Calculating Ancestral Influence in Man

Laughlin, Harry Hamilton

doi:10.1073/pnas.6.5.235

Cited by 2 publications

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“…Continuing this process, this individual has five ancestors three generations back and eight ancestors four generations back ( Figure 1). In general, a present-day female's X genealogical ancestors is growing as a Fibonacci series (Basin, 1963;Laughlin, 1920), such that k generations back she has F k+2 X genealogical ancestors, where F k is the k th Fibonacci number (OEIS A000045; Sloane, 2010). We can demonstrate that one's number of X genealogical ancestors grows as a Fibonacci series by encoding the X inheritance rules for the number of males and females (m k and f k , respectively) in the k th generation as a set of recurrence relations:…”

Section: Number Of Genealogical X Ancestorsmentioning

confidence: 99%

A Genealogical Look at Shared Ancestry on the X Chromosome

Buffalo

Mount

Coop

2016

Preprint

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Close relatives can share large segments of their genome identical by descent (IBD) that can be identified in genome-wide polymorphism datasets. There are a range of methods to use these IBD segments to identify relatives and estimate their relationship. These methods have focused on sharing on the autosomes, as they provide a rich source of information about genealogical relationships. We can hope to learn additional information about recent ancestry through shared IBD segments on the X chromosome, but currently lack the theoretical framework to use this information fully. Here, we fill this gap by developing probability distributions for the number and length of X chromosome segments shared IBD between an individual and an ancestor k generations back, as well as between half-and full-cousin relationships. Due to the inheritance pattern of the X and the fact that X homologous recombination only occurs in females (outside of the pseudo-autosomal regions), the number of females along a genealogical lineage is a key quantity for understanding the number and length of the IBD segments shared amongst relatives. When inferring relationships among individuals, the number of female ancestors along a genealogical lineage will often be unknown. Therefore, our IBD segment length and number distributions marginalize over this unknown number of recombinational meioses through a distribution of recombinational meioses we derive. We show how our results can be used to estimate the number of female ancestors between two relatives, giving us more genealogical details than possible with autosomal data alone.

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Section: Number Of Genealogical X Ancestorsmentioning

confidence: 99%

A Genealogical Look at Shared Ancestry on the X Chromosome

Buffalo

Mount

Coop

2016

Preprint

View full text Add to dashboard Cite

show abstract

“…In general, a present-day female's X genealogical ancestors are growing as a Fibonacci series (Laughlin 1920;Basin 1963), such that k generations back she has F kþ2 X genealogical ancestors, where F k is the kth Fibonacci number [where k is 0 indexed and the series begins F 0 ¼ 0; F 1 ¼ 1; . .…”

Section: Ancestrymentioning

confidence: 99%

A Genealogical Look at Shared Ancestry on the X Chromosome

2016

View full text Add to dashboard Cite

Close relatives can share large segments of their genome identical by descent (IBD) that can be identified in genome-wide polymorphism data sets. There are a range of methods to use these IBD segments to identify relatives and estimate their relationship. These methods have focused on sharing on the autosomes, as they provide a rich source of information about genealogical relationships. We hope to learn additional information about recent ancestry through shared IBD segments on the X chromosome, but currently lack the theoretical framework to use this information fully. Here, we fill this gap by developing probability distributions for the number and length of X chromosome segments shared IBD between an individual and an ancestor k generations back, as well as between half-and full-cousin relationships. Due to the inheritance pattern of the X and the fact that X homologous recombination occurs only in females (outside of the pseudoautosomal regions), the number of females along a genealogical lineage is a key quantity for understanding the number and length of the IBD segments shared among relatives. When inferring relationships among individuals, the number of female ancestors along a genealogical lineage will often be unknown. Therefore, our IBD segment length and number distributions marginalize over this unknown number of recombinational meioses through a distribution of recombinational meioses we derive. By using Bayes' theorem to invert these distributions, we can estimate the number of female ancestors between two relatives, giving us details about the genealogical relations between individuals not possible with autosomal data alone.

show abstract

Calculating Ancestral Influence in Man

Cited by 2 publications

References 0 publications

A Genealogical Look at Shared Ancestry on the X Chromosome

A Genealogical Look at Shared Ancestry on the X Chromosome

A Genealogical Look at Shared Ancestry on the X Chromosome

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