text: **Genealogies improve ancestry modelling**
  By definition,*f*-statistics count the occurrence of local genealogical 
  relationships that are implied by how mutations are shared between 
  individuals42. This inherent relationship between*f*-statistics and local 
  genealogies makes it straightforward to compute*f*-statistics directly on 
  inferred genealogies43. Instead of computing*f*-statistics on observed 
  mutations, they are now calculated on the inferred branches of these 
  genealogies, some of which may not be directly tagged by mutations 
  but are inferred by resolving the local haplotype structure (Methods). 
  We develop mathematical theory and simulate a simple admixture 
  model, in which the ancestry proportion is constrained in a single ratio of 
  two*f*4-statistics19, to test this approach (Fig. 1b and Supplementary Note). 
  While unbiased, we find that using*f*-statistics computed on genealogies 
  by itself does not yet yield a large improvement in statistical power to 
  quantify admixture events. However, we show, through both theoretical 
  prediction and simulation, that large improvements in power can be 
  gained without bias by restricting to recent coalescences, which are most 
  informative for recent admixture events (Fig. 1c,d and Extended Data 
  Figs. 2 and 3). We show that coalescences older than the time of diver- 
  gence of the sources carry no information with respect to the admixture 
  event and only add noise to the*f*-statistics. Excluding these therefore 
  increases statistical power, without introducing bias, in principle. 