Randomness in Evolution: Valid and Invalid Usage

[sol invictus]

And why in the blue hell do you have this definition ?

That is a good question - but in the realm of psychology, not biology of math.

It's rather ironic that mijo doesn't realize that even when the probabilities are 1 or 0, that is STILL random by his definition, since those are perfectly good probability distributions.

 

[sol invictus]

Works for me, but I tried that strategy a few months ago and only got back -- if it's a probability distribution, then it's random.

Heads 1.0, tails 0.0 is a probability distribution too.

 

[mijopaalmc]

That is a good question - but in the realm of psychology, not biology of math.

An equally interesting question is why you continue to deny that the definition I give is not a real definition, even thought it is in any probability theory text book that includes the measure-theoretic basis for the field.

It's rather ironic that mijo doesn't realize that even when the probabilities are 1 or 0, that is STILL random by his definition, since those are perfectly good probability distributions.

Again, this show that you do not understand the definition that I have given. In order for a event to exist its opposite must also exist (see: almost surely).

 

[sol invictus]

An equally interesting question is why you continue to deny that the definition I give is not a real definition, even thought it is in any probability theory text book that includes the measure-theoretic basis for the field.

I do indeed deny that the definition you gave is not a real definition.

But what's relevant not whether it's "real", but whether it's useful, appropriate, or even correct in the statement "evolution is random".

Again, this show that you do not understand the definition that I have given. In order for a event to exist its opposite must also exist (see: almost surely).

That page - so far as it's relevant at all - supports my (correct) statement that probability 1.0 for heads and 0.0 for tails is a perfectly valid probability distribution for the results of a coin flip.

 

[mijopaalmc]

I do indeed deny that the definition you gave is not a real definition.

Funny, it appears in several dictionary and is easily derived from from the measure-theoretic descriptions given in probability theory textbooks.

But what's relevant not whether it's "real", but whether it's useful, appropriate, or even correct in the statement "evolution is random".

Look, calling evolution "random" is a simple statement that you can't simply take a phenotype and say that an individual possessing it is guaranteed to reproduce.

That page - so far as it's relevant at all - supports my (correct) statement that probability 1.0 for heads and 0.0 for tails is a perfectly valid probability distribution for the results of a coin flip.

Then you didn't read the dart board example. It made a really clear distinction between a sure event and an almost sure event.

 

[jimbob]

mijo: don't forget to not fail to count the number of negatives in Sol's post

 

[Ichneumonwasp]

Look, calling evolution "random" is a simple statement that you can't simply take a phenotype and say that an individual possessing it is guaranteed to reproduce.

Well, then you are not using words correctly, because looking at a single phenotype and noticing that an individual is not guarunteed to reproduce is not evolution. That is the struggle for survival/reproduction.

 

[sol invictus]

Funny, it appears in several dictionary and is easily derived from from the measure-theoretic descriptions given in probability theory textbooks.

Looks like even you can't not misunderstand your own words.

Then you didn't read the dart board example. It made a really clear distinction between a sure event and an almost sure event.

The dartboard example is perfect - it makes my point precisely. The odds of a (n infinitely thin) dart hitting the precise center are zero, and yet that's obviously a perfectly good probability distribution.

The only distinction they're drawing there is whether the other option is possible to consider. Obviously we can consider coins with odds other than 0 for tails - indeed, we might have a set of coins, some of which have 0 odds of tails and some which have 1/2. According to you, all of them are random.

 

[zosima]

Important caveat: I'm jumping into this thread late, and have not (yet) read it through, and - more importantly - have not absorbed or understood what has already been said.

Question re randomness etc: given genetic drift (and a moderately small population with a very narrow ecological niche), given that fixation one way spells extinction (no accessible genetic path to an adaptation that leads to survival/speciation) but the other leads to survival/speciation, how could this not be (or lead to) a (potentially) purely contingent history? The variation that is fixed, one way or the other, is selectively neutral.

ETA: intended principally as a question for zosima.

I'm not entirely clear about the details of your situation. Why is there drift? Why do you presuppose that the species must bifurcate in a single direction? What causes the bifurcation?

