At least two statistical reasons are motivating this model. First, it usually leads to a decrease in the variance of the estimate [@rod99]. In coalescent-based inference, the smaller the number of extant lineages in a given time interval, the greater the variance of our estimate of the interval length, and consequently, the greater the variance of any estimate that depends on that length such as $(N_e(t))_{t\geq 0}$. By including heterochronous samples, we can increase the number of active lineages in the past, and thus obtain better estimates. Second, [@par19] show that including heterochronous samples is necessary (in some cases) to make the parameters describing $(N_e(t))_{t\geq 0}$ identifiable.

The Tajima heterochronous $n$-coalescent fundamentally differs from the Tajima *isochronous* $n$-coalescent in that sequences sampled at different times are not exchangeable. The Tajima isochronous $n$-coalescent distinguishes between singletons and *vintaged* lineages, where a singleton lineage refers to a lineage that subtends a leaf in [**g**]{}, and a vintaged lineage refers to a lineage that subtends an internal node in [**g**]{}. Singletons are indistinguishable while vintages are labeled by the ranking of the coalescence event at which they were created. When dealing with heterochronous samples, singletons are instead implicitly labeled by their underlying sampling 