Selected substitutions at one locus can induce stochastic dynamics that res
emble genetic drift at a closely linked neutral locus. The pseudohitchhikin
g model is a one-locus model that approximates these effects and can be use
d to describe the major consequences of linked selection. As the changes in
neutral allele frequencies when hitchhiking are rapid, diffusion theory is
not appropriate for studying neutral dynamics. A stationary distribution a
nd some results on substitution processes are presented that use the theory
of continuos-time Markuv processes with discontinuous sample paths. The co
alescent of the pseudohitchhiking model is shown to have a random number of
branches at each node, which leads to a frequency spectrum that is differe
nt from that of the equilibrium neutral model. If genetic draft, the name g
iven to these induced stochastic effects, is a more important stochastic fo
rce than genetic drift, then a number of paradoxes that have plagued popula
tion genetics disappear.