From: Hal Fulton <hal9000@...>
Date: 2004-12-07T10:25:01+09:00
Subject: Ruby (quiz?) simulation idea

This is just off the top of my head. I thought I'd post it instead of
emailing, in case people want to discuss it and/or think about it.

This is "life" in a sense, but not John Horton Conway.

Imagine you have N lifeforms to start with, each with a certain
genotype. For simplicity, we could assume simple dominance, no
sex-linked traits, and panmictic mating (probability of mating is
random based on the population). Purists out there: Please don't
flame any slight misuse of terms unless it's really relevant.

Flashback to the first day of Genetics 101:

   AA = homozygous dominant
   Aa = heterozygous
   aa = homozygous recessive

The population's genotype frequencies are obviously
   pAA + pAa + paa = 1

A few seconds of thought should show that the gene frequencies
are
   pA = pAA + 0.5pAa
   pa = paa + 0.5paa
and also
   pA + pa = 1

I imagine modeling each individual as an object running in a
thread. For the heck of it, give each individual a location in
a grid. Let them wander around. When a nature male bumps into a
mature female, a probability function determines whether they mate
and how many offspring they have.

Assume each individual has a known average lifespan and a typical
mating age. (I'd favor expressing these in millisec for purposes
of the simulation). Let the "children" have certain probabilities
of surviving to mating age: qAA, qAa, and qaa. Typically, these
are all near 1.0 -- in many situations, the heterozygote will be
a little less likely to survive, and the homozygote least of all.
(This is the trivial case in which "A" is good or healthy and "a"
is bad or unhealthy.)

All things being equal, such a population will eventually reach
what is called Hardy-Weinberg equilibrium, in which the genotype
frequencies reach a constant and stay there (for a suitable value
of epsilon).

Run the simulation with large numbers of individuals. Sample the
population once in awhile and check the numbers. Watch for
equilibrium.

Write a pure deterministic (algebraic) model that will predict when
equilibrium occurs. See how well it matches your simulation. An
iteration in the deterministic model is simply a "generation" -- I
think we can consider that equal to a lifespan (or perhaps, hmm, the
lifespan minus the mating age?).

Just a thought...


Hal