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Evolution: Technically Random?

Vorticity said:
2) For the mathematically inclined: Consider the stochastic differential equation (SDE)

dv/dt = v + W(t), v(0) = 10,

where W(t) is a standard white noise process. The solution will look roughly like a jagged, increasing exponential, i.e. v(t) = 10*e^t + noise. Just because v(t) has an overall trend that can be predicted does not suddenly make it a non-stochastic process.
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Thanks for this example (been a long time since ODEs!).

For a nice reference on some aspects of this (with numerical results), see: "Forecast and control of epidemics in a globalized world", PNAS, vol 101 no. 42. (Not my paper, but a good one.)
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Sounds interesting. I'll check it out, thanks.
 
Loon said:
-Mutation arise randomly (or at least can't be specifically predicted at any level beyond mutation rate).

-The quality of the mutations is random with respect to the environment. This was what separated Darwin from Lamark. Larmark thought that only the necessary mutations would arise. Darwin thought that all sorts of mutations arose and that only the good ones survived.

-The location of mutations is random. Imagine you have a population spread over a varied environment (say the forest extending into the savannah). A mutation arises that causes the organism to blend in really well with the trees. If it arises in the forest, then it has a good chance of spreading because it lets the organism hide from either predators or prey. (It may not spread, though, because the organism may not breed for one reason or another.) If the same mutation arises in an organism living in the savannah, it's not going to help that organism or its offspring survive. The mutation may or may not spread, depending on chance.

Another thing is that evolution is not the same as natural selection. Evolution is the change of gene frequencies over time. There are different ways for this to happen. One is selection. Another is gene flow. Another is drift.
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Good points Loon.
 
T'ai said:
But I do.
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Then where are you heading with this?

I have no problem agreeing that evolution is mathematically a random process. However, talking about a random process without giving some indication about "how random" it is is a recipe for vast misunderstanding. To see this, ask the next person who says evolution is random to explain how it works. See if he gives a reasonable explanation.

Vorticity, is there some sort of measure of the "level of randomness" in a process? A measure of the stationarity perhaps?

~~ Paul
 
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How about: Evolution is a stochastic process where mutations are random with respect to the environment but selection is highly non-random with respect to the environment.

Does that summarize the situation?

~~ Paul
 
Vorticity said:
Also, regarding evolution, someone suggested that the randomness is inherent only at the "micro" level, i.e. the small time or individual level, whereas it gets washed out by the time we get to the "macro" level, i.e. the species level.
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That was me, but I was using micro and macro as they are used in QM, not as they are used to refer to evolution.

This does not necessarily follow. It is easy to think of many situations where micro randomness does indeed wash out by the time we get to the macro level, leaving us with what is, for all intents and purposes, a non-random system.
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Agreed. And indeed, biology is a system where individual QM-level effects can be amplified right up to the level of speciation. So I was kind of, uh, wr... Wr... Wrgn. You know. ;)

Among other things, I've been studying the propogation of diseases in human poulations by computer simulation. For these kinds of systems, the way the disease spreads, and the final numbers of the infected, depend very strongly on the (largely random) actions of individual humans ("agents", we call them), e.g. whether one of the first people to be infected decides to take that vacation to Europe or not.
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That's a really lousy example. Or a very good counter-example, I'm not sure which. The individual actions of humans aren't random; you just don't have enough information.

Evolution may or may not behave qualitatively as a spreading disease. However, one cannot blithely assert that micro-randomness MUST wash out.
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Agreed.

So to sum up: I think that Tai Chi is perfectly right to say that evolution is random. It is a stochastic process, and thus inherently random. This is not a "technicality" or a "nitpick", but follows unambiguously from the mathematical definition of these terms.
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If Tai said "Mathematically speaking, evolution is a random process.", then few of us would seriously disagree.

But on the larger scale, it's natural selection, and not genetic variation, that gives evolution its shape. So biologically speaking, evolution is not random.

Evolution is a theory of biology, of course, so to say "Evolution is random", without qualification, is more wrong than to say "Evolution is non-random" without qualification. The latter is justified in the standard context in which evolution is considered, which is not mathematical physics. The former is not justified at all.

So: Evolution is non-random.
 
