Date: Mon, 16 Aug 1999 10:28:02 +0200
From: "Gatherer, D. (Derek)" <D.Gatherer@organon.nhe.akzonobel.nl>
Subject: RE: Defection Rates and Classes (was Parody of Science)
To: "'memetics@mmu.ac.uk'" <memetics@mmu.ac.uk>
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.
Derek:
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
classes
P'new_money = W * D-up ie. the number of workers moving up to fill the
vacancies
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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