Randomness

[sfs]

A randomn variable is one where for a certain experiment the results is not predictable. In the case of a coin the experiment is flipping it once. Randomn variables follow a distribution function such that if a number of experiments are done then colletively the data will mimic the distribution function which in the coins case ideally should by 50 heads and 50 tails.

No, the probability distribution for a coin tossed one hundred times is not 50 heads and 50 tails; that's the average number of heads and tails expected, over a large number of trials. The probability of actually getting 50/50 in a particular trial is about 8%.

 

[Chalnoth]

No, the probability distribution for a coin tossed one hundred times is not 50 heads and 50 tails; that's the average number of heads and tails expected, over a large number of trials. The probability of actually getting 50/50 in a particular trial is about 8%.

Yup. But the probability of getting between 45 and 55 heads is about 68%, the probability of getting between 40 and 60 heads is about 95% (if I'm doing my math right).

If you bump the number of coin flips by another factor of a hundred, we get:

Average number of heads from many runs of 10,000 flips: 5,000
68% of runs will be between 4950 and 5050.
95% of runs will be between 4900 and 5100.

Notice how it's tightening up? When you get to very large numbers, the deviation from the mean won't even be noticeable. For example, let's take 10^10 flips:

Average number of heads from many runs: 5,000,000,000
68% of runs will be between 4,999,950,000 and 5,000,050,000
95% of runs will be between 4,999,900,000 and 5,000,100,000

So, there you have it. Flip a coin 10 billion times, and you'll get the mean back within a tiny fraction of a percent. This is an argument that's used in teaching statistical mechanics, which is a way of deriving thermodynamics from first principles. In this discipline, you're typically talking about on the order of 10^23 atoms or molecules at a time, so the deviation from the mean behavior is essentially zero.

Evolution isn't too dissimilar. You're still talking about large numbers of members of a population (typically a hundred thousand or more for a healthy population), and you have each new member of the population get a slight random change to their genome. Some overall statistics of how the population changes are therefore completely predictable, since random process + large number of tries = predictability.

Not everything is predictable, of course, due to the fact that life is a highly nonlinear system, but some general things are, such as the fact that if the environment remains the same, the fitness of a population will increase.

 

[Late_Cretaceous]

Why is there such a phobia about randomness?

Plants disperse their seeds randomly.
Seeds that fall in areas favorable for growth - for that particular species - grow well, those that fall on unfavorable areas don't grow well or not at all.
Jesus taught this very concept!
If we look at a forest, we don't find that the product of this random dispersion is chaos do we? No, we find that shade loving plants grow on shady slopes, sun loving plants grow on sun drenched slopes, moisture loving plants grow in boggy areas and plants that prefer well drained soil grow on sandy areas.
Just look at any river valley. One side might get more sunlight, and the other receive less - and you will find entirely different communities of plants growing. All that results from random dispersion of seeds!

 

[Wiccan_Child]

Why is there such a phobia about randomness?

Plants disperse their seeds randomly.
Seeds that fall in areas favorable for growth - for that particular species - grow well, those that fall on unfavorable areas don't grow well or not at all.
Jesus taught this very concept!
If we look at a forest, we don't find that the product of this random dispersion is chaos do we? No, we find that shade loving plants grow on shady slopes, sun loving plants grow on sun drenched slopes, moisture loving plants grow in boggy areas and plants that prefer well drained soil grow on sandy areas.
Just look at any river valley. One side might get more sunlight, and the other receive less - and you will find entirely different communities of plants growing. All that results from random dispersion of seeds!

Because it is not true random. Truely random systems are on the quantum scale. Mathematical systems, however, are utterly predicatble. Since mutation is not affected directly by quantum fluctuations (although chaos theory tells us that a single incident of autogenesis in the quantum foam will have drastic consequences in the long run (though for such a small event, the run must be very long indeed. But you get the point)), it is, in theory, predictable. It's just very very hard to do so. So, we call it random, and save ourselves the quite impossible task of predicting such complex molecular movement.

