Posted: Aug 11, 2010 3:33 am
The average is a quantity based on looking at extant data, it doesn't determine the data itself, what part of this do you not understand? Averages are never used to predict what may happen, to the point of scientific reliability at least, averages, at best, are used to highlight what is the most likely outcome in a Bayesian probability distribution is based on observed data, this however can only be done when the function which results in the data is conserved, it isn't the case in population dynamics.
Doubling is true only for the exponential phase, where N (number of individuals) is 2n, where n= number of generations, but even this linear function is oversimplified and suitable only for asexually reproducing organisms like bacteria which divide by binary fission, where doubling takes place and the death rate is negligible, as soon as death rate begins to pick up and nR/t = nD/t (number of living and dead cells wrt time) the population doesn't double, it stays constant (nR/t / nD/t = 1) , if death rate begins to exceed growth rate then nR/t / nD/t < 1
Even in such a simplistic model, the average doubling time is dependent on the constraint of there being no deaths at all and resources being suitable enough, and an average during the exponential phase, or the doubling time, indicates sweet fuck all about the other phases.
In humans of course, there are other factors that come to the fore, firstly, the time available for reproduction (for women are limited to reproduction between puberty and the menopause) , child mortality (wiping out a significant portion of those who could reproduce affects more than one generation) , fertility , which can be dependent on nutrition, for instance, as malnourishment can impose constraints on fertility. The fact that the average is skewed by an explosion where the influence of such constraints was supressed doesn't allow the same average to be applied throughout human history to assert that growth ought to be exponential throughout with a doubling time blah blah blah, as you've glibly done.
In other words, while averages tell someone about the most likely outcome, they don't determine it, you need to get yourself to a population dynamics instructor.
Doubling is true only for the exponential phase, where N (number of individuals) is 2n, where n= number of generations, but even this linear function is oversimplified and suitable only for asexually reproducing organisms like bacteria which divide by binary fission, where doubling takes place and the death rate is negligible, as soon as death rate begins to pick up and nR/t = nD/t (number of living and dead cells wrt time) the population doesn't double, it stays constant (nR/t / nD/t = 1) , if death rate begins to exceed growth rate then nR/t / nD/t < 1
Even in such a simplistic model, the average doubling time is dependent on the constraint of there being no deaths at all and resources being suitable enough, and an average during the exponential phase, or the doubling time, indicates sweet fuck all about the other phases.
In humans of course, there are other factors that come to the fore, firstly, the time available for reproduction (for women are limited to reproduction between puberty and the menopause) , child mortality (wiping out a significant portion of those who could reproduce affects more than one generation) , fertility , which can be dependent on nutrition, for instance, as malnourishment can impose constraints on fertility. The fact that the average is skewed by an explosion where the influence of such constraints was supressed doesn't allow the same average to be applied throughout human history to assert that growth ought to be exponential throughout with a doubling time blah blah blah, as you've glibly done.
In other words, while averages tell someone about the most likely outcome, they don't determine it, you need to get yourself to a population dynamics instructor.