The infinite alleles model revisited: a Gibbs sampling approach

The SARS-CoV-2 outbreak started in late 2019 in the Hubei province in China and the first viral sequence was made available to the scientific community on early January 2020. From there, viral genomes from all over the world have followed at an outstanding rate, reaching already more than 105 on early May 2020, and more than 106 by early March 2021. Phylodynamics methods have been designed in recent years to process such datasets and infer population dynamics and sampling intensities in the past. However, the unprecedented scale of the SARS-CoV-2 dataset now calls for new methodological developments, relying e.g. on simplifying assumptions of the mutation process. In this article, I build on the infinite alleles model stemming from the field of population genetics to develop a new Bayesian statistical method allowing the joint reconstruction of the outbreaks effective population sizes and sampling intensities through time. This relies on prior conjugacy properties that prove useful both to develop a Gibbs sampler and to gain intuition on the way different parameters of the model are linked and inferred. I finally illustrate the use of this method on SARS-CoV-2 genomes sequenced during the first wave of the outbreak in four distinct European countries, thus offering a new perspective on the evolution of the sampling intensity through time in these countries from genetic data only.