 

[shernren]

Yup. But the probability of getting between 45 and 55 heads is about 68%, the probability of getting between 40 and 60 heads is about 95% (if I'm doing my math right).

[geek]

Yeah, should be about right. Standard deviation of a binomial distribution = sqrt(npq), and since a large binomial distribution approximates a normal distribution, 68% of data ends up within 1s.d. and 95% within 2s.d. Note that since p and q remain constant, as n changes the standard deviation changes according to sqrt(n), which is a mathematically formal (and illegible ) way of saying what Chalnoth was saying.

 

[Chalnoth]

Because it is not true random. Truely random systems are on the quantum scale. Mathematical systems, however, are utterly predicatble. Since mutation is not affected directly by quantum fluctuations

Actually, all chemical reactions are inherently quantum-mechanical. The only thing is, when we have large numbers of them (for example, large numbers of members of a population), the result becomes predictable. Mutations are highly random. That's why evolution doesn't ever talk about what happens to single organisms: it talks about populations. Random events + large numbers = predictable behavior.

For example, if you tried to guess the outcome of one roll of a die, you'd be wrong most of the time. But if you average many die rolls, the result suddenly becomes very predictable.

 

[Late_Cretaceous]

So why then do evolutionists think of evolution as the Christian's cryptonite? Evolution proves nothing of value for anyone seeking to answer a God question.

The first part is simply untrue. The second part is true, but then again it would be true for any scientific theory. Just because science does not answer questions about God is no reason to reject science - nor is it fair to say that science rejects God.



As far as purpose and non-purpose goes. Are rainfall patterns on Earth a result of concious purpose or non purpose. Does it require intellect and contant tinkering to make sure that the coast of Cameroon gets several feet of rain a year, while the coast of Namibia never sees a drop for centuries? Or can that all be explained by naturalistic explanations?

 

[Loudmouth]

Actually, all chemical reactions are inherently quantum-mechanical. The only thing is, when we have large numbers of them (for example, large numbers of members of a population), the result becomes predictable. Mutations are highly random. That's why evolution doesn't ever talk about what happens to single organisms: it talks about populations. Random events + large numbers = predictable behavior.

I, like Gould, think this definition of "random mutations" is highly erroneous. The randomness of mutations has to do with the link between the creation of variety and the direction of evolution. Mutations are random with respect to the direction of evolution. Ironically, I found this Gould quote while reading for a supersport thread:

Textbooks of evolution still often refer to variation as “random.” We all recognize this designation is a misnomer, but continue to use the phrase by force of habit. Darwinians have never argued for “random” mutation in the restricted and technical sense of “equally likely in all directions,” as in tossing a die. [Rather it means statistical frequencies around a modal norm, like the bell curve for example, which does not imply that the underlying cause is totally random like tossing die.] But our sloppy use of “random” (see Eble, 1999) does capture, at least in a vernacular sense, the essence of the important claim that we do wish to convey -- namely, that variation must be unrelated to the direction of evolutionary change; or, more strongly, that nothing about the process of creating raw material biases the pathway of subsequent change in adaptive directions. This fundamental postulate gives Darwinism its “two step” character, the “chance” and “necessity” of Monad’s famous formulation the separation of a source of raw material (mutation, recombination, etc.) from a force of change (natural selection). Gould, Stephen J. (2002) The Structure of Evolutionary Theory. Cambridge: Harvard University Press. pp. 137-150.​

So this is why "random mutations" needs the additional qualifier "with respect to fitness". And again, the best way to illustrate this definition in an experimental and objective way is the Luria-Delbruck fluctuation assay. In this assay, mutations conferring phage resistance occurred in an environment where they were neutral, or even slightly deleterious. The experiment demonstrated that bacteria did not guide mutations so that they could gain phage resistance when it was needed. Random, in the case of mutations, denotes the lack of a demonstratable mechanism linking the formation of mutations and the needs of an organism in a specific environment.​

 

[bluetrinity]

The first part is simply untrue. The second part is true, but then again it would be true for any scientific theory. Just because science does not answer questions about God is no reason to reject science - nor is it fair to say that science rejects God.



