# Mathematical Ecology and Evolution

### Overview

As the current revolution in biological information progresses, there is a well recognized need for new quantitative approaches and methods to solve problems in ecology. One challenge is to model complex ecological systems--systems which depend upon a myriad of inputs, but often with incomplete details regarding the inputs. Such systems range from spatial disease dynamics (eg. influenza, tuberculosis) to the response of biota to global environmental change (eg., vegetation shifts), to the impact of habitat fragmentation on species survival. Mathematical tools for addressing such biological problems include stochastic processes, nonlinear dynamical systems, adaptive dynamics, scaling methods from individuals to populations, statistical inference (particularly in the area of inverse problems), and parallel computational methods. Our primary goal in this period of concentration is to develop and strengthen the synergistic interactions between mathematics and ecology in PIMS universities. Research in any interdisciplinary field brings its own particular set of challenges: (i) The rigorous and unambiguous aspects of mathematics vs the overwhelming complexity of the biological world. (ii) The different languages of mathematics and biology can provide a major barrier to interdisciplinary research.

With this in mind, an interdisciplinary research program that significantly impacts both mathematics and biology has some basic requirements: (i) the opportunity for training outside the core discipline of mathematics or biology and (ii) a mechanism for effective collaborations and cross-communication between empiricists and theoreticians.

These requirements are, of course, in addition to mathematical and biological expertise. The above ingredients are central to the training of personnel in this research plan.

This period of concentration will incubate significant new original research, foster local interactions, provide leadership to the new researchers, and strengthen the international profile of mathematical ecology and evolution in our universities. Areas of mathematical ecology research at PIMS universities include: Nonlinear population dynamics; Spatially structured populations; Adaptive dynamics; Model selection and validation and inverse methods, Stochastic models for populations; Scaling laws--from individuals to populations.

### PIMS Distinguished Chair

The period of concentration has funded two distinguished chairs at approximately 10K each. The first Bryan Grenfell, is described below. We have not yet determined the other PIMS distinguished chair and would welcome suggestions. We are also hoping to have additional visitors with other funding. If you have suggestions for these visitors or for other funding please inform us. Contact Thomas Hillen mathecol@math.ualberta.ca.

Bryan Grenfell is a preeminent mathematical epidemiologist at the University of Cambridge, UK. His specialty is analysis of patterns in epidemiological data, and understanding the spatio-temporal dynamics of diseases and populations using mathematical and statistical models. Recent awards include the Order of the British Empire for services to epidemiology and the control of infectious diseases. Recent research includes mathematical analysis of foot-and-mouth disease, measles modeling, and analysis of nonlinear population dynamics. In the year 2001 alone, five of his published papers appeared in "Science" or "Nature".

The goal of the PIMS Distinguished Chair is to have Grenfell visit for 3.5 weeks in September 2003 to interact with mathematicians and mathematical ecologists at PIMS universities. The two host of mathematics, statistics and epidemiology. Interactions arising from Grenfell's visit will help catalyze new research interactions between PIMS researchers.

Distinguished chairs are to spend time at multiple PIMS sites.

### Faculty

**Coordinator:**Dr. Thomas Hillen, Associate Professor, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Phone: (780) 492-3395 Fax: (780) 492-6826, Email: mathecol@math.ualberta.ca- Co-Organizers
- Dr. Michael Doebeli, Associate Professor Departments of Zoology and Mathematics, University of British Columbia Phone: (604) 822-3326, Fax: (604) 822-2416, Email: doebeli@zoology.ubc.ca
- Dr. Mark Lewis, Professor, Dept.of Math.Stat. Sci. and Biological Sciences University of Alberta, Edmonton, T6G 2G1, Phone: (780) 492-0197, Fax: (780) 492-6826, Email: mlewis@math.ualberta.ca
- Dr. Edward McCauley, Professor, Department of Biological Sciences University of Calgary, Phone: (403) 220-5583, Email: mccauley@ucalgary.ca

- Faculty Participants (tentative)
- University of Alberta:
- Mark Boyce boyce@ualberta.ca,
- Herb Freedman hfreedma@math.ualberta.ca,
- Thomas Hillen thillen@math.ualberta.ca,
- Subhash Lele slele@ualberta.ca,
- Mark Lewis mlewis@math.ualberta.ca,
- Michael Li mli@math.ualberta.ca,
- Jens Roland jroland@gpu.srv.ualberta.ca,
- Joseph So Joseph.So@ualberta.ca

- University of Calgary:
- Ed McCauley mccauley@ucalgary.ca,
- Shane Richards richas@ucalgary.ca

- University of British Columbia:
- Fred Brauer brauer@math.ubc.ca,
- Michael Doebeli doebeli@zoology.ubc.ca,
- Leah Keshet keshet@math.ubc.ca,
- Dolph Schluter schluter@zoology.ubc.ca

- University of Washington:
- James Anderson jim@cbr.washington.edu,
- Carl Bergstrom cbergst@u.washington.edu,
- Daniel Grunbaum random@u.washington.edu,
- Ray Hilborne rayh@u.washington.edu,
- Mark Kot kot@amath.washington.edu

- Simon Fraser University:
- Eirikur Palsson epalsson@sfu.ca,
- Bernard Roitberg bernard_roitberg@sfu.ca

- University of Victoria:
- Pauline van den Driessche pvdd@math.uvic.ca

- University of Alberta:

**PIMS Postdoctoral Fellow**

- For 2004-06, Mario Pineda-Krch, was a postdoc at UBC.
- For 2003-04 our POC has been awarded two PIMS PDFs. Both of these PDFs may be renewed for 2004-05.

The value of the PIMS fellowship is $20,000 per year (salary including benefits). This must be matched this with a minimum of $20,000 from non-PIMS sources to provide a minimum annual salary of $40,000 (including benefits). Approximately 20% of the postdocs time will be spent helping in activities associated with the POC (summer school, Banff ecology retreat, interacting and communicating with visitors and so forth). Some of this will require extended travel to PIMS sites or BIRS where the activities are being held.

The funding cycle of the Institute runs from April 1 to April 1. Therefore, PIMS requests that each fellowship commence prior to January 1 of the fiscal year for which it is allocated. For example, the 2003-04 fellowships should commence before January 1, 2004. PIMS strongly urges the PIMS CRGs not to apply for additional PDFs through the general competition, so as to ensure access to the programme for other PIMS members.

**Notes**

There are two postdocs associated with the program. These are funded 50% from the program, and the other 50% is to come from private research grants and teaching. On August, 1, 2003 Dr. Frithjof Lutscher started as PIMS postdoc. He works 50% at U of Calgary with Ed McCauly and 50% at U of Alberta with Mark Lewis. On November, 1, 2003 Dr. Joanna Renclawowicz will start as PIMS postdoc. She will work 33 % at U of Victoria with Pauline van den Driesche and 66 % at U of Alberta with Thomas Hillen and Mark Lewis. Note that, besides research and teaching, duties of the postdocs include 15% of the time devoted to helping with the POC (see below). As outlined in the proposal to PIMS, the postdocs are to work in interdisciplinary mathematical ecology and evolutionary biology. Note that these postdocs are only available to Canadian Universities - sorry to UW.