Can one hear the shape of a population history?
  Reconstructing past population size from present day genetic data is a major goal of population genetics. Recent empirical studies infer population size history using coalescent-based models applied to a small number of individuals. Here we provide tight bounds on the amount of exact coalescence time data needed to recover the population size history of a single, panmictic population at a certain level of accuracy. In practice, coalescence times are estimated from sequence data and so our lower bounds should be taken as rather conservative. 
Junhyong Kim, Elchanan Mossel, Mikl\'os Z. R\'acz, Nathan Ross
q-bio.PE math.ST stat.TH