Imitating biology

[rossum]

No, the average of any walk is zero, seek the example on Wikipedia of flipping coins.

Blessings,
Lee

This is your problem. The 'average' of a single walk is just the result of that walk. For a real average you need a number of different walks, which you combine and find the average.

Take a random walk of one single step in a random direction. Have you moved? Yes, you have moved the distance of the step you took. Your 'average' for that one short random walk was definitely not zero.

Find 99 friends and get them all to take a random walk of a single step. In that case the average of all those different walks will be zero. Though the average is zero, none of the 100 single step walks have zero travel distance.

You are reading too much into the average. Very few if any random walks will conform exactly to the average.

[shunyadragon]

This is your problem. The 'average' of a single walk is just the result of that walk. For a real average you need a number of different walks, which you combine and find the average.

Take a random walk of one single step in a random direction. Have you moved? Yes, you have moved the distance of the step you took. Your 'average' for that one short random walk was definitely not zero.

Find 99 friends and get them all to take a random walk of a single step. In that case the average of all those different walks will be zero. Though the average is zero, none of the 100 single step walks have zero travel distance.

You are reading too much into the average. Very few if any random walks will conform exactly to the average.

This is going off the cliff of the thread subbject. These examples have no relatinship as to how randomness plays a role in mutations.

[shunyadragon]

Yes, I understand your points, and I still disagree with you, as evidenced by the article on evolutionary algorithms having a problem with local optimums.

Blessings,
Lee

You are groosely misrepresenting your sources and using sources describing randomness that have no relationship to genetic mutation and the processes of evolution.

No, you either do not understand The Lurch's posts, or you are intentionally ignorant of The Lurch's responses. It is compounded by the fact that you so not have the educational background to address the topic with a religous ID agenda. Behe is a far worse case. He knows his science is groosely dishonest, because he has the educational background in science to know this.

You mentioned the flip of a coin? as an example of what? The outcome of each flip of a coin is indeed random, the sequence of coin flips follow a fractal pattern and are NOT random.

[lee_merrill]

I don't know whether genetic drift is a "major" source of evolutionary change. But it is obviously a source. And how major it is should be determined by observation, rather than by overly simplistic mathematical models.

Well, I think the random walk does show that drift, on average, is not going to get very far.

The average of many random walks will be approximately zero, because the odds that you will move in one direction on one walk are balanced out by the odds that you will move in the opposite direction on another walk.

That's not true, see the Wikipedia explanation again, about one one-dimensional random walk by flipping a coin.

If you flip a coin very many times, the odds are extremely low that the number of heads will exactly equal the number of tails.

But I am after the average, not the value of the sum after n turns. The average tends to zero.

Blessings,
Lee

[lee_merrill]

What makes you think you understand this better than someone with a PhD in it? I would like to have that answered.

Because people with PhDs can sometimes be mistaken.

In any case, evolutionary algorithms are only an approximation of biological evolution - they do not recapitulate all its features. Things that are problems for algorithms may not be issues for actual, biological evolution.

Well, how so?

Random walks end up being directional in biology because you have things like population isolation, genetic linkage to favored/unfavored traits, founder effects, etc. etc.

There's a paradox here, if you stop a random walk anywhere, and say we're going to start another random walk from this point, then the average motion from that point will be zero! That would be like a founder effect, or population isolation. But the average of such starting points will still be zero.

... so he thinks that a mathematical random walk is a good analogy for genetic drift, and he's convinced that if something's true for an analog, it must be true for the actual thing.

There are good analogies, and bad analogies, I think a random walk is a good analogy for genetic drift.

Blessings,
Lee

[lee_merrill]

This is your problem. The 'average' of a single walk is just the result of that walk. For a real average you need a number of different walks, which you combine and find the average.

Or I can take an average of all the positions in a single walk.

You are reading too much into the average. Very few if any random walks will conform exactly to the average.

But the actual average will tend to the theoretical average, and will get closer to the theoretical average, the more steps that are taken.

Blessings,
Lee

[lee_merrill]

You mentioned the flip of a coin? as an example of what? The outcome of each flip of a coin is indeed random, the sequence of coin flips follow a fractal pattern and are NOT random.

The sequence follows a random distribution, though the walk itself can be seen as a fractal.

Blessings,
Lee

[Stoic]

Well, I think the random walk does show that drift, on average, is not going to get very far.

You think that, but you are wrong. Even if the random walk was a decent model of genetic drift (and it isn't), it wouldn't prove what you want it to. You would have to take the step size and the number of steps into account.

That's not true, see the Wikipedia explanation again, about one one-dimensional random walk by flipping a coin.

The Wikipedia article on random walks shows that the more steps you take, the further you can expect to be from the origin.

But I am after the average, not the value of the sum after n turns. The average tends to zero.

As has been pointed out repeatedly, the average doesn't matter.

