Replies

First, I'd like to say that unlike a lot of anti-evolutionists I've discussed things with over the years, you manifestly have a very good intuition for math. You make quite a few correct conclusions, even on things that most people would not find obvious, apparently by intuition alone (since I don't see any sign that you've cranked through the actual numbers or equations, or rely on any pre-discovered laws -- in fact, you seem quite distrustful of them).

However, intuition alone can often be a risky thing. Many things in math and science work in counterintuitive ways -- subtle effects can have larger consequences than seems obvious at first look, or can combine in completely unexpected ways, which can only be discerned if you take a much closer look and work through full rigorous proofs, or carefully simulate thousands of trials on a computer, or run experiments to check how things really work instead of the way you'd presume they work.

Intuition can take you far, but it's absolutely no substitute for actually checking your presumptions against reality.

This is especially the case when your intuition takes you to a conclusion which seems to prove a point you'd like to support... The temptation is very strong to declare victory and examine it no further, rather than truly dig as deep as possible to make certain that you haven't overlooked something which makes the case not as simple as you'd first presumed.

And now, back to the discussion.

So what, over several generations it will average out.

No, actually, it doesn't. Random walks aren't like running tallies of coin flips. Because each new step picks up where the last one left off, any deviation from the "average" at any step permanently offsets the "baseline" and becomes the new "center". Any initial (or subsequent) deviation permanently biases all future results, making it impossible even in theory for an "average" position to be maintained or returned to or "averaged out". Once a random walk wanders "off" its initial position, which it generally does very soon, it has no more "incentive" to wander back to its original position than it does to wander off in the other direction entirely. This is *not* a process that "evens out over time". You can get a good feel for this property of random walks by playing with this Java applet.

This leads to very counterintuitive results, but a careful examination of actual random walk behavior (either by rigorously derived math, or by carefully conducted computer simulations) reveals that while the results are hardly "obvious", they are nonetheless true.

For example, let's consider the simplest possible type of random walk. Mark a spot on the ground and call it "zero". Stand on the spot. Now flip a coin. If you get heads, take one step to the right. If you get tails, take one step to the left. Now that you're at your new spot, flip the coin again and repeat. Then keep repeating, following where the coin leads you.

Now let's examine the actual properties of such a walk.

1. At the end of, say, 1000 flips/steps, what do you think your *single* most likely position is? Intuition says, "on point zero", which happens to be correct. But that's about the *only* intuitive answer that is correct for random walks.

2. After 1000 random steps, what's your most likely *distance* from point zero? Intuition says the most likely distance is zero, or close to it. Actual analysis shows that your most likely distance is actually square-root(1000), or 32 feet away. Quite counterintuitive.

3. As you perform more and more random steps, are you more and more likely to end up near point zero, or not? Intuition says you should more likely "average out" to someplace near point zero. Actual analysis shows that your position becomes more and more likely to be farther and farther from point zero. The longer you do the random walk, the farther afield you are likely to end up. The reason is that the distribution curve, although centered on point zero, becomes flatter and flatter and wider and wider -- after a large number of random steps, the vast middle of the distribution curve becomes so flat that you're just about as likely to end up anywhere at all as opposed to point zero itself. Although point zero itself always has a somewhat greater probability than any other single spot, the odds of actually being *at* point zero (or even close to it) continue to shrink the more random steps you take. A really nice "look-see" Java demonstration of this can be found here.

4. How many times are you likely to cross over point zero? That is, how often will you randomly wander from the left of point zero to the right of it, or vice versa? Intuition says that you'll cross over it many, many times if you do the random walk a long time. Actual analysis shows that the most likely number of crossings is *zero*, the next most likely number of crossings is one, then two, and so on.

Don't try to rely on intuition alone when doing analysis on random processes, it too often leads to seemingly reasonable, but wrong, results.

For good introductions to random walks, see:

Random Walks - 1-dimensional
Random Walks - 2-dimensional
The One-Dimensional Random Walk
Chemistry 531 The One-dimensional Random Walk

Also it means that many mutations will dissappear.

Yes, of course they will. But it matters not how many vanish, it matters how many manage to persist. There's no harm in "losing" mutations if enough do survive to drive evolution.

As I previously showed, small populations retain a larger percentage of mutations but produce fewer to work with, while large populations retain fewer mutations (as a percentage) but produce more overall. The net effect is that although many mutations are lost in either case, the population as a whole will acquire mutations at a rate equal to the mutation rate in a single individual.

