Here’s a simple experiment one can actually try. Take a bag of M&M’s, and without peeking reach in and grab one. Eat it. Then grab another and return it to the bag with another one, from a separate bag, of the same colour. Give it a shake. I guarantee (and if you tell me how big your bag is I’ll have a bet on how long it’ll take) that your bag will end up containing only one colour. Every time. I can’t tell you which colour it will be, but fixation will happen.
This models the simple population process of Neutral Drift. Eating is death, duplication is reproduction, and the result is invariably a change in frequencies, right through to extinction of all but one type. You don’t have to alternate death and birth; choose any scheme you like short of peeking in the bag and being influenced by residual frequencies (ie: frequency-dependent Selection), and you will end up with all one colour.
Is Chance a cause here? Well … yes, in a sense it is, in the form of sample error. Survival and reproduction are basically a matter of sampling the genes of the previous generation. More random samples are a distortion of the larger population than aren’t, so, inexorably, your future populations will move away from any prior makeup, increasing some at the expense of others till only one variant remains.
Selection is a consistent bias upon this basic process. If different colours also differed a little in weight, say, more of some would be at the bottom of the bag than others, so you’d be more likely to pick one type than another. In more trials, the type more likely to be picked would be picked more often, to express it somewhat tautologously. You’d get a sampling bias.
Both of these processes are random – or stochastic, to use the preferred term. In reality, they are variations of the same process, with continuously varying degrees of bias from zero upwards. It makes no sense to call selection nonrandom, unless by ‘random’ you mean unbiased. Where there is no bias, all is Drift. But turning up the selective heat does not eliminate drift – sample error – and so does not eliminate stochasticity.
With a source of new variation, these processes render evolution inevitable. Even with a brand new mutation, with no selective advantage whatsoever, 1/Nth of the time (where N is the population size) it will become the sole survivor. That’s the baseline. If there is a selective advantage, it will be more likely and quicker to fix, on the average. If at a selective disadvantage, it will be less likely and slower.
Conversely, without a source of new variation, all existing variation would be squeezed out of the population, and evolution would stop.
No that’s not accurate at all. What law says the rest of the population will be eliminated in 2N? You have zero reason for making that statement. While one is getting a mutation for black, another is getting a mutation for ivory. And another is getting a mutation for rainbow. Why is only the black going to spread, while the others aren’t?
The fixation rate is not the mutation rate. And furthermore you don’t even know the mutation rate, just because 1 in 1000 got THAT particular mutation, the rate might actually be 1 in a million, and it just so happens that this is the one unlikely time, and next time, it will be some other unlikely mutation. If you have enough unlikely mutations eventually you will get one of them.
Is it also fine to be rude towards the person, and not just the argument, as long as you aren’t accusing them of being disingenuous in their utter stupidity or incompetence?
I can tell someone they are making a complete ass of themselves, or they don’t know what they are talking about because they their mother was retarded, as long as the meaning is that they can’t help being so dam dumb?
Because if that is NOT ok, then don’t just save your criticism for my posts.
phoodoo,
The rules are as hotshoe states, phoodoo. “Attack ideas, not commenters” is the guiding principle. I’m sorry that moderation is patchy. I (and other admins, I suspect) would prefer to err on the side of freedom of expression rather than censorship so transgressions do get overlooked.
Why not make any suggestions you may have for improving matters in the sandbox? Perhaps some kind of “flagging” system? Leading by example is also worth trying. 😉
Take N blue M&Ms. Remove two and replace them with one black and one ivory. The probability of the population staying blue is (N−2)/N, getting black 1/N, and getting ivory 1/N.
phoodoo,
It’s a mathematical expectation.The process of sampling with removal and replacement is a probabilistic process. For a haploid population (which this is), the expected time to fixation works out at 2N ***. There is a mathematical derivation, but you could observe it if you could be arsed to write the simple computer program we have been urging upon you. I’ll write it for you – have you got Excel?
*** In individual replicates it will be greater or less than this. 2N is the mean. It’s a probability distribution.
http://en.wikipedia.org/wiki/Genetic_drift#Time_to_fixation_or_loss
The treatment there is for a diploid population, hence there is a factor of 2 difference – 4N instead of 2N, because each individual has 2 alleles.
Your default position for any statement I make is that I have “zero reason” for making it!
