For a recent publication, the authors identified a seven-region model of mammal family distribution patterns, in which each unit contributes equally to the system's overall statistical characteristics of diversity, despite its individual units having measurably different levels of diversity and endemism. This systemization presents a highly efficient descriptive model that can possibly be interpreted as a form of natural classification. An additional analysis of the same mode is described here, in which the seven-region model of the distribution of mammal families' spatial affinities is shown to closely approach a most-probable-state arrangement, as assessed through combinatorics, raising some important questions about how macroevolutionary patterns might self-organize spatially. One of the possible practical applications of the overall approach is to areal representation; statistical moments of the underlying world patterns can be used to characterize faunal statuses at any individual location by relating the latter to the former. Through this approach, classical concepts such as corridors, tracks, and transition zones might be re-examined in a manner that better lends itself to hypothesis testing. An arbitrarily chosen bounded area, the conterminous United States, is treated in this fashion by way of illustration.
Keywords: distribution patterns; evolution; faunal classification; mammals; maps; natural systems.