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.
To make the claim that the human eye is actually not that special of a mechanical device seems to me to be a stunningly weak argument to address the notion that random mutations could have formed all the parts the way they are.
Is there any camera made today that can focus faster than a human eye, as well as track movement with such precision? I don’t think so.
That would be your ignorance talking again. The fastest a human eye can focus is about 350msec for children which slows considerably when we get older. The Fujifilm X1000 camera can autofocus in 80 msec.
The human eye doesn’t track continuously but moves in jumps called saccades that move the eye anywhere from 1 to 20 degrees. Human built optical tracking devices move smoothly with an accuracy of +/-6 microradians.
These facts don’t have any meaning whatsoever for the veracity of evolutionary theory.
Indeed there are.
They are up in space in satellites, in the Hubble space telescope, on Mars, in surveillance systems, in the sensing systems used by the military, and they are used throughout industry.
There are high speed cameras that operate well over 40,000 frames per second, and they can track and focus faster than any living thing and can see in various parts of the electromagnetic spectrum where no human eye can respond.
I was involveed in the devlopment of some of these devices. Science and technology have come a long way.
phoodoo,
Oh dear, you are terribly confused. If you think there is something wrong with the math in my “3 mutations per individual per generation” example, point it out. But you will have to be a little bit more specific than just saying “the assumption you are making is that the rate of mutations equals the rate of mutation is not correct”, which is simply gobbledygook.
I will try writing slowly:
The number of new mutations that arise per generation is
{# mutations per individual per generation} X {population size}
e.g. 3 X 1,000 = 3,000
The number of mutations that become fixed in a generation is on average
{# of mutations per generation} X {1/population size}
e.g. 3,000 X 1 / 1,000 = 3
which equals {# mutations per individual per generation}
Or you could think about yet another way, if it helps (hope springs eternal):
The probability that a single member of the present population (we don’t know which one) becomes, at some future date, the ancestor to the entire population = 1. This is the (admittedly counter-intuitive) point of the OP. Which we encourage you to verify on your own.
In a population of N individuals, the probability that the future universal ancestor happens to be this particular individual (e.g. your black M&M) has to be 1/N.
Just by symmetry.
phoodoo, have you studied probabilities even a little bit? It seems like you are confused about the very basics of probability theory.
Your confusion boils down to this.
Take a fair coin and toss it twice. What is the probability that both tosses yield heads? The answer is 1/4.
What if the first coin came up tails? What is then the probability to get two heads after the second toss? Well, 0.
Are these two answers (1/4 and 0) mutually contradictory? If not, why not?
phoodoo,
It’s perfectly possible to stop a run at a particular point, but that’s not really what happens in nature, is it? Ignoring, of course, extinction.
As I have repeatedly noted (it has become my mantra!)
p(fixation) = current frequency.
Paste that inside your hat. So of course it changes with time. When current frequency drops to zero, then yes probability of fixation drops to zero. That is, effectively, extinction (extinction is the flipside of fixation, because frequencies, like probabilities, add up to 1 (or 100, if you’re using percentage).
So, I run my little Excel vba version (I offered you the code, but you didn’t seem interested). I tell it N (population size). I tell it how many times I want it to repeat the experiment. For that number of times, it does this: it generates a population of N members, and then to keep tabs on them, it gives them each a different number – its ordinal position in the array. Then on that population I just run the M&M model. I don’t do ANY mutation. Mutation is a red herring at this stage. The population starts off fully varied, with effectively, N different alleles, so all frequencies are the same – 1/N.
None of these runs goes on for ever. They take a varying number of times, but every single one results in fixation of a single ‘ancestor’. That iteration stops when that happens, and I’m not still waiting for any previous runs to finish (nor do I cheat and kill them if they take too long!). If you haven’t weighted things in any way, it makes perfect sense that each ordinal position label ends up being represented, on average, as many times as every other as the last one standing. ie, the probability from any starting population is 1/N for every member. How could it be anything else? Given that fixation is inevitable, and the alleles are not involved in their selection, the chance to be the-one-to-be-fixed must be equally distributed amongst the members.
Mutation comes in when you start to think of what each member might represent. None of these need be mutants. They could all be the same colour. The run end simply represents fixation of one ancestor, not its class (that fixation may have already happened). But if that ancestor is a mutant, it has the same probability as if it isn’t. If my process randomly chose one of the N to be the mutant – “you’re ‘it'”! – it would fix with the same probability as if my process didn’t make such a distinction.
Olegt, have you studied the English language? How about critical thinking?
Your confusion boils down to this:
Two fish are swimming in a pond.
One guy is fishing in a completely different pond .
Is a motorcycle fast or slow?
This is how confused and irrelevant your post is.
