Genetics puzzle

I study and work in the field of genetics and was curious if anyone would like to attempt to calculate the probability of the following event occurring:

On average you share 50% of your genes with your brother / sister, although the actual figure can range from 0-100%. If you are not a monozygotic twin what is the probability that you will be 100% related?

I don’t have the answer yet (working on it) but thought others might like to attempt in the meantime.

Assumptions:

Species = Human
No mutation events
No non-disjunction
No translocation / inversion / insertions / deletions etc
No change in parents for each child

Originally posted by timebombted
I study and work in the field of genetics and was curious if anyone would like to attempt to calculate the probability of the following event occurring:

On average you share 50% of your genes with your brother / sister, although the actual figure can range from 0-100%. If you are not a monozygotic twin what is the probability that you will be 100% rel ...[text shortened]...
No translocation / inversion / insertions / deletions etc
No change in parents for each child

wouldnt it be in the trillions and trillions? so many dnas...do you have an estimate?

a 100% chance you'll be "related" to your twin . .but i bet you meant .. .100% identical genes.

Now, that will be some really big odds!

Originally posted by coquette
a 100% chance you'll be "related" to your twin . .but i bet you meant .. .100% identical genes.

Now, that will be some really big odds!

"a 100% chance you'll be "related" to your twin"

Only if your monozygotic twins.

Yes the odds are huge.

Originally posted by jvanhine
wouldnt it be in the trillions and trillions? so many dnas...do you have an estimate?

Yes the probability will be astronomical....... no estimate yet

Originally posted by timebombted
On average you share 50% of your genes with your brother / sister,

I thought we shared up to 98.6% of our genes with chimpanzees? That we even share genes with a pine tree, a spider, a champignon, gonorhea bacterium etc...?

What about the brother and sister, where a whole chromosome is not shared?

I'm not an expert of genetics, but I use it everytime me and my girlfriend are having ... you know.

The chance you will be 100% the same as your monozygotic twin would be, on average, 6!/number of genes!(6)x6!/number of genes!(6) all divided by number of genes-5

In other words, it doesn't happen.

Originally posted by timebombted
I study and work in the field of genetics and was curious if anyone would like to attempt to calculate the probability of the following event occurring:

On average you share 50% of your genes with your brother / sister, although the actual figure can range from 0-100%. If you are not a monozygotic twin what is the probability that you will be 100% rel ...[text shortened]...
No translocation / inversion / insertions / deletions etc
No change in parents for each child

I don't know too much about genetics, so I'll make some simplifying assumptions:

1. The average person has about 25,000 genes.
2. One gene from either parent is required to fill each "gene slot".
3. No "gene slot" is empty or double filled.
4. Order is pre-set by the nature of the "gene slots", so order is not important. (this is probably my worst assumption)

The number of genetic makeups possible using these rules is 2^25000. For a given genetic makeup, the probability of the second offspring repeating this makeup is 1/2^25000. This is vanishingly small. For reference, the number of particles in the known universe is estimated at 10^81. Using logs to compare these numbers directly, we have log10(10^81) = 81, and log10(2^25000) = 7525.75. Therefore, the number of combinations is approximately 7526 - 81 = 7445 orders of magnitude bigger than the number of particles. Yikes!

Originally posted by PBE6
I don't know too much about genetics, so I'll make some simplifying assumptions:

1. The average person has about 25,000 genes.
2. One gene from either parent is required to fill each "gene slot".
3. No "gene slot" is empty or double filled.
4. Order is pre-set by the nature of the "gene slots", so order is not important. (this is probably my worst ass ...[text shortened]... 7526 - 81 = 7445 orders of magnitude bigger than the number of particles. Yikes!

"The number of genetic makeups possible using these rules is 2^25000"

However most genes will move together as they are linked on the same chromosome / chromatid so its 2^23 for both the male and female gamete production - but then of course there are numerous crossing over events during meiosis. Still looking for data to find the average number of crossovers for each chromosome.........

Originally posted by doodinthemood
The chance you will be 100% the same as your monozygotic twin would be, on average, 6!/number of genes!(6)x6!/number of genes!(6) all divided by number of genes-5

In other words, it doesn't happen.

Monozygotic (identical) twins come from a cell splitting after fertilization, which then proceeds to develop as seperate indivdiuals, so at this point in time they are 100% the same (Assuming there has been no error in replication, no non disjunction). After this point errors in replication / mutation etc make them less than 100%. Dizygotic (non identical) come from 2 eggs and 2 sperm but same pregnancy, so no more related than standard brother & sister etc.

We are trying to work out the probability of being identical if you are NOT a monozygotic twin.

One thing you would need to find is how many genes 2 average (non-related) people would tend to share, as those genes would not factor into the equation at all, because it would not matter if you and your sibling got them from different parents or not, you'd have the same gene.

There is also the issue of sex-related genes, which would be dependent on the sex of the child, thus also simplifying chances.

The odds would still be astronomically high though, despite these things. They just wouldn't *AS* astronomically high.

Originally posted by geepamoogle
One thing you would need to find is how many genes 2 average (non-related) people would tend to share, as those genes would not factor into the equation at all, because it would not matter if you and your sibling got them from different parents or not, you'd have the same gene.

There is also the issue of sex-related genes, which would be dependent on ...[text shortened]... stronomically high though, despite these things. They just wouldn't *AS* astronomically high.

To keep things simlpe (ish) lets ignore the inbreeding coefficent (genes identical by descent). I should have included this as an assumption: parents have no genes identical by descent F=0

Originally posted by geepamoogle
One thing you would need to find is how many genes 2 average (non-related) people would tend to share, as those genes would not factor into the equation at all, because it would not matter if you and your sibling got them from different parents or not, you'd have the same gene.

There is also the issue of sex-related genes, which would be dependent on ...[text shortened]... stronomically high though, despite these things. They just wouldn't *AS* astronomically high.

The sex chromosome also make it slightly easier as there is only one region of crossover = pseudoautosomal region

Originally posted by timebombted
To keep things simlpe (ish) lets ignore the inbreeding coefficent (genes identical by descent). I should have included this as an assumption: parents have no genes identical by descent F=0

I'm not so much talking about inbreeding as I am genes which define humans in general.

Even assuming every gene is set randomly, any two individuals will tend to have around 50% of their genes identical (sex genes aside for couples). Throw in potential common ancestry (even if such ancestry is not recent), and the percentage of genes in common likely to be even higher (although perhaps not by much).

So I would humbly submit that this assumption isn't a meaningful one, like "no mutations" or any of the others.

we have 26 pairs of chromosomes, so we would have had to get exactly the same set of chromosomes from each parent. The likely hood of getting the exact same set from the father is 1/(2^26), the likelyhood of getting the same set from the mother is also 1/(2^26). Do we then just add the exponents? If so it would hem be 1/(2^52). I'm not sure if that's right. We could also have to use the combinatorial equation.