A partial order approach for summarizing landscape quality

Abstract

We propose a simple mathematical framework to define consistently the environmental quality of a given landscape based on the relative abundances of the constituting land cover classes. Unlike traditional diversity measures, the new method does not evaluate the simple dispersion of the relative abundances of land cover classes, but assigns a weight to each land cover class according to the rank along a gradient of environmental quality. To clarify the ideas discussed, the method is illustrated with data from a pilot study to assess landscape changes in an Italian periurban area over the last 50 years

The role of environmental and socio-demographic indicators in the analysis of land use changes in a protected area of the Natura 2000 Network: the case study of Lake Trasimeno, Umbria, Central Italy

“…In many cases very rapid socio-demographic dynamics have caused the creation of new landscapes whose changes have been studied by means of territorial analysis and modellistic approaches (Sui and Zeng 2001). It is also necessary to mention that landscape environmental quality often depends on the variety and dominance of land use classes (Ricotta et al 2003).…”

Using the natural capital index framework as a scalable aggregation methodology for regional biodiversity indicators

“…This relationship is relatively straightforward in the case of the habitat hectares approach and the hemeroby index, but it also holds in the case of ILC (and IVN) as it is shown in Appendix A. Ricotta et al (2003) provide further justification for the ILC approach, showing that ILC based landscape evaluation naturally conforms to the partial Lorenz ordering arising from the order of the naturalness categories-which can be seen as an important sanity criterion for any potential aggregation schemes. It can be shown that this partial Lorenz ordering is also preserved by all well defined NCIs (Appendix B).…”

“…To show this, we first prove an even stronger lemma: that the formula of natural aggregation (NCI) equals to the Lebesgue integral of the function underlying the intrinsic Lorenz majorisation for landscapes suggested by Ricotta et al (2003). In other words, we show that ∀T ∈ T : NCI(T ) = [0,1]…”

“…If for A and B the cumulative relative areas (starting from the most natural category) are all larger for A than for B, then landscape A is said to majorise (dominate) landscape B in terms of naturalness. Ricotta et al (2003) provides a proof that the Index of Landscape Conservation (ILC, Pizzolotto & Brandmayr 1996) conserves this majorisation intrinsic to the naturalness scale used. We will show here, that the aggregation scheme of the NCI formula using any well-defined quality weights will also conserve this majorisation.…”

“…As Ricotta et al (2003) pointed out, the preservation of this intrinsic partial Lorenz ordering ( ) of the landscapes is an important sanity criterion that any spatial aggregation scheme should preserve. We prove here that this ordering is preserved by the natural aggregation scheme, thus:…”