Evolution: Technically Random?

[T'ai Chi]

Thought people might find this interesting for discussion. I've posted the page over at Skepticfourm a while ago for discussion too and got some good comments.

I basically got tired of reading a lot of popular books that saying evolution is random is beyond wrong. Now, I do believe it is incorrect to say that natural selection is random. But evolution is more than natural selection from what I understand.

I reason that if Evolution can be mathematically conceived as

Evolution = NS(RM, OS)

where NS is Natural Selection, RM is Random Mutation, and OS is Other Stuff,

(That is, NS is a function acting on things, some of which are random. Or put another way, evolution is the non-random selection of random variation and some other things)

the going by this conception, doesn't that make Evolution random (ie. unable to be predicted with certaintly beforehand), and therefore saying evolution is random is not wrong, but in fact a true and reasonable statement?

For example, say I have fair coin, with Heads or Tails which I code as 0 or 1. Then I calculate some function, I choose 2^outcome+10. The output is still random, either 11 or 12.

Take any non-trivial function f, and calculate f(something random). Won't the output f be random?

I write about this here http://www.statisticool.com/evolution.htm

 

[kevin]

If you have a function that takes a random number as it's input and filters out all numbers except the number 2 for output, is the output random?

 

[sphenisc]

If you have a function that takes a random number as it's input and filters out all numbers except the number 2 for output, is the output random?

The time between outputs may be random, given eg, a fixed finite time between inputs and for 'processing'.

 

[kevin]

and what do you mean by a non-trivial function? your example seems trivial to me, at least as trivial as discarding all numbers that are not 2.

if we make your function 1^(outcome) + 10 then the result is always 11. Still random?

The randomness of the output depends on the function it's put through (trivial or not). You have to evaluate the results of natural selection to determine if it is random, not the inputs.

Natural selection is a filter, bad mutations discarded, beneficial mutations allowed through. The output is non-random for beneficial mutations.

 

[kevin]

The time between outputs may be random, given eg, a fixed finite time between inputs and for 'processing'.

yeah, i almost put that in my note then discarded it. Of course natural selection has the same issue. The timings between beneficial mutations is probably random (although I think punctuated equilibrium might address this).

 

[T'ai Chi]

and what do you mean by a non-trivial function? your example seems trivial to me, at least as trivial as discarding all numbers that are not 2.

if we make your function 1^(outcome) + 10 then the result is always 11. Still random?

The randomness of the output depends on the function it's put through (trivial or not). You have to evaluate the results of natural selection to determine if it is random, not the inputs.

Natural selection is a filter, bad mutations discarded, beneficial mutations allowed through. The output is non-random for beneficial mutations.

Trivial in the sense that if the equation is

Evolution = NS(RM,OS)

is always being a constant, as in your example, isn't realistic in terms of modelling, since we know evolution is capable of producing change. I think I'll add your comment to the page though.

I'm not sure at all what a very realistic model would be, but I don't believe it should always be constant no matter what. Having f specified as is at least allows for the possibility for f's to be the same at some point or points in time, but not always be the same.

 

[sphenisc]

and what do you mean by a non-trivial function? your example seems trivial to me, at least as trivial as discarding all numbers that are not 2.

if we make your function 1^(outcome) + 10 then the result is always 11. Still random?

The randomness of the output depends on the function it's put through (trivial or not). You have to evaluate the results of natural selection to determine if it is random, not the inputs.

Natural selection is a filter, bad mutations discarded, beneficial mutations allowed through. The output is non-random for beneficial mutations.

Natural selection is a statistical filter; sometimes bad mutations aren't discarded, sometimes beneficial mutations are. The output still as elements of randomness (I'd prefer the term stochastic) in it.

 

[kevin]

there will be randomness in the result of evolution -- which particular mutations arise, when they arise, etc... Just as in my example their is still randomness in how often a 2 will be output.

In your example a coin flip will always produce a 0 or 1. The possible outputs are only 2 numbers, how random is that? For your function it's the order of the numbers that is random, the individual numbers aren't so random.

Not sure why you claim a constant result is trivial. Natural selection has 3 types of mutations to act on: a detrimental mutation, a non-beneficial/non-detrimental mutation, or a beneficial mutation. In coin flipping, if we had a 3 sided coin, this would be a 0, 1, or 2.

Natural selection filters these: 0's are discarded, 1's generally won't make it through, 2's always make it through.

The output of this filter is fairly constant -- 2's. If we use your definition of trivial then we have to discard natural selection as a possible function.

 

[kevin]

Natural selection is a statistical filter; sometimes bad mutations aren't discarded, sometimes beneficial mutations are. The output still as elements of randomness (I'd prefer the term stochastic) in it.