To be clear:
I've really been taking two different tacks in my previous post a sort of strong determinism, based on punctuated equilibrium, and a weaker one.

Weak:
I guess it would depend on what is causing the drift. I would argue that directed drift does not occur spontaneously. When people talk about mutations being indifferent, they're essentially saying that in absence of selection the gene pool drifts in all directions(ie the standard distribution of the gene pool increases to the limits allowed by the niche, but the median stays fixed.) So if you postulate that the median of the gene pool is shifting, then I would assert that this is either because some external cause made it possible for the species to enter a new niche and the species adjusting to a new equilibrium or that some external selective pressure has been applied to the species in its current niche and this is causing the species to adjust to the new pressure.

Strong(which assumes everything the weak position does):
Punctuated equilibrium suggests that as far as our evidence is concerned, we don't see drift, we see discrete changes. So one species, pivotal event, new species. This may be because drift never occurs or it may be because the scales of evolution and our evidence is so many orders of magnitude larger than the time scale of genetic drift that it is highly improbable that we'll see a smooth continuum of transitions. Either way, this sort of drift is not significant to the theory of evolution. All that needs to be considered is the characteristics of a species at ecological equilibrium, just like the macroscopic study of a gas.

 

[zosima]

An equally interesting question is why you continue to deny that the definition I give is not a real definition, even thought it is in any probability theory text book that includes the measure-theoretic basis for the field.



Again, this show that you do not understand the definition that I have given. In order for a event to exist its opposite must also exist (see: almost surely).

Fine, for the sake of discussion, I will take your "almost surely" definition of random to be true. Anything that can be described with a probability distribution, regardless of the values taken by the distribution, is random.

Can you name one system that isn't random by that definition?

 

[mijopaalmc]

Fine, for the sake of discussion, I will take your "almost surely" definition of random to be true. Anything that can be described with a probability distribution, regardless of the values taken by the distribution, is random.

Can you name one system that isn't random by that definition?

Ballistics.

You, like sol invictus, are relying on uncertainty in the initial conditions to declare that my definition is meaningless. However, my point is that, in the case of a stochastic process, each possible value in the distribution of initial condition yields at least two distinct outcome, not just one, as would be the case with a deterministic system.

 

[zosima]

Ballistics.

ROFLCOPTER! Are you really serious? Ballistics is deterministic by your definition? I'm going to request that you be clearer as to how that is the case.

The following is the definition of ballistics from the wikipedia page on ballistics:

"Ballistics (gr. βάλλειν ('ba'llein'), "throw") is the science of mechanics that deals with the motion, behavior, and effects of projectiles, especially bullets, gravity bombs, rockets, or the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance."

Just one post ago you were claiming that the landing location of a dart on a dart board is a perfect example of random behavior. You do understand the path(and landing point) of a dart thrown at a dartboard is a classic example of ballistics? Right? See how it says from the greek "to throw", as in throw a dart?

Even you must admit that that is a clear contradiction ya?

You, like sol invictus, are relying on uncertainty in the initial conditions to declare that my definition is meaningless. However, my point is that, in the case of a stochastic process, each possible value in the distribution of initial condition yields at least two distinct outcome, not just one, as would be the case with a deterministic system.

I've done nothing of the sort. I simply asked you if your definition of random applied to everything. Being as broad as it is, it appears to.

 

[Walter Wayne]

...

If the probability distribution is largely determined by the environment, then calling it simply "random" is misleading, I think. The probability distribution is dependent on the environment.

~~ Paul

True, but simply calling it "non-random" is also misleading, and I would go so far as to ay that non-random is in fact wrong. Of course, wether random or non-random is more descriptive, nobody I recall in this thread has left the statement and just random or just non-random.

I don't mean to imply that there are not other interpretations of the spectrum percentage you gave. I think often what happens is that, the probability ends representing a stable solution. So that the equilibrium population is 15% species 1, 13% species 2,...1% species n.

But its hard to construct a situation where we're talking about the probability of the fate of a species and have that situation be one that we think of as random.

