Maths and global population

[KenDodd]

Anyone good at maths?

If fertility rate was 1.9 per women and average age to give birth is 30, how long before the human race is extinct ?

Need more info. Assume 1 kid per woman?

Otherwise at face value 630 years.

Assumes no man or woman is gay and every man and woman is fertile.

And carbon neutral by 2050.

Assume 1 kid per woman?
1.9 fertility rate.
Fertility rate is falling in almost every country, its 1.6 in high income countries and 2.4 globally, so still above replacement level.
data.worldbank.org/indicator/SP.DYN.TFRT.IN

Ok, I'm going to try to work this out myself. World population 7.9 billion (call it 8)

Ahh, it's hard!

Ok, I think I'm coming at this the wrong way.
If fertility rate is 1.9 for every woman (so actually every two people) that's a 5% reduction every generation (?)
If we say a generation is 30 years, that a 5% reduction every thirty years. So in 20 generations you have zero (?)
20×30 = 600 years
So man goes extinct in year 2,621 (???)

Really, is anyone good at maths?

BTW I know I've made an awful lot of assumptions here.

You are assuming that nobody dies in childhood or before reproducing, and that nobody is infertile. Those are obviously wrong assumptions that will affect the answer.

Average age for first time birth across the world is lower than that, that's the average here and a lot of western countries however across Africa the average is still under 20 as is countries like Bangladesh (18.1)

You’re ignoring that societies will likely collapse into anarchy, war and starvation as the population ages and there are not enough young people to work to pay and support the top heavy aged population.

Or that if we avoid anarchy, north rates will probably rise if everyone feels the planet has plentiful resources.

Just told my husband the date man goes extinct.
He was very alarmed!
Then he realised I wasn't talking about mangos, I was talking about the human race, he was visibly relieved. He really likes mangos.

It isn't 5% of the same though.
If you have a population of 100 declining by 5
Year 1 is 5 people so 95 left
Year 2 4.75 so 91.25 people left
Year 3 is 4.56 so 86.68. Not 75

Also, I forgot, we're 2022 now so the date of our end is 2,622. An extra year!

The maths is fairly easy, but posting a coherent explanation would be too time consuming for me to be arsed, but the factors will be average number of births per woman and average time between generations.

The population will decline slowly over many years, but with a very long tail to become totally extinct, rather than a defined cut off. I do think your 2621 calculation is in the right ball park.

However, as the population reduces the variables will become more signficant, eg differences between a woman in one country having 1 DC at age 40 vs one elsewhere having 6 between ages 15 and 35, with not all of them surviving to adulthood.

Plus when the population becomes really sparse, it could slow down the birth rate, as there may not be sufficient healthy adults to get together to make babies!

@SleepingStandingUp

Yes, I did think of that while I was just on the loo. Its 5% of a declining number.

The maths is fairly easy

It not, it's really hard! For me.

Answer 1: never.

After n years the population has changed by a factor of 0.95^(n/30). This never reaches zero, no matter how large n is.

Answer 2: After 13350 years there will be one person left on Earth. I guess our days are numbered then.

Very easy to do if you use a spreadsheet to do your calculations.

Column 1, increases by 30 on each row
Column 2, multiply the number above by 0.95 (using your assumptions of average 1.9 children per woman, and average age of birth of 30, you could also change the number of DC and average age of DC and see what affect this has by changing 1.9 and 30 accordingly).

You can also add a column to work out the actual population by multiplying each line of column 2 by 8 billion

The total number of rows gives you the number of generations to get down to zero (very many, but would show you get down below 1 billion after about 1200 years and 100 million after about 2500 years).

@5pot6pot7potmore

Answer 1: never.

After n years the population has changed by a factor of 0.95^(n/30). This never reaches zero, no matter how large n is.

Answer 2: After 13350 years there will be one person left on Earth. I guess our days are numbered then.

Also as 6.42 people can't procreate do you remove the decimals at each point? 100 people make 95 people make 90, 85, 80, 76 vs 100 people make 95 make 90.25, 85.74, 81.45, 77.37

13350 years from now sounds a lot more optimistic!
So, year 15, 372 by you're calculation.

@KenDodd

13350 years from now sounds a lot more optimistic! So, year 15, 372 by you're calculation.

Probably less tho, you need to add in mortality of say before 40 so they don't get to procreate. I'd make it year 15,072, just to be safe.

The formula on a basic level, as in your op, is

0.95^n

I.e. 0.95 to the power of n, where n is the number of generations. This takes account of the 5% of a decreasing number thing. Multiple this by current population to find population at any generation:

7.9 billion x 0.95^n

You can choose n to be whatever you want, type it in, and that gives you population in n generations. I.e. let's say in 100 generations, then the population will be 46,772,181

Or pick a number that you consider 'effectively extinct' (because mathematically it will never get to zero, but in numbers of humans half is a good as zero!). I'll say 1000 humans, but you could choose 1 or 2 or whatever.

So
7.9 bill x 0.95^n =1000

Now some a level maths...

n log 0.95 = log(1000/(7.9 bill))
n = log(1000/(7.9 bill) ) / log0.95
n = 310

That's 310 generations , so 30 x 310 years

Of course there are lots of real factors such as the birth rate declining BUT if we take 1.9 at face value this already accounts for people dying or not procreating

@Babdoc

You are assuming that nobody dies in childhood or before reproducing, and that nobody is infertile. Those are obviously wrong assumptions that will affect the answer.

The 1.9 figure is an average for all adult women including the infertile and intentionally child-free ones, but it doesn't include the ones who die as children, which is why the replacement fertility rate is c.2.1 not just 2.