# calculating numbers of decendents **URL:** \ **Category:** Factual Questions\ **Created:** [January 15, 2005, 6:40am UTC](https://boards.straightdope.com/t/calculating-numbers-of-decendents/284840 "2005-01-15T06:40:05Z")\ **Posts on this page:** 4\ **Page:** 1
**Author:** ![HPL](https://avatars.discourse-cdn.com/v4/letter/h/3da27b/32.png) [@HPL](https://boards.straightdope.com/u/HPL)\ **Post date:** [January 15, 2005, 6:40am UTC](https://boards.straightdope.com/t/calculating-numbers-of-decendents/284840/1 "2005-01-15T06:40:05Z")
Okay, suppose I want to get an estimate of the number of decdendents a person after a period of time. Say a man has two childern, and those two childern have an average of two childern each(and I know people used to have more childern the that, but a lot of those died as well). So two living childern who then grow up to have their own childern. Say each of those childern procreate around the age of 20 on average(I’m assuming here that people used to have kids more or less around that age for a long time, if not earlier. 20 seems decently midrange). Then extraporlate over 1000 years(say 1000 AD to 2000 AD), probably for a person of Europeon descent. I’m not sure how to correctly calculate this to get a fairly correct range assuming 1 generation per 20 years over 1000 years, with 2 childern to each generation. I know the resulting number will likely be lower, so if somewhat wants to supply more accurate numbers for averages. I just want a decent low-end estimate. ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [January 15, 2005, 8:27am UTC](https://boards.straightdope.com/t/calculating-numbers-of-decendents/284840/2 "2005-01-15T08:27:53Z")
Each generation will have twice as many descendants as the previous. Since each generation takes 20 years to procreate, take our 1000 year period and divide it in to fifty 20 year intervals. That means the generation in 1000 years will have 2^50 = 1,125,899,906,842,624 descendants in it (a bit over 1 quadrillion). The total number of descendants throughout the entire 1000 year period will be 2^51 - 1 = 2,251,799,813,685,247. These figures are obviously _way_ too high, as they do not take into account “inbreeding”. I’m not sure exactly how it should be adjusted to take that into account, however. ---
**Author:** ![AllShookDown](https://avatars.discourse-cdn.com/v4/letter/a/d9b06d/32.png) [@AllShookDown](https://boards.straightdope.com/u/AllShookDown)\ **Post date:** [January 16, 2005, 3:32pm UTC](https://boards.straightdope.com/t/calculating-numbers-of-decendents/284840/3 "2005-01-16T15:32:27Z")
Cecil discussed this [here](http://www.straightdope.com/classics/a2_083b.html). It has a paragraph on estimating the numbers. ---
**Author:** ![K364](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k364/32/5_2.png) [@K364](https://boards.straightdope.com/u/K364)\ **Post date:** [January 16, 2005, 7:03pm UTC](https://boards.straightdope.com/t/calculating-numbers-of-decendents/284840/4 "2005-01-16T19:03:58Z")
You might be interested in [Fibonacci’s Rabbits](http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#Rabbits): > [@](#): > > Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was… > > How many pairs will there be in one year? and the answer is based up the “Fibonacci Series”: 1-1-2-3-5-8-13…