I dealt with this. I suggested you view all the mutations as a shade of grey; original alleles as coloured. 1/1000th of the N=1000 population can be black, because it is an individual. But I would not propose that ‘black’ is the only mutation that can happen. So let’s label all mutants as a shade of grey. There are 1000 of them in N=1,000,000 for every 1 in the N=1000 population. A single ‘shade-of-grey’ has the probability 1 in a million of being fixed. But there are 1000 ‘shades-of-grey’ in the larger population. 1/1000th of the population is a mutant in both cases, and hence (because p(fixation) = current frequency – remember?) the chance of a mutant being fixed is identical, even though the chance for a specific mutant goes down.
Yes it is. “the rate of fixation for a mutation not subject to selection is simply the rate of introduction of such mutations”. That’s irrespective of population size.
I anticipated, and dealt with, this. I said:
If you want to compare a large population with one mutation rate against another smaller population with a different mutation rate, that’s fine, but it’s best to compare like with like – if you’re actually trying to argue for or against the role of a particular variable, don’t cheat by changing another one at the same time, unless they are correlated. Which they aren’t in this case. For the same mutation rate, a large population will experience exactly the same proportion of mutations as a small one – ie, more, in direct ratio of their respective sizes. The same proportion of its individuals will be mutated, and hence mutants as a class will have the same frequency and probability of fixation.
Allan Miller,
Whats the probability that no new mutation will get fixed in your population?
Elementary, Watson. Take the probability of fixation and subtract it from one.
Or subtract it from 4, since 4 = 1 according to you.
If the message you are trying to convey is really true, why do you have to misrepresent other posters to show this?
The rules also say don’t imply that the poster is stupid. But you can say that the post is wrong, or doesn’t make sense.
The rules also say don’t imply that the poster is stupid is. But you can say that the post is wrong, or doesn’t make sense.
That’s silly, phoodoo. Probabilities add up to 1. Don’t you know that?
ETA: You also seem to have no idea about units. I never said that 4 = 1. I said that 4 deaths = 1 generation (in a population of 4).
Saying that 12 inches = 1 foot is not the same as saying that 12 = 1.
No phoodoo, what Allan says is accurate. Try thinking of it this way: while one is getting a mutation for black, another is getting a mutation for peanut. And another is getting a mutation for crinkly, etc., etc., etc. ALL of these mutations are equally likely to spread (we have stipulated neutral mutations, remember).
You are confused as to how these things scale.
Here’s another way of thinking about it that might help:
Imagine a population of 100, in which each offspring carries 3 new neutral mutations. That’s 300 new mutations each generation – 3 are destined to be fixed (please test this for yourself), and the remaining 297 are destined for extinction.
Suppose that the average time to fixation is 100 generations (this, I think, is true), and the average time to elimination is 10 generations (this depends on the degree of culling per generation).
Therefore, at any one time, the population of 100 contains, thanks to its past mutations, (297 mut/gen x 10 gen= ) 2,970 mutations that are destined for extinction and (3 mut/gen x 100 gen= ) 300 that are destined to fix. In this generation, one tenth of the losers (= 297) will be extinguished and one in 100 of the winners (= 3) will fix.
Now let’s make the population ten times bigger:
Population size is now 1,000. Each offspring still carries 3 new neutral mutations. That’s 3,000 new mutations each generation – 3 are destined to be fixed, and 2,997 are destined for extinction.
The average time to fixation has increased to 1,000 generations, but we’ll keep the average time to elimination at 10 generations. Not that it matters.
At any one time, the population of 1,000 contains 29,970 mutations that are destined for extinction and 3,000 that are destined to fix. In this generation, 2,997 will be extinguished and 3 will fix.
IOW, the probability that any one neutral mutation will fix is 1/N, but as the chance that any one particular mutation will fix gets smaller and smaller, the number of ‘shots on goal’ or ‘at bats’ increases proportionally. As you put it: “If you have enough unlikely mutations eventually you will get one of them.”…to fix, that is.
The fixation rate is the mutation rate.
[Prediction: next up, genetic entropy]
ETA: I see Allan responded himself while I was typing. Apologies for the duplication…and I am off by a factor 2 in the expected time to fixation. Which, of course, washes out in the result: just double my prevalent population of “future winners”.
Just curious, why did you qualify your statement to say ToE explains “virtually all” of the empirical observations? Are you aware of any empirical observations that ToE does not explain?
