A Comment on Quinn and Hastings: Extinction in Subdivided Habitats

In a review of the question of habitat subdivision for the conservation of a target species, Quinn and Hastings (Conservation Biology 1:198-208) review the SLOSS (Single Large Or Several Small) controversy and add a new view of their own. By likening reserve design to production line engineering and species to failure-prone components, they conclude that redundancy is the best policy in planning reliably for the persistence of a species. Following models of stochastic population growth developed by Leigh (1981), they derive a formula that specifies that the number of equally sized subdivided habitat patches be equal to the square root of the numeric carrying capacity of the target species. For example, given sufficient habitat to support 1000 individuals, it would be best to divide this habitat into 32 small patches of 32 individuals each. For black rhinos, down to about 8000 individuals, this works out to 90 reserves of 90 rhinos each. Thus, they push the old controversy of SLOSS to a more extreme dichotomy, SLOPP (Single Large Or Plentifully Patchy). While they do caution that their square root result should not be taken too seriously, they add that "the important point is that considerable redundancy in reserve systems may be effective in preventing overall extinction." I challenge the foundations of this theoretical finding. For the purposes of this discussion, I define Single Large as 1 or 2 patches (100), Several Small as 3 to 10 patches (101), and Plentifully Patchy as 10 to 100 patches (102). Quinn and Hastings' support for Plentifully Patchy is based on the view that each population is isolated and dynamically independent. That is, there is no movement of individuals, which would allow gene flow, rescue (in the sense described by Brown & Kodric-Brown [1971]), and recolonization; nor are their populations assumed to share in any way a common environment. Further, Quinn & Hastings ignore genetics, which would affect isolated small populations earlier and more seriously than large populations, and demographic stochasticity, which would also have a disproportionately larger effect on small populations. With regard to demographic stochasticity, it must be understood that it is always a factor in extinction, for it applies whenever a population becomes small, which it must do at least once on the way to extinction. Together, these omissions mean that their Population Vulnerability Analysis (Gilpin & Soule 1986) is incomplete probably seriously so and that it cannot, therefore, be taken as an unalloyed management recommendation. There might, however, be a small subset of species for which all of the considerations mentioned above are of secondary importance. For these possible cases, I wish to criticize Quinn and Hastings' model in the context of their own assumptions. For concreteness, I refer to a situation where the habitat will support 256 individuals of the species of concern. Thus, the Plentifully Patchy strategy is for 16 habitat subdivisions of 16 individuals each. Figure la shows the Single Large configuration, while Figures lb and lc show two differently spaced versions of Plentifully Patchy, which I term Close Separated and Far Separated, respectively. Because they assume isolation and independence, Quinn and Hastings accept the two separated cases (Figs. lb and Ic) as equivalent, and both, according to their reasoning, as superior to the Single Large. Quinn and Hastings have reached their conclusion based on the ideas of reliability theory, which is a successful and important branch of engineering and economics. Reliability theory speaks to the failure time of a system fashioned of components each of which has its own characteristic probabilities of failure. This theory assumes that it is possible to place components in parallel. For several identical components in parallel, the