Using mathematical models to explore cross-scale biological dynamics: A conversation with Daniel Cooney

The NSF-Simons National Institute for Theory and Mathematics in Biology is composed of investigators at the forefront of innovative research at the interface of mathematics and biology. NSF-Simons NITMB Affiliate Members each bring unique perspectives vital for developing new mathematics and inspiring biological discovery. One such NITMB Affiliate Member using mathematics to study evolutionary biology is Daniel Cooney. 

Daniel Cooney, assistant professor, Department of Mathematics, University of Illinois Urbana-Champaign

Daniel Cooney is an assistant professor in the Department of Mathematics at the University of Illinois Urbana-Champaign. He is also an affiliate member of the Carl R. Woese Institute for Genomic Biology at Illinois. Professor Cooney’s research involves studying evolutionary game theory and modeling biological and social systems, often using PDEs and dynamical systems.  

We spoke with Daniel Cooney to explore his work using mathematical models to expand our understanding of evolutionary biology. 

What is a big question you’ve been asking throughout your research? 

“One of the main research questions I have explored is what can be learned by using mathematical models to explore cross-scale biological dynamics, with an emphasis on problems in evolutionary biology when natural selection operates simultaneously across multilevel levels of biological organization. This question about competition and cooperation across levels of selection has allowed me to explore topics ranging from the evolution of early cells and origins of chromosomes to the emergence of cooperation in complex animal societies. I have particularly enjoyed using evolutionary game theory as a window for understanding the conflicts between the individual incentive to cheat and a collective incentive to achieve cooperation, and it has been really fun to use a range of mathematical techniques to explore this tug-of-war between traits and behaviors favored by individuals or groups.” 

What disciplines does your research integrate? 

“Scientifically, a lot of my research involves techniques from game theory that were originally developed in economics, and applying these game-theoretic ideas to questions related to population dynamics, ecology, and evolutionary biology. Mathematically, I like to use a mix of techniques from stochastic processes and differential equations to understand how the rules for interactions between individuals give rise to interesting emergent behavior at the population level.” 

Where do you find inspiration? 

“I have really enjoyed reading work from lots of different fields in the life and social sciences, learning what kinds of questions are of interest to researchers in these fields and trying to see how ideas from game theory and population dynamics could lead to interesting new applications. I have also found inspiration by learning about techniques in dynamical systems and trying to expand my mathematical toolkit by using these techniques to solve a fun problem in biology.” 

What aspects of your work could be interesting to mathematics or applied to biology? 

“I think cross-scale evolutionary dynamics provide a lot of interesting problems for mathematicians and theorists with the goal of striking a balance between coming up with a meaningful description of a complex biological phenomenon and the mathematical tractability of resulting models. While I have mostly used partial differential equations in my attempts to study multilevel aspects of the evolution of cooperation, I think that there are lots of related ways for mathematicians to use probability theory or numerical analysis to explore these biological systems. On the biological side, I think there are a range of possible settings to which multilevel models could be used to explore questions of interest, from gene-level competition in plasmids to group-level dynamics in primate societies.” 

What about the NITMB do you find exciting? 

“I particularly like the viewpoint set forth by NITMB through their slogan of ‘Math Inspires Biology’ and ‘Biology Inspires Math’, placing a dual emphasis on the use of math to learn about biology and mathematical developments that arise with the goal of understanding complex biological systems. So far, I have been able to participate in the NITMB MathBio Convergence Conference and several NITMB workshops, and I have felt that these events provide a great opportunity to interact with researchers with a variety of disciplinary backgrounds and to explore the coupled mathematical and biological goals of the institute. I am also looking forward to organizing a workshop at NITMB in 2026 related to evolutionary game theory, and one of the major goals of this meeting will be to try to identify new biological questions that can be addressed with existing game-theoretic frameworks and to chart out possible problems in mathematics that arise by extending the biological scope of evolutionary games.” 

What career achievement are you most proud of? 

“I have really enjoyed the opportunity to work with a few groups of undergraduate students on problems related to evolutionary game theory and spatial pattern formation as part of the Illinois Mathematics Lab. It has been so much fun getting to share what I have learned in this field with enthusiastic students, and I am really proud that several of my students have written preprints on their results.” 

Outside of your research, what other interests do you have? 

“I have always really enjoyed baseball, and I played on my school's club baseball team as both an undergraduate and graduate student. Because I was a catcher for the team in graduate school, I liked to tell my advisor that calling pitches during the games counted as practical experience in game theory. Now that I have graduated, I have only been watching baseball as a fan, but I have continued my interest in ‘applied game theory’ by trying to learn more about chess.” 

What are you hoping to work on in the future? 

“I have really enjoyed getting more involved in research related to spatial pattern formation, using a mix of stochastic processes and differential equations to understand more about complex emergent behaviors in spatial models of cooperation. I am looking forward to learning more about this field and trying to work on a mix of applications to both biology (from the evolution of multicellularity to the management of shared natural resources) and to various questions in the social sciences (including economics, sociology, and anthropology). I have had some nice discussions about the mathematics of patterns with several fellow NITMB affiliate members, and I look forward to chatting with others at NITMB about this topic as well.” 

Is there anything else you would like the NITMB community to know about you? 

“I am only a few hours away from Chicago, so I would be happy to meet anyone at NITMB if they would like to chat about research. In addition, I help to co-organize a virtual seminar series (the Midwest Mathematical Biology Seminar) and an in-person seminar in Urbana (the Illinois Mathematical Biology Seminar) so I would be happy to host you for a virtual or in-person talk if you would like to share more about your research.” 

More information on Daniel Cooney’s work is available on his website and on his Google Scholar profile. Professor Cooney also posts about his research and other topics in mathematical biology on Bluesky.