Two questions, really:
- Does the game explain at some point where those red "eggs" come from?
- Where does these red "eggs" come from?
The eggs are being spit by the flower-like things. You can destroy the flowers.
Also, the big slow flying monsters ("Spore Generators") lay them.
All the red stuff is either a virus, or something infected by it (in the case of red darwinians)
Here's an enemy guide I found
to answer your first question: no, the game won't explain about the origin of the eggs. But it will explain the origin of virus in the end - but I don't want to spoil it for you, let's just say I liked it
Like everything else, they are created by the virus.
They are some sort of "plant" that drop them where they detect your activity.
spoilers
tag to the question. If you don't want spoilers, you won't want to see the answers anyway, and therefore won't click the question.