From: "Tim Rhodes" <proftim@speakeasy.org>
To: <memetics@mmu.ac.uk>
Subject: Defection Rates and Classes (was Parody of Science)
Date: Fri, 13 Aug 1999 12:34:08 -0700
Derek,
Yes, the results are counter-intuitive. I wouldn't have predicted them
myself before running the model. (In fact, after reading your post I went
back and ran them again to see if maybe I'd done something wrong the first
time. Nope -- I get the same results every time.)
Rather than try to persuade you with words, why don't I just give you the
values and equations I've used and you can set up a simple for-next loop and
check them yourself. Run at least 30+ cycles and watch what happens. Yes,
in the first few generations the proportions in the population change
dramatically, but after 15 or 20 cycles those ratios stabilize.
Again, I wouldn't have predicted it either, so I can understand your
skepticism. Here's what I'm working from (and, of course, if you can spot
an error in my equations, please let me know):
The terms I 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.
-Tim Rhodes
P.S. This effect seems to work for any non-zero D value where Rp is not the
same as Rw. Try playing with the starting values a bit and see what
happens.
P.P.S. I'm guessing that we could work backwards from the ratios we see a
given population stabilize around, to derive the defection value (D) present
in that population. What do you think?
-----Original Message-----
From: Gatherer, D. (Derek) <D.Gatherer@organon.nhe.akzonobel.nl>
To: 'memetics@mmu.ac.uk' <memetics@mmu.ac.uk>
Date: Friday, August 13, 1999 4:34 AM
Subject: RE: Parody of Science
>Tim:
>If 25% of children from the labor classes enter the professional classes
>(and
>adopt their reproductive rates) and the same is true the other way
>round--with 25% of the children of professional parents also entering the
>working class and adopting their reproductive strategies--then any effects
>on their respective gene pools disappear entirely after few generations.
>
>Derek:
>Is this possible? Imagine a society where there are 10% upper class and
90%
>lower class. To keep it simple, assume the reproductive rates of each
class
>are the same, and the population is static. If there are 1000 individuals,
>and 25% move each way per generation, then:
>
>25% of 100 upper class move downwards = 25 move down
>25% of 900 lower class move upwards = 225 move up
>
>Then in the 2nd generation, the size of the population would be (assuming
>total assortative mating and net reproductive rate of 1):
>
>Upper: 100 - 25 + 225 = 300
>Lower: 900 - 225 + 25 = 700
>
>so the proportional class division in the society would have changed
>radically. You have to keep the proportions the same per generation.
>
>If you ditch one of my assumptions above (that the relative reproduction of
>the classes is the same) and replace it with the more realistic assumption
>that the reproductive rate of the lower classes is higher, then the problem
>becomes even worse - since there are even more lower class children.
>
>So I don't think you can have that degree of gene flow between your class
>populations. Unless I've interpreted you wrongly....
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