I dont think negative points would be a good idea to carry, since it's something that if not written down will be forgotten through the playtime. negative point should perhaps be applicable if the events are still in effect when the game ends and the scores are being tallied.
I think a better option would be for certain event cards to only function if you play them on one of your own species, much like sacrificing units in standard game terminology, or have other caveats that protect what you have but limit your play options. That would bring a layer of strategy to some more powerful event cards. For example, we could have an "Endangered Wildlife Preserve" event that can be played on any card of score value X or higher. However, it is removed from play should either player play a second copy of that species (which is representative of it being delisted as endangered and becoming fair game).