Simulation analyses using matrix models can examine how such factors as environmental stochasticity can interact with demographic characteristics, such as deterministic growth rate (λ), to influence the persistence of small populations. Using stage-structured matrix models, Menges (1990, 1991, 1992) explored how the persistence of plant populations is affected by environmental stochasticity and how the effects of environmental stochasticity are modulated by variation in rates of increase. Using life-table data on several plant species, Menges (1992) found that, except for very small populations with deterministic growth rates near 1.0, demographic stochasticity was much less important than environmental stochasticity in causing chance extinction. Moderate environmental stochasticity was found to cause extinction even in populations with positive deterministic growth rates. By systematically varying environmental stochasticity in a series of simulations, he demonstrated that populations with deterministic growth rates near 1.0 are much more likely than populations with higher growth rates to go extinct when exposed to moderate environmental stochasticity. Populations with deterministic growth rates greater than 1.2 were affected only by extreme environmental stochasticity. The potential importance of that final result to invasion biology is that if the deterministic growth rate of a newly established population of invaders is much greater than 1.0 (say, 1.5 or higher) the likelihood of chance extinction is much reduced.

THE ENVIRONMENTAL CONTEXT

Against the continuous backdrop of stochastic forces that affect a fledgling population are the environmental characteristics of the new range. Abiotic factors–such as climate and landscape–will determine whether a new range is at least minimally habitable by an immigrant. Biotic factors–including the availability of hosts or pollinators and the presence of competitors, predators, and plant-pathogen antagonists–challenge the biological tolerance and competitive abilities of the newcomer. The following discussion is by necessity abridged and serves only to illustrate the breadth of environmental factors that affect establishment.

Abiotic Factors

The likelihood of establishment will be affected by the general climatic match between the donor habitat and the new habitat of the immigrant species. Moreover, the geographic distribution and range of climatic conditions known to have been suitable for the immigrant species in its native range or in previously invaded regions provide some indication of potentially suitable habitats. Prediction of establishment and invasiveness based on climate-matching between original and potential ranges of nonindigenous species is a subject of active research (Kriticos and Randall 2001). This correspondence is related to the potential



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