 05106 Armando G. M. Neves, Carlos H. C. Moreira
 Percolation Model for the Existence of a Mitochondrial Eve
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Mar 16, 05

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Abstract. We look at the process of inheritance of mitochondrial DNA as a
percolation model on trees equivalent to the GaltonWatson
process. The model is exactly solvable for its percolation
threshold $p_c$ and percolation probability critical exponent. In
the approximation of small percolation probability, and assuming
limited progeny number, we are also able to find the maximum and
minimum percolation probabilities over all probability
distributions for the progeny number constrained to a given $p_c$.
As a consequence, we can relate existence of a mitochondrial Eve
to quantitative knowledge about demographic evolution of early
mankind. In particular, we show that a mitochondrial Eve may exist
even in an exponentially growing population, provided that the
average number of children per individual is constrained to a
small range depending on the probability $p$ that a newborn child
is a female.
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