Quasispecies theory predicts that slower replicators will be favored if they give rise to progeny that are on average more fit; these populations occupy short, flat regions of the fitness landscape … Flat quasispecies accept mutation without a corresponding effect on fitness … A flat quasispecies with an expansive mutant repertoire can explore vast regions of sequence space without consequence and is poised to adapt to rapid environmental change.

Lauring, A., & Andino, R. (2010). Quasispecies Theory and the Behavior of RNA Viruses PLoS Pathogens, 6 (7) DOI: 10.1371/journal.ppat.1001005

(My emphasis)  RNA viruses in general form quasispecies because they have such high mutation rates.  Many (though by no means all) emerging infections are the result of RNA viruses. I’ve pointed before to aspects of viruses that might help them jump from species to species (for example, here — though this is a DNA virus, not an RNA virus, and I don’t think it runs in quasispecies — and the string of posts I link to inside that one).

One example Lauring and Andino point to is influenza virus hemagglutinin (HA). Influenza mutates very rapidly, of course, but most of the changes are harmful to the virus. But changes in HA seem to be very well tolerated. Since HA is a major target of the immune system, this property allows influenza to avoid the immune system without getting hit by defects in fitness associated with the immune evasion.  This is a contrast to, say, HIV (generalizing here! This isn’t always true). HIV within a patient undergoes constant changes to avoid the immune response, but many of these changes reduce the overall viral fitness. If you take the mutated HIV into an environment without that particular immune response, the virus quickly mutates back to its original, more-fit, form.

I’m not sure how we would assess, in advance, which viruses are more “flat” than others and that are therefore more able to adapt to new species, but it’s something to think about as we look at new viruses and new viral variants. I would be interested in SARS, for example — what happened to mutation tolerance as the virus adapted to humans? Was the virus that originally jumped into humans different in this was from the ones that normally infect bats? Not easy to measure, though.