During the first million years of the Pleistocene climate changes, our ancestors' brain size doubled. Enlargement continued at the same rate, suggesting a self-sustaining process with a rate-limiting component. For large grazing animals and their predator Homo erectus, I analyzed the brush-fire cycle behind grasslands' brushy frontier, seeking a feedback loop. The burn scar's new grass is an empty niche for grass-specialized herbivores, which evolved from mixed feeders only in the early Pleistocene. The frontier subpopulation of grazers discovering the auxiliary grassland quickly multiplies. Following this boom, a bust occurs several decades later when the brush returns; it squeezes this offshoot population back into the core grasslands population. For both prey and predators, such a feedback loop can shift the core's gene frequencies toward those of the brush explorers. Hunters of both browsers and grazers spend more time in the brush than those specializing in grazers; this versatility becomes a candidate for differential amplification. Any brush-relevant allele could benefit from amplifying feedback by such trait hitchhiking, so long as its phenotypes also concentrate near where empty niches can open up in the brush for grazers and their predators. Increased versatility likely correlates with larger brain size on the evolutionary time scale. Among the tasks likely to need the shade of brush are toolmaking and food preparation. The more versatile, larger-than-average brains need only spend more-than-average time in the catchment zone for this recursive evolutionary process to keep average brain size increasing even further, making advance room for some future functionality in the cerebral cortex.