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In this paper, we apply a special application of the Rao quadratic diversity for multiscale analysis of land use changes in a mixed agricultural-forest landscape in Central Italy. The proposed approach is similar to a block-size analysis of compositional diversity for which a given landscape is overlaid with a series of square grids composed of increasingly larger boxes. The combination of land cover classes in each box is recorded, and the Rao quadratic diversity is computed for the frequency distribution of the land cover classes at each box-size. Plotting compositional diversity

It has been widely recognized that landscape structure is spatially correlated and scale-dependent; that is, it changes with the scale of observation [

Besides scale dependence, to be useful, a measure of landscape structure should imply something on the amount of “correlation” between the landscape components that generate a pattern. As a rule of thumb, the larger and more intricate the correlations between the landscape components, the more “complex” (structured) the system [

Out of the many methods for summarizing multiscale landscape structure [

Imagine a landscape composed of M land cover classes that is overlaid with a grid of square boxes of linear size, δ. The combination of LCCs in each box is recorded to obtain the frequency distribution p_{i} = (p_{1}, p_{2},..., p_{N}) of the N combinations of LCC at the given scale of observation, where p_{i} is the relative abundance of combination i (

A drawback of this procedure is that, with usual diversity indices, all observed LCC combinations are considered equally distinct. For instance, the hypothetical combination, ABC, is equally distinct from both combinations ABD and DEF. However, ABC and ABD share two LCCs, while ABC and DEF do not have any LCC in common, such that the dissimilarity between ABC and ABD is lower than the dissimilarity between ABC and DEF.

One solution to overcome the mutually exclusive nature of LCCs consists in using instead an index, like the Rao quadratic diversity [_{ij}_{ij}_{ji}_{ij}_{ij}_{i}_{j}^{2}, quadratic diversity reduces to the variance of

If ^{N}− 1, _{ij}

The value of the proposed measure is illustrated to the multiscale analysis of landscape changes taking place from 1954 to 2000 in the municipality of Isernia (Central Italy). The study area (6,874 ha in Central Italy;

Location of the study area.

The municipality of Isernia consists of a small town of roughly 22,000 inhabitants surrounded by a hilly landscape with agricultural land cover in the alluvial plain and more natural LCCs at higher elevations. Using aerial photographs, two land cover maps (scale 1:25,000) of the study area were produced. Ten land cover classes were identified in the study area, and their distribution in 1954 and 2000 is shown in

Land cover maps of the study area in 1954 and 2000.

In 1954, the study area can be described as a prevalently rural landscape constituted by a mosaic of annual crops together with olive groves and vineyards. At higher elevations, the dominant land cover classes were composed of natural and semi-natural vegetation types, such as extensive grasslands and broadleaved forests. In 2000, landscape heterogeneity tends to increase. Following the abandonment of the agro-silvo-pastoral practices in the least accessible areas, transitional shrublands became a significant constituent of the 2000 landscape. On the other hand, on lowlands and alluvial plains, traditional farming methods were extensively replaced by more intensive agricultural practices, leading to a homogenization of the former heterogeneous rural matrix into large crop fields. For a thorough analysis of the temporal dynamics of the study area, see [

The land cover maps of _{ij}_{Jac}

The plots of

Plot of the Rao index

During 1954–2000, the region of Isernia experienced intense land cover changes that were mainly related to the marginalization of traditional agricultural practices due to ongoing socioeconomic shifts, like the aging and diminishing of the agricultural population, as more people become increasingly employed in manufacturing, construction and service sectors [

Given the direct relationship between Rao’s quadratic diversity and variance, the proposed method may be interpreted as an extension of block-size analysis of variance (ANOVA; see, e.g., [

In the proposed multivariate version, the most important methodological decision is about the method to be used to calculate dissimilarity, as the results obtained will depend to a certain extent on the multivariate measure, _{ij}

Finally, unlike traditional methods of landscape change analysis, which are usually based on transition matrices (see [

We gratefully acknowledge three anonymous referees for helping to improve the original version of the manuscript.

The authors declare no conflict of interest.