I get lots of people who ask about those little white and black spots on their dolls and miniatures. I've asked Nick Hill, a chemist who has researched and come up with products for cleaning and restoring dolls about this problem. Over time in some less than optimun formulations some of the plasticizer migrates or moves to the surface of the plastic. Plasticizer in PVC is good food for micorooorganisms like bacteria and fungi.
Fungi derive their color from chlorophyll and from ingredients into the vinyl.
The black dots are the roots of fungal organisms. The white dots are baby fungus. A new colony is called a mycelial mat. Since the organisms are ubiquitious is appears that the spots are contagious. In fact if the conditions are right and a nutrient source is available, growth would take place no matter how many dolls are in a given location.