Note that this is for neutral mutations -- beneficial mutations are accumulated in the population at large at a faster rate.

Also, interesting things happen when a large population is split up into separate breeding subpopulations, called "demes".

The laws of statistics are very strict, and we know they work. They built the casinos in Las Vegas.

Certainly, but you must take care to apply them properly. Many people have gone broke in Vegas through their misapplication of statistics to a given game. Check out the book "Scarne on Gambling" for a long list of gambler's fallacies and "betting systems".

Sampling error is way too small for it to have any effect on the matter at hand. The most you might get is that in a population of one million the sampling error will end up providing you a proportion of the allele of 1/500,000 instead of 1/1,000,000 this is not taking over the population.

Intuitively, yes, that makes sense and seems reasonable. In actual practice, it doesn't work that way.

It also means that many mutations will die also due to 'sampling error'.

Yes it does. But this is of no consequence as long as enough mutations persist to drive evolution. And studies of how many mutations have actually entered the gene pool for various populations indicates that the real-world mutation acquisition rate is indeed sufficiently high to account for evolution.

Intuition is a fine thing, but eventually it needs to reality-checked.

As I keep saying, genetic drift is total bunk.

As Galilleo replied when faced with similar obstinance, "and yet it still moves".

You can declare it bunk as much as you like, but countless different sorts of studies (mathematical analysis, simulation, examinations of real-world genetics, etc.) show that no matter how much you may disbelieve it, it still works.

You need to pause and actually test your intuition from time to time.

You are starting with ONE (1) mutation you cannot get it to take over the whole population except by a miracle.

Intuition says that. Intuition is wrong in this case. The actual dynamics are more interesting than intuition would lead you to believe.

Such miracles do not happen every day as evolution would require.

This misstates the issue. Evolution does not require it to happen "every day". Nor is the introduction of new mutations into the population a "miracle".

Actual measurements of non-fatal mutation rates are on the order of 1 per 1000 alleles per generation, or 4 per each human birth (1.6 deleterious). This means that each human generation introduces *fourteen billion* new neutral-or-beneficial mutations into the population. True, most of the neutral ones will sputter out, but surely you can see that there are so bloody many that *some* will hit the mutation lottery and become established. And the beneficial ones will (statistically) grow in frequency through selection.

That makes for a *lot* of raw material for evolution to sift and select and build on.

Let's do some quick estimates. Let's be conservative and say that all of the non-deleterious mutations are merely neutral, and not beneficial. Using the statistics from our last post, we find that 2.4 neutral mutations per generation will become "fixed" in the human gene pool eventually. It has been roughly 5 million years since we shared a common ancestor with chimpanzees. For most of human history, a generation has been no more than 15 years or so long. That means we've had 333,000 generations since our kinship with the chimps, and at 2.4 "successful" mutations per generation (out of billions lost through chance) we've accumulated 800,000 mutations to separate us from the chimps (and the chimps have accumulated about the same number in *another* direction).

Is it reasonable to presume that 1.6 million acquired mutations would be enough to turn a man into a chimp or vice versa? I think it is. More likely, we're separated by far *fewer* genetic differences. In fact, actual comparison between human DNA and chimp DNA turns up less than 0.5% differences, or 150,000 allele base pairs. So the *actual*, *measured* neutral mutation acquisition rate is *ten times* greater than that necessary to split humans and chimps from their presumed common ancestor.

You were saying?

You can postulate one or two miracles, but to postulate that not only will they happen once but numerous times to build and change one gene in one species a little bit is ludicrous.

So says intuition. But see above.

To postulate that such miracles happen all the time in all species all the time just shows that evolution is totally false.

Again, you're working way too much on intuition here. You jump from "rare and unlikely per single event" to "impossible" or "totally false", which is not a valid transition. Unlikely things still do happen, and over enough time or a large enough population, they happen at a pretty steady rate.

Again, please do a reality-check every once in a while.

BTW - the reason these folk have to write so much nonsense is that they are trying to obscure the truth. The truth is usually very simple, you do not need reams of nonsense to show it.

Now this is just beneath you. I have more respect for your intelligence than that.

It's just intellectually dishonest to try to dismiss reams of evidence and study as being merely attempts to "obscure the truth".

That's just an excuse to avoid having to examine it, and deal with what it reveals.

As for the "truth is usually very simple", I think you know better than that. Things only seem simple to simple minds. The more we actually examine something, especially things in nature, the more wondrous and intricate we discover them to be.