#3. AviApics 101 [population, engineering, evolutionary psychology]

PO     EN     EP     

Red, theory; black, fact.

Here, I go into detail about the human population controller introduced in the previous post.

I assume that, like everything in the natural (i.e., evolved) world, it is a masterful piece of engineering, as Leonardo Da Vinci declared.

The way to build an ideal controller is the inverse plant method, where the controller contains the mathematical inverse of a mathematical model of the system to be controlled.  To derive the model, you take the Laplace transform of the system's impulse response function. For populations, a suitable impulse would be the instantaneous introduction of the smallest viable breeding population into an ideal habitat.

What happens then is well known, as least in microbial life forms too simple to already have a controller: unrestrained, exponential population growth as per Malthus, with no end in sight.

This exponential curve is then the impulse response function we need, and its Laplace transform is simple: 1/(S - r), where S is complex frequency and r is the Malthusian constant, that is, percent population growth rate per year. The mathematical inverse is even simpler: S - r, which is calculated as set point X minus controlled variable Y. The result is summed with perturbation P and made equal to Y. The result is usually simplified to permit predictions about controller performance, but that is not needed in this discussion.

The control effort is E(S - r), which can be multiplied out as ES - Er. Remember that everything has been Laplace transformed in these expressions, and that ES becomes the time differential of e when transformed back into the real world. Multiplication by a constant such as r stays multiplication, however. Control effort in the real world is then rate of change of e minus r times e. (Lowercase variables are the un-transformed versions.) Since e = x - y, and since x is constant, x becomes zero when differentiated, and drops out of the expression. Control effort is then -dy/dt - er. <Corrected 5 Jun '16.>

I theorize that women calculate -dy/dt, and men calculate er. When they get together, the complete population control effort is exerted, resulting in stability, which the world rewards. However, on average, the men and the women will be pulling in opposite directions exactly 50% of the time, if we model population variation as a sine wave centered on the set point.

A prediction is that women unconsciously react to evidence of increased birth rate or decreased death rate by wanting fewer children. Men react to excess absolute population relative to set point by violence, and to breathing room under the set point by partying.

That negative sign in front of the male contribution was puzzling at first, until I realized that it must derive from the married state itself, and not from the base male response to population error. This could be the origin of statements such as: "Marriage is the exact opposite of the way you think it will be." 

The level of the noise produced so copiously by small children is probably the signal that women unconsciously integrate to estimate birth rate, and the wailing and long faces following a death probably serve the same purpose for estimating death rate, aided by reading the tabloids. [My (married) older brother once showed me the developmental time course of child noise in the air with his hand, and it looked like an EPSP, the response of a neuron to an incoming action potential. The EPSP is the convolution kernel by which a neuron decodes a rate code.] The men have to calculate absolutes, not rates, however. The male proprietary instinct causes them to divvy up the limiting resource for breeding (jobs in our present society) into quanta that can be paired off with people like pairs of beads on adjacent wires of an abacus. Excess people left over at the end of this operation spells trouble. Politicians are right to worry about jobless rates.