As far as purpose and non-purpose goes. Are rainfall patterns on Earth a result of concious purpose or non purpose. Does it require intellect and contant tinkering to make sure that the coast of Cameroon gets several feet of rain a year, while the coast of Namibia never sees a drop for centuries? Or can that all be explained by naturalistic explanations?

My point exactly. I could never understand why many Creationists are so threatened by the Theory of Evolution. Evolution merely describes one path that a God may have chosen to create, yes? After all, we can explain much of it, but not one vital aspect, i.e. the one about mutations being random. Of course, that raises the thorny question of harmful mutations.

 

[bluetrinity]

I, like Gould, think this definition of "random mutations" is highly erroneous. The randomness of mutations has to do with the link between the creation of variety and the direction of evolution. Mutations are random with respect to the direction of evolution. Ironically, I found this Gould quote while reading for a supersport thread:

Textbooks of evolution still often refer to variation as “random.” We all recognize this designation is a misnomer, but continue to use the phrase by force of habit. Darwinians have never argued for “random” mutation in the restricted and technical sense of “equally likely in all directions,” as in tossing a die. [Rather it means statistical frequencies around a modal norm, like the bell curve for example, which does not imply that the underlying cause is totally random like tossing die.] But our sloppy use of “random” (see Eble, 1999) does capture, at least in a vernacular sense, the essence of the important claim that we do wish to convey -- namely, that variation must be unrelated to the direction of evolutionary change; or, more strongly, that nothing about the process of creating raw material biases the pathway of subsequent change in adaptive directions. This fundamental postulate gives Darwinism its “two step” character, the “chance” and “necessity” of Monad’s famous formulation the separation of a source of raw material (mutation, recombination, etc.) from a force of change (natural selection). Gould, Stephen J. (2002) The Structure of Evolutionary Theory. Cambridge: Harvard University Press. pp. 137-150.​

So this is why "random mutations" needs the additional qualifier "with respect to fitness". And again, the best way to illustrate this definition in an experimental and objective way is the Luria-Delbruck fluctuation assay. In this assay, mutations conferring phage resistance occurred in an environment where they were neutral, or even slightly deleterious. The experiment demonstrated that bacteria did not guide mutations so that they could gain phage resistance when it was needed. Random, in the case of mutations, denotes the lack of a demonstratable mechanism linking the formation of mutations and the needs of an organism in a specific environment.​

So, are mutations following something like a normal distribution (or some other sort of distribution) or not? If yes, then presumably where we are today is the expected outcome of billions of mutations.

 

[I_Love_Cheese]

So, are mutations following something like a normal distribution (or some other sort of distribution) or not? If yes, then presumably where we are today is the expected outcome of billions of mutations.

Mutations of any given genome will have some sort of distribution, however where we are today is not the mean of a distribution but the result of multiple random events.
These are not multiple trials of one event but a sequential product of multiple different events.

 

[Loudmouth]

So, are mutations following something like a normal distribution (or some other sort of distribution) or not?

It's impossible to say. Environmental factors, such as mutagens in the environment and UV exposure, can increase or decrease mutation rates and the types of mutations that occur. Genetic factors can also increase or decrease mutation rates, such as the SOS mechanism in E. coli. However, biologists like to study model organisms with consistent genomes under controlled conditions, and in these situations mutations on a nucleotide basis do fall into a normal distribution, or something close to it. Every genome I am aware of has mutation hotspots, so the mutation distribution across a single genome will not be normally distributed.

It is interesting to note that in the Luria-Delbruck experiment they were able to derive consistent mutation rates for the resistant phenotype.

The big point that Gould and others have stressed is that mutations are not linked to what an organism requires in a given environment. For example, you are just as likely to spontaneously acquire the sickle cell allele through mutation in an area that is devoid of malaria as you are in an area that has endemic levels of malaria. However, the subsequent proliferation of that mutation through subsequent generations is influenced by the environment. This is the two-step function of evolution that Gould was talking about.

