On parametric fragmentation measures

In the landscape ecological literature, a number of measures have been proposed for quantifying landscape fragmentation based on distinct objectives and motivations. However, none seems to be generally preferred. The main reason for this disagreement is that, from a statistical viewpoint, by mapping fragmentation into a single scalar, information is necessarily lost and no ideal function is able to uniquely characterize all aspects of landscape fragmentation. A more complete summarization of fragmentation is possible if, instead of one single index, a parametric index family is applied whose members have varying sensitivities to the presence of large and small landscape patches. While traditional indices supply point descriptions of fragmentation, according to a parametric fragmentation family H(alpha), there is a continuum of possible fragmentation measures that differ in their sensitivity to the presence of large and small patches as a function of the scaling parameter alpha. Therefore, changing alpha allows for vector description of fragmentation. The purpose of this paper is to introduce a parametric generalization of Shannon's entropy to summarize landscape fragmentation. A small set of artificial landscapes is used to clarify our proposal.