Why genetic diversity barely grows with population size
In plain words
Simple theory says a species with a billion times more individuals should carry far more genetic variation, but diversity differs only about a hundredfold across animals whose numbers differ by more than ten orders of magnitude. What compresses diversity in large populations is unknown.
Precise statement
Neutral theory gives nucleotide diversity $\pi=4N_e\mu$ ($N_e$ = effective population size, $\mu$ = mutation rate per site per generation), yet across metazoans $\pi$ varies over roughly two decades while census size $N_c$ varies over more than ten (Lewontin, 1974). Account quantitatively for the slope of $\log \pi$ versus $\log N_c$ through linked selection (genetic draft from sweeps, as in traveling-wave theory, and background selection), population-size fluctuations, and mutation-rate scaling.
What would settle it
A model with measured recombination maps, mutation rates and demographic histories across many species that reproduces the observed $\pi$ versus $N_{c}$ relation.
Status in the literature
Buffalo (eLife 2021, doi 10.7554/eLife.67509) found that linked selection, even assumed strong and frequent, cannot explain the relation across 172 taxa; this remains disputed.