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"Cosmopolitan" is referring to the plants being found in nature world wide. This includes natural or even an unnatural presence. Can you imagine trying to keep duckweed from spreading? Many of the VERY fast growing plants, especially floating plants, are now found in almost every environment that will support them. Because of this is it is or almost is impossible to say where some plants are originally from, geographically speaking. So the catch all term "cosmopolitan is used. You could almost sub the word "invasive" for "cosmopolitan", but it wouldn't be 100% accurate.