Retrotransposons have had a considerable impact on the overall architecture of the human genome. Currently, there are three lineages of retrotransposons (Alu, L1, and SVA) that are believed to be actively replicating in humans. While estimates of their copy number, sequence diversity, and levels of insertion polymorphism can readily be obtained from existing genomic sequence data and population sampling, a detailed understanding of the temporal pattern of retrotransposon amplification remains elusive. Here we pose the question of whether, using genomic sequence and population frequency data from extant taxa, one can adequately reconstruct historical amplification patterns. To this end, we developed a computer simulation that incorporates several known aspects of primate Alu retrotransposon biology and accommodates sampling effects resulting from the methods by which mobile elements are typically discovered and characterized. By modeling a number of amplification scenarios and comparing simulation-generated expectations to empirical data gathered from existing Alu subfamilies, we were able to statistically reject a number of amplification scenarios for individual subfamilies, including that of a rapid expansion or explosion of Alu amplification at the time of human-chimpanzee divergence.