Just because I express doubts about the sufficiency of current evolutionary theory to explain all of life doesn’t mean I’m making an argument for Creationism or any other theory. Was horizontal gene transfer a part of the original evolutionary theory? Kind of screws up the simple tree of life that we all grew up with. Was punctuated equilibrium (or at least the acknowledgement that evolution may not always be gradual) part of the original evolutionary theory? Evolutionary theory has changed over the years, and I anticipate that it will change in the future.
Of course there are areas of natural science where we still have unknowns. One quick example is the timing of the life cycle for the seventeen year cicada. There are also species of cicada that have a thirteen year life cycle. Biologists have some hypotheses as to how these large unusual emergence times came about but no definitive answer yet. That’s why we do science, to investigate and gain knowledge.
And how many times per day do you think this rule gets violated by Thorton and hotshoe and Olegt per day, with zero mention from you?
olegt,
Olegt, Allan and DNA Jock:
You think that my question of what is the probability of no new mutation spreading through the population was perhaps a silly question, but it goes exactly to the heart of the misunderstanding you all have about the whole problem, and why you are confused. The problem is this:
In the formula you are using for fixation rates which says its equal to the number of the individuals with that mutation in the population divided by the population, there is one important criteria, that is that we assume that a mutation MUST drift through the population one way or the other. There is NO probability for none drifting, because the formula works under the assumption that we look at an INFINITE number of mutations-thus we eliminate the option of NONE. This is Allans mistake, this is Olegts mistake and this is now DNA Jocks.
You see, one way to look at this probability of fixation is to imagine the situation of a bag of M& M’s first with NO black M&M’s inside. At this point the probability for fixation of a black M&M is zero! It can’t happen, its statistically impossible. And then bingo, one mutation arises and suddenly its no longer zero. The impossible became possible. How can that be? Its because the fixation rate you are using does not calculate the possibility of NO mutation drifting, it simply calculates the odds of one mutation compared to another, not compared to zero.
So the odds change with each and every new addition or subtraction. Because we have to assume an infinite number of generations, an assumption which discounts the option of NONE. So a black can go from zero probability, to 80% probability, and back to zero probability with each successive round of generations. But obviously an infinite number of generations is not actually possible, because we have a finite number of time that the species exists. If we start talking about what can happen theoretically given an infinite number of generations, of course anything is possible, but that is not reality, that is just numbers grinding by seeing how long our computer can run. We have removed the option of zero, to give every mutation a chance to run to infinity. So any mutation at some point has a zero probability and at some point can have a 100% probability.
An illogical assumption. If you change your computer to stop at a certain number of generations, then suddenly the odds change completely. They are not the odds of 1/N. This is why you have been getting it wrong. You are presetting your computer to insist it must happen But no such insistence exists.
I’m not following your line of reasoning, and am not sure you are responding to one of my comments. Are you saying that through unguided macroevolution, we should expect to see only a few design patterns? I thought evolution theory was supposed to explain the great diversity of life.
He’s mostly talking about the “nested hierarchy” design pattern which has been observed across the whole of Life on Earth. Under the presumption of “descent with modification”, a nested hierarchy is the design pattern we’d expect to see; under the presumption of “the Designer did it”, we’d expect to see pretty much any design pattern whatsoever, depending on how the Designer happened to feel about it.
phoodoo,
There is a lot that is wrong in your latest post. You appear unable to understand the most basic math.
The calculation that everyone, including you, has been discussing is the probability of a specific individual mutation fixing, given that it has occurred. (Actually the OP discusses the probability that a single variant will achieve fixation, assuming that there are no new mutations. This probability = 1. But starting with more than one ‘black’ M&M upset you, so we moved on to explaining that the probability of a single, novel mutation fixing is 1/N.)
We have more recently been trying to explain to you that the rate of fixation equals the rate of mutation. You are now complaining that IF there are zero mutations, then no mutations will fix. I think we all agree about that. You might even notice that it is a logical consequence of the statement: “rate of fixation equals the rate of mutation”.
Your complaint about our assuming INFINITE numbers of mutations and of generations makes no sense. The assumption that leads to “rate of fixation equals the rate of mutation” is the Steady State Assumption, but rather than rely on the SSA, we have demonstrated that it is a good approximation via simulations. The simulation I wrote this morning stopped itself after 2*N generations, but had no problems in getting a single mutation to fix in a population of 1,000. Obviously, I didn’t need infinite numbers of mutations, nor generations.