You are suffering from the same problem as Olegt and DNA Jocks:
Your numbers are not correctly attached to the concepts being discussed, so all meaning is lost. Discussing whether or not some mutation will become fixed into a population is not the same as discussing whether or not ONE PARTICULAR mutation has enough time and opportunity for this to happen.
In your program, if you start with one black M&M in a population of 1000, of the 1 time in 1000 chances that the black becomes fixated, how many generations were required?
(please don’t answer this Olegt, you already tried, and your answer is logically impossible).
phoodoo,
Well, I don’t know phoodoo. I’m pretty bad at math and have had almost no training in statistics but I find Oleg’s point pretty simple to grasp. If you make a prediction based on a series of events, you can get a probability of the whole series by multiplying the probability of each link in the series. The chance of a head or a tail is .5 so the chance of a head followed by another head is .5 x .5 = .25. But, knowing that the first event was a tail, there is absolute certainty it wasn’t a head (probability 0). Anything multiplied by zero is zero et voilà
Did you think about leading by example on the invective content?
Citation please, for how fast a human eye can focus?
Sorry, as I do not follow this, could you explain what the difference is. The general case is some arbitrary non-lethal mutation. When one goes from the general to the particular non-lethal mutation, what changes (apart from the allele)?
phoodoo,
“What really matters is that no camera has yet exceeded the capabilities of the human eye with respect to focusing speed, color range, depth of field or it’s ability to see wide ranges of light levels. In photography, this matters because your camera will not be able to see things the same way your eye does. Your camera is always hiding something – just like a shifty con-artist.”
http://www.shutterphoto.net/article/the-cameras-not-as-good-as-the-human-eye/
Evolution isn’t searching for “ONE PARTICULAR” mutation.
I am curious Allan, why haven’t you used even a minimum of your time trying to tell those whose positions you apparently agree with to control their comments, instead of reminding me? Why do I need to lead by example? I am following by example.
Secondly, the heads tails problem has nothing whatsoever to do with the discussion of whether or not it is likely for a novel mutation to fixate in a population. There is not much other way of stating it other than you are talking about two completely different concepts.
They’re workin’ on it
Well, Rumraket just gave a perfect example of why their logic is flawed.
If the question was whether or not ANY mutation (we don’t care which one, as long as at least one does it) will fixate through a population, instead of will a particular mutation do that, then of course you are talking about two completely different things.
That they can’t see this distinction, tells me they lack the proper reasoning skill to address the problem.
In a population of 1 million people, the odds that someone might win the lottery are not so bad. The odds that YOU will win the lottery however are very very low.
Because I’m a very unenthusiastic censor. I was hoping that commenters would pick up on my hints. Addressing a remark to you does not make it only visible to you.
Well, of course. Analogies can be taken too literally as Dawkins’ weasel illustration amply demonstrated. As I said, I am no mathematician.
I agree.
Thus I feel anyone arguing that actually the humans eye is not so remarkable, is probably willing to deny just about any reality in front of them, which might cause their worldview into question.
I see we agree on the question. What I do not see is your response to my wondering what the difference is. A general case is just that. If there are examples that render the general case shot through with exceptions, then a better model is needed. Is your problem that we can’t talk in general terms about alleles, for example talking generally about a beneficial, neutral or deleterious allele?
ETA exceptions changed to examples
It’s not an assumption. It’s a derivation and it has been confirmed by simulation.
The simulation results have been presented here. For the derivation see, e.g. Lecture 16 : Fixation of a neutral mutation and Fixation of New Mutations in Small Populations. There are lots of other resources that you can easily locate if you are interested.
I doubt anyone is arguing that the human eye and it’s associated neural structures and it’s evolutionary origins and development (the eye can be regarded developmentally as a part of the brain) are not remarkable, fascinating, only partly understood. There is no reason to assume that further study will not lead to further insights. ID explanations are absent in the visual field. 😉
Alan Fox,
Yes, well, one problem I see is that often people who are mathematicians or in the field of chemistry or biology are so accustomed to looking at the world within their narrow focus of specialty, that they struggle with assimilating those ideas into broader picture concepts.
It is often said about many mathematical theorists, they have no idea what their numbers actually mean. Its not just a joke. The stereotype of them not even knowing how to dress themselves is not a stereotype for no reason.
I have many friends who work in the bio-technical industry and have PHD’s in biology. They have told me on numerous occasions in casual conversation that they have no idea what is really happening in biology, because no one person studies all aspects, they each just concentrate on knowing about one particular part that pertains to the work they need to do. That is by no means an isolated assessment.
http://en.wikipedia.org/wiki/Accommodation_(eye)
And see Dynamics of Accommodation Responses of The Human Eye, Table 1 on the fifth page.
