RE: Defection Rates and Classes (was Parody of Science)

Gatherer, D. (
Mon, 16 Aug 1999 10:28:02 +0200

Date: Mon, 16 Aug 1999 10:28:02 +0200
From: "Gatherer, D. (Derek)" <>
Subject: RE: Defection Rates and Classes (was Parody of Science)
To: "''" <>

The terms Tim used:

P = number of people in the professional class
W = number of people in the working class
Rp = the reproduction rate for individuals in P
Rw = the reproduction rate for individuals in W
D = defection rate across classes (as a decimal)

The equations:

P' = ( ( P * (1-D) ) * Rp ) + ( ( W * D ) * Rw )
W' =( ( W * (1-D) ) * Rw ) + ( ( P * D ) * Rp )

Some of the values used:

Starting P = 100
Starting W = 900
Rp = 1
Rw = 2
D = 0.05

As I said, run at least 30 or more cycles and tell me what results you get.
I think you will be quite surprised.


It does, as you say, stabilise, and often very close to the starting
proportions. For instance for the values you suggest above, the population
grows at a rate of 90% per generation (!!), but the proportion of
professional classes is maintained at an equilibrium of close to 9.4% which
is largely achieved (to 2 decimal places) within 6 generations.

But what does D mean above? and what justifies using 1-D? Surely you need
to have several Ds, D-up which would be the drift of workers upwards, but
this would have to be a variable rather than a constant, since it would
depend on how many spaces are available in the professional classes. D-down
could be more of a constant, as there is always room for more poor people
(in fact for simplicity we could set it to zero and ignore it).

So how about?

P'old_money = P * Rp ie. the self-replenishment of the existing professional

P'new_money = W * D-up ie. the number of workers moving up to fill the

where of course P'total = P'old_money + P'new_money

and D-up = P'new_money/W

and hold P'/(P'+W) constant at say 0.1

Also I'm not sure why you have W * D * Rw as a component of P' Rw is the
reproductive rate of the workers, so why should that contribute to P'?

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