Hybridization between humans and Neanderthals has resulted in a low level of 
Neanderthal ancestry scattered across the genomes of many modern-day humans. 
After hybridization, on average, selection appears to have removed Neanderthal 
alleles from the human population. Quantifying the strength and causes of this 
selection against Neanderthal ancestry is key to understanding our relationship 
to Neanderthals and, more broadly, how populations remain distinct after 
secondary contact. Here, we develop a novel method for estimating the 
genome-wide average strength of selection and the density of selected sites 
using estimates of Neanderthal allele frequency along the genomes of modern-day 
humans. We confirm that East Asians had somewhat higher initial levels of 
Neanderthal ancestry than Europeans even after accounting for selection. We find 
that the bulk of purifying selection against Neanderthal ancestry is best 
understood as acting on many weakly deleterious alleles. We propose that the 
majority of these alleles were effectively neutral-and segregating at high 
frequency-in Neanderthals, but became selected against after entering human 
populations of much larger effective size. While individually of small effect, 
these alleles potentially imposed a heavy genetic load on the early-generation 
human-Neanderthal hybrids. This work suggests that differences in effective 
population size may play a far more important role in shaping levels of 
introgression than previously thought.