The nested subset hypothesis was formulated to describe and explain patterns in the community structure of insular mammal faunas which are in the state of ‘relaxation’. The hypothesis states that the species comprising a depauperate fauna should constitute a proper subset of those in richer faunas, and that an archipelago of such faunas arranged by species richness should present a nested series. The non‐randomness of this pattern is evaluated for montane mammals in the American Southwest using Monte Carlo simulations under two sets of conditions. First, we constructed model archipelagos with the observed distribution of species richnesses, drawing individual species at random (without replacement) from the species pool (RANDOM0). Secondly, we constructed model archipelagos having the observed distribution of species richnesses, but weighted the selection of species by their actual frequencies of occurrence (RANDOM1). The degree of nestedness in the model archipelagos was then used to assess the non‐randomness of the observed structure. Actual Southwestern mammal faunas have a far more nested structure than model archipelagos produced by either RANDOM0 or RANDOM1, and there is virtually zero probability that observed structure is represented in the distribution of scores from either simulation run. Similar analyses were conducted on other archipelagos to determine the generality of this relationship and to identify variables putatively responsible for its production. Mammal faunas of large islands off the coast of Maine, U.S.A., studied by Crowell (1986) also comprise nested subsets, as do those inhabiting islands off the coast of Baja California, Mexico, studied by Lawlor (1983). Significantly, when the Baja archipelago is divided into landbridge islands (which are presumed to be relaxing to lower species level) and oceanic islands (where species number is limited by successful overwater dispersal), only the former show significant nestedness under the more stringent conditions of RANDOM1. These results and theoretical considerations suggest that selective extinction of species may be chiefly responsible for the nestedness in natural archipelagos. Our conclusions have obvious implications for the design of natural preserves (e.g. SLOSS): several small fragments of a single biota can be expected to support nested subsets of the species originally present or that would likely be retained in a single large preserve. Even more sobering are arguments raised which suggest that the faunas of preserves established in different habitats within the same biome might be expected to converge in composition via selective ext