Table 1. Main notations for the observations and the model.

	Designation (unit) [reference value]
Observed variables
${\mathit{x}}^p\left(t_d\right)=(x_1^p\left(t_d\right),\dots ,x_{n_{var}}^p\left(t_d\right))$	Variant sequence counts in virus population p at sampling time td (seq a)
${\mathit{f}}^p\left(t_d\right)=(f_1^p\left(t_d\right),\dots ,f_{n_{var}}^p\left(t_d\right))$	Variant frequencies in virus population p at sampling time td (no unit)
State variables
${\mathbf{\lambda }}^p\left(t\right)=({\lambda }_1^p\left(t\right),\dots ,{\lambda }_{n_{var}}^p\left(t\right))$	Theoretical variant frequencies in virus population p at time t of a Wright-Fisher model (no unit)
Parameters of interest
$\mathit{r}=(r_1,\dots ,r_{n_{var}})$	Variant relative intrinsic rates of increase (generation−1) a
${\mathit{\eta }}_e=({\eta }_e^{IO},{\eta }_e^{S_1},{\eta }_e^{S_2},{\eta }_e^{S_3})$	Successive virus effective population sizes (individuals) b
Fixed parameters
λinoc	Vector of variant frequencies in the virus inoculum (no unit)
T	Vector of measurement dates (day) [(0, 6, 10, 14, 20, 27, 34)]
Additional notations
Ne = (Ne(1), …, Ne(34))	Vector of virus effective population sizes (piecewise constant function of ηe)
$N_e^h\left(t_d\right)$	Harmonic mean of virus effective population sizes at sampling time td
$\sigma \left[f_i^{•}\left(t_d\right)\right]$	Standard deviation of the frequencies of virus variant i at sampling time td over the virus populations p
${\lambda }^{det}(t)=({\lambda }_1^{det}(t),\dots ,{\lambda }_{n_{var}}^{det}(t))$	Vector of variant frequencies at time t for an infinite size Wright-Fisher model

^a The abbreviation “seq” is the number of sequences representing the virus population or a given variant in this population.

^b The mean intrinsic rate of increase $\overline{r}$ of all virus variants is one.

^c With the full model ${\mathfrak{M}}_4$, ${\eta }_e^{IO}$ in the inoculated organ for t ∈ [1, 6], ${\eta }_e^{S1}$ at the onset of systemic infection for t ∈ [7, 10], ${\eta }_e^{S2}$ for t ∈ [11, 14] and ${\eta }_e^{S3}$ for t ∈ [15, 34].