I read this story in 2011 and haven't stopped trying to find it. It may have been in an older anthology book from around the 1970s or '80s, and may have been titled "The Lottery".
It was about a scientist sent to the distant past, with a machine which gave out evolutionary lines to make extinct. The scientist was on a boat and the machine spit out humans as one of the lines. The scientist plucked a creature out of the ocean that was an early human ancestor, and then climbed into the water to float while feeling herself fade out of existence.