The measure of order and disorder in the distribution of species in fragmented habitat.

Species distribution patterns within naturally fragmented habitat have been found to often exhibit patterns of pronounced nestedness. Highly predictable extinction sequences are implied by these nested species distribution patterns, thus the patterns are important to both the philosophy and practice of conservation biology. A simple thermodynamic measure of the order and disorder apparent in the nested patterns is described. The metric offers (i) a measure of the uncertainty in species extinction order, (ii) a measure of relative populational stabilities, (iii) a means of identifying minimally sustainable population sizes, and (iv) an estimate of the historical coherence of the species assemblage. Four presumptions govern the development of the metric and its theory: (i) the fragmented habitat was once whole and originally populated by a single common source biota, (ii) the islands were initially uniform in their habitat heterogeneity and type mix, and have remained so throughout their post-fragmentation history, (iii) no significant clinal (latitudinal) gradation exists across the archipelago so as to promote species turnover across the archipelago, and (iv) all species of interest are equally isolated on all islands. The violation of these conditions promotes species distributions which are idiosyncratic to the general extinction order expected in fragmentation archipelagos. While some random variation in extinction order is to be expected, idiosyncratic distributional patterns differ from randomness and are readily segregatable from such noise. A method of identifying idiosyncratic species and sites is described.