Statistical phylogenetic analysis currently relies on complex, dedicated software packages, making it difficult for evolutionary biologists to explore new models and inference strategies. Recent years have seen more generic solutions based on probabilistic graphical models, but this formalism can only partly express phylogenetic problems. Here we show that universal probabilistic programming languages (PPLs) solve the model expression problem, while still supporting automated generation of efficient inference algorithms. To illustrate the power of the approach, we use it to generate sequential Monte Carlo (SMC) algorithms for recent biological diversification models that have been difficult to tackle using traditional approaches. This is the first time that SMC algorithms have been available for these models, and the first time it has been possible to compare them using model testing. Leveraging these advances, we re-examine previous claims about the performance of the models. Our work opens up several related problem domains to PPL approaches, and shows that few hurdles remain before PPLs can be effectively applied to the full range of phylogenetic models.In statistical phylogenetics, we are interested in learn-1 ing the parameters of models where evolutionary trees-2 phylogenies-play an important part. Such analyses have a 3 surprisingly wide range of applications across the life sci-4 ences 1,2,3 . In fact, the research front in many disciplines is 5 partly defined today by our ability to learn the parameters 6 of realistic phylogenetic models. 7 Statistical problems are often analyzed using generic 8 modeling and inference tools. Not so in phylogenetics, 9 where empiricists are largely dependent on dedicated soft-10 ware developed by small teams of computational biolo-11 gists 3 . Even though these software packages have become 12 increasingly flexible in recent years, empiricists are still 13 limited to a large extent by predefined model spaces and 14 inference strategies. Venturing outside these boundaries 15 typically requires the help of skilled programmers and in-16 ference experts. 17 If it were possible to specify arbitrary phylogenetic mod-18 els in an easy and intuitive way, and then automatically 19 learn the latent variables (the unknown parameters) in them, 20 the full creativity of the research community could be un-21 leashed, significantly accelerating progress. There are two 22 major hurdles standing in the way of such a vision. First, we 23 must find a formalism (a language) that can express phyloge-24 netic models in all their complexity, while still being easy to 25 learn for empiricists (the model expression problem). Sec-26 ond, we need to be able to generate computationally efficient 27 inference algorithms from such model descriptions, draw-28 ing from the full range of techniques available today (the 29 automated inference problem).30In recent years, there has been significant progress to-31 wards solving the model expression problem by adopting 32 the framework of probabilistic graphi...