Wednesday, February 28, 2007

Rocks off v Off this rock

Here's a question I posed tonight, and couldn't quite be arsed to work out an answer to: Given current levels of mortality, what is the average number of children per couple needed to maintain the total population at a steady state? I suspect it's somewhat less than two.

This may ultimately be an important question if we don't get off this rock...

(and is population growth control the only sure way to limit carbon emissions?)

4 comments:

Chip said...

The only sure way to limit carbon emissions is to stop using fossil fuels at all (and, technically, all hold our breath on a permanent basis). And that probably won't ever happen - even if we stop burning them, they're too useful for making plastics, medicines and the like.

A couple of items in the way you've worded your question mean I'd be very surprised if it's less than two.

Per couple would rule out several percent of the population, and that percentage seems to be growing over time too (at least in Western countries).

Ignoring that, on current levels of mortality, everybody dies eventually, so a stable state must average out at exactly 1 person reproducing per person dying.

However, mortality before puberty is non-zero, so not every child born will get to reproduce itself - need to have more than 1 child born per person to ensure that 1 survives to reproduction age per person.

2.1ish is the usual figure quoted, but I don't think that's particularly scientifically derived. As a first stab, you could say it's 2 * 1/(0p20ish) / (1-%ge of non-couples).

Throw in mortality improvements, and you're in a greyer area though. Improvements will asymptotically tend to zero mortality for everyone, at which point the replacement level must be zero, so there will be some level of mortality improvement for which replacement level falls below 2 per couple.

Can you tell I've had a rubbish day?!

Another question in the same general ballpark - are there currently more or fewer people alive than dead? There are some obvious definitional issues there, which, like you, I can't be arsed to sort out, so answer as you see fit.

Lint said...

It's never good when the comments are longer and more interesting than the post...

I think I'd read somewhere that there were broadly the same number of live people as dead people... if the population has doubled in the last 60 years or so (which I think is true) then no of dead people = half the current population (ie all the people who were alive 60 years ago are now dead, asuming average world life expectancy of 60) plus all the dead people before them. You might assume this gives a sum like 1/2 + 1/4 + 1/8 +... which sums to 1.

Hence.

Or I might be talking bollocks due to being hungry (and dumb).

Chip said...

Coincidentally, this arrived in one of my RSS feeds over the weekend :

http://www.sciam.com/article.cfm?chanID=sa004&articleID=09E07C6F-E7F2-99DF-3AD087F0DA77D94F&ref=rdf

Lint said...

That sounds more sensible...