Bierne (1975), in a widely cited retrospective analysis of the role of initial colony size in establishment, reviewed Canadian biological control programs. He found that if fewer than 5000 individuals were released, about 9% of the species became established—a percentage that is similar to the 10% estimated for accidental introductions (Williamson 1996). If at least 30,000 individuals were released, 79% of the species became established. The average number of individuals per release site also seemed to be important; establishment rates increased from 15% to 65% of species if at least 800 individuals were released at a single location. Bierne’s (1975) approach has limitations: the role of the number of individuals released in each case might be confounded by the traits of particular species; and these traits also contribute to establishment, such as a high reproductive rate or abundant distribution in their native range (Crawley 1986, 1989b). Grevstad (1999a) took an experimental approach in assessing relationships between population size and persistence. She followed the fate of 92 experimental releases of two chrysomelid beetles for three full generations and found that the probability of establishment increased over the range of initial beetle density (20, 60, 180, and 540 beetles). Population growth rates varied among environments but were positively related to release size. In a second experiment, in 20 releases of single gravid females, only one female founded a population that persisted for the duration of the 3-year study.
Although Levine and D’Antonio (1999) contend that any community, given enough propagules, can be invaded, nonindigenous insects are usually introduced accidentally and presumably arrive in low numbers in most cases. Small populations have a greater random chance of extinction than large populations and are more vulnerable to inbreeding depression, so the descendants of founders might also need propitious conditions to survive. Liebhold et al. (1995) and MacArthur and Wilson (1967) suggest that the probability of establishment can be simply described as a continuous function of initial population size. Translating these conclusions into practical terms is currently difficult because the small immigrant population that is detected may be only one of a large group of small populations that arrived at the same time. Although many may soon go extinct, some may survive unless they are deliberately eradicated.
Not only a large number of immigrants per introduction, but also frequent introductions will mitigate stochastic processes and increase the likelihood of establishment. Crawley (1986) found that the probability of establishment increased with both the sizes and the number of population releases. Repeated introductions increase the chance that an immigrant species will encounter a combination of resources, scarcity of competitors, and low density of predators or pathogens that will permit establishment. That expectation appears to be borne out in the release of insects for biological control. In the Canadian biological control programs, nonindigenous species that were released in at least 10 episodes established in 70% of the cases; those released in fewer than 10 episodes established in only 10% of the cases (Bierne 1975).