Environmental stochasticity can reduce populations to the level at which demographic stochasticity becomes important. Models derived for plants suggest that when deterministic growth rates of newly arrived species exceed 1.2, effects of environmental stochasticity will be reduced and extinction will occur only as a result of extreme environmental events.

Weather, the random expression of the amplitude of climate, is an important source of adverse environmental stochasticity.

Natural catastrophes—such as fires, floods, and earthquakes—are difficult to predict but can cause the extirpation of populations of less than several thousand individuals.

An Allee effect arising from low reproductive success or survival in low-density populations can strongly influence the ability of a newly arrived, nonindigenous species to persist. Whether a founder population persists or is driven to extinction can depend on the strength of this inverse density dependence, the population process that is subject to the Allee effect, and interactions with environmental stochasticity.

Phenotypic plasticity, including acclimation, may buffer populations from environmental stochasticity.

Human-generated disturbance can reduce populations to the point where demographic stochasticity causes extinction. But cultivation, whether deliberate or inadvertent, can promote persistence of nonindigenous plant pests by increasing resource availability and decreasing environmental stochasticity.

Spatial distribution of newly arrived populations can affect the influence of stochastic forces. Small populations that are restricted to a specific habitat or host are more susceptible to extinction from stochastic forces than populations distributed across a large geographic area or populations that occupy multiple habitats or infest several hosts.

Demographic, environmental, and other stochastic forces can be overcome by repeated introductions of a species that increase its population number, by introductions that spatially distribute the population, and by the life-history traits (such as diapause and dormancy) that minimize the consequences of stochasticity.

Estimates (based on interception or other data) of the size of an immigrant population, the frequency of introduction, and opportunities for it to be introduced in multiple locations could be useful in determining the likelihood that a nonindigenous population will become established.

The geographic distribution and range of climates known to be suitable for the immigrant species in its native range or in previously invaded regions provide some indication of new habitats in which the immigrant population could