Benjamin Allen

Associate Professor of Mathematics - Chair

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. 

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

  • MATH1101 College Algebra
  • MATH1111 Calculus I
  • MATH2103 Calculus III
  • MATH2109 Discrete Methods
  • MATH4157 Senior Seminar

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

  • Fotouhi, B., Momeni, N., Allen, B., & Nowak, M. A. (2018) "Conjoining uncooperative societies facilitates evolution of cooperation" Nature Human Behavior, in press
  • Allen, B. (2017, September 5) Global cooperation depends on the strength of local connections. Aeon, retrieved from https://aeon.co/ideas/global-cooperation-depends-on-the-strength-of-local-connections. Also published as Allen B. (2017, September 6) A mathematical model of altruism. The Atlantic, retrieved from https://www.theatlantic.com/science/archive/2017/09/cooperation-networks/538842.  
  • Allen, B., Kon, M. A. (2017). The Marr Conjecture and Uniqueness of Wavelet Transforms. Annals of Mathematical Sciences and Applications, in press.  
  • Allen, B., Lippner, G., Chen, Y. T., Fotouhi, B., Momeni, N., Yau, S. T., & Nowak, M. A. (2017). Evolutionary dynamics on any population structure. Nature, 544(7649):227-230.  
  • Allen, B., Stacey, B. C. and Bar-Yam, Y. (2017). Multiscale Information Theory and the Marginal Utility of Information. Entropy, 19(6):273.  
  • Nowak, M. A., McAvoy, A., Allen, B., & Wilson, E. O. (2017). The general form of Hamilton's rule makes no predictions and cannot be tested empirically. Proceedings of the National Academy of Sciences, 114(22):5665-5670.  
  • Sample, C., & Allen, B. (2017). The limits of weak selection and large population size in evolutionary game theory. Journal of Mathematical Biology, online ahead of print.  
  • Stacey, B. C., Allen, B., & Bar-Yam, Y. (2017). Multiscale information theory for complex systems: Theory and applications. In M. Burgin, C. S. Calude (Ed.) Information and Complexity (pp. 176-199) Hackensack, NJ, USA: Word Scientific.  
  • van Veelen, M., Allen, B., Hoffman, M., Simon, B., & Veller, C. (2017). Hamilton's rule. Journal of Theoretical Biology, 414:176-230.   Makohon-Moore, A. P., Zhang, M., Reiter, J. G., Bozic, I., Allen, B., Kundu, D., Chatterjee, K., Wong, F., Jiao, Y., Kohutek, Z., Hong, J., Attiyeh, M., Javier, B., Wood, L., Hruban, R., Nowak, M. A., Papadopolous, N., Kinzler, K. W., Vogelstein, B., Iacobuzio-Donahue, C. A. (2017). Limited heterogeneity of known driver gene mutations among the metastases of individual patients with pancreatic cancer. Nature Genetics, 49:358-366.  
  • Allen, B. (2016). Statistical Inference Is Not Needed When the Solution Is Already Known. BioScience, 66(3):186-186.  
  • Allen, B., & Nowak, M. A. (2016). There is no inclusive fitness at the level of the individual. Current Opinion in Behavioral Sciences, 12:122-128.  
  • Cooney, D., Allen, B., & Veller, C. (2016) Assortment and the evolution of cooperation in a Moran process with exponential fitness. Journal of Theoretical Biology 409:38-46.  
  • Olejarz, J. W., Allen, B., Veller, C., Gadagkar, R., & Nowak, M. A. (2016). Evolution of worker policing. Journal of Theoretical Biology, 399:103-116.    
  • Allen, B. (2015). Inclusive Fitness Theory Becomes an End in Itself. BioScience, 65(11), 1103-1104.  
  • Allen, B., Sample, C., Dementieva, Y., Medeiros, R. C., Paoletti, C., & Nowak, M. A. (2015). The molecular clock of neutral evolution can be accelerated or slowed by asymmetric spatial structure. PLoS Computational Biology, 11(2):e1004108.  
  • Allen, B., & Nowak, M. A. (2015). Games among relatives revisited. Journal of Theoretical Biology, 378:103-116.  