This is the general pattern we see. But the development of some of the engineering feats like vision, flight, and echolocation have not been adequately explained in my view. And since these features appear in separate branches of the nested hierarchy, all the more reason to believe the known evolutionary mechanisms may be inadequate to explain all the diversity of life. Especially since evolutionary mechanisms don’t explain how life began in the first place.
What about the evolutionary explanations for them is inadequate? Just that we don’t know every last detail? Pick an example and be as specific as you can as to why you reject the scientific consensus. Please remember that personal incredulity is not an argument.
Non-sequitur. Science doesn’t offer evolutionary theory as an explanation for OoL.
AFAIK you are the only one in this thread who has called others stupid. Plenty have noted that based on your answers you seem woefully ignorant of both evolutionary theory and basic probability but that is not the same thing.
phoodoo,
What DNA Jock said. The probabilities that have been discussed are for the fixation of n black M&Ms to take over a population, assuming no new mutations. Black ones give rise to black, blue to blue and so on. That is how the model is formulated.
We can add mutations to this model, making it more complex. In fact, some of that has been discussed by DNA Jock and Allan. But I see no point in doing that as you do not even understand the simpler version with no new mutations.
“n black M&Ms” means “a given number of black M&Ms.”
Correct. Life could have been created in its most-primitive form by a god entity who had created the planet with the capacity to sustain life once it provided the first spark of life.
Evolution is what explains what happened after that. Life took about 3 billion years to do much of anything interesting after that, so that’s pretty good evidence that god entity had no desire to interfere in the results of the natural process of evolution. What was it waiting for, if its desire was to see interesting things like flight and echolocation and brainpower and ultimately, special humanity? Why didn’t that god entity perform any of its “engineering feats” 3 billion years sooner?
I admit that god entity may have interfered in the natural process in ways that were subtle enough that they remain undetectable by scientific observation. Maybe its game was to wait so long precisely because .3+ billion years later, when it finally got down to creating humans, some of the curious humans would see from the evidence that life had had plenty of time to evolve complexity without needing an “engineer’s” shortcuts. Hiding its light under a bushel?
But it simply did not create “flighty” creatures out of thin air and plop them down into the existing biosphere, so what exactly did it do? How exactly did it construct its “engineering feats”? How does a god entity outside of an animal insert “flight capabilities” into that animal? IF it did engineer in “flight”, then it took enormous pains to see that flight first showed up in organisms that appear as if they share an unbroken chain of common descent from flightless ancestors, while not leaving any unbridgeable gaps between the apparent ancestors’ anatomy (and DNA) and that of its “newly-constructed” flight-capable ones. Pretty clever work, I’d say.
Well, however that god entity did its work, since by definition it had/has the capabilities to do it in a fashion invisible to human understanding, I guess we shouldn’t be too hard on the IDists for their lack of answers. Nor even for their apparent lack of curiosity in trying to get any answers more accurate than “Interior-Decorator-didit”.
It’s quite Zen in a way. We can’t know the answers, so cease searching for answers and you’ll cease suffering the pangs of unanswered curiosity. Stop striving, stop suffering. Yeah, I can see how that sounds like good advice to some.
Curous, why don’t you think that the fact they “evolved” – that is, appeared – more than once is sufficient reason to accept they are relativelly easy to evolve and therefore no need to invoke an intentional designer?
As an example, the lens of the eye is a particular stumbling block for me, has to be clear and develop the ability to focus.
But solving this part of the puzzle may offer insight into other processes at work here.
I agree.
Just curious, are you on track towards solving the OoL puzzle?
Molecules evolve.
You are free to accept these things as relatively easy. The research involving genome sequencing is relatively new, I’ll be interested to see where it leads.
Again, why do you think this is some sort of problem? We have plenty of examples of transparent cells in biology and we have plenty examples of muscles that allow the alteration of physical forms. Why couldn’t these have started extremely simply and evolved improved function over time?
No, just wasted a couple hours thinking about it.:)
The eye lens is just a bag of fluid, with some muscles to distort its shape.
That’s the theory. Everything just fell into place, over time, by natural selection acting on random mutations.
Piltdown2,
As cubist explained, I am talking about the implications of the objective nested hierarchy.
You didn’t answer my questions:
How many bags of biological fluid would stay clear for decades?
I’ll ask again – do you have any technical reason to doubt the scientific evidence-based explanation? Anything besides your own personal disbelief?
Here is a pretty neat site from the U. of Utah with a good overview of what is known about eye evolution.
