Genetics question

I’m trying to understand something about genetics to get an idea of how many of my lousy genes my relatives are saddled with until they can breed them out. For simplicities sake, lets say I have a sibling and we share both parents. Each of us gets 50% of our genes from each individual parent. However, we do not get the same 50% (unless we are identical twins, we are not). As I understand it, our parents gametes randomly take one gene from either of two pairs they possess, a 1/2 chance for each gene. A quick check online suggests there are about 25,000 genes in the human genome. Here is are my questions:

  1. does that mean the chance of producing identical twins or “Mirror Children” Who share the same parents, but share not a single gene, in separate fertilization’s of eggs is 1 in 2 to the 25,000th power?
  2. Whether I am wrong or right, is there a bias statistically towards children sharing 25% of each parents genes and having 50% of total genes in common? if so, how strong is that bias?

Thanks in advance to anyone who can help

A couple factors will reduce your estimate for question 1.

  • First, most human genes are homozygous, that is, they are represented by only one variant (allele). Therefore both parents will have identical copies. I’ve been having some trouble finding a cite for the level of homozygosity in human populations, but there will be many fewer than 25,000 genes at which variability occurs.

  • Second, the genes on the same chromosome do not segregate completely independently. Although the phenomenon of crossing over serves to shuffle genes, genes that are close to one another on the chromosome are less likely to show crossing over (that is, they are linked). This will also serve to increase the probability of similar genomes between siblings.

Thank you very much Colibri. I do wonder though if someone could give me a better idea of how close the percentage of genes adhere to the 50% mix past the first generation. I have great-nieces and nephews from my half-brother. I want them to succeed in life of course, so I would like to know a good estimate of how many of my genes they are burdened with.

One thing I forgot though, while fantastically unlikely, the chance of children with identical genes or completely opposite genes (amongst those genes that differ in the population) is real isn’t it?

No. The calculation would be much more complicated and depend on crossover statistics and how you define genes.

Your non-twin full-sibling will share 50% of your “abnormal” alleles on average. Are you asking for the variance of this proportion? It will be small as number of alleles grows large. (It’s simplest to consider “abnormal” alleles; define this if you wish as an allele which occurs only once in any stage of your pedigree. There are webpages that may explain this; Googling “Wright’s Inbreeding Coefficient” might be one way to start.)

Each has a 1/16 chance of possessing any one of your “abnormal” alleles.

General formula: Your k’th full-cousin m times removed will possess a given one of your abnormal alleles with probability 1/2^(2k+m+1), or 1/2^(2k+m+2) for half-cousin.

A great-nephew via half-brother is “0th half-cousin 2x removed”, so k=0, m=2; prob = 1/2^(0+2+2)

Thank you so much septimus, that was a great answer. 1/16 isn’t too bad, I can always hope they got the rare good genes and future generations are safe.

While the probability might be finite, for practical reasons it would probably never be observed, except perhaps in an extremely inbred population. It would only take a few dozen unlinked heterozygous genes before the probability was reduced to less than one in several billion (and therefore unlikely to occur within the entire present population of the Earth).

While the OP’s figure of 2^(25000) is an overestimate, it can serve as an upper bound. As a lower bound, you can take 2^46, since even with no crossover at all, each chromosome is independently assorted, and you can assume that all of your parents’ chromosomes are distinct.

Epigenetics play an important role as well. Two people with identical genes may not display identical phenotypes.