In a randomly-mating biparental population of size $N$ there are, with high
probability, individuals who are genealogical ancestors of every extant
individual within approximately $łog_2(N)$ generations into the past. We use
this result of Chang to prove a curious corollary under standard models of
recombination: there exist, with high probability, individuals within a
constant multiple of $ łog_2(N)$ generations into the past who are
simultaneously (i) genealogical ancestors of each of the individuals at
the present, and (ii) genetic ancestors to none of the individuals at the
present. Such ancestral individuals - ancestors of everyone today that left no
genetic trace -- represent `ghost' ancestors in a strong sense. In this short
note, we use simple analytical argument and simulations to estimate how many
such individuals exist in Wright-Fisher populations.
%0 Generic
%1 gravel2014existence
%A Gravel, Simon
%A Steel, Mike
%D 2014
%K biparental_ancestry biparental_mrca pedigrees
%T The existence and abundance of ghost ancestors in biparental populations
%U http://arxiv.org/abs/1401.3668
%X In a randomly-mating biparental population of size $N$ there are, with high
probability, individuals who are genealogical ancestors of every extant
individual within approximately $łog_2(N)$ generations into the past. We use
this result of Chang to prove a curious corollary under standard models of
recombination: there exist, with high probability, individuals within a
constant multiple of $ łog_2(N)$ generations into the past who are
simultaneously (i) genealogical ancestors of each of the individuals at
the present, and (ii) genetic ancestors to none of the individuals at the
present. Such ancestral individuals - ancestors of everyone today that left no
genetic trace -- represent `ghost' ancestors in a strong sense. In this short
note, we use simple analytical argument and simulations to estimate how many
such individuals exist in Wright-Fisher populations.
@misc{gravel2014existence,
abstract = {In a randomly-mating biparental population of size $N$ there are, with high
probability, individuals who are genealogical ancestors of every extant
individual within approximately $\log_2(N)$ generations into the past. We use
this result of Chang to prove a curious corollary under standard models of
recombination: there exist, with high probability, individuals within a
constant multiple of $ \log_2(N)$ generations into the past who are
simultaneously (i) genealogical ancestors of {\em each} of the individuals at
the present, and (ii) genetic ancestors to {\em none} of the individuals at the
present. Such ancestral individuals - ancestors of everyone today that left no
genetic trace -- represent `ghost' ancestors in a strong sense. In this short
note, we use simple analytical argument and simulations to estimate how many
such individuals exist in Wright-Fisher populations.},
added-at = {2014-01-20T18:18:15.000+0100},
author = {Gravel, Simon and Steel, Mike},
biburl = {https://www.bibsonomy.org/bibtex/2af3623eb040b6c20bb3bcd83a961c88c/peter.ralph},
interhash = {337105ad668fe105b91b9fb8a3405bf5},
intrahash = {af3623eb040b6c20bb3bcd83a961c88c},
keywords = {biparental_ancestry biparental_mrca pedigrees},
note = {cite arxiv:1401.3668},
timestamp = {2014-01-20T18:18:15.000+0100},
title = {The existence and abundance of ghost ancestors in biparental populations},
url = {http://arxiv.org/abs/1401.3668},
year = 2014
}