An accurate genetic clock
Our method for ``Time to most recent common ancestor'' TMRCA of genetic trees for the first time deals with natural selection by apriori mathematics and not as a random factor. Bioprocesses such as ``kin selection'' generate a few overrepresented ``singular lineages'' while almost all other lineages terminate. This non-uniform branching gives greatly exaggerated TMRCA with current methods. Thus we introduce an inhomogenous stochastic process which will detect singular lineages by asymmetries, whose ``reduction'' then gives true TMRCA. Reduction implies younger TMRCA, with smaller errors. This gives a new phylogenetic method for computing mutation rates, with results similar to ``pedigree'' (meiosis) data. Despite these low rates, reduction implies younger TMRCA, with smaller errors. We establish accuracy by a comparison across a wide range of time, indeed this is only y-clock giving consistent results for 500-15,000 ybp. In particular we show that the dominant European y-haplotypes R1a1a $\& $ R1b1a2, expand from c3700BC, not reaching Anatolia before c3300BC. This contradicts current clocks dating R1b1a2 to either the Neolithic Near East or Paleo-Europe. However our dates match R1a1a $\& $ R1b1a2 found in Yamnaya cemetaries of c3300BC by Svante P\"{a}\"{a}bo et al, together proving R1a1a $\& $ R1b1a2 originates in the Russian Steppes.