study outlininghow the model works and comparing our method to state-of-the-art alternatives. In Section \[app\], we analyze modern and ancient bison sequences described in [@fro17]. In Section \[covid\], we apply our method to SARS-CoV-2 viral sequences collected in France and in Germany. Section \[concl\] concludes. An open-source implementation is given in `R` package `phylodyn`, which is available for download at `https://github.com/JuliaPalacios/phylodyn.`

The Tajima heterochronous $n$-coalescent {#sec:hettaj}
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The Tajima heterochronous $n$-coalescent is an inhomogeneous continuous-time Markov chain that describes the ancestral relationships of a set of $n$ individuals sampled, possibly at different times, from a very large population. The set of ancestral relationships of the sample is represented by a ranked genealogy as the one depicted in Figure \[fig:hetTaj\]. Every organism is dated and labeled according to the time in which the organism lived (if ancient, by radiocarbon date) or in which the living organism was sequenced. In this generalization of the Tajima coalescent, each pair of extant ancestral lineages merges into a single lineage at an instantaneous rate which depends on the current effective population size $N_e(t)$, and new lineages are added when one of the prescribed sampling times is reached. In this work, we do not model the 