large increases in population that have been documented for many species in new ranges (Thebaud and Simberloff 2001). When biological control of an invasive species, which involves the deliberate introduction of parasites and predators of the species from its native range, is successful, it is powerful confirmation of the potential role of biotic constraints in curbing a species’ abundance and distribution.

In this chapter, we first review the stochastic character of forces that determine the establishment or persistence of populations, especially the small populations that typify immigrants. We then illustrate how biologists have attempted to categorize the role of a population’s spatial structure in interacting with the stochastic character. Without attempting to be inclusive, we next proceed to illustrate the breadth of environmental factors, both abiotic and biotic, that form the specific forces that immigrant populations encounter. Finally, we provide illustrations of life-history traits that can influence immigrants’ tolerance of a new range. In compiling this chapter, we were aware that some aspects of the discussion of persistence are equally pertinent to the proliferation and spread of a species, the topic of Chapter 4. As a result, we introduce these shared properties or circumstances here and mention them only briefly in Chapter 4. Although additional observations, new hypotheses, and empirical testing are needed to confidently predict the net effect of these countervailing forces on the outcome of a specific species’ introduction, a body of data that underlie the basis for establishment is slowly emerging.

STOCHASTIC EXTINCTION— THE PERILS OF SMALL POPULATIONS

The defining demographic of an introduced species is typically its small population. Even the planet’s most abundant and widespread invasive species commonly began as “rare” species in their new ranges, compared with the size of their populations in their native ranges. (There are exceptions; see Eckert et al. 1996). Although population extinction can result from deterministic processes— ranging from direct eradication by humans to fire or flooding—a pervasive threat to the persistence of small populations is stochastic extinction. This risk of extinction for small populations transcends the taxonomic groups we examine here. For plants and arthropods, the topic is often examined in terms of the minimal viable population (see Box 3-1); for pathogenic microorganisms, it is referred to as the minimal infective dose. Consequently, our remarks should be interpreted as relevant for all taxonomic groups unless stated otherwise.

Demographic models have relied on such quantities as the mean population growth rate and the variance in growth rate (Leigh 1981, Goodman 1987) and predict that persistence time increases slowly with increasing carrying capacity. As a result, extinction is predicted to be much more likely at lower population numbers, a conclusion that is biologically realistic. To facilitate discussion of the importance of stochastic extinction in the early stages of establishment, the forces



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