It is a universal property of the extinction process, including populations on islands, that the smaller the population, the more likely extinction is to happen, all other things being equal. This is a fundamental assumption underlying the area prediction of the MacArthurWilson equilibrium model, and it has been observed in some of the systems we have been discussing, including Channel Island birds and Bahamian spiders.
We can better understand the reasons for this relation if we examine the key processes responsible for extinction. First, demographic stochasticity, the chance occurrence of a series of deaths before any member of a population can give birth, acts at low population sizes and can cause the population randomly to go to zero. Second, environmental stochasticity, represented as variation in species traits generated by extrinsic environmental factors that themselves are varying, is important at moderate-to-large population sizes. The environmental variation can be chronic, occurring more-or-less continuously over time, or catastrophic, occurring very infrequently but being much more severe. Finally, population ceilings are important: no population has the capacity to increase indefinitely, but rather negative feedback (density-dependence) will set in as it expands, eventually forcing the population to hover at or near some ceiling in numbers. With lower and lower values of the ceiling, a population would be correspondingly more and more vulnerable to demographic-stochastic extinction.
Many models ofpopulation extinction exist that can be applied to islands, but rarely has a single model encompassed both kinds of stochasticity as well as population ceilings. An international collaboration recently attempted to apply such a model to data for spider populations on 77 islands, censused annually over a continuous 20 year period. Two species were contrasted, one with larger populations sometimes crashing quickly to extinction and having a much weaker relation of extinction likelihood to population size than the other species. A simple model ignoring life cycles and a more complex model with detailed life-cycle characteristics estimated from the field were constructed; both models did well for large population sizes, but the complex model was necessary to fit data from small population sizes, as the life cycles interact with the various forms of stochasticity. In particular, the prediction that extinction probabilities are very sensitive to juvenile survivorship emerged from the analysis. This is in contrast to a similar approach for a noninsular species, Bonelli's eagle (Hieraatus fasciatus), which predicted sensitivity to adult survivorship. Conclusions such as these are in fact detailed expectations about extinction likelihood, in turn guiding conservation efforts in preserving species.
See also: Metapopulation Models.
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