A thematic semester on “Biodiversity and Evolution” recently ended at the CRM (Centre de Recherches Mathématiques) in Montreal. It was packed with activities, drawing both mathematicians and biologists to a stimulating exchange of recent results, methodologies and open problems.
One of the challenges for a mathematician interested in this topic is the range of biological questions that are associated with this area. The concept of evolution—the change in inherited characteristics of populations over successive generations—affects every level of biological organization, from the molecular to organismal and species level. It is also associated with a variety of questions about how and why humans have evolved to what we are today (evolutionary neuroscience, physiology, psychology), as well as in our understanding of health and disease (evolutionary medicine). Since diversity of life on Earth is crucial to human well-being and sustainable development, evolution is also highly connected to the impacts of climate change. This goes to show the importance of fully comprehending fundamental evolutionary mechanisms.
The driving processes of evolution—mutation, genetic drift and natural selection—are, independently, relatively easy to understand. However, when combined they lead to different phenomena, and it is remarkably tricky to unravel the role of the different evolutionary causes from their signatures. At the molecular level, most of the complexity is due to exchanges of genetic material (recombination, gene duplication, gene swapping, etc.). At the organismal/ecological level the interactions between the species (food webs, predator-prey systems, specialists vs. generalists) or between individuals with different organizational/social roles (cooperators, defectors, etc.) lead to complex dynamics of population structures.
All of these issues were extensively discussed in the six workshops held at the CRM from August to December, 2013:
1) “Random Trees” focused on stochastic techniques for analyzing random tree structures;
2) “Mathematics for an Evolving Biodiversity” discussed probabilistic and statistical methodologies for drawing inferences from contemporary biodiversity;
3) “Mathematics of Sequence Evolution” presented computational approaches to investigation of function and structure of genetic sequences;
4) A minicourse on “Theoretical and Applied Tools in Population and Medical Genomics” gave an introduction to modern population genetics and genomics;
5) “Coalescent Theory” focused on the probabilistic techniques for reconstructing evolutionary relationships using a backwards in time approach; and
6) “Biodiversity and Environment — Viability and Dynamic Games Perspectives” combined biological, economical, social and interdisciplinary perspectives in mathematical modeling of individual or species interactions and their consequences for biodiversity and the environment.
A sequence of special lectures were given during the term by Aisenstadt chairs: David Aldous (UC Berkeley) and Martin Nowak (Harvard), as well as by Clay senior scholar: Bob Griffiths (Oxford). Abstracts and slides of the presentations can be found here.
What was apparent to anyone following all of the above workshops was the varied combination of approaches from distinct scientific disciplines: genomics, ecology, economics, computational biology, statistical genetics, and bioinformatics. Given the production and analysis of massive environmental, genetic and genomic data, it is clear that mathematical techniques are extremely useful in the advancement of these scientific areas. As randomness plays a prominent role in evolutionary processes, stochastic processes and random combinatorial objects are key players in its analysis and development. For young mathematicians interested in the area I would highly recommend a solid background in probability and stochastic processes, and some practice in simulating random processes.
Dept of Mathematics and Statistics