Ask HN: Dense Tree Layout Algorithms

I recently bought a poster which features a really beautiful rendering of a phylogenetic tree of the world's bird families (a rooted binary tree).

https://lynxnaturebooks.com/product/orders-and-families-of-the-birds-of-the-world-poster/

I am sure it was carefully designed by hand. What algorithms could automatically generate a layout like this? The graphviz layout algorithms are poorly suited to the problem because they cannot seem to avoid edge/node coincidence beyond a certain node density.