# How long does it take for a person to lose all offsprings due to inheritance?

From this I know we will only inherit some genetic informations from parents, which is about 50 percent. But the problem is, gene has finite size, after some generations a person leaves only $0.5 \times 0.5 \times 0.5$ parts of genes to the offsprings, and it will be casted into zero. My question is, how long does it required for a person to lose all genetic information in the world?

• Why would someone (a lineage) lose all genetic information in the world? Definitely the person will mate with someone else from the same world and not from another galaxy. Mar 23, 2016 at 11:57

I think your question conveys some misunderstanding.

A child is related to each parent by a factor of ½. Humans have a diploid genome, meaning they have two copies of each chromosome (see: autosome). When two humans reproduce, they each contribute one copy of each chromosome to the offspring, in other words, they contribute a haploid genome to make a diploid child. Genetic information is not "lost" - the genome is not shrinking by a factor of ½ every generation.

However, relatedness does decrease from generation to generation. You are related to each of your parents by a factor of ½, each of your grandparents by a factor of ½ $\times$ ½, your great-grandparents by a factor of ½ $\times$ ½ $\times$ ½... You are also related to your children by a factor of ½, you are related to your grandchildren by a factor of ½ $\times$ ½... You get the picture, right?

For example, imagine the genome carries just one gene. Your father carries alleles $AA$ at that locus, and your mother $aa$. You would then be $Aa$ and, because half of your alleles came from your father and the other half from your mother, be related to each by a factor of ½, but all three of you have the same number of genes (1) and that gene is the same length (in nucleotides, barring mutations) in all three.

• But at some point, your offspring will have increased in number to the point that they're a significant fraction of the population, and will start mating with each other. So if two of your great-great-grandchildren marry (each 1/16 of your genes, if I counted right), their offspring have 1/16 + 1/16 = 1/8 of your genes, not 1/32, no? Mar 23, 2016 at 17:55
• @jamesqf Right idea, but the fractions add up a little differently. Two of your great-great-grandkids marrying would each provide 1/2 of the 1/16 of your DNA they have, giving their progeny 1/16 of your DNA still. If two of your children, each with 1/2 of your DNA, were to have kids (gross, I know), the child would have 1/2 of your DNA, and not be your genetic clone (100% of your DNA). Oct 9, 2017 at 17:53

I feel rg255 answered your question very well, however my mind snapped to an exponential relationship, which is part of what I feel your asking and what rg255 has said (but I have a pretty picture to add).

An exponential graph illustrates the relationship you are speaking of where a substance is infinitely divided by itself.

In this way it will never reach zero. It will inevitably and exponentially shrink but not disappear.