Physics – Biological Physics
Scientific paper
2011-09-13
Physics
Biological Physics
Scientific paper
To calculate the number of ancestor of one individual from any biparental reproduction specie is necessary to use an statistical approach. It's not possible to build the progenitor's tree only assuming that the spice has a sexual biparental reproduction. In particular it not true that the simple progression of $2^{t+1}$ describes in a realistic way the number of ancestors after a few generations. The reason is that when we go back in generations the probability of some ancestors been relatives has an increase. This implies a restriction in the ancestor's mean number respect of $2^{t+1}$. Although this number correspond to the maximum ancestor's number in the $t$-generation. Considering the possibility of blood relationship between the ancestors, we show how to re-build the progenitor's tree by modeling our problem with a Markov's Chain. First we work in a continuous time variable and then by doing a discretization process we obteined the ancestor's distribution. Using covariant derivative in a proper way we normalized the distribution and included the interaction's scale. Also we obtained the ancestor's distribution it's first and second moments. Finally we calculated the entropy associated to the distribution in order to ensure that it's grows with the generation's number.
Caruso M.
Jarne C.
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