This theory, championed by Tomoko Ohta, argues that at the molecular level, most evolution occurs via changes which are not completely selectively neutral, but effectively so. Specifically, when s is the selection coefficient and Ne is the effective population size, if:

s < 1/2Ne

than the mutation will behave as if it is neutral. In other words, it will be effected by genetic drift and not natural selection.

Evidence for nearly neutral theory comes from codon bias. Specifically, codon bias is much higher in organisms with larger population sizes. For example, E. coli has a high degree of codon bias, while humans have much less.