  • Nowak M. A. and Allen, B. (2015) Inclusive Fitness Theorizing Invokes Phenomena That Are Not Relevant for the Evolution of Eusociality. PLoS Biology 13(4):e1002134.  
  • Olejarz, J. W., Allen, B., Veller, C., & Nowak, M. A. (2015). The evolution of non-reproductive workers in insect colonies with haplodiploid genetics. eLife 4:e08918.  
  • Szabó, G., Bodó, K. S., Allen, B., & Nowak, M. A. (2015). Four classes of interactions for evolutionary games. Physical Review E, 92(2):022820.  
  • Vukov, J., Varga, L., Allen, B., Nowak, M. A., & Szabó, G. (2015). Payoff components and their effects in a spatial three-strategy evolutionary social dilemma. Physical Review E, 92(1):012813.   Allen, B. and M. A. Nowak (2014).  Games on graphs.  EMS Surveys in Mathematical Sciences 1:113-151.  
  • Allen, B. and C. E. Tarnita (2014). Measures of success in a class of evolutionary models with fixed population size and structure. Journal of Mathematical Biology, 68:109-143.  
  • Jeong, H. C., S. Y. Oh, B. Allen, and M. A. Nowak (2014). Optional games on cycles and complete graphs. Journal of Theoretical Biology 356:98-112.  
  • Rosenbloom, D. I. S. and B. Allen (2014).  Frequency-dependent competition can lead to the evolution of high mutation rates.  American Naturalist 183: E131-E153.  
  • Szabó, G., Bodó, K. S., Allen, B., & Nowak, M. A. (2014). Fourier decomposition of payoff matrix for symmetric three-strategy games. Physical Review E, 90:042811.  
  • Allen, B., J. Gore, and M. A. Nowak (2013). Spatial dilemmas of diffusible public goods. eLife 2:e01169.  
  • Allen, B. and M. A. Nowak (2013). O brave new world with such games. Science 341:844.   Allen, B. and M. A. Nowak (2013). Cooperation and the fate of microbial societies. PLoS Biology 11:e1001549.  
  • Allen, B., M. A. Nowak, and E. O. Wilson (2013). Limitations of inclusive fitness. Proceedings of the National Academy of Sciences, 110:20135-20139.  
  • Allen, B., M. A. Nowak, and U. Dieckmann (2013). Adaptive dynamics with interaction structure. The American Naturalist 181:E139-E163.  
  • Anton, B. P., Chang, Y. C., Brown, P., Choi, H. P., Faller, L. L., Guleria, J., et al. (2013). The COMBREX project: design, methodology, and initial results. PLoS Biology, 11(8):e1001638.  
  • Bozic, Ivana, J. G. Reiter, B. Allen, T. Antal, K. Chatterjee, P. Shah, Y. S. Moon et al (2013). Evolutionary dynamics of cancer in response to targeted combination therapy. Elife 2:e00747.  
  • 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., 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.

In 2021, Dr. Allen was awarded $240,000 from the John Templeton Foundation for his project "Natural Selection for Collective Purpose." The project seeks to mathematically model collective, cooperative purpose as is widely exhibited in living systems from microbes to metazoans. A key output of this work will be a new modeling framework that is generally applicable to diverse biological scenarios and helps to unify existing theoretical resources for the evolution of agential features in living systems. The project was part of a larger, $15 million grant by the Templeton Foundation's “Science of Purpose” initiative.

In 2017, Dr. Allen and Dr. Christine Sample were awarded a three-year $285,161 grant from the National Science Foundation (NSF) to study evolution as a mathematical process. Their project may aid the understanding and treatment of cancer, which can be seen as unwanted evolution occurring inside the body. Dr. Allen was the lead author of an article on the topic recently published in Nature, a prestigious multidisciplinary scientific journal.

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.