#3. Human Reproductive Control [population, engineering, evolutionary psychology]

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Red, theory; black, fact

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

The Relevance of Engineering 

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

Application of Filter Theory

The way to build an ideal feed forward 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.

The Impulse Response Function 

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 per year. 

The Inverse Model

The mathematical inverse is even simpler: S - r, which is multiplied by the sensor-error Laplace transform to get the controller output. Multiplication by S followed by subtraction of the zero-time signal is equivalent to differentiation in the time domain. The effect of S-domain subtraction and multiplication by a constant remain the same when transferred to the time domain.

In humanly engineered systems, a feedforward controller typically operates in conjunction with a downstream feedback controller.

  

The Sensor Signal

The level of the noise produced so copiously by small children is probably the signal that people unconsciously use to estimate birth rate, and the wailing and long faces following a death probably serve the same purpose for estimating death rate.  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. This suggests that the differentiation operation is telescoped into the sensing operation.