And @vmminin.bsky.social! Somehow I couldn't find you before.

Ultimately, direct comparison between the approaches is hard since their three models are so different, but that's what makes them so complementary. With @matsen.bsky.social @yun-s-song.bsky.social @wsdewitt.github.io, and others I can't find on here, but may have missed!

they infer what we call an "effective" birth rate (left column) that is more biologically interpretable than the "intrinsic" rate inferred by deep learning (center column), but which also varies with time and across GCs.

It also turns out there's some subtleties in comparing to the more analytic traveling wave and branching process approaches:

The results consist of a curve, or rather, two versions of (hopefully) the same curve: one infers the parameters of a sigmoid shape, the other infers independent bin values.

Finally, we applied the model to real data, inferring the affinity-fitness response curves for many potential parameter values, choosing the best combination based on summary statistic matching.

We then trained a deep learning model on simulation samples with a wide variety of parameter values.

Here I'll focus on the deep learning approach. We first built a birth-death-mutation simulator and carefully matched it to data to ensure we understood the processes underlying the experimental results.

whereas a branching process model arxiv.org/abs/2508.09519 and deep learning (this thread) zoom in to use detailed lineage trees to inform inference.

A traveling wave model takes a very high level view, essentially modeling histograms of affinity (Fig 6 in doi.org/10.1101/2025...)

Higher affinity antibodies, on average, have more offspring. But what exactly does this relationship look like? We used three complementary approaches to measure it:

In the weeks after we're exposed to a pathogen, our antibodies evolve toward higher affinity. The cellular mechanisms here are fairly well understood, but a recent experiment from @victora.bsky.social gave us the opportunity to also learn about the mathematical dynamics of this selection.