Our Faculty

Benjamin Allen

Assistant Professor of Mathematics

Contact Information


Office Hours

Office: Cardinal Cushing Library, Room G14

Office hours: Monday and Wednesday: 11:00 a.m.-12:00 p.m. and 3:00 p.m.-4:00 p.m.; Friday: 11:00 a.m.-12:00 p.m.


Ph.D., Boston University; M.A., Bryn Mawr College; B.A., Haverford College


I have always loved mathematics - at first for its own sake, and later for how it can help us understand real-world processes and relationships. I am interested in connections between mathematics and the sciences, especially biology. My current work uses mathematical modeling to illuminate the organisms, patterns, and behaviors that emerge from evolution. 

What I Love About Emmanuel:

I love that Emmanuel is both intellectual and caring. We support each other as scholars and as people. 

Courses I Teach

  • MATH1111 - Calculus I
  • MATH2103 - Calculus III

slideshowWhat I'm Working On

Publications + Presentations

A continuously updated and linked list of my publications can be found here.

  • Allen,B., M.A. Nowak and E.O. Wilsin. 2013. Limitations of inclusive fitness. Proceedings of the National Academy of Sciences. 110: 20135-20139.
    Allen, B. and M. A. Nowak. 2013. Cooperation and the Fate of Microbial Societies. PLoS biology 11:e1001549.
  • Allen, B., M. A. Nowak, and U. Dieckmann. 2013. Adaptive Dynamics with Interaction Structure. The American Naturalist 181:E139-E163.
  • Bozic, I., J. G. Reiter, B. Allen, T. Antal, K. Chatterjee, P. Shah, Y. S. Moon, A. Yaqubie, N. Kelly, D. T. Le, E. J. Lipson, P. B. Chapman, J. Luis A Diaz, B. Vogelstein, and M. A. Nowak. 2013. Evolutionary dynamics of cancer in response to targeted combination therapy. eLife 2.
  • Dickinson, B. C., A. M. Leconte, B. Allen, K. M. Esvelt, and D. R. Liu. 2013. Experimental interrogation of the path dependence and stochasticity of protein evolution using phage-assisted continuous evolution. Proceedings of the National Academy of Sciences 110:9007-9012.
  • Leconte, A. M., B. C. Dickinson, D. D. Yang, I. A. Chen, B. Allen, and D. R. Liu. 2013. A population-based experimental model for protein evolution: effects of mutation rate and selection stringency on evolutionary outcomes. Biochemistry 52:1490-1499.
  • Reiter, J. G., I. Bozic, B. Allen, K. Chatterjee, and M. A. Nowak. 2013. The effect of one additional driver mutation on tumor progression. Evolutionary applications 6:34-45.
  • Allen, B. and M. A. Nowak. 2012. Evolutionary shift dynamics on a cycle. Journal of Theoretical Biology 311:28-39.
  • Allen, B. and D. I. S. Rosenbloom. 2012. Mutation Rate Evolution in Replicator Dynamics. Bulletin of Mathematical Biology 74:2650-2675.
  • Allen, B. and C. E. Tarnita. 2012. Measures of success in a class of evolutionary models with fixed population size and structure. Journal of Mathematical Biology:1-35.
  • Allen, B., A. Traulsen, C. E. Tarnita, and M. A. Nowak. 2012. How mutation affects evolutionary games on graphs. Journal of Theoretical Biology 299:97-105.
  • Bozic, I., B. Allen, and M. A. Nowak. 2012. Dynamics of targeted cancer therapy. Trends in Molecular Medicine 18:311-316.
  • Diaz Jr, L. A., R. T. Williams, J. Wu, I. Kinde, J. R. Hecht, J. Berlin, B. Allen, I. Bozic, J. G. Reiter, and M. A. Nowak. 2012. The molecular evolution of acquired resistance to targeted EGFR blockade in colorectal cancers. Nature 486:537-540.
  • Allen, B., M. Kon, and Y. Bar‐Yam. 2009. A new phylogenetic diversity measure generalizing the Shannon index and its application to phyllostomid bats. The American Naturalist 174:236-243.
  • Allen, B. 2008. The Category-Theoretic Arithmetic of Information. arXiv preprint arXiv:0803.3608.

Research Focus

I use mathematical modeling to help illuminate the organisms, patterns, and behaviors that emerge from evolution.  I am interested in both theoretical and practical questions within this topic.

On the theoretical side, I am interested in how the spatial or social structure of a population affects its evolution. These structures can influence the processes of adaptation and neutral drift, as well as the kinds of social behaviors favored by natural selection. Using the theory of stochastic processes, I develop mathematically general approaches that can address these questions across different organisms. 

On the more empirically motivated side, I use stochastic models to study the genetic evolution of cancer as tumors grow and develop within an organism. This question is particularly important in understanding how tumors develop resistance to targeted cancer therapies. I also use mathematical modeling to study evolution in E. coli and other microorganisms.