Appendix 1

Our first discussion centered on the apparent lag phase observed in many invasions. Lags of years to decades early in the invasion process could occur or be perceived to occur for a number of reasons. Possible mechanisms include:

• An invader maintains a more or less stable population at relatively low levels for a number of years, during which time various genotypes are tested against the environment until one "breaks through" and begins to spread actively.
• An invader is more or less stable until the right set of environmental conditions (a wet year, a hurricane that opens sites, the right kind of anthropogenic disturbance) occurs - whereupon the invasion spreads.
• An invader grows slowly at first due to the "Allee effect," many populations grow slowly at low densities due to difficulties in finding mates (for plants, pollinating successfully). Once a threshold population size is reached, normal exponential growth begins.
• Normal exponential growth can easily be interpreted as containing a lag phase; population could grow more or less continuously, but not be noticed until the last doubling or two makes it obvious.

While the first case has been discussed widely (and is possible), none of us is impressed that there is evidence for its importance. That's somewhat encouraging, because the fourth case can be identified if monitoring is adequate, and the second and third are at least potentially identifiable if enough is known about the species and system.

We then discussed how the most damaging invasions could be predicted. All invasions represent change, but we are concerned most strongly with those that affect human health or wealth, ecosystem structure and function, and/or the biological diversity of natives, populations, species, communities, or landscapes. We are impressed with the progress that has been made in identifying which organisms are likely to become established if they are introduced, at least for some groups of organisms; we are particularly impressed with the potential for development of quantitative models that identify likely invaders. However, we need to go beyond that to identify the subset of invaders that should be controlled first, with the limited resources available (and the available resources will always be limited). To address this set of issues, we need to develop a sharper understanding of what makes communities either subject or resistant to invasion, and which interactions between invader and community can cause fundamental changes in biological diversity and/or ecosystem function.

Overall, it was the sense of the group that what we need is a combination of case studies (called 'anecdotes' when there are too few of them, or when they are one-sided), experiments, and models based on the fundamental dynamics of populations and communities. There was some discussion of trying to develop a "universal (well, at least global) model" that incorporates attributes of invaders, invaded communities, and the environment; there was agreement that while we cannot develop a model that is general across all invaders and ecosystems, there can well be generic models that have features in common for a very broad range of species and ecosystems.

We believe it would be rewarding to begin the development of such a modelling effort by focusing on a set of relatively well-studied groups of invaders. We identified several groups for which there are plenty of cases of introductions and invasions that are reasonably well documented as to failures as well as successes, for which there are ongoing introductions that could be evaluated experimentally, and for which we have some strong ideas of controlling mechanisms. These include: pasture grasses, insects used for biological control, crayfish, and upland game birds. An effort to gather information, synthesize, and predict invasions and their consequences could be rewarding for any of these groups; an interactive effort on several of them could move us towards the development of a generic model.

We then turned towards considering what should go into the "environment" and "effects" portions of such models. For invaders that can alter ecosystem properties, we are interested in resources - both because their availability determines the success of invaders, and because invaders that alter resource supply (or its variation in space and/or time) thereby have ecosystem-level consequences. For plants, the major resources that need to be considered are water, light, and nutrients. Additionally, alterations in the fire regime or in the frequency and/or intensity of other disturbances affects the ability of plants to use resources, and so has ecosystem-level effects; changes in substrate stability can be similarly important. Introduced animals could alter a number of these resources directly. In addition, animals could alter ecosystems by being effective "engineers" - altering soils and or sediments by bioturbation, altering hydrology by controlling water levels (as beavers do). Finally, organisms that alter the trophic structure of an ecosystem, often by adding or removing a top carnivore, also alter ecosystems. When considering the possibility that an invader might alter ecosystems, the major questions are:

• What potential invaders (or types of invaders) could alter the availability of limiting resources?
• What systems could be affected substantially by an alteration in the supply of a particular resource?
• What native species already present in an area affect resources more or less as the invader would? If such native species exist, invasion may be less likely; much more solidly, an invasion would be less likely to alter ecosystem structure and function even if it succeeded.

Overall, we agreed that while identifying those invasions that are likely to alter ecosystem structure and function is difficult, we do have both theory and experience to bring to bear on the problem, and can hope to make substantial progress. In contrast, predicting the effects of invasion on biological diversity is more difficult, in large part because idiosyncratic interactions are likely to be important. Certainly any invader that alters ecosystems is likely to affect diversity - but many that do not change ecosystem processes appreciably could still affect diversity. Is there a way to construct anything but idiosyncratic models about this phenomenon?

The key to a predictability may lie in identifying the resources that generate (or permit) diversity in different ecosystems. Where resource levels control diversity, alterations in ecosystem dynamics and diversity are likely to go together. Where the composition of the plant community controlled more by the availability of sites for seed germination and establishment than by factors influencing seedling or sapling growth rates, an invader that alters the number or nature of such sites could affect composition and diversity substantially without changing productivity, nutrient cycling, or hydrology directly. Other topics that arose in our discussion but were not resolved include:

• Can we encourage ecosystem restoration in degraded and invaded systems by establishing long-lived organisms, and using their effects on resources to encourage colonization by desirable native species?
• Can we manage disturbance regimes in a way that encourages colonization by natives and works against particular invaders?
• How can we determine (rationally) the utility of toxicants in the control of destructive introduced animals? Many North Americans shrink from this prospect - but we know that the costs (economic and environmental) of some invaders are substantial, and if toxicants work to control them, there may be instances in which their use is appropriate.

Similarly, how do we weigh the direct and indirect effects of pesticides versus biological controls, when both are employed on introduced organisms in near natural ecosystems?