This, extremely counter-intuitively, doesn't actually change anything at all in terms of population change. All it does is cause some brief noise as you hit the 'equilibrium point.' It's easiest to explain this with an example. Let's take it to a ridiculous extreme and say people live to 200 years old, yet otherwise maintain the same general fertility trends of having about 20 years of peak fertility. And to keep things simple, we'll assume a fertility rate of 1, which means the total population would halve every generation. We'll also assume everybody has all their children at age 20, and then dies at age 200.
So start at the bottom. And say we have exactly 2 twenty year olds. Since there are 2 twenty year olds there must be 4 forty year olds, 8 sixty year olds, and so on. This generalizes to there being a total of (2^n) people of age (20*n). So there are 512 people of age 180. The entire population is 512 + 256 + 128 + ... 1 = 1023. So what happens when this 180 year old generation dies? Your population declines by half. What happens twenty years later when the 256 population group dies? Your population decreases by half. So each generation, you start seeing an exponential halving of your population.
So how long people live doesn't actually matter. All it does is add some noise/delay as you shift from an equilibrium between fertility rates. And once that equilibrium is reached, your population will shift by a factor of fertility_rate/2 every breeding generation (~20) years. This holds true whether people live for 40 years, or 40,000. So with a fertility rate of e.g. 1 your population will exponentially decline by 50% every 20 years, until you go extinct or start having babies.
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This, extremely counter-intuitively, doesn't actually change anything at all in terms of population change. All it does is cause some brief noise as you hit the 'equilibrium point.' It's easiest to explain this with an example. Let's take it to a ridiculous extreme and say people live to 200 years old, yet otherwise maintain the same general fertility trends of having about 20 years of peak fertility. And to keep things simple, we'll assume a fertility rate of 1, which means the total population would halve every generation. We'll also assume everybody has all their children at age 20, and then dies at age 200.
So start at the bottom. And say we have exactly 2 twenty year olds. Since there are 2 twenty year olds there must be 4 forty year olds, 8 sixty year olds, and so on. This generalizes to there being a total of (2^n) people of age (20*n). So there are 512 people of age 180. The entire population is 512 + 256 + 128 + ... 1 = 1023. So what happens when this 180 year old generation dies? Your population declines by half. What happens twenty years later when the 256 population group dies? Your population decreases by half. So each generation, you start seeing an exponential halving of your population.
So how long people live doesn't actually matter. All it does is add some noise/delay as you shift from an equilibrium between fertility rates. And once that equilibrium is reached, your population will shift by a factor of fertility_rate/2 every breeding generation (~20) years. This holds true whether people live for 40 years, or 40,000. So with a fertility rate of e.g. 1 your population will exponentially decline by 50% every 20 years, until you go extinct or start having babies.