Eye Evolution
Note that in the real world we have a whole spectrum of eye types from the simplest light spots on up.
You are wrong again. the assumption you are making is that the rate of mutations equals the rate of mutation is not correct. What you mean to say is that it is the odds of fixation compared to the few others in your sample. That’s an entirely different meaning.
What if you have 3 black M&M’s in your population, and then all three die, now what is the probability of a black M&M become fixed at that moment? The probability becomes zero. And then once you get another black mutation its not zero anymore. Furthermore, if you run your program like Olegt already has, you will see that if your start with population N, in a population of 1000 you need to have around 1,000,000 birth and death substitutions to get it to happen just once in a thousand times. What if you limited the birth and death substitutions to 2000? It never happens.
You have defined the fixation rate by insisting have ever long it takes, that is how many we allow. And you don’t allow new mutations, so its meaningless.
What happens if the lights fail and you can’t tell which M&Ms are black?? Huh?? HUH??
What happens if the sun goes supernova and all the black M&Ms melt?? Huh?? HUH??
Where’s that leave your so-called EVILution theory??
keiths,
Thanks for the link. Apparently, you’ve been down this road before a time or two.
Piltdown, you’ve named yourself after a common Creationist talking point (red flag #1). Your I just have doubts about certain aspects of evolutionary theory approach is, whether you realize it or not, an approach commonly used by Creationists (red flag #2). And your “doesn’t mean I’m making an argument for Creationism” statement here, which is clearly intended to give the impression that you’re not a Creationist while, at the same time, not actually being a, you know, direct denial of being a Creationist? That statement is, whether you know it or not, exactly and precisely the sort of slippery plausible-deniability verbiage commonly found in Creationists’ writings for public consumption (red flag #3).
It’s like this, Piltdown: From where I sit, you give every indication of being a Creationist who’s tryna hide their Creationism. Could I be wrong about that? Sure I could. But the fact that I could be wrong doesn’t mean that I am wrong, nor does it alter the unrelated fact that you do display a variety of different signs which indicate that you really are a Creationist. So you’ll just have to forgive me for thinking that someone who has gone out of their way to closely resemble a Creationist might, instead, be a non-Creationist who has innocently assembled, and chosen to wear, a highly detailed, highly realistic Creationist costume. And if you find that being mis-identified as a Creationist is a problem for you, perhaps you might want to take off your costume.
Just sayin’.
You think the eyeball of a human is just a bag of fluid? Even just the composition of that fluid is complicated. http://www.glaucoma.org/uploads/eye-anatomy-2012_650.gif
And this says nothing about eyelids, and tear ducts, and irises with pupils that regulate light, and the nerves needed to control them, and the color sensors, and on, and on…
And what kinds of random mutations have you ever heard of before which cause bags of fluid to exist appear in precise positions as a heritable feature in multicellular organisms? And then those mutations have to be bundled together and placed in a part of the DNA which would highly preserve and protect that particular massive configuration from continual change. Was that also a random mutation which put it in exactly the right part of the dna to preserve it and allow hox genes to completely control its expression at exactly the right time?
If you really think its just any old bag of fluid, I can see why people would think evolution is easy.
Sorry that you don’t have the scientific or mathematics chops to understand these discussions. You could correct that if you wanted to.
We get it. For whatever reason you personally don’t accept the evidence that has convinced 99.9% of all science professionals who have ever studied the subject. But if you can offer no other reasons for rejection save your personal incredulity you’re no better off than the flat-Earthers and the geocentrists.
Did you read that U. of Utah site on eye evolution and follow some of the links to the other evidence?
The fluid is being replaced over time, which is what keeps it clear.
The main point here is that the eye lens is far simpler than a typical camera lens.
Wow. I consider myself a skeptic, but you can label me as you please. There is a continuum between what I know as fact, what I believe to be true (or false) and what I believe might be true (or false).
Your original comment was only about the lens, and I replied to that.
In most respects, the eye is a lot simpler than a camera. The one part that is complex, is the neural system, which corrects for many of the deficiencies in the lens.
Piltdown2,
Indeed I have.
I consider it a public service. ID supporters are like those scattered Japanese soldiers who fought on for decades in the jungle, thinking that victory was still a possibility. Someone needs to let them know that the war is over, and that ID lost decisively and conclusively.
It is impossible to be an intellectually fulfilled IDer. The evidence simply doesn’t allow it.
I’m still interested in hearing your answers to my questions.