In this article we discuss the ancestry of sequences sampled fr om the coal
escent with recombination with constant population size 2N. We have studied
a number of variables based on simulations of sample histories, and some a
nalytical results are derived. Consider the leftmost nucleotide in the sequ
ences. We show that die number of nucleotides sharing a most recent common
ancestor (MRCA) with the leftmost nucleotide is approximate to log(1 + 4N L
r)/4Nr when two sequences are compared, where L denotes sequence length in
nucleotides, and r the recombination rate between any two neighboring nucle
otides per generation. For larger samples, the number of nucleotides sharin
g MRCA with the leftmost nucleotide decreases and becomes almost independen
t of 4N Lr. Further, we show that a segment of the sequences sharing a MRCA
consists in mean of 3/8Nr nucleotides, when two sequences are compared, an
d that this decreases toward 1/4Nr nucleotides when the whole population is
sampled. A measure of the correlation between the genealogies of two nucle
otides on two sequences is introduced. We show analytically that even when
the nucleotides are separated by a large genetic distance, but share MRCA,
the genealogies will show only little correlation. This is surprising, beca
use the time until the two nucleotides shared MRCA is reciprocal to die gen
etic distance. Using simulations, the mean time until all positions in the
sample have found a MRCA increases logarithmically with increasing sequence
length and is considerably lower than a theoretically predicted upper boun
d. On the basis of simulations, it turns our that important properties of t
he coalescent with recombinations of the whole population are reflected in
the properties of a sample of low size.