If yes, then presumably where we are today is the expected outcome of billions of mutations.

The frequency of each mutation over several generations is not guaranteed to fit a normal distribution because of natural selection. Natural selection will skew the numbers of each mutation in each subsequent generation. Shifting environmental conditions will then change selective pressures.

Neutral mutations, OTOH, tend to fit normal distribution and are part of an effect called Genetic Drift.

 

[shernren]

So, are mutations following something like a normal distribution (or some other sort of distribution) or not? If yes, then presumably where we are today is the expected outcome of billions of mutations.

Also, some types of mutations are inherently more likely to occur than others. Among point mutations, transitions, which change purines to purines (A <-> G) or pyrimidines to pyrimidines (C <-> T) are more likely than transversions which interchange between pyrimidines and purines (A/G <-> C/T). [Wikipedia] And the chances of a large indel happening is intuitively smaller than the chances of a small indel happening (though of course I could be wrong about that).

Even then, mutations are still random, in the sense that a loaded dice is random. Not that all outcomes have equal probability, but the outcome is not determined by the desired outcome. No matter how a dice is loaded there's still a chance that I'll roll a 6, even if what I want is a 1 or 2. In the same way a bacterium can't mutate a particular gene to yield antibiotic resistance when it senses antibiotics nearby. The gene just mutates or doesn't mutate, fullstop, irrespective of whether the bacterium is going to get blasted by antibiotics today or tomorrow or not at all.

 

[bluetrinity]

It's impossible to say. Environmental factors, such as mutagens in the environment and UV exposure, can increase or decrease mutation rates and the types of mutations that occur. Genetic factors can also increase or decrease mutation rates, such as the SOS mechanism in E. coli. However, biologists like to study model organisms with consistent genomes under controlled conditions, and in these situations mutations on a nucleotide basis do fall into a normal distribution, or something close to it. Every genome I am aware of has mutation hotspots, so the mutation distribution across a single genome will not be normally distributed.

It is interesting to note that in the Luria-Delbruck experiment they were able to derive consistent mutation rates for the resistant phenotype.

The big point that Gould and others have stressed is that mutations are not linked to what an organism requires in a given environment. For example, you are just as likely to spontaneously acquire the sickle cell allele through mutation in an area that is devoid of malaria as you are in an area that has endemic levels of malaria. However, the subsequent proliferation of that mutation through subsequent generations is influenced by the environment. This is the two-step function of evolution that Gould was talking about.



The frequency of each mutation over several generations is not guaranteed to fit a normal distribution because of natural selection. Natural selection will skew the numbers of each mutation in each subsequent generation. Shifting environmental conditions will then change selective pressures.

Neutral mutations, OTOH, tend to fit normal distribution and are part of an effect called Genetic Drift.

Fair enough. Ultimately, it seems to me that, in layman's terms and for practical purposes, mutations are random. Their occurance can be observed to more or less likely in certain situations but not in others. This means to me that what exists today is the result of a long chain of random mutations influenced by natural selection. Now please explain natural selection to me. But be sure to avoid expressions like: natural selection does this, that or the other thing because unless natural selection has an address and a phone number, by itself it cannot do anything. It is not a person with a purpose, I think.

 

[Loudmouth]

Now please explain natural selection to me. But be sure to avoid expressions like: natural selection does this, that or the other thing because unless natural selection has an address and a phone number, by itself it cannot do anything. It is not a person with a purpose, I think.

Gravity is not a person with a purpose and yet gravity moves the Earth towards the Sun. It is just a literary device for explaining concepts.