True, the fate of a species may be the result of more than one "coin-toss" but that doesn't necessarily make the situation more predictable. We are used to thinking of the casino analogy, where the casino relies on large numbers of trials to make a profit. But that doesn't reflect the evolutionary process accurately.

You may look at a species, and think even though they individually have a high mortality rate before maturity, through the benefit of large numbers, some will make it there to reproduce. From the gamblers perspective, if I told him he had a 100 tries to draw the Ace of Spades from a deck of cards he'd love this game. He's virtually guaranteed to win.

But then look at the long term. The survival of a species depends on a long chain of events happening. When looked at from the perspective of a chain of events, we can see uncertainty arise. Each time we see significant environmental change, a species has an almost certain chance of surviving. The odds of lossing are tiny, but the cost is life. The odds of winning are huge, but the prize is ... getting to play again. Now if you have a 99.9% chance of winning, but lossing costs you everything, do you want to play a thousand times?

That unbroken chain each species has going back may be a huge number of highly probably events. But the odds of all those events happening is very low.

Walt

 

[Earthborn]

Why does anyone "need" evolution to be "random"?

I don't think anyone "needs" evolution to be random, it is just that some people understand "randomness" in such a way that it simply is.

You claim that many of the people who understand evolution consider it non-random because that supposedly leads to less misunderstanding of evolution. I disagree; calling it "non-random" instead of "random" does not make it more likely that people understand evolutionary concepts.

When you said: "--just as there is no one who teaches people how to play poker that would describe the game as random." you missed an important issue. Poker is considered non-random (despite random elements) because it involves intelligent decision makers, working towards a specific goal. Intelligent designers in other words.

For all the confusion the word "random" causes, I think the word "non-random" is even more problematic when discussing evolution. "Non-random" is often understood to mean "pre-planned by intelligent decision makers" instead of letting things just run their natural course. I choose to conceptualise evolution as "random", because if you can explain how certain patterns can arise from random influences, one does not need to assume any intelligence behind it.

You asked "if one wanted to be understood, why wouldn't one use the definitions of those who ARE understood?" To that I say, that I would use such definition if there was one, but there isn't. Whether one calls evolution "random" or "non-random" makes no difference when trying to explain evolutionary concepts to people who have no prior understanding of them. With either you'll still have to explain very carefully what you mean by it.

 

[mijopaalmc]

ROFLCOPTER! Are you really serious? Ballistics is deterministic by your definition? I'm going to request that you be clearer as to how that is the case.

The following is the definition of ballistics from the wikipedia page on ballistics:

"Ballistics (gr. βάλλειν ('ba'llein'), "throw") is the science of mechanics that deals with the motion, behavior, and effects of projectiles, especially bullets, gravity bombs, rockets, or the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance."

Just one post ago you were claiming that the landing location of a dart on a dart board is a perfect example of random behavior. You do understand the path(and landing point) of a dart thrown at a dartboard is a classic example of ballistics? Right? See how it says from the greek "to throw", as in throw a dart?

Even you must admit that that is a clear contradiction ya?

No, you didn't actually read what I wrote or what I referred to (which seems to be a huge problem with those who argue that evolution is non-random.

A sure event (e.g., hitting the dart board universe) is deterministic, because one, and only one, outcome exists). An almost sure event (e.g., hitting a specific point or line the dart board universe) is random, because strictly more than one outcome exists. You can never not hit the dart board universe (deterministic event), but you could get really lucky and hit a specific point or line on the dart board universe (random event)

Do try and actually read before you post.

 

[Ichneumonwasp]

True, but simply calling it "non-random" is also misleading, and I would go so far as to ay that non-random is in fact wrong. Of course, wether random or non-random is more descriptive, nobody I recall in this thread has left the statement and just random or just non-random.


Walt

You know, I think this sums it up for many people. I don't think many are comfortable with random or non-random. Why must we choose between the two?

Really, when it comes down to it, 'evolution' being an abstraction, does either word apply?

