Yeah, I agree with the others, it's rim grime spreading outwards, not the treads bleeding color. It's pretty common on tan sidewalls in general. I just scrub them occasionally, when it starts to bug me. It happens the most after riding in the rain, so if this is your wet weather bike, you are going to see this pretty constantly.
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1964 JRJ (Bob Jackson), 1973 Wes Mason, 1974 Raleigh Gran Sport, 1986 Schwinn High Sierra, 2000ish Colian (Colin Laing), 2011 Dick Chafe, 2013 Velo Orange Pass Hunter