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{version = 1.02; (* of migrate.p 1999 Dec 22}
(* begin module describe.migrate *)
(*
name
migrate: selective migration of drunkard's walk
synopsis
migrate(migratep: in, output: out)
files
migratep: parameters to control the program. The file must contain the
following parameters, one per line:
The version number of the program. This allows the user to be
warned if an old parameter file is used.
range: (integer) +/- range of the world
This is the region that will be displayed. A constant in the
program (see technical notes) defines the range of the array.
displaymax: (integer) vertical display maximum
How many vertical lines are devoted to the display.
pagejump: 'l' means produce a page jump
maxgens: (integer) maximum number of generations to run
initpop: (integer) initial population placed at zero
survival rate: (two integers)
probability of survival for negative and positive steps
iseed: (real) initial random seed
delaycount: (integer) number of times to do a futile addition to
slow the display. Start with a small value and work up to a
reasonable delay. 3000000 gives near a 1 second delay on a Sun
Sparcstation 20/61.
touchhalt: stop the program when this location is touched This
allows one to determine how many steps of selective evolution
are needed to get a particular distance from the origin.
output: messages to the user
description
The migrate program shows evolutionary selection in the context of the
classical drunkard's walk. In the drunkard's walk, a population of drunks
comes out of a bar and starts stepping to the left or the right randomly.
The drunks don't bump into each other, and so are really ghosts ...
Statistics text books demonstrate that the distribution will approach a
Gaussian distribution.
The program adds only two new factors. Each drunk really doesn't move.
Instead "it" divides in two like a bacterium, and the two progeny are born
one step to the left or the right of the parent. The other new factor is
that there are survival probabilities for the two directions. By playing
with these probabilities, the population can be made to migrate to the
left or right.
A natural example if this is the mechanism that bacteria use to find
food. They have two modes of movement, either tumbling or swimming.
Which happens depends on the direction that they rotate their flagella.
(Yes, it is a rotating part! See Eisenbach1990.) The trouble for the
bacterium is that it is too small to sense chemical gradients. So it
swims for a while and compares the new situation to the previous
situation. If things are getting better, it keeps going. If not, it
tumbles and then tries to swim again.
This program demonstrates natural selection, and it also makes clear the
falsity of the following argument. Creationists often want to argue that
the "probability" of forming a biological system is impossibly low. For
example, the E. coli genome is 4638858 basepairs long in GenBank entry
U00096. The probability of generating this sequence by equally probable
choices for the 4 bases is
1/(4^4638858) = 1/340282346638528859811704183484516925440 = 3.4x10^38
(assuming that my computer really did the computation correctly!) This is
then cited as evidence against evolution and for creationist views of how
living things came into existance.
The program here adds the missing factor to this argument, which is that
there is selection at every generation. This makes the probability
computation given above invalid, BECAUSE THE PROBABILITIES ARE NOT
INDEPENDENT. That is, it is only valid to multiply probabilities if they
are independent. But selection at each generation means that the
condition of THIS generation is not independent of what happened in the
past.
examples
Example migratep.1 BROWNIAN DRIFT
1.00 version of migrate that this parameter file is designed for.
27 range: +/- range of the world
40 displaymax: vertical display maximum
l pagejump: 'l' means produce a page jump
100 maxgenss: maximum number of generations to run
10000 initpop: initial population placed at zero
0.5 0.5 survival rate: probability of survival for negative and positive steps
5 iseed: initial random seed
0 delaycount: number of times to do a futile addition to slow the display
25 touchhalt: stop the program when this location is touched
At the first generation, the population looks like this:
maximum population density = 10000 is at location = 0
------------------ ++++++++++++++++++
222222221111111111--------- +++++++++111111111122222222
7654321098765432109876543210123456789012345678901234567
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|*******************************************************| 0
generation 1
This example reaches 25 from the origin in 44 steps.
The final population looks like:
maximum population density = 1264 is at location = -1
------------------ ++++++++++++++++++
222222221111111111--------- +++++++++111111111122222222
7654321098765432109876543210123456789012345678901234567
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|*******************************************************| 0
generation 44
the population touched 25
program halt.
The population has spread out and reached 25 that way. The average is still
zero. If there were other factors keeping the population homogenous, the
variants would be trimmed away.
Example migratep.2 SELECTION
1.00 version of migrate that this parameter file is designed for.
27 range: +/- range of the world
40 displaymax: vertical display maximum
l pagejump: 'l' means produce a page jump
100 maxgenss: maximum number of generations to run
10000 initpop: initial population placed at zero
0.1 0.9 survival rate: probability of survival for negative and positive steps
5 iseed: initial random seed
0 delaycount: number of times to do a futile addition to slow the display
25 touchhalt: stop the program when this location is touched
This example reaches 25 from the origin in 26 steps.
The final population looks like:
maximum population density = 2674 is at location = 21
------------------ ++++++++++++++++++
222222221111111111--------- +++++++++111111111122222222
7654321098765432109876543210123456789012345678901234567
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|*******************************************************| 0
generation 26
the population touched 25
program halt.
The population reached 25 steps at almost one per generation. More
importantly, the ENTIRE population migrated, and the average changed
significantly.
documentation
@article{Eisenbach1990,
author = "M. Eisenbach",
title = "Functions of the flagellar modes of rotation in bacterial
motility and chemotaxis",
journal = "Molec. Microb.",
volume = "4",
pages = "161-167",
year = "1990"}
atchange program:
https://alum.mit.edu/www/toms/atchange.html
E. coli genome:
ftp://ncbi.nlm.nih.gov/genbank/genomes/bacteria/ecoli.gbk
see also
migratep
migratep.1
migratep.2
author
Thomas Dana Schneider
bugs
technical notes
The easiest way to run the program is under a Unix operating system. Put
the migratep file into your favorite editor. Set up an atchange program
running in a different window that will run the program whenever you write
the migratep file out. This allows one to play with the variables and
watch the results without mousing around (which wastes an enor-mousE
amount of time ;-).
The populations are not stable. They can grow or shrink exponentially
depending the selection values. The reason for the instability is that
the population is not part of a balanced ecology. This could be added to
the model, but it would reduce the clarity of the results. (Fortunately
balanced ecologies obviously exist or the creationists would probably
argue that this program demonstrates their impossibility!)
There is a global constant (worldsize) that determines the maximum width
of the world.
*)
(* end module describe.migrate *)
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