PixyMisa said:
If Tai said "Mathematically speaking, evolution is a random process.", then few of us would seriously disagree.

But on the larger scale, it's natural selection, and not genetic variation, that gives evolution its shape. So biologically speaking, evolution is not random.

Evolution is a theory of biology, of course, so to say "Evolution is random", without qualification, is more wrong than to say "Evolution is non-random" without qualification. The latter is justified in the standard context in which evolution is considered, which is not mathematical physics. The former is not justified at all.

So: Evolution is non-random.
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I disagree that one is more wrong than the other. Evolution is non-random is inaccurate and misleads about randomness, evolution is random is accurate but misleads about both. I would also point out that "evolution is random" is only misleading considering the ignorance of the general population on one or both subjects.

When talking about the randomness of evolution, one isn't discussing just math or just biology. One is discussing both.

A question for the "non-randomites". Do you think that the rise of humanity was inevitable, given the conditions when life first crawled onto land.
 
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PixyMisa said:
If Tai said "Mathematically speaking, evolution is a random process.", then few of us would seriously disagree.
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From my page:
(bold mine)

"To summarize, while evolution could reasonably be considered and described as biologically or practically non-random, it is technically, mathematically random. To say that calling evolution random is "the opposite of truth" and "false" could itself be viewed as the opposite of truth and false."
 
Paul C. Anagnostopoulos said:
Then where are you heading with this?
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I've presented a logical argument for discussion. I'm not sure why I'd need to head anywhere.

How about: Evolution is a stochastic process where mutations are random with respect to the environment but selection is highly non-random with respect to the environment.
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I agree, and point out that stochastic means random.

Stochastic is synonymous with "random." The word is of Greek origin and means "pertaining to chance" (Parzen 1962, p. 7). It is used to indicate that a particular subject is seen from point of view of randomness. Stochastic is often used as counterpart of the word "deterministic," ...
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http://mathworld.wolfram.com/Stochastic.html
 
Yes, stochastic does mean random.

Pondering this some more this morning, I realize one thing that is bothering me. All natural processes are random,* so to say that a natural process is random conveys no information. I think we're obliged to describe any given process in more detail, so that the "type of randomness" is clear, as Walter said.

~~ Paul

* Or, with more knowledge, we may come to say that all natural processes are deterministic.
 
T'ai Chi said:
I've presented a logical argument for discussion. I'm not sure why I'd need to head anywhere.
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Then this thread is rather trivial and rather meaningless. Vorticity made this point early when he wrote that your stochastic process conclusion is by definition. Nothing more to discuss, is there? Stupid topic, isn't it? Unless, methinks, the Woodini doth protesteth too much.

"T'ransparent Chi."

We should all keep in mind that the news of recent weeks has now given us two concretely documented examples of creationists lying through their dentures as they sneakily try to ramrod ID into our kids' heads.
 
CFLarsen said:
That's Intelligent Design.
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No. At no point have animal fanciers ever had the ability to design biochemical alterations. All they've ever done is acted as a form of artificial selection, favoring the traits that mutation and recombination have made possible.
 
PixyMisa said:
But on the larger scale, it's natural selection, and not genetic variation, that gives evolution its shape. So biologically speaking, evolution is not random.
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I'm not quite sure what you mean by "gives evolution its shape." Evolution is possible through a couple of mechanisms that are not natural selection (adaptation, on the other hand, is fantastically unlikely w/o natural selection). Natural selection in a varied population is the only one that really allows you to make meaningful predictions.

Melendwyr said:
CFLarsen said:
That's Intelligent Design
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No. At no point have animal fanciers ever had the ability to design biochemical alterations. All they've ever done is acted as a form of artificial selection, favoring the traits that mutation and recombination have made possible.
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You're right here, Melendwyr, but c'mon, "Intelligent Design" -- that's funny.
 
I'm sorry, but I don't understand. Could you please explain how interspecies hybrids represent an example of "designing biochemical alterations"?
 
Melendwyr said:
I'm sorry, but I don't understand. Could you please explain how interspecies hybrids represent an example of "designing biochemical alterations"?
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I'm talking about new species.

What alterations are you talking about?
 
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