Last week, the United Nations announced that the world’s population had reached seven billion, but there have been times when it headed in the opposite direction, and not in pleasant ways. The savagery of the Mongol conqueror Genghis Khan may have culled the global population by about 11 percent; two bloody upheavals in China — the An Lushan Rebellion and the collapse of the Xin Dynasty — each may have felled about 6 percent of humanity. Those are but 3 of the 100 worst atrocities in history, as cataloged by Matthew White in “The Great Big Book of Horrible Things,” an amusing (really) account of the murderous ways of despots, slave traders, blundering royals, gladiators and assorted hordes. Estimating the tolls from such horrors is an inexact science, given war’s nature and the mysteries of antiquity. The deadliest “multicides” are more plentiful in recent centuries, given that there were more people to kill and better ways to kill them on a grand scale. Even so, killings as a percentage of all humanity are probably declining. Here is a look at the sweep of human brutality presented in a timeline.