My model is obviously simplistic, but it would be fair to say that each pass through the statistical filter would reduce randomness? Would a bad mutation not discarded in the first generation be more likely to be discarded in the 2nd generation?

 

[T'ai Chi]

Just as in my example their is still randomness in how often a 2 will be output.

I was talking about the example of 1^(outcome) + 10 then the result is always 11. That is always 11.

In your example a coin flip will always produce a 0 or 1. The possible outputs are only 2 numbers, how random is that?

My point was to show that it is random. One cannot predict with 100% certainty which number will be output.

Not sure why you claim a constant result is trivial.

No, the constant function is trivial. A constant result is not.

The f I propose allows for variety, and also allows for the output to be the same from time period to time period (for example if there is no mutation, or there is and just by chance). The other example that was offered only produces constant outputs (11). It doesn't allow for any variety.

 

[sphenisc]

My model is obviously simplistic, but it would be fair to say that each pass through the statistical filter would reduce randomness? Would a bad mutation not discarded in the first generation be more likely to be discarded in the 2nd generation?

Yes, but more likely to doesn't mean it will be. It is possible for detrimental mutations to, by chance, become fixed in a population. This 'genetic drift' is discussed here:
http://darwin.eeb.uconn.edu/eeb348/lecture-notes/selection-drift/selection-drift.html

 

[kevin]

My point was to show that it is random. One cannot predict with 100% certainty which number will be output.

I don't think evoluion can predict with a 100% certainity if a particular mutation would even arise (i.e. on another planet are aliens guarenteed to have eyes?) So in that aspect I do think the output of NS is random because the mutations that are put in are random.

But in the aspect of, is this a beneficial mutation or a detrimental mutation, I do think NS will reduce the randomness and select towards beneficial mutations. So a prediction could be made as if to a particular mutation would survive a particular enviornment.

I also think that randomness is furthur reduced with each pass through NS filter. In each generation of a population, the older a particular mutation is, the more likely it is beneficial to their current environment.

 

[CFLarsen]

One cannot predict with 100% certainty which number will be output.

That's not the point of evolution. Evolution doesn't predict that there will be a specific "number". It predicts that, under certain given conditions, certain "numbers" (traits) could develop.

 

[Paul C. Anagnostopoulos]

the going by this conception, doesn't that make Evolution random (ie. unable to be predicted with certaintly beforehand), and therefore saying evolution is random is not wrong, but in fact a true and reasonable statement?

Evolution is not random with respect to the environment.

~~ Paul

 

[T'ai Chi]

Evolution is not random with respect to the environment.

~~ Paul

I believe mutations are part of the environment.

 

[CFLarsen]

I believe mutations are part of the environment.

How so?

 

[Mojo]

I believe mutations are part of the environment.

The mutations are not really relevant as far as the non-random nature of evolution by natural selection is concerned. It's the selection part that is going to produce non-random results, even if the mutations are random replacements of one nucleotide with another. Individuals that survive and successfully breed are more likely to be those best suited to survive in the environment in which they find themselves, and they will be able to pass these traits on to their descendents. The genes and traits of those individuals that produce the most descendents will have more representation in subsequent generations. The result will be that traits which enable an organism to survive and breed in its environment will be selected for, rather than random traits with no survival value.

 

[Mojo]

I reason that if Evolution can be mathematically conceived as

Evolution = NS(RM, OS)

where NS is Natural Selection, RM is Random Mutation, and OS is Other Stuff

Could you say what you mean by "Other Stuff"?

the going by this conception, doesn't that make Evolution random (ie. unable to be predicted with certaintly beforehand), and therefore saying evolution is random is not wrong, but in fact a true and reasonable statement?

The fact that it cannot be predicted with certainty does not make it entirely random. It is quite possible to make predictions about the sort of traits that are likely to be successful in a given environment. The fact that the environment is a very complex system (including as it does all interacting species, all of which are also being acted upon by evolution by natural selection) will make it pretty much impossible to predict exactly how it will eventually pan out. This does not mean that it's random though.

As an analogy here, while the action of gravity on orbiting bodies is pretty well understood, in a system with many orbiting bodies (such as our Solar System) the further ahead you try to predict the position of the planets, the more difficult it gets to produce an accurate prediction, because they're all attracting each other to some extent, and the effect of small uncertainties in the current positions lead to ever increasing margins of error the further into the future you try to predict. This does not mean that the behaviour of the planets is random.

 

[Melendwyr]

I believe mutations are part of the environment.

No, mutations are part of the organism. Mutations can be caused by the environment.

 

[T'ai Chi]

Could you say what you mean by "Other Stuff"?

I'm thinking things like genetic drift, migration, and other mechanisms of change that I've left out because I don't know what they are.