This is something I debated a long time whether or not to actually write anything about, mainly because the subject matter is not something that interests me, but the situation and story behind it is certainly something worth thinking about. Neverthless, this will likely be far too many words on a matter that deserved much less.
Thinking about population models, a relatively basic model would be to assume that the rate of growth of a population is proportionate to the size of the population. That is, at a given time t, for some characteristic constant k,
That constant encapsulates a lot of information about the population, such as gestation rates, reproduction rates, etc.
Skipping the mechanics of actually solving it, you get the following,
Where P0 is the population size at time t = 0.
Now, this solution allows us to answer an interesting question, given a population – how old is that population? How long must it have been in existence to reach the population size it is at now? The model is predictive forwards and backwards, and we can project when the population was at a given size.
We assume that the population had to start at some small value, say P = 1 for an asexually reproducing organism, P = 2 for a sexually reproducing organism, and P = 3 for a hedonistic, liberal organism. We’ll assume sexual reproduction. Then we simply solve for the time at which the population would’ve been that size.
We can then say that the age of the population is whatever time it is currently, minus the time given above. Which is all very interesting.
“Well, Fox,” I hear you say, “that’s all well and good, but where’s the proverbial beef?”
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