# ) in equations (5) and (six) (nonetheless restricting to genetic

However, the geometric growth of r(n) means that small uncertainties in n have large effects on the estimated numbers of genealogical common ancestors--and we have large uncertainties in n. Despite these difficulties, we can still get some order-ofmagnitude estimates. For instance, we estimate that someone from Hungary shares on average about five genetic common ancestors with someone from the United Kingdom between 18 and 50 generations ago. Since 1/r(36) = 5.86107, we would conservatively estimate that for every genetic common ancestor there are tens of millions of genealogical common ancestors. Most of these ancestors must be genealogical common ancestors many times over, but these must still represent at least thousands of distinct individuals.the observed variance sxy, for all pairs of populations x and y with at least 10 individuals in Selonsertib site population y. (B) The ``z score,* which is observed value sxy minus mean value divided by standard deviation, estimated using 1,000 replicates. The population x is shown on the vertical axis, with text labels giving y, so for instance, Italians show much more substructure with most other populations than do Irish. Note that sample size still has a large effect--it is easier to see substructure with respect to the Swiss French (x = CHf) because the large number of Swiss French samples allows greater resolution. A vertical line is shown at z = 5. Only pairs of populations with at least three samples in country x and 10 samples in country y are shown. Because of the log scale, only pairs with a positive z score are shown, but no comparisons had z,22.5, and only three had z,22. (PDF)Figure S3 (A) Mean numbers of IBD blocks of length at least 1 cM per pair of individuals, shown as a modified Cleveland dotchart, with 62 standard deviations shown as horizontal lines. For instance, on the bottom row we see that someone from the United Kingdom shares on average about one IBD block with someone else from the United Kingdom and slightly less than 0.2 blocks with someone from Turkey.) in equations (five) and (6) (nevertheless restricting to genetic ancestors around the autosomes). These inform us that provided the distribution m(n), the mean number of genetic prevalent ancestors coming from generation n/2--that is, the imply variety of IBD blocks of any length inherited from such P common ancestors--is N(0) m(n) 22 Gk z1 where Gk is k 1 the total sex-averaged genetic length on the kth human chromosome. Because the total sex-averaged map length from the human autosomes is about 32 Morgans, this can be about m(n)(32nz22). This procedure has been made use of in Figures four and 5. Converting shared IBD blocks to numbers of shared genealogical frequent ancestors is far more problematic. Suppose that modern-day people a and b each have c as a grandnparent. Utilizing equation (6) at x = 0, we know that the imply number of blocks that a and b both inherit from c is r(2n), with r(n) : 2{n (32nz22), since each block has chance 222n of being inherited across 2n meioses. First treat the endpoints of each distinct path of length n back through the pedigree as a grandnparent, so that everyone has exactly 2n grandnparents, and some ancestors will be grandnparents many times over.*