Azaele et al. 2012), data for 16 different British plant species at grid-sizes of 40000, 10000 and 2500 km2 were sufficient to give good predictions for occupancy rates at grid-sizes down to 0.25 km2. The method currently exists in the form of computer code to be implemented in the software Mathematica.

Upscaling biodiversity estimates
A range of methods have been proposed for predicting species richness in a contiguous region using species richness values from isolated local surveys within the region. Kunin reviewed sixteen of these, including the main published methods, in competition, to see which could best predict species richness values for vascular plants in different regions of Great Britain using samples representing only 0.0002% of the island's total area. The best predictions of total species richness came from the incidence-based sampling-without-replacement method of Shen and He (2008), with average errors of 10%, while the best predictions of values along the entire average species-area curve came from the log-normal ranked-species-abundance method of Ulrich and Ollik (2005), with average errors of about 27% (and 21% for total richness). Other methods are in development.

Downscaling climate
micEuroclim is a method for relating local soil surface temperatures to physical variables that are readily-available at coarse spatial scales. Digital elevation data are used in a projection of the coarse-scale variables to a fine-scale spatial resolution, with the resolution of the elevation data determining the degree of "downscaling". Predictions may be made for two different temporal resolutions: monthly means (a kind of temporal upscaling) and instantaneous points (a kind of temporal downscaling).

Downscaling environmental variables to optimise sample sites
The spatial-downscaling conditioned Latin hypercube sampling (sdcLHS) method uses available spatial data for a set of environmental variables to recommend a sample of locations that will optimally capture the variation in the environmental variables. The sdcLHS method uses experimental variograms to downscale measured variables to a continuous plane and then seeks a set of locations expected to represent the full distributions of the environmental variables. These locations may then be used as the basis of a data-collection programme for statistically fitting species distribution models, for example.

Scaling habitat prioritisation
There are two geographical methods for prioritising areas of habitat to be protected under various constraints. Each of these can be used for a kind of scaling in which the total area under consideration is varied while observing how the priority attributed to some focal habitat patch(es) varies. The National Responsibility Tool, created within SCALES, calculates scores for the relative importance of a specified habitat type within specified geographical areas (typically countries), by comparing local coverage with broarder-scale (e.g. global) coverage of the habitat. ZONATION is a flexible tool that can account for a wide range of prioritisation factors and ranks locations for their priority. As expanded within SCALES, ZONATION now allows species to be weighted differently in different parts of the landscape.


Figure 1; Various types of upscaling and downscaling. (a) Two forms of upscaling: (i) extrapolating data from a single small region (dashed enclosure) to predict some quantity in a target region of larger extent (solid enclosure), or (ii) upscaling from a number of samples (dotted enclosures) that have incomplete coverage of the target region. In some situations, corresponding forms of downscaling might be useful. (b) Downscaling by resolution: relating information at a coarser resolution (dark blue grid) to that at a finer resolution (pale blue grid). In some situations, a corresponding form of upscaling might be useful.

References

Azaele S., Cornell S.J. & Kunin W.E. (2012). Downscaling species occupancy from coarse spatial scales. Ecological Applications, 22, 1004-1014.

Shen T.J. & He F.L. (2008). An incidence-based richness estimator for quadrats sampled without replacement. Ecology, 89, 2052-2060.

Ulrich W. & Ollik M. (2005). Limits to the estimation of species richness: The use of relative abundance distributions. Diversity and Distributions, 11, 265-273.

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