The study of plant dispersal is undergoing a renaissance because of advances in models, computing power and empirical methods, but also because of the urgent environmental problems outlined above. This has been evidenced by the prominence of long-distance dispersal as a key issue at scientific meetings in ecology and evolution. The problems are of pressing concern, especially in Canada, which is a highly-invaded northerly nation where climate change impacts have the potential to be very significant. Recent new research in plant dispersal modeling has the potential to provide crucial components for modeling the problems.
The purpose of this meeting is to address the problems in modeling dispersal described in the `Overview' section in a cross-disciplinary research environment. We will bring together a group of expert mathematicians and quantitative biologists with the following goals:
(i) communicate recent advances in the mathematical analysis of dispersal problems, and advances in the application of these results to real ecosystems (ii) give the opportunity for cross-pollination between different approaches (iii) propose future directions for research in the mathematics of plant dispersal with a view to developing areas where the interaction between models and science is strong.
Our strategy will be to bring to the meeting a number of empirical seed dispersal data sets (supplied by Bullock, Clark, Greene, Nathan, and Tackenberg), together with associated wind data. We will examine how each of the three modeling approaches outlined above in the `Overview' section can be used to explain the observed data and to extrapolate reliably to distances beyond the furthest seed dispersal observation. To do this, the team will split into three (circa four member) groups, each of which will target one of the three approaches. The groups will examine mathematical, computational, modeling and data-model aspects. This will be followed by group-wide comparison of the three approaches, analysis of interfaces between approaches, and discussion and possible development of new methods. We believe that this cross-disciplinary approach will be highly productive.
Some of the mathematical underpinnings for the above approaches include nonlinear stochastic spatial processes, turbulent fluid flow and wave-type solutions to nonlinear parabolic PDE and related integral models. Through focusing on the interaction between the biological problem of plant spread and the mathematical formalisms used to describe this process, the group hopes to develop new ways to connect aspects of these different mathematical areas.
The meeting will produce an overarching review paper presenting a critical evaluation and advances in modeling seed dispersal, and also subsidiary papers on particular model developments. The goal would be to solicit sections of the review paper before the meeting from various authors, to spend the first few days of the meeting making short presentations on the `state of the art', and to spend the remainder of the first week on the team work and group discussion described above. Several members of the group would remain for the second week of the meeting to complete a draft of the paper.
Final Report (in PDF format)