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...

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.

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.

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...

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...

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...

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.

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...

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.

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.

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...

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...