I think it unquestionable that random applies to what occurs at the level of organisms and species (the real stuff). But does it apply to 'evolution', which is really just a description of allele change over time? Allele change is so thoroughly assured that I don't think the word random applies even though all the lower level changes are clearly random (is Boyle's law random?). What alleles? Evolution doesn't care. It is the accumulation of change that will occur where most folks don't like the word 'random' applied. It is too often used to mean -- one-stop random jump.

I still think this is all much ado about nothing.

 

[zosima]

No, you didn't actually read what I wrote or wqhat I referred to (which seems to be a huge problem with those who argue that evolution is non-random.

A sure event (e.g., hitting the dart board universe) is deterministic, because one, and only one, outcome exists. An almost sure event (e.g., hitting a specific point or line the dart board universe) is random, because strictly more than one outcome exists. You can never not hit the dart board universe (deterministic event), but you could get really lucky and hit a specific point or line on the dart board universe (random event)

Do try and actually read before you post.

I did read it. You didn't say "my contrived dartboard example" you said ballistics and I took you literally. I have no idea what you meant. But if your only example of a non-random event is when there is a single entity(or two if you want to get technical), it really is completely devoid of meaning.

While we're at it, I'll one up you, I'll argue there are two outcomes in your dartboard world too. With a probability of 1 the dart hits the board and with a probability of 0 the dart hits nothing. By your definition this is a probabilistic system. Thus, all examples proposed,so far, are random under your definition, and we can conclude the definition is useless and unrealistic. Also, its not at all how the author's intended the almost surely article to be used.

 

[zosima]

Do try and actually read before you post.

While we're goin at it, before you ask me how I know what the authors on the "almost_surely" article were thinking. I'll let you know. I read the discussion page and you wouldn't believe what I found.

Statement one:

I think it should be mentioned on this page that the need for perplexing terminology only arises if probability is defined as the limit of frequency. However, there is no need to define probability in terms of infinite sets (cf. Cox's derivation of probability theory, in his book "The Algebra of Probable Inference"). Given a finite set of propositions, probability 0 always implies a false proposition ("an impossible event" in your terms) and vice versa, and probability 1 always implies a true proposition ("a certain event"). If you wish to consider what happens with probabilities when a set of propositions (events) becomes infinite, you should pass to the limit in a well-defined fashion. "Well-defined fashion" requires specifying the operation by which you extend the originally finite set to approach infinity. Better yet, restrict yourself to finite sets of propositions in your applications and avoid the need for metaphysical terminology altogether.

Statement two:

Two comments: Almost sure is a concept that is valid whether you define probabilities based on "limits of frequency" or from a purely mathematical/topological viewpoint. Second, "probability 0" and "impossible" are synonymous in countably infinite sets as well as finite. The issue only arises when we have a space that is larger. - grubber 17:22, 11 February 2007 (UTC)

Any now your claim:

A sure event (e.g., hitting the dart board universe) is deterministic, because one, and only one, outcome exists). An almost sure event (e.g., hitting a specific point or line the dart board universe) is random, because strictly more than one outcome exists.

:

It sounds like you just said that the cardinality of the set of outcomes in a system must equal one to be non-random. But these guys(the guys that have written the article you are citing so vigorously), seem to claim that actually the set of outcomes can have many outcomes, in fact infinitely many outcomes, just as long as its not uncountably infinite. And they provide a reference, Ouch! Thats a sick burn huh? It's like an iced lightning burn.

So guess what? If we can map a set of probability relations to a countable infinite set, then that has nothing to do with your silly silly dart board. And we can talk about impossible and inevitable as much as our merry little hearts desire without that system being random.

 

[Paul C. Anagnostopoulos]

True, but simply calling it "non-random" is also misleading, and I would go so far as to ay that non-random is in fact wrong. Of course, wether random or non-random is more descriptive, nobody I recall in this thread has left the statement and just random or just non-random.

I think "nonrandom full stop" is better than "random full stop," but I agree that we should not use either of these simplistic terms, and certainly not in a serious discussion of evolution.

So what is Mijo's full description of evolution? Perhaps I missed it.

~~ Paul

 

[Paul C. Anagnostopoulos]

I still think this is all much ado about nothing.

Yeah, but it's fun, random ado about nothing.

~~ Paul