I would like to start posting on this blog more frequently. Currently the only blog post (that is not along the lines of “Hello world”) includes some pictures of birds. More of that to come, probably.

But I’m hoping to post more than bird pictures, too, and hopefully it is of interest to others.

Ducks CDMX

To start, I thought I could share a few papers that I have recently enjoyed reading. Among other pieces of content that I have consumed and would like to share.

  1. Evans, S. (2000). Kingman’s coalescent as a random metric space. Here, Evans shows that realizations of the coalescent process, where lineages merge pairwise at rate 1 back in time (i.e., find shared genetic ancestors), can be understood as a metric space with an associated topology. In particular, the coalescent induces induces a random (ultra)metric and, thus, topology on the set of individuals. It turns out that, in this topology, sequences of individuals whose pairwise coalescence times are getting closer and closer (i.e., Cauchy sequences of individuals in this space) don’t have limits in the space*. (The same thing happens when one considers sequences of rational numbers approximating irrationals. It is in this sense that the rationals are incomplete and the reals, their completion, are closed under limits.) Evans completes the random metric space induced by the coalescent by adding, in some sense, a continuous array of leaves to each coalescent genealogy. There are good technical reasons to care about the completed space, but I find the fact the coalescent induces a random metric topology striking on its own! And the fact you can characterize features of the space, e.g., various ways of measuring it’s “dimension” — super cool!

*The reason is related to my favorite fact about the coalescent: it comes down from infinity. Starting with infinitely many individuals that have not found shared genetic ancestors with each other (i.e., are in their own blocks when the process starts running), we have $\Pr(\text{number of blocks that have yet to coalesce} < \infty) = 1$ for all $t > 0$. (In other words, when we start with infinitely many blocks, only finitely few are left after a positive amount of time.) This means there is an infinite amount of coalescence in every interval $[0,t]$. From these rapid coalescences, one can construct Cauchy sequences which have limits at time $t=0$. But there is, in fact, no coalesce at $t=0$ itself! Instead, coalescence begins as soon as the clock starts running. As a consequence of the infinitely fast coalescence occuring away from time zero, sequences of individuals whose coalescence times go to zero converge to points which are not in the space.

  1. Goldberg, A. (2026). Rare variation in malaria parasites biases population-genetic inference. The Kingman coalescent is a remarkably useful model for the evolution of many species, but convergence to this coalescent requires that the reproductive variance of individuals doesn’t blow up as $N \to \infty$ too fast. When the reproductive success of individuals is highly skewed, multiple-merger coalescents pop out. This paper shows that these coalescents are better fit to malaria population genomic data in Africa, South Asia, and Southeast Asia. The extent of deviations from binary-merger model appear to vary with geography, with greater signal of reproductive variance in Africa and South Asia. Interestingly, differences in vector density and the magnitude of co-infection may explain this pattern.

  2. This video by 3Blue1Brown.

  3. Stroustrup, S. et al. (2025). Stochastic Phylogenetic Models of Shape. I have been thinking about the evolution of function-valued traits for a couple of years now — primarily in the context of the landscape of recombination along the genome. I was delighted to see this work on bioRxiv a couple months ago, and have found myself returning to it for inspiration. (If the authors could devise a principled model for two-dimensional shapes, then I surely can make some progress in 1D?!) When the preprint came out, I excitedly emailed several colleagues who are interested in how shape varies and evolves. I forget what the subject line was but it wasn’t too far from “the most important paper in phylogenetic methods development of the decade!” Given widespread interest in studying the evolution of shape, I stand by the sentiment. Moreover, I think the approach of coupling Brownian motions at all locations in the plane (to ensure shapes stay, well, shapes) is very cool!

  4. Judd, J., Spence, J. et al. (2025). Allele Frequencies at Recessive Disease Genes are Mainly Determined by Pleiotropic Effects in Heterozygotes. This paper uses the wealth of human genetic data to test if predictions under mutation-selection balance hold up. Surprisingly, they do not: almost all frequencies of recessive LoF variants are too low. The authors carefully nullify alternative explanations (inbreeding, drift, compound effects) and provide evidence that 1) recessive alleles have pleiotropic effects in heterozygotes and 2) the majority of negative selection may be via heterozygotes. I was particularly awe-struck by the fact the authors could estimate a lower bound on the fraction of selection in heterozygotes and the strength of the evidence against predictions of the mutation-selection balance model at equilibrium.

  5. This profile about playwright Jeffery O. Harris. I had just seen “Slave Play” in Toronto and was eager to learn more about Harris. The profile was a really interesting look into his creative process and to the controversy around his work. I was particularly moved by Harris’ time at Yale, which culminated in “Yell: A Documentary of My Time Here”. I read “Yell” on a flight from Buenos Aries to Toronto and, like “Slave Play”, have kept thinking about it for months.

  6. This Numberphile video about smoothed asymptotics and the freedom we have in mathematics to define things how we please. One of the first moments I fell in love with math was watching this video about how, in a certain sense, the sum of all natural numbers equals $-1/12$. Many people took issue with the claims of this video when it came out, including friends of mine with whom I excitedly shared the video in high school! But, as the follow up video illustrates, there are multiple senses in which the sum of all natural numbers is meaningfully defined as $-1/12$. The rules are for us to decide!

  7. This article about the use of children’s genetic data in race pseudoscience circles. One can write entire books about the methodological flaws of this kind of “research”; there is nothing meaningful that can be learned from this kind of analysis. At the same time, this kind of application of human genetic data is not nearly surprising as it should be. Many human genetic datasets have gotten into the hands of racist freaks and, in the process, the privacy of study participants compromised. One aspect of the story that did surprise me, however, was that investigators who collected the data to study brain development did not inform the children or their families of how the data was used. And it doesn’t end there. The final lines of the article were among the most disturbing: “Within weeks of Mr. Trump taking office, the N.I.H. made a little-noticed revision to the guidelines on access to a large genetic database. Its description of what constituted stigmatizing research no longer included any reference to skin color, ancestry and ethnicity.”

  8. This blog post about if AI leaves space for human flourishing.

Bugs BA

And that’s all for now!