Daniel Cooney

Hi everyone! I'm co-organizing this retreat/workshop June 15-19 for those looking to get started in mathematical/computational modeling of biological processes. Location is a beautiful farm in NC. Please share with students and others who want to build modeling skills. Interdisciplinarity welcome!

Right now, @tedloch.bsky.social from Rice University is giving a talk on a coordination game approach to studying symbiosis.

Please see below for more information about joining the talk.

This is such a compelling game to follow on play-by-play while taking a train in the snow back to Champaign.

Big congratulations to Dr Nikhil Sharma on receiving the Kiel Life Science Postdoc Award 2025! His outstanding work in theoretical biology and evolutionary graph theory makes us proud. Well deserved! 👏 #KLS #MPIEvolBio
www.evolbio.mpg.de/3847270/kiel...

(Photo: Christian Urban, Kiel University)

This Plasmid Project was directly inspired by the results on multilevel selection that Dan introduced me to! In this thread he explains some fundamental theoretical results that were so influential to me as a Scientist. Looking forward to more Math-driven experiments!!! Thanks Dan!

Its very exciting to see this paper out in @behavecol.bsky.social. These conversations, expertly led by @delphinedemoor.bsky.social, have really shaped how I now think about working with social network data. Check out Delphine's thread to learn more!

Postdoc position in individual-level incentives, social
learning, and payoff-biased imitation shape group-level accuracy in complex prediction and decision-making tasks in Konstanz

files.newsletter2go.com/l3slzozn/s_i...

I really enjoyed the discussions that led to this model, and it was really fun to think about how these kinds of multilevel selection models can describe systems ranging from replication competition between genes in cells to the evolution of cooperative social norms in complex animal societies.

Right now, Dr. Farshad Shirani from Emory University is giving a talk on "Infinite-Dimensional Dynamics, Spatiotemporal Gamma Oscillations, and Balance of Excitation and Inhibition in Cortical Networks".

Please see below for information to join the seminar.

By the way, in case you are still interested in models of ecology and evolutionary biology, I am co-organizing a conference session at Boston College in March 2026 with Alex McAvoy and Thomas Zdyrski.

www.ams.org/meetings/sec...

Thanks for sharing, @blakestacey.myatproto.social. I am particularly looking forward to the chapter on invasion fitness with a pair-approximation approach, as well as the discussion on different interpretations of MLS.

Multiscale Structure in Eco-Evolutionary Dynamics In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independ...

Wow, that takes me back to an earlier research life...

arxiv.org/abs/1509.02958

Multilevel mutation-selection systems and set-valued duals - Journal of Mathematical Biology A class of measure-valued processes which model multilevel multitype populations undergoing mutation, selection, genetic drift and spatial migration is considered. We investigate the qualitative behav...

Donald Dawson also explored the behavior of the Fleming-Viot limit, using a dual process to study the extinction or survival of cooperation due to selection, mutation, and drift at both the individual and group levels.

link.springer.com/article/10.1...

Maintaining diversity in structured populations Abstract. We examine population structures for their ability to maintain diversity in neutral evolution. We use the general framework of evolutionary graph

Very cool--a systematic study of coalescence and consensus times on graphs, with new theoretical bounds, from @david-brewster.bsky.social et al academic.oup.com/pnasnexus/ar...

Two level natural selection with a quasi-stationarity approach Aiming at a simplified model where natural selection at the individual level is confronted with selection effects at the group level, we consider certain individual-based models of large populations s...

Analysis of this two-level Moran model has led to a lot of other interesting work in probability and PDEs. In one interesting paper, Aurélien Velleret studied quasi-stationary distributions in a diffusive PDE model that arises in the limit of weak selection.

www.aimsciences.org/article/doi/...

Slide presenting the PDE model of the three-type multilevel selection model featuring slow genes, fast genes, and dimers consisting of a linked pair of the two genes. The slide illustrates the advection terms describing gene-level replication and a nonlocal term describing the effects of protocell-level competition.

Slide illustrating numerical solutions of the three-type protocell model over time, showing that a mix of slow genes, fast genes, and dimer replicators could occur in this model.

We saw that the shadow/ghost(👻) prevented coexistence of the fast and slow genes if protocell success most favored an even mix of the genes.

However, introducing a third replicator (a dimer linking together the two genes), we saw that coexistence could occur in three-type multilevel dynamics.

A PDE Model for Protocell Evolution and the Origin of Chromosomes via Multilevel Selection - Bulletin of Mathematical Biology The evolution of complex cellular life involved two major transitions: the encapsulation of self-replicating genetic entities into cellular units and the aggregation of individual genes into a collect...

The three of us ended up writing a paper with Simon Levin on applying these PDE models to protocell evolution, considering competition between "fast genes" and "slow genes" that were complementary for protocell-level replication.

link.springer.com/article/10.1...

