I have seen some very strongly and brightly colored pearls: are they naturally colored?

While pearls can naturally occur in every hue and be very saturated in color, pearl colors can be treated to alter their appearance. The most common color treatment is dyeing, and it is more common with freshwater pearls than saltwater pearls.
 
While freshwater pearls do come in a wide range of beautiful natural colors and can be quite saturated, they typically are not naturally dark in tone and do not naturally occur outside of the warm purplish, pink, orange, and yellowish hues. So if you come across freshwater pearls that are gray or black, very vibrant purple or pink, deep red or orange, or any green or blue colors, you should inquire as to whether the color is natural or treated.
 
It is a good idea to inquire whether color is natural or treated when shopping for any pearls, and to always ask for any declarations in writing upon purchase.