Scribd
Upload
93 views11 pages

Dynamics of Human Ancestry

This document discusses mathematical models of human ancestry and the most recent common ancestor. It notes that a binary tree model of ancestry leads to more ancestors than the historical world population. It then discusses pedigree collapse over generations which leads to a directed acyclic graph structure rather than a tree. It also discusses the Y-chromosomal Adam and Mitochondrial Eve as the most recent common ancestors in direct paternal and maternal lines. Models are presented for the probability of an unbroken lineage extending over generations based on probabilities of daughters versus multiple offspring. The models show decreasing probabilities of an unbroken lineage extending many generations into the past.

Uploaded by

Woof Dawgmann
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
93 views11 pages

Dynamics of Human Ancestry

This document discusses mathematical models of human ancestry and the most recent common ancestor. It notes that a binary tree model of ancestry leads to more ancestors than the historical world population. It then discusses pedigree collapse over generations which leads to a directed acyclic graph structure rather than a tree. It also discusses the Y-chromosomal Adam and Mitochondrial Eve as the most recent common ancestors in direct paternal and maternal lines. Models are presented for the probability of an unbroken lineage extending over generations based on probabilities of daughters versus multiple offspring. The models show decreasing probabilities of an unbroken lineage extending many generations into the past.

Uploaded by

Woof Dawgmann
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 11

Dynamics of Human Ancestry

Mathematical Models

Lineage A Paradox
You

Parents

Grandparents

Past

Binary tree with nodes at Level

. billion > (past) world population!

Pedigree Collapse

Past

Collapse in tree

DAG

Adam and Eve


Y-chromosome inherited only from father,
mitochondrial DNA inherited only from
mother.
Y-MRCA or Y-chromosomal Adam:
The MRCA from whom all people (in the
present) are descended patrilineally.
mt-MRCA or Mitochondrial Eve: The
MRCA from whom all people (in the
present) are descended matrilineally.
3

Most Recent Common Ancestor

Most Recent Common Ancestor

Probability of Unbroken Matrilineal


Descent
Let the probability be .
Let probability of one daughter be and two
daughters be .
Then = + 2 1 + 2 .
Solution:
+
=

provided + 2 1.
6

Probability of Unbroken Matrilineal


Descent

2(1 )

= + +
7

Probability of Unbroken Matrilineal


Descent

0.5
0.55
0.25

0.3
0.25
0.4

. = %
. = %
. = . %

Are the probabilities unrealistically high?

Smaller probabilities lead to = .


Perhaps infinite descent is impossible.
8

A Finite Model
Let the probability be that the lineage
extends to further generations.
Then = + .
For = 0.4 and = 0.15
10 = 1.58 102 1.6%
20 = 4.42 104 0.04%

30 = 1.24 105 0.001%


9

Conclusion
What is the probability of your existence?

According to Ali Binazir1, it is around

in ,,
Translation: Mathematically, you probably dont
exist!
In other words, you are here against all odds.

1. http://blogs.law.harvard.edu/abinazir/2011/06/15/what-are-chances-you-wouldbe-born/

10

You might also like