Table 4.

Modeling of unobserved processes in the simultaneous phylogenetic family. For the sequence mutation process, the user could either use a single substitution model or choose. Within-host evolution (modeled or not) includes whether the transmission bottleneck is complete or weak. When transmission is modeled, we mention the states hosts can find themselves in (S: susceptible, E: latent, I: infectious, R: removed). In addition, either geographical distance (spatial kernel), contact data, or random mixing are considered. Finally, the transmission model mentions whether there is only one index case possible (single introduction) or multiple. * means multiple sequences can be considered per epidemiological unit.

Method (Name) [Reference]	Sequence Mutation	Within-Host Evolution	Transmission	Case Observation	Inference Method
Ypma et al., 2013 [5]	Mutation rate	Coalescent process	SEIR (latency/infectious period)	All cases are observed and sampled	Bayesian
		Complete	Spatial kernel
			Single
Hall et al., 2015 (beastlier) [18]	User’s choice	Coalescent process	SEIR (latency/infectious period)	All cases are observed but not always sampled	Bayesian
		Complete *	Spatial kernel
			Single
De Maio et al., 2016 (SCOTTI) [41]	User’s choice	Coalescent process	Migration model	Maximum number of hosts	Bayesian
		Weak *
Klinkenberg et al., 2017 (phybreak) [26]	Mutation rate	Coalescent process	SI (generation times)	All cases are observed but not always sampled	Bayesian
		Complete	Random mixing
			Single
Morelli et al., 2012 [23]	Jukes Cantor model	No explicit model	SEIR (latency/infectious period)	All cases are observed and sampled	Bayesian
		Complete	Spatial kernel
			Single
Mollentze et al., 2014 [1]	Kimura model	No explicit model	SEIR (latency/infectious period)	Observed cases contribute to transmission after removal time	Bayesian
		Complete	Spatial kernel
			Multiple
Lau et al., 2015 [42]	Kimura model	No explicit model	SEIR (latency/infectious period)	All cases are observed but not always sampled	Bayesian
		Complete	Spatial kernel
			Multiple
Firestone et al., 2020 (BORIS) [29]	Kimura model	No explicit model	SEIR (latency/infectious period)	All cases are observed but not always sampled	Bayesian
		Complete	Spatial kernel
			Multiple
Montazeri et al., 2020 [43]	Jukes Cantor model	No explicit model	No explicit model	All cases are observed and sampled	Bayesian
		Complete