I continue to be fascinated by the common creationists preference for making stuff up rather than finding things out, and the tenacity with which they defend what they’ve made up as if anything they make up automatically becomes established fact.
(HTML tables not allowed but LaTex is? Boo!)
Scientific references, please.
JonF,
” Approximately 1/68 or .015th of a second.”
http://wiki.answers.com/Q/How_fast_does_human_eye_refocus?r2as=1#slide=2
Yes, and in evolution every individual is a carrier of mutations, as in everyone is a player in the lottery. Someone will win that lottery.
New mutations are constantly arising, in every individual in every generation. Every one of these, if they’re not lethal or strongly deleterious, will start drifing through subsequent generations. Many will be lost, some few will be fixed. But mutations are constantly fixed through drift, because mutations constantly arise through this ongoing process of reproduction. So in almost every generation, some allele which has been drifting through countless generations in the past, is becoming fixed. This process just keeps going as long as mutations arise and the population doesn’t go extinct.
JonF,
“Fujifilm claims that the camera can focus in 0.08 seconds thanks to its new EXR Processor II and its new X-Trans II sensor (which is equipped with new phase detection pixels). That figure seems to be accurate.”
http://petapixel.com/2013/01/10/the-blazing-fast-autofocus-speed-of-the-new-fujifilm-x100s/
The problem here is that you posed your question about the eye, rather than about the visual system as a whole. The eye itself is not particularly remarkable, other than to remark on its relative simplicity in comparison with our cameras.
Again, scientific references please. Especially not anonymous claims with no reference or evidence. For example, the paper I linked to is a scientific reference. Did you look at it?
Unverified and unreferenced one-line response someone posted on Wiki answers noted.
But if it’s on the Internet it must be true, right?
It’s a mystery why phoodoo is on about human eye performance. We can build machines that can mechanically outperform humans in virtually every area – strength, speed, range, etc. Does anyone see his argument besides “gee, it’s complicated so EVILution could not have done it”?
Yes, I already referred to that in a post which I requested be deleted because another poster had provided the same information. I have presented scientific evidence that this is much faster than the human eye can do (note that the camera focuses starting from a no-focus condition so small changes in human eye focus are not relevant; the best we can do is to compare infinity-to-close or the reverse in human eyes).
You have posted three unsupported opinions. Let’s see some actual measurements. Oh, wait, I already supplied those and you have no rebuttal other than anonymous unsupported opinion!
You’d have look at specifics, but convergence has been part of the theory of evolution since Darwin. It’s a result of natural selection.
It would limit possible Design mechanisms, including the canonical view of Biblical ex nihilo creation of kinds.
PhooDoo wrote:
And we have been pointing out to you ad nauseam that p(a single individual will become the universal ancestor) = 1, and p(THIS PARTICULAR individual will become the universal ancestor) = 1 / N
Well, my program was a little different, in that a culled M&M was replaced by duplicating a randomly selected member of the *offspring* already produced for that generation, which makes the frequencies unstable. I think it’s an interesting model of stochastic reproduction.
I saw fixation of the lone black M&M in 55, 59, and 87 generations (pop size N=1,000).
Just to make you happy, I modified my vba to duplicate a randomly selected member of the parental generation, but I did not prevent the vba from duplicating a culled member (which would be a ‘shuffle’): fixation of the lone black M&M took 897, 1214, 1764, 2591, 2592, and 2616 generations
“But it takes millions of births and deaths to fix a single mutation” you cry. But you are conveniently ignoring the presence – in a real world scenario – of all the other mutations that are drifting to fixation over the same time period.
I suspect that you have not wrapped your brain around the second counter-intuitive result: at steady-state, it does not matter how long it takes for an individual mutation to fix:
If it takes ten years for an individual mutation to fix, then the population contains, on average, ten years worth of mutations that are destined to fix.
If, OTOH, it takes a thousand years for a mutation to fix, then the population contains a thousand years’ worth of mutations steadily plodding along on their way to fixation (and a few years’ worth of mutations destined for extinction)
In either case, the number that achieve fixation in one generation is on average the same as the number generated (per individual per generation).
Please go step by step through the example calculation I offered here, and be very very specific about what you think is wrong. Waffling about specialization amongst biotech PhD’s hardly seems on point.
[next up: genetic entropy]
DNA_Jock,
WTF? You are now saying that your program does something COMPLETELY DIFFERENT than the stated proposal at the very beginning of the thread, and you are saying I am wrong? In other words you have adjusted the program to make sure that a mutation gets fixed in as short a time as possible?
Why have you changed it from the program that olget has been arguing for this whole time? Better yet, why are you involved in this discussion at all, if you are making some entirely different argument that you haven’t even said what it is.
