Singular Lineages

Molecular clocks give “Time to most recent common ancestor” TMRCA of genetic trees. By Watson-Galton most lineages terminate, with a few overrepresented singular lineages generated by W. Hamilton’s “kin selection”. Applying current methods to this non-uniform branching produces greatly exaggerated TMRCA. We introduce an inhomogenous stochastic process which detects singular lineages by asymmetries, whose reduction gives true TMRCA. This implies a new method for computing mutation rates. Despite low rates similar to mitosis data, reduction implies younger TMRCA, with smaller errors. We establish accuracy by a comparison across a wide range of time, indeed this is only clock giving consistent results for both short and long term times. In particular we show that the dominant European y-haplotypes R1a1a & R1b1a2, expand from c3700BC, not reaching Anatolia before c3300BC. While this contradicts current clocks which date R1b1a2 to either the Neolithic Near East or Paleo-Europe, our dates support recent genetic analysis of ancient skeletons by Reich.