Text 1276, 228 rader
Skriven 2004-12-31 15:03:00 av Tim Tyler (1:278/230)
Ärende: Re: The "fuel" of evoluti
=================================


Perplexed in Peoria <jimmenegay@sbcglobal.net> wrote or quoted:
> "Tim Tyler" <tim@tt1lock.org> wrote in message
news:cquoj6$u8q$1@darwin.ediacara.org...
> > Perplexed in Peoria <jimmenegay@sbcglobal.net> wrote or quoted:

> > > Clearly, to have any hope at all of preserving the original information,
it
> > > must be the case that any one tape in the population will sire on average
> > > more than one error-free descendent.  To complete the analogy, we need a
> > > selection process that is biased toward chosing error-free descendents as
> > > the sources for the next generation of copies.
> >
> > Yes, but a way of increasing the variance of the number of mutations in
> > individuals would help selection do its job in this area.
> >
> > If the deleterious mutations are concentrated in some individuals,
> > fewer members of the population need to fail for the gene pool to
> > remain in good working order.
> 
> I fully agree that IF recombination increases the variance in number of
> mutations per individual, then your argument works.  What I don't
> agree with is that recombination *will* increase the variance, unless you
> make some totally artificial assumptions regarding the source of
> mutations.  For example, if your mutation process inserts *exactly* one
> mutation per individual (low variance), then recombination obviously
> will redistribute the mutations so that you have (in the simplest model)
> 25% with no mutations, 50% with one, and 25% with two mutations.  The
> variance per individual has increased.  But the initial assumption
> regarding the statistics of the mutations is unrealistic, IMO.

Fortunately, your query can easily be dealt with by a more sophisticated
model.

Here's a model where mutations occur with much greater biological
realism - where mutations occur in individuals with some fixed
probability - and individuals can have 0, 1 or more mutations
per generation.

Heavily mutated individuals - with more than some threshold number
of mutations - are eliminated - and new individuals take their
place.

The results (which are highly repeatable):

Asexual experiment
Deaths: 538260
-----
Sexual experiment
Deaths: 422799
-----

I.e. the sexual population needs many fewer selective deaths to keep its
gene pool in good order.

The mutation model here is pretty good - and making it even more realistic 
would not alter the results - the effect is one that really does exist.

What /could/ be criticised is the idea that there is a mutation threshold 
- beyond which you are dead.  Making this more realistic would 
reduce the magnitude of the effect - but would not eliminate it.

Fairly simple Java 1.1 (or greater) source code appended
for your inspection:

import java.util.Random;

public class GeneRepair {
  final int pop_size = 100;

  final int mutation_attempts_per_generation = pop_size;

  int[] population;

  final double mutation_rate = 0.1;

  final int generation_max = 10000;

  int generation = 0;

  int death_count;

  final int death_threshold = 4;

  boolean sex;

  Random random = new Random();

  private void main() {
    this.sex = false;
    experiment("Asexual");
    
    this.sex = true;
    experiment("Sexual");
  }

  private void experiment(String name) {
    log(name + " experiment");

    init();
    do {
      iterate();
    } while (this.generation < this.generation_max);

    printStats();
  }

  private void init() {
    this.generation = 0;
    this.death_count = 0;
    this.population = new int[this.pop_size];
  }

  private void iterate() {
    mutateAll();
    selectionAll();
    this.generation++;
  }

  private void selectionAll() {
    for (int idx = this.pop_size; --idx >= 0;) {
      selection(idx);
    }
  }

  private void selection(int idx) {
    int total_bits = countBits(getMember(idx));
    if (total_bits > this.death_threshold) {
      deathAndReproduce(idx);
    }
  }

  private void deathAndReproduce(int idx) {
    death();
    reproduction(idx);
  }

  private void reproduction(int idx) {
    this.population[idx] = reproduce();
  }

  private int reproduce() {
    int parent_1 = chooseParent();
    if (this.sex) {
      return sexual(parent_1);
    }

    return getMember(parent_1);
  }

  private int getMember(int parent_1) {
    return this.population[parent_1];
  }

  private int sexual(int parent_1) {
    int bit_mask_maternal = this.random.nextInt();
    int bit_mask_paternal = (-1 ^ bit_mask_maternal);
    int parent_2 = chooseParent();

    int genes_maternal = getMember(parent_1) & bit_mask_maternal;
    int genes_paternal = getMember(parent_2) & bit_mask_paternal;

    return genes_maternal | genes_paternal;
  }

  private void death() {
    this.death_count++;
  }

  private int chooseParent() {
    //  using "%" is poor style - but is good enough here...
    return (this.random.nextInt() >>> 1) % this.pop_size;
  }

  private void mutateAll() {
    for (int idx = this.mutation_attempts_per_generation; --idx >= 0;) {
      simulateCosmicRays(idx);
    }
  }

  private void simulateCosmicRays(int idx) {
    if (this.random.nextFloat() < this.mutation_rate) {
      mutate(idx);
    }
  }

  private void mutate(int idx) {
    int bit_mask = 1 << (this.random.nextInt() & 31);
    this.population[idx] ^= bit_mask;
  }

  private void printStats() {
    log("Deaths: " + this.death_count);
    log("-----");
  }

  private void log(String s) {
    System.out.println(s);
  }

  private int countBits(int value) {
    int bit_count = 0;
    for (int idx = 32; --idx >= 0;) {
      int bit_mask = 1 << idx;
      if ((value & bit_mask) != 0) {
        bit_count++;
      }
    }

    return bit_count;
  }

  public static void main(String args[]) {
    new GeneRepair().main();
  }
}

-- 
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