The Origin of Chromosomes I. Selection for Linkage A model is analysed of cells containing independently replicating genes, which segregate randomly when the cell divides. We follow the fate of a primi…

Later on in grad school, I had many fun discussions with @fernpizza.bsky.social and Dylan Morris about applying multilevel selection models for coexistence to topics like the origins of chromosomes (such as in the linked paper by Maynard Smith and Szathmary).

www.sciencedirect.com/science/arti...

Basically, no level of group-level competition can fully erase the shadow of the individual incentive to defect.

Overall, it seemed like it was very hard to sustain coexistence of strategies that are complementary at the group level in the presence of an individual-level selective advantage.

Slide illustrating the steady state densities achieved by the PDE model for multilevel selection when groups are best off with a composition of 75 percent cooperators. The densities all concentrate around a composition of less than 50 percent cooperation, even in the limit of really strong competition between groups.

Slide illustrating the result that the long-time collective payoff of the population cannot exceed the average payoff of the all-cooperator group. This includes a statement "If groups are best off with an intermediate level of cooperation, no level of between-group competition can fully erase the shadow / ghost of lower-level selection".

When groups are best of with an intermediate mix of cooperators and defectors, no level of group-level selection could allow the population to achieve this optimal composition, and the population could not achieve an average payoff greater than the payoff achieved by an all-cooperator group.

Modeling Natural Selection at Multiple Levels of Organization | SIAM Game theory shed light on the evolutionary competition between the interests of individuals and groups.

Here is a blog post that I wrote with Yoichiro Mori, @jplotkin.bsky.social, and Simon Levin on the dynamical behaviors of this cross-scale model. In particular, we highlight a behavior that I like to call the shadow/ghost(👻) of lower-level selection.

www.siam.org/publications...

Slide illustrating the partial differential equation model for multilevel selection with payoffs determined by two-player, two-strategy games. It describes the probability density of having groups with a given fraction of cooperators, and has two terms describing the effects of selection at each level. The individual-level dynamics are described by an advection term with characteristic curves given an individual-level replicator equation, and the group-level dynamics follow a replicator equation for group-level competition (with x-cooperator groups increasing in frequency if the average payoff of such a group exceeds the average group payoff in the population).

The PDE model was really fun to explore, because it was basically a two-level replicator equation: individual-level selection depends on personal payoff within groups and group-level selection favors groups whose achieve higher average payoffs.

The replicator dynamics for multilevel selection in evolutionary games - Journal of Mathematical Biology We consider a stochastic model for evolution of group-structured populations in which interactions between group members correspond to the Prisoner’s Dilemma or the Hawk–Dove game. Selection operates ...

I made an extendsion the Luo-Mattingly model to incorporate individual and group replication rates based on the payoff of two-strategy, two-player games.

Such games can feature dominance of defectors, coexistence of both strategies, or bistability within groups.

link.springer.com/article/10.1...

Group-level events are catalysts in the evolution of cooperation Group-level events, like fission and extinction, catalyze the evolution of cooperation in group-structured populations by creating new paths from unco…

Early in grad school, Carl Veller pointed me to the Luo-Mattingly model and related cross-scale models by Burt Simon. Carl thought that evolutionary game theory could be helpful to describing different tugs-of-war between individual and group incentives.

www.sciencedirect.com/science/arti...

Luo and @jonathancm.bsky.social derived and analyzed PDE and Fleming-Viot scaling limits in the limit of infinitely many groups and infintie group size, characterizing the strength of group-level selection required for survival of cooperation in the PDE model.

iopscience.iop.org/article/10.1...

Mathematically, Luo's model is particularly tractable due to the choice of a nested birth-death process of individuals and groups.

Biologically, the plasmid system of @fernpizza.bsky.social et al fit this approach so nicely because the plasmids replicate independently but impact cellular fitness.

Schematic diagram from Shishi Luo's paper describing group-structured population dynamics in a population consisting of three three-member groups, illustrating individual-level and group-level birth events based on the strategic composition of groups.

Luo considered two strategies: cheaters with an individual-level replication advantage and cooperators that conferring a collective replication advantage to its group. Luo formulated a stochastic model for individual and group dynamics, deriving ODE and PDE models in the large population limit.

A unifying framework reveals key properties of multilevel selection Natural selection can act at multiple biological levels, often in opposing directions. Viral evolution is an important example, with selection occurri…

Here is one of my favorite papers, "A unifying framework reveals key properties of multilevel selection" by Shishi Luo. Luo highlights examples of multilevel selection and introduces a nested birth-death process to model evolutionary competition across scales.

www.sciencedirect.com/science/arti...

I'm really excited to see this paper by @fernpizza.bsky.social, @baym.lol, et al. This is a great model system for studying multilevel selection, and the experimental work builds nicely on cross-scale theoretical modeling approaches that I've enjoyed learning about over the past few years. 🧵

Cultural evolution postdoc alert 🚨