successful if there was a single introduction of many individuals. In contrast, when environmental stochasticity was great, establishment was more likely to occur if there were many introductions of low numbers. Interactions between an Allee effect and environmental variability in larger colonies were more deleterious than the sum of their independent influences; a few years with bad conditions reduced population density to a level where negative population growth eventually led to extinction (Grevstad, 1999a,b). The need to estimate the influence of Allee effects on any immigrant population depends on the species and the circumstance, thereby complicating the population state in a new range.

Effects of Spatial Structure

Models estimating the persistence of a population typically consider only aggregate population statistics, not the spatial distribution of individuals. As a result, the question arises as to whether the extinction dynamics of spatially structured populations (such as a patchy distribution) might differ from those with little spatial structure (such as an aggregate).

The answer is frequently yes. Effects of environmental stochasticity can be reduced if the species is patchily distributed in such a way that not all members in any age class are affected equally by environmental perturbations. The potential for spatial patchiness to function as a buffer against extinctions caused by environmental stochasticity depends, however, on the degree to which environmental fluctuations are correlated across patches (Gilpin 1987, Stacey and Taper 1992). If environmental conditions are correlated across the region occupied by subpopulations of a newly arrived species, “Moran effect” dynamics could lead to a tension between synchronizing effects of extrinsic environmental stochasticity and desynchronizing effects of nonlinear density dependence (Hudson and Cattadori 1999, Ranta et al. 1999). In the Moran effect, originally proposed as a mechanism to explain synchronized fluctuations in Canadian lynx populations (Moran 1953, Royama 1992), when disjunct populations have the same endogenous structure (such as density dependence), a correlated exogenous, density-independent factor (such as weather) will bring population fluctuations into temporal synchrony (Earn et al. 1998, Heino et al. 1997, Hudson and Cattadori 1999, Williams and Liebhold 1995). Thus, when a species is strongly influenced by Moran effect dynamics, a period of unfavorable environmental conditions will promote extirpation of all colonies. A newly arrived immigrant species will persist, therefore, only if at least some subpopulations experience “good times” while other subpopulations suffer reduced population growth during “bad times”. In contrast, spatially structured populations may be subject to inverse density dependence regardless of environmental conditions if subpopulations are diluted by dispersal. Such a scenario could increase the probability of extinction due to stochasticity or Allee effects (Hopper and Roush 1993, Lewis and Kareiva 1993).

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