[hat type="canine professional" duration="40 years"]
There's a great deal of apocrypha about origin of dog breeds. Supposedly Rottweilers were the "ancient cart dogs of Rome" but there's really no proof; rather it was an assumption based on where they were common when Europeans started writing down such observations. Sometimes even a history that was "never in doubt" is disproved by DNA studies, such as were done on Pharaoh and Ibizan Hounds -- turns out they're not 5000 year old breeds after all, but rather are relatively modern recreations of an ancient type, probably only a few hundred years old.
I expect that Rotts will prove to be a variant/descendant of the landrace Molosser type that survives in its most ancient form as the Cão de Castro Laboreiro (an Iberian flock-guardian breed which aside from its brindle markings, most people would mistake for its most immediate descendant, the American-type fieldbred Labrador Retriever). DNA studies show the Castro to be the primary ancestor of most European breeds of its general type. The Castro itself is probably an archeological remnant, or cousin, of the medieval "St.Hubert's Hound". [The "St. John's Water Dog" usually credited as the Labrador's ancestor probably never really existed either as a breed or landrace, but rather was a remnant from Castros left in Newfoundland by Portuguese sailors.]
The mosaic appears to be one of the basic herding/pursuit landrace types (ie. a type that naturally develops in response to local conditions and demands of work) which today we might call a Border Collie.
Aren't there Roman writings about their war dogs? These, per at least the descriptions I remember (which may not be authentic, but...) would be the basic Molossor type, shading toward mastiffs -- a big strong dog-of-all-work, with dropped ears and most typically a short coat (tho the Estrela is, per DNA, just a Castro crossed with some longhaired type). Today we see the same type mainly as mastiffs and various flock guardian breeds. The Rottweiler's known historical work, as German droving and cart dogs, is consistent with the Molossor type and temperament.
Anyway, I expect the Romans had the same basic landrace types and variants as have appeared anywhere that dogs are expected to work for a living -- herding, flock guardian (also used for military and property guarding), hunting, vermin control, and companion. (Yes, companion is a job, of sorts. It generally included a part-time job as indoor vermin control.) With assorted local variations, which today we would call "breeds". Dogs are so useful that no post-Stone-Age culture has done without them for long.
Tho as a general rule, the more useful the dogs, the less they're talked about historically, being more in the realm of livestock.
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