Anyway, natural selection is the second step in evolutionary two-step. The first step we have already talked about which is random mutations. The second step is the amplification of beneficial mutations. Natural selection acts as a sieve. As an analogy, random mutations are equivalent to breaking a rock into pieces. When you break a rock the pieces will fall into a random distribution of different sizes. When you pass these broken rocks through a sieve only the rocks below a certain size will pass through. What results is a non-random distribution. The same for natural selection. Only certain variations produced by random mutations are passed on through several generations. The ones that are passed on with the best success are almost always beneficial mutations. Those that don't get passed on to future generations are almost always detrimental mutations. Therefore, beneficial traits become more and more common in a population with each generation. That is how natural selection works. The viral resistance mutation in the Luria-Delbruck experiment is a perfect example.

 

[Chalnoth]

Even then, mutations are still random, in the sense that a loaded dice is random. Not that all outcomes have equal probability, but the outcome is not determined by the desired outcome. No matter how a dice is loaded there's still a chance that I'll roll a 6, even if what I want is a 1 or 2. In the same way a bacterium can't mutate a particular gene to yield antibiotic resistance when it senses antibiotics nearby. The gene just mutates or doesn't mutate, fullstop, irrespective of whether the bacterium is going to get blasted by antibiotics today or tomorrow or not at all.

To take the loaded dice idea a little bit further, it's sort of like the die is always loaded to prefer 1, set by the properties of chemistry, but in some cases I might want a 6 instead, set by natural selection.

 

[Ondoher]

Fair enough. Ultimately, it seems to me that, in layman's terms and for practical purposes, mutations are random. Their occurance can be observed to more or less likely in certain situations but not in others. This means to me that what exists today is the result of a long chain of random mutations influenced by natural selection. Now please explain natural selection to me. But be sure to avoid expressions like: natural selection does this, that or the other thing because unless natural selection has an address and a phone number, by itself it cannot do anything. It is not a person with a purpose, I think.

In any population of organisms there is variability, and environmental stressors such as competition for resources, competition for mates, parsitism, predation, etc. Some individuals have traits that increase the likelihood of having offspring within their environment. Those individuals with traits most likely to benefit reproductive success are most likely to reproduce and thus pass those traits on to their offspring. Those with traits most detrimental towards reproductive success tend not to reproduce, thus not passing on those detrimental traits to the next generation. This differential reproductive success is called natural selection.

 

[Dr.GH]

So then randomness doesn't really exist, if I understand you all correctly. What we call random is merely our inability to understand fully the process. Which means, I suppose, that, if we understood it properly we might find out that they are not random at all.

Not quite. First, there are events and systems having properties that are random. These events are well understood, but unpredictable from moment to moment. For example, if I flip a "fair" coin, there will over time be equal numbers of "heads" and "tails." The number of "heads" or "tails" in a row will form a Poisson distribution.

So, we know alot about the toss of a coin, but we cannot predict how the next toss will turn out any better than "random."

There are much more complex examples. Among these are examples in biology.

 

[Dr.GH]

For practical purposes I agree. But the relevance of the outcome of this question might be my eternal destiny.

Then you are so messed up.

 

[Chalnoth]

Here's my little description of natural selection:

Consider a population. Let's just take some wolves to start with. Some members of the population will have slightly thinner fur, and others will have slightly thicker fur. If the weather changes, or if a group moves to an area with different weather, the ideal fur thickness will change.

For example, if the climate gets colder, then the members of the population with thin fur will have a harder time surviving than the members of the population with thicker fur. Those with fur that is too thin will have a greater chance of freezing to death. Thus, over time, the average thickness of the fur will increase.

Similarly, if the population moves to an area with a warmer climate, the population members will have a risk of dying of heat stroke if their fur is too thick, so the average thickness of the fur will get thinner.

This is what way of most evolutionary changes, as most survivable mutations are those that only affect small changes in traits. There are more drastic changes, but just take us for a moment, and compare us to chimpanzees. What is the difference? Well, we're a little bit larger, have shorter arms and longer legs, have slightly different bone shapes, have significantly larger and more complex brains, and have much less hair. All of these differences can easily be explained by our ancestors living in different areas for 5-7 million years, and thus being subject to different evolutionary pressures.