I don’t know what your program does, and I don’t even particularly care what your program does, but its fairly certain that if you claim a new mutation becomes fixed in an entire population of 1000 individuals in 59 generations, it most definitely does not mirror reality.
phoodoo,
You may like to have a look at OMagain’s program here. It does seem to confirm Allan Miller’s M&M claim. Ramp the simulation up to top speed for the best viewing experience.
Features are not gene sequences. It’s the sequences that form the nested hierarchy.
A million of births and deaths in a population of one thousand is a thousand generations. Not a million as phoodoo stubbornly, and incorrectly, claims.
59 generations to fixation is way too soon, indeed. But DNA Jock explained that his code was doing something unorthodox. When he went back to the original model, things went back to normal:
That’s precisely what one expects in a population of 1000.
4 does not equal 1.
Now I’m a bit confused. I can see that in a stable population each individual would effectively leave one offspring, on average. Otherwise the population size would rise or fall.
But in real populations, the number of births per individual is higher than the replacement rate, and the death rate compensates. So I assume you are speaking of some kind of effective birth and death.
Programs are meaningless if it is not stated what is being represented, and what the logic is behind what it is representing. So far we can’t seem to get past what they are even calling a generation. Thus we are getting wildly contradictory claims.
We are discussing an equilibrium situation, in which the population size stays fixed.The number of deaths and the number of births are equal over time. Some individuals have several offspring, others die before they get a chance to produce a single offspring.
Everyone except you, phoodoo, is in agreement on what we mean by a generation. Even though my recipe differs from Joe’s, the two agree in the limit where N is large compared to 1.
So far (amazingly) you have given zero rationale for your claim of what a generation is. You have arbitrarily said it is equal to your number, for no reason whatsoever other than you claim its your formula. Saying that everyone agrees with you (they do?) is a crazy appeal to authority which makes no sense.
I have explained it several times, phoodoo. You simply can’t seem to grasp it. I will try again below, but before I do that, I will note that you seemed to find Joe Felsenstein’s definition reasonable. Curiously, his definition and mine give essentially the same results when population size is large compared to 1. That ought to be enough for you even if you do not understand my reasoning.
Another leading candidate for understatement of the year.
So, once again, what’s my rationale for defining a generation in the problem with N M&Ms as the number of deaths divided by N?
Let’s put our M&Ms on the squares of a chessboard. Half are on white squares and half on black.
We start at t = 0.
At t = 15 seconds, we remove the M&Ms residing on white squares.
At t = 30 seconds, the M&Ms on black squares give birth to one child each and place them on an adjacent white squares.
At t = 45 seconds, we remove the M&Ms residing on black squares.
At t = 1 minute, the M&Ms on white squares give birth to one child each and place them on an adjacent black squares.
We have replaced all M&Ms. Thus 1 minute can be reasonably counted as 1 generation.
How many deaths have happened during that time? N/2 in the first half of the minute and N/2 in the second half. For a total of N deaths. Thus we conclude that 1 generation = N deaths (and N births).
Is this clear, phoodoo?
No, phoodoo. I mentioned, as an aside, a variant of the ‘M&M problem’ that I had modeled. I then edited my model to conform to the parameters under discussion. Did you not understand that bit?
The ‘variant’ does that. In the ‘standard’ version fixation of the lone black M&M took 897, 1214, 1764, 2591, 2592, and 2616 generations.
I note your abject failure to address the substance of my post; you appear unable to discuss mathematics at all.
You hit me with several, but I’ll comment on this one (mainly because I like how you aren’t asking which is true):
Of these two possibilities, I would go with B – at least it adds another element to the equation! As I’ve stated, I think there will be changes to the accepted evolutionary theory. Here’s a good book review by Adam Wilkins of James Shapiro’s Evolution: A View from the 21st Century (http://gbe.oxfordjournals.org/content/4/4/423.full). Although Wilkins disagrees with several of Shapiro’s ideas, he goes on to state, “Let me end on a positive note. Jim Shapiro has made a well-documented case against the sufficiency of random mutations (arising irrespective of potential need) as the source material for genetic variation and has discussed a wide variety of mechanisms by means of which, in some degree, genetic change is evoked in direct response to environmental challenge.” After seeing Allan’s genetic drift argument and reading a couple of your posts and the 29+ page, this is the direction of my own thoughts. There can be natural explanations for non-random variations driven by environmental pressures. This would greatly increase the odds of beneficial mutations being fixed in the genome. And could help explain why macroevolution mimics a designer.
I sure wished my eyes focused that fast. My eye tissues are a lot stiffer than they used to be, and a lot more distorted. Thus, my dependence on technology for clear sight.