Organizers: Mark Lewis (Univ. Alberta), Mark Kot (University of Washington), Pauline van den Driessche (University of Victoria).
The purpose of this meeting is to bring together a group of expert mathematicians and quantitative biologists with the following goals: (i) communicate recent advances in the mathematical analysis of invasion problems, and advances in the application of these results to real ecosystems (ii) propose future directions for research in the mathematics of biological invasions with a view to developing areas where the interaction between models and science is strong. Because the field of biological invasions is immense, we start by focusing of four subareas where the interaction between models and science is already promising.
The following four problems regarding the spread of invasive organisms are fundamental to present and future diversity and biological integrity of the highly-invaded North American ecosystem:
1. How do invader life-history details affect spread, and are there particular stages that are most sensitive to control measures?
2. How do secondary ecological interactions with other species impact spread, and what is the impact of the invader on these other species?
3. Given available resources and a well-defined management goal, what is the optimal strategy for controlling a particular invasion, and how can this problem be formulated and analysed mathematically?
4. What is the impact of rare, long-distance dispersal events on the rate of spread, and the precision of spread rate estimates?
Some results of these efforts will give us a detailed understanding of biological invasions, including the spatial spread of disease, new methods to predict the response of vegetation to climate change, suggestions for methods to prevent the spread of genetically engineered strains used in agriculture, and new methods for spatial biocontrol of pest species.
Our workshop will be focused around the above four themes, and will involve a range of participants, ranging from mathematicians to quantitative biologists. We anticipate the synergistic interaction between mathematics and biology will lead to major advances in both fields.
As shown below, we will have an introductory session and a closing session, and then an evening and one morning on each subject. Day 1: morning: introduction, overview, classical PDE, integral models, stochastic models
evening: 1A stage-structured integrodifference models: theory --- wave speed, stage structure, elasticity, sensitivity Day 2: morning: 1B stage-structured integrodifference models: fitting theory with biology
evening: 2A secondary ecological interactions: theory
Day 3: morning: 2B secondary ecological interactions: fitting with theory with biology
evening: 3A biocontrol/conservation in an invasion context: theory
Day 4: morning: 3B biocontrol/conservation in an invasion context: fitting theory with biology
evening: 4A long distance dispersal: theory
Day 5: morning: 4B long distance dispersal: fitting theory with biology
afternoon: final discussion and commentary
Afternoons will be reserved for small group discussions and one afternoon there will be a field trip to the Columbia Ice Fields to see the "invasion" of recolonizing vegetation behind the retreating ice sheets.
Programme (pdf file)
Final Report (pdf file)
Open Questions (pdf file)