On parametric fragmentation measures

In the land scape ecolo gical litera ture, a numb er of measures have bee n proposed for quantifying land-scap e fragmen tation ba sed on distinct objec tives and motiv ations. Howeve r, non e seems to be general ly pre-ferred. The main reaso n for this dis agreemen t is that, from a statisti cal viewpoi nt, by map ping fragmen tation into a single scalar , informat ion is neces sarily lost and no ideal fun ction is ab le to uniqu ely char acterize all aspe cts of land scape fragmen tation. A more compl ete summa rization of fragmen tation is possible if, ins tead of one sin gle index, a paramet ric index fam ily is applied whose memb ers have varyin g sensitiviti es to the prese nce of larg e and small land scape pa tches. While tradition al indices supply point description s of fragmen tation, accord ing to a pa rametric fragmen tati on fam ily H a , there is a cont inuum of possible fragmen tati on measur es that diff er in their sensiti vity to the prese nce of large and small pa tches as a func tion of the scalin g paramet er a. There fore, changing a allows for vector descrip tion of fragmen tation. The purpose of this pape r is to introd uce a pa rametric general ization of Shann on’s entropy to summa rize landscap e fragmen tation. A small set of artific ial landscap es is used to clarif y our proposal .