A Malthusian would predict that rising GDP per capita would lead to a rising population, whilst rising population would (with a smaller lag) lead to falling GDP per capita. The data for an African sample... suggests that there is no significant link from GDP per capita growth in decade one to population growth in decade two and a significant but small impact of population growth in decade one on GDP per capita growth in decade two using a pooled sample. This provides scant evidence to support a theory that the region is caught in a Malthusian cycle.
That said, I've heard a lot of good things about A Farewell to Alms. With luck, the Malthusian Zombie will be too lethargic to cannibalize the rest of the book.