3. geographical and environmental spread

3.1 POTENTIAL CONTRIBUTION OF INDIVIDUAL PLANNING UNITS

When calculating summed irreplaceability, C-Plan can already weight features according to the proportion of target met for each feature (Ferrier et al. in press). This weighting can now be further adjusted to account for geographical/environmental spread. The analytical approach employed is largely new, but was inspired by recent work by Faith and Walker (1996) on the measurement of environmental diversity. The adjustment is applied only to those features for which a configuration goal has been specified, in terms of the level of spread required. Such a goal is specified in C-Plan by assigning a ‘spread radius’ to the feature concerned. For this feature, the proportion of target met for a given planning unit is then estimated for that part of the region falling within the specified radius of the unit rather than for the region as a whole. The proportion of target met for a given feature therefore varies between planning units, reflecting the extent to which reservation has been evenly spread across the range of the feature. This effectively adjusts feature weights to give emphasis to planning units in those parts of the region with poorest reservation of the feature.

For a given feature, the adjusted proportion of target met p_x in planning unit x is calculated as follows (see Figure 3 for an illustration of some of these parameters):

where d_max = the specified radius around the unit of interest
n_r = the number of reserved planning units within the specified radius
n_a = the total number of planning units within the specified radius
A_i = the area of the feature in planning unit i
d_i = the distance between planning unit i and the unit of interest
C = a user-specified constant (between 0 and 1) that determines how quickly the weight applied to surrounding planning units diminishes with increasing distance from the unit of interest
A_target = the reservation target for the feature, for the entire negotiation region
A_total = the total area of the feature, across the entire region

In the current implementation of the above approach all distances are simple geographical distances. The weighting therefore considers geographical spread but not environmental spread (although the former is likely to function reasonably well as a surrogate for the latter). The approach could be readily extended to incorporate consideration of environmental spread by replacing the underlying inter-unit distance matrix based on geographical distance (see Section 4) with one based on some amalgam of geographical and environmental distance, e.g. predicted biological dissimilarities derived from modelling of biological survey data in relation to geographical and environmental separation of sites (see report on separate CRA project: Evaluation of effectiveness of derived forest ecosystems as biodiversity surrogates and analysis of biological variation within forest ecosystems).

^{Figure 3. Parameters used to calculate the proportion of target achieved for a given feature, adjusted to reflect the geographical spread of reservation. Light shading indicates areas currently selected for reservation. Dark shading indicates the distribution of the feature of interest.}

3.2 CURRENT CONFIGURATION OF RESERVE SYSTEM

For any given feature assigned a spread radius, C-Plan can also calculate (and report on) an overall measure of the spread of reservation across the feature’s range. This index is derived using the ‘adjusted proportion of target met’ values calculated for individual planning units (see Section 3.1). The index is essentially a measure of the evenness of these values, and ranges from 0 (very uneven, biased spread of reservation) to 1 (very even, unbiased spread of reservation):

n = total number of planning units in the region (including reserved units)
p_i = proportion of target met within specified radius of planning unit i
A_i = area of feature in planning unit i

As for the patch size/connectivity index described in Section 2.2 this spread index must always be interpreted in conjunction with information on the total area of the feature reserved

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