[shunyadragon]

Because people with PhDs can sometimes be mistaken.


Well, how so?


There's a paradox here, if you stop a random walk anywhere, and say we're going to start another random walk from this point, then the average motion from that point will be zero! That would be like a founder effect, or population isolation. But the average of such starting points will still be zero.


There are good analogies, and bad analogies, I think a random walk is a good analogy for genetic drift.

Blessings,
Lee

These are horrendously terrible meaningless analogies with relationship to genetic mutation, genetic drift nor evolution.

The lack of education, and a religious agenda is the worst possible combination. 97%+ of all scientists in the science think your line of reasoning is hogwash, The Lurch and I join them.

In fact your examples do not represent true randomness.

[TheLurch]

Because people with PhDs can sometimes be mistaken.

How many times have i been wrong so far? How many times have you been wrong?

Well, how so?

Evolutionary algorithms, for computational reasons, necessarily use relatively small populations compared to those that live in the natural world. For most programs, a single error can disable the entire program, while a single mutation is unlikely to damage more than one gene. Programs are optimized to solve a single problem, while evolution optimizes for multiple problems simultaneously. Evolutionary algorithms only deal with individual programs, while evolution optimizes across a gene and its entire interaction network....

I could go on, but i think that's enough to make the point.

There's a paradox here, if you stop a random walk anywhere, and say we're going to start another random walk from this point, then the average motion from that point will be zero! That would be like a founder effect, or population isolation. But the average of such starting points will still be zero.

That's not a paradox. It's just stupid. It distills down to "I want to claim that random drift can't have direction, so i'm doing that by redefining any mechanism that can provide it direction as not doing so."

Basically, since your original contention is wrong, you're trying to come up with a description of things that has no logical foundation and isn't any way biologically relevant, all in the hope you can salvage it. It doesn't work. You can't arbitrarily define every mechanism that provides a direction to random drift as resetting the clock and think it has any meaning. All it is is you trying to make up arbitrary rules in the hope of salvaging your argument. There's no logic to it whatsoever.

It's also a demonstration - one of a large number that's possible - that a mathematical approximation is a bad model for genetic drift, since you have to do something incredibly stupid in order to encompass the things we know happen during drift.

There are good analogies, and bad analogies, I think a random walk is a good analogy for genetic drift.

Given that you've just demonstrated it isn't, i feel that this statement nicely illustrates how bad your judgement is in this matter.

[lee_merrill]

That's not a paradox.

It is a paradox, how can picking a point in a path change the average motion for that path? I think the picture becomes clearer if you consider a walk of coin flips, as Wikipedia does. The average is going to tend to 50%, regardless of the starting point along the path. So if you call heads 1 and tails -1, the average position will be zero, independent of the starting point! Thus even taking into account population isolation etc., drift isn't getting very far, I would say.

Blessings,
Lee

[lee_merrill]

You would have to take the step size and the number of steps into account.

Not so, the average position would tend to zero.

The Wikipedia article on random walks shows that the more steps you take, the further you can expect to be from the origin.

So flipping a coin, say, the more you flip it, the further you expect to be from 50%?

As has been pointed out repeatedly, the average doesn't matter.

It does matter, it reflects your current position.

Blessings,
Lee

[TheLurch]

It is a paradox, how can picking a point in a path change the average motion for that path? I think the picture becomes clearer if you consider a walk of coin flips, as Wikipedia does. The average is going to tend to 50%, regardless of the starting point along the path. So if you call heads 1 and tails -1, the average position will be zero, independent of the starting point! Thus even taking into account population isolation etc., drift isn't getting very far, I would say.

And you say that, frankly, because you're being stupid, and you think a coin flip is a good approximation of evolution. It's not.

In your world, there are almost no genetic differences between humans and chimps, because the drift would all average out over 7 million years, right? Only things under selection would have changed, after all - everything else would average out.

I cannot begin to even express how wrong that is. Drift without selection has resulted in tens of millions of differences between us and chimps. You're so committed to your desire to believe something that you've completely lost touch with reality.

[Stoic]

It is a paradox, how can picking a point in a path change the average motion for that path?

It's not a paradox. It's a misunderstanding, on your part.

I think the picture becomes clearer if you consider a walk of coin flips, as Wikipedia does. The average is going to tend to 50%, regardless of the starting point along the path. So if you call heads 1 and tails -1, the average position will be zero, independent of the starting point! Thus even taking into account population isolation etc., drift isn't getting very far, I would say.

The average is going to tend towards 50% heads, but the position of the random walk isn't going to tend towards the origin.

[Stoic]

So flipping a coin, say, the more you flip it, the further you expect to be from 50%?

No, the more you flip it, the closer you get to 50%, but the further away from the origin you get.

Flip a coin a thousand times, and you can expect to be farther away from the origin than after you flip it a hundred times, even though you can expect to be closer to 50% after a thousand flips than after a hundred flips.