Pink petri dish.

The petri dish is infected with two kinds of bacteria: pink and purple. Each spreads in random clusters across the dish, the pink bacteria patches and the purple grow quite happily over top of oneanother. Both kinds grow faster exponentially, but then the growth rate of the purple bacteria slows down drastically as the growth rate of the pink accellerates steadily.

What colour do you expect will fill the petri dish in the end?

The culture (if you will excuse the pun) that reduces population growth to static or shrinking will be rapidly supplanted by the culture that promotes population growth. Meme die-out? Probably. Will the reduced population growth meme inevitably recur? Not likely given the dwindling resources at our disposal. There may not be time - and less time if a larger population/fast population increase culture prevails.