Biological invasions are the unintended consequence of globalization; as rates of world trade and travel increase, non-native species are accumulating in virtually every corner of the world.  While most of these species are relatively innocuous, a significant number of alien species profoundly alter ecosystem properties and processes, resulting in considerable socioeconomic impacts.  Given the ecological complexity of biological invasions, mathematical models are critical tools for the development of effective strategies for managing invasions.  Here, I describe the ways that models are currently being used to manage each of the three major invasion phases.

Results/Conclusions

Arrival is the first stage of any biological invasion and it is managed via risk assessment, the application of quarantines and inspections of incoming commodities.  Managing arrival is perhaps the most efficient approach to mitigating the invasion problem.   Niche modeling plays a critical role in risk assessment and  biogeographical models play increasingly important roles in explaining patterns of invader establishment and identification of particularly risky pathways where quarantine and inspection  activities should be targeted.

The second invasion stage is establishment, during which populations grow to an extent such that extinction is no longer possible.  Establishment is managed via detection of new populations followed by eradication, the total elimination of a species from an area.  Modeling of Allee dynamics provides critical information for designing eradication strategies that focus either on reducing populations below extinction thresholds or increasing Allee thresholds above current population levels; in either situation, populations can be expected to decline towards extinction.

Invasion spread is the stage during which an invading species expands into its potential range and spread is managed through containment strategies.  Models have provided critical information to the development of containment strategies; these models have allowed managers to optimize the allocation of resources between the suppression of the production of outlier populations vs. the suppression of outlier populations themselves.

Part of the success of the use of models for devising invasion management strategies can be attributed to the simplicity of the population processes that underlie the invasion process.  The spatial dynamics of invading populations are largely driven by simple reproduction and dispersal and are not subject to the complexities of intricate trophic interactions.   Furthermore, the simplicity of invasion models lends themselves to incorporation into bioeconomic models that allow the identification of optimal management strategies.