What is the probability that your bloodline will last the next billion years?

[drumbo]

Intuitively it should be very close to zero if not exactly zero. There are three reasons your bloodline could end. The first being that you or your children or your grandchildren just end up not having children for some reason. It happens. However once you get past that hurdle and you have quite a few descendants it is almost impossible that your bloodline would end solely because nobody had children, and then the next reason your bloodline could end would be some catastrophic event such as a war, asteroid impact, or some other high fatality event. For example, my grandfather was one of 13 children, and 6 of his siblings died during WWII. It's not hard to imagine that some families which had only a few children might have had their entire bloodline wiped out during WWII, especially Jews. The city, Novi Sad, where my grandparents lived pretty much had zero Jews after WWII ended. Now consider how often these high fatality events happen. The black death wiped out 50% of the population of Europe, and that wasn't that long ago when we're considering a scale of a billion years. The third reason your bloodline could end is if the humans species, or whatever is descended from us, just gets totally wiped out. Assume a 50% fatality event happens every 100,000 years. Also assume that 5% of the population is descended from you the first time there is a 50% fatality event. What is the probability of your bloodline lasting the next billion years?

1st 50% fatality event - This could either greatly reduce or greatly increase the proportion of your descendants. It would depend on factors like geographic distribution of your descendants, if they are specifically targeted by the event for some reason, etc... If you're lucky this could double, or ever more than double, the proportion of your descendants. If it doubles and 10% of the population is descended from you during the 2nd 50% fatality event then you have a better shot of your bloodline not getting totally wiped out than you did at 5%. Say you get lucky again and you double up, now 20% of the population is descended from you, and you can see where this is going. The probability that your bloodline survives the next billion years is high dependent on them surviving the first few 50% fatality events. If they survive the first few, then your descendants become so prevalent in the population that it becomes almost impossible for them to be wiped out unless the entire species gets wiped out.

Therefore the probability is P(you, your immediate children, and grandchildren all have kids) * P(your descendants survive the first few 50% fatality events) * P(the species doesn't get wiped out within a billion years).

Now let's plug in example numbers.

P(you, your immediate children, and grandchildren all have kids) = 0.7

P(your descendants survive all of the 50% fatality events) = 0.1

P(the species doesn't get wiped out within a billion years) = 0.01

So it's got to be pretty close to zero.

[joigus]

You forget mutation (slow) and recombination (fast). In a billion years almost nothing of your "bloodline" will be left because of mutation and recombination alone (half our bloodline genes on average is discarded every time one of our gametes is produced). One billion years up your (and my) family line all our ancestors were minute eukaryotes swimming around in aqueous solution.

Natural (man-made included) catastrophes and migrations are just another major factor of change, punctuating evolution, mainly acting as filters or local amplifiers, introducing a bottleneck effect. "Founder effect" it is called.

But you're right in your conclusion. (Grand)^N-children (N representing the number of generations in a billion years) will probably look nothing like us and won't look nearly as cute as we do in a family picture.

1 billion years is the domain of so-called deep time.

 

[Strange]

Why don't you include your siblings children (and they and their siblings' children) in this? That brings the probability closer to 1 (over sensible timescales, although perhaps not a 1 billion years).

It may be helpful to look at it from the other end. How many people alive today are descendants of some notable figure in the past? Let's say Charlemagne. Well he had some children, and some of them had some children, and so on. By your math, his bloodline should have pretty much died out by now, right?

But actually, pretty much everyone of European descent alive today is descended from Charlemagne: https://www.theguardian.com/science/commentisfree/2015/may/24/business-genetic-ancestry-charlemagne-adam-rutherford