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Q: Population genetics and heredity ( Answered,   2 Comments )
Subject: Population genetics and heredity
Category: Science > Biology
Asked by: melim42-ga
List Price: $20.00
Posted: 04 Apr 2006 08:36 PDT
Expires: 04 May 2006 08:36 PDT
Question ID: 715343
How many generations apart do two "relatives" have to be before
they're no more closely related than two people chosen at random from
the population? ($20)
Here's the idea:  people are related to their children and their own
parents by 50% (i.e., they share 1/2 of their genes).  What percentage
of genes do two randomly chosen humans share, and how many generations
does it take to get to that point?  I'm looking for an anwer like "5"
or "10" or whatever is correct.  Thanks!  Hope you think this is as
interesting a question as I do!
Subject: Re: Population genetics and heredity
Answered By: alanna-ga on 05 Apr 2006 12:51 PDT
Hi Melim42-ga -

First off, I'd like to say that I do find this question interesting
and enjoyed researching it for you.

Your question: How many generations apart do two "relatives" have to be before
they're no more closely related than two people chosen at random from
the population?

Your answer is found in an algebraic expression called the
"coefficient of relationship."  This is " the proportion of genes that
are held in common by two individuals as a result of direct or
collateral relationship."

I can't write the formula here because it uses subscripts and
superscripts, but the degree of relationship (shared blood) between
any two people who are descended from the same person decreases by
double between generations.

For siblings, as you rightly say, the coefficient is .5; for first
cousins it is .25; for second cousins .125.  By the 5th generation it
is .03125; by the 7th it is .0076125.

It is never 0, but gets close.  Please refer to the table at: [scroll to the
very bottom of the page].

When we think of the general population, we infer a coefficient of
relationship of 0.  That may be.  But chances are that in the mist of
time, a common ancestor or ancestors exist for any two people as noted
in one of the comments below.

As to your question about the percentage of genes that any two people
share, I'd say it's quite high.  After all, there are 20,000-25,000
genes in the human genome. They are not all different.  We pay
attention primarily to the genes whose expression we can see (the
phenotype) like hair, eyes, length of nose, skin color, etc.  But
there are many more genes in the (hidden) genotype.  These are the
genes that govern metabolic functions or bone formation or most of
what goes on inside of us. When a mutation occurs in one of these
workhouse genes, disease often strikes.

Estimates have been made of DNA elements (base pairs) that make up the
genes that reside on the human chromosome.  There are  50 - 250
million base pairs on each of the 24 human chromosomes. Thus far
scientists have identified about 1.4 million locations on various
chromosomes that show a single-base difference.

It's a vast and fascinating subject.  I hope I've helped you come to
an understanding of some of the mysteries of life.

Here are some other websites that may be of interest

Formula for coefficient of relationship [scroll 1/4 way
down the page; it starts with Rxy]

The Human Genome Project

Genotype and Phenotype Definition

Genetic andQuantitative Aspects of Genealogy

Birgid Schlindwein's Hyperglossary of Genetic Terms

All the best,


Request for Answer Clarification by melim42-ga on 12 Apr 2006 08:18 PDT
I was looking for a number of generations, like mikewa-ga's answer. 
Do you agree with him, and why or why not?  I would also like to know
if my own calculations are similar in concept to mikewa-ga's, if he
will respond again.

From my calcuations, I'd say 6 to 8 is a good estimate.  I get 5 to 9
generations, assuming all of the "variable" genes are inherited
independently and ignoring new mutations -- bad assumptions, I know.

Assume 25,000 genes, 99% of which any two humans have in common.  A
relative can, therefore, share (or not) 250 genes with the index
individual.  After 9 generations, the index individual's "relatives"
will have (on average) 250*(.5^9)<1 gene out of the original 250.

Assume 25,000 genes, 99.9% in common.  After 5 generations, the number
of common genes is 25*(.5^5)<1.

Clarification of Answer by alanna-ga on 13 Apr 2006 16:52 PDT
I don't disagree with mikewa-ga's comment.  As a Google Answers
researcher, I am charged with giving you the answer plus the
background information and web sites that will back up my information.
 If you felt you had an answer from the comments section, you did have
the option of withdrawing the question.

I gave you the link to a table showing the coefficient of relationship
for 13 generations. You can choose the point on that table where you
feel the relationship is small enough to be close to considered
"random."  Remember, it approaches but never is 0.

I believe that mikewa-ga is referring to nucleotide bases (the
components of each gene). His range hits  the estimate of the Human
Genome Project, which is 99.9% nucleotide bases.  Those 99.9% string
out on the chromosome in various combinations to form the 30,000 genes
of the human genome and a lot of junk DNA.

Nonetheless I would also state that 6-7 generations are sufficient for
any two descendents to be considered "non-related."

I'd like to add that because 99.9% of the nucleotide bases are the
same in all of us, that is not to say that 99.9% of the genes are the
same.  A lot of the bases (at last 50%) are "dead space" or junk DNA.

Here are some numbers from the Human Genome Project:

   " *   The human genome contains 3164.7 million chemical nucleotide
bases (A, C, T, and G).
    * The average gene consists of 3000 bases, but sizes vary greatly,
with the largest known human gene being dystrophin at 2.4 million
    * The total number of genes is estimated at 30,000 ?much lower
than previous estimates of 80,000 to 140,000 that had been based on
extrapolations from gene-rich areas as opposed to a composite of
gene-rich and gene-poor areas.
    * Almost all (99.9%) nucleotide bases are exactly the same in all people.
    * The functions are unknown for over 50% of discovered genes.

   " *   Less than 2% of the genome codes for proteins.
    * Repeated sequences that do not code for proteins ("junk DNA")
make up at least 50% of the human genome.
    * Repetitive sequences are thought to have no direct functions,
these repeats reshape the genome by rearranging it, creating entirely
new genes, and modifying and reshuffling existing genes.
    * During the past 50 million years, a dramatic decrease seems to
have occurred in the rate of accumulation of repeats in the human
Subject: Re: Population genetics and heredity
From: kottekoe-ga on 04 Apr 2006 20:26 PDT
It depends entirely on your assumptions about the amount of
inbreeding. Until quite recently, most humans lived in rather small
communities with extensive inbreeding. If you go back 40 generations
(~1000 years) you would have one trillion ancestors alive at that time
if it were not for inbreeding. Obviously that makes no sense.
Subject: Re: Population genetics and heredity
From: mikewa-ga on 05 Apr 2006 04:30 PDT
Estimates of the similarity of DNA between two randomly chosen people
vary depending on what is being counted,, but usually are in the
99-99.9% range. Since each generation halves the variation attributed
to a specific ancestor then just 6-8 generations should be enough to
make it statistically similar to the general population. there are
enough variables in this to provide lots of argument, but this should
be in the right ballpark.


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