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.
I am a mathematical biologist, not a mathematician. I have written books full of equations, and I hope they are correct equations. I teach courses in theoretical population genetics and in phylogenetic inference to graduate students, and I hope I teach them correctly. And I’ve been doing this for about 50 years.
I don’t see the point of your retort. I was pointing out that your position was one that would also conclude that humans have a generation time of one week. (And in the next town, where the population is 10x larger, humans have a generation time of less than 9 hours). Olegt, a skilled and knowledgable mathematical physicist, agrees that yes, this is what you are saying.
You have, in effect simply redefined “generation time” to be what you want it to be. You are free to do that, but no one else agrees with you. And therefore we are free to ignore your redefinition, especially since it leads to silliness as shown by the human generation time example. Can you point us to anyone in the scientific literature who agrees with your definition?
Piltdown2,
My meaning was clear:
Piltdown2:
The only kind of common descent that explains the objective nested hierarchy is unguided common descent — unless the guiding intelligence is mimicking unguided evolution. This is explained in my OP and the ensuing comment thread.
keiths:
Piltdown2:
In my OP, I explained what’s wrong with that sort of hypothesis:
I am going to assume that you were completely sober when you wrote this, although feel free to correct me.
When did a unit of time ever get included in this discussion? You realize we are talking about a bag of M&M’s correct. People aren’t actually getting pregnant in this model. No one is buying maternity clothes or needing to get c sections, you got that right? The M&M’s aren’t the size of Jennifer Lopez, you understand that right?
If you think these M&M’s are actually people, then why do you think its ok, to leave open the possibility in your “people” model that a great great great great grand daughter exists in the same time frame as a grandmother from 5 generations back?
You have redefined generation times by giving them some imaginary clock. And your appeal to ‘the majority rules, is just the worst argument possible.
You haven’t even attempted how you defend a notion that you can select one new offspring, and in the same “generation, allow that offspring to have a baby, and then in that same generation allow its offspring to have an offspring.
And you are complaining that my definition is illogical? Yea right teach.
Honestly, phoodoo, you do not understand mathematical modeling.
It is entirely normal practice to make some simplifying assumptions when modeling.
In real life, death can be described as random. And in the model it is also random.
In real life, the probability of death increases with age. In the model, the probability of death remains constant. That’s a simplifying assumption, but it doesn’t seriously affect the usefulness of the result.
In real life, new mutations occur. In the model, there are no new mutations. That was a deliberate change to see how the population would change without new mutations.
The model is not used to predict what will happen in real life. It is used to explore the processes involved, and aid our understanding. Personally, I found it very informative, though your disagreement about generations was a distraction.
If the piano ain’t blue, you can’t play the blues.
I find it interesting that IDists like to abstract life to information, until you start demonstrating the consequences of that abstraction.
phoodoo,
Time is not explicit, but is contained within the fact that we are taking a succession of population states. Any population is a collection of members alive at the same moment in time. If you take a start population and assign them as ‘generation zero’, then taking a future population, each individual will have a specific number of generations connecting it to the individual from gen 0 from whom they descend – 1 for a parent, 2 for a grandparent etc. They won’t all be the same, in a non-overlapping population – there will be a distribution of values. The metric for the entire population will be the mean of this distribution, and the mean generation length will be the total time elapsed divided by the mean generation count. We don’t record these variables in the models (because they are irrelevant), but we could.
If you count a generation as one birth/death, you end up with a mean generation length (the average time between being born and becoming a parent) substantially shorter than the actual time it takes, and largely dependent upon population size – a sure sign that you are barking up the wrong tree.
So then you agree with me, that Joe is off his rocker with his complaint that humans can’t reproduce in 9 hours?
So a better model is one in which we can have overlaps of ten, twenty, thirty, 100 generations all existing in the same time?
And you are worried about my tree?
No. You are somehow confused about the model, which results in your misunderstanding what’s a generation in the model.
I am not confused in the slightest Nick. You can’t do a population model which allows for the newest addition to the population, to be the next one to sire offspring, while all the others in the populations remains stagnant. And furthermore also call it the same generation!. Its a nonsense concept.
phoodoo,
The better model is the one that best approaches the actual number of nodes in descent for an individual.
There will be a distribution. Just as there is in a real population. Precisely because actual generation lengths vary from the mean, different descendants of your great-great-great-grandfather, all alive today, can be separated by 4, 5 ,6, 7, 8 generations, while you yourself are separated by precisely 6.
Your intuition concentrates on populations with huge variances. They will not constitute the majority of permutations. In practice (and I’ve checked this) the variance is not that great, even with the unnatural persistence and fecundity of the elderly in my model. By actually keeping track of all generations in all lineages, by each offspring inheriting its generation count from a parent + 1, here is a typical result:
Population of 1500 after fixation of new mutation:
Births/deaths: 1693584
Generations by approximation (births/deaths divided by N): 1129
Mean generations by counting: 1160
Minimum count: 1112
Maximum count: 1199
It’s a common feature of your thinking to regard the extreme case as the norm. The more trials performed, the less probable, and the less significant, extremes become. It’s the centre that matters most.
Prof Felsenstein was pointing out the absurdity of your interpretation of the model and how generation is counted. Take the computer sim written by OM. Have you tried it. If you leave the speed at 1 and a small bag size (150) and small number of colours (10) you can easily see how the number of trials relates to the parameter “generations”. Its’s just n° of trials divided by bag size. Try then changing the bag size to 300.
If you want to talk about evolutionary theory in general and wish to claim there is not enough time for evolutionary processes to account for life’s current diversity then why not make it explicit. Attempting to debunk a computer program will not affect the validity of evolutionary theory.
Your definition of a generation is completely fabricated and arbitrary, so your premises from your fabricated numbers hold no meaning. You seem to think one has to except your formula for a generation, simply because you say this is what it is. Your logic is totally circular because you made up how long a generation is, and then say it has to be this because this is what a generation is.
And I was pointing out the absurdity of his. Did you miss that?
Again, you wish to make up what a generation will be, and then say this is what a generation is because we just defined it as this.
If you wish to just makeup a formula to show the feasibility of neutral drift causing loads of fixed traits, then why not make it explicit.
Your hand waving is tedious.
phoodoo,
My definition of a generation is entirely in accord with common usage. Your children are your generation +1; their children are your generation + 2, and so on till your line becomes extinct. I didn’t make up that definition.
My definition is the only one that makes sense of a statement such as “the human generation time is about 20 years”. Circular? It isn’t circular to define a generation as the time between two comparable points in a life cycle between parent and offspring. That’s simply a definition. But having defined it so, it follows that n generations take an average of n * genlength to elapse. You don’t have to ‘except’ my definition, but I don’t see what use yours is. If your generation does not relate to time, why are you so attached to it?
Look at a single individual and trace its lineage. This one here is from the original bag, count that as zero generations. This one has a mother, a mother who was from the original bag, so count that as one generation. This one has a mother, a mother who had a mother who was from the original bag, so count that as two generations.
Now, let’s look at the same situation where we have a hundred M&Ms, each of which are second generation. That means there have been two hundred replications, two in each lineage. We don’t count a hundred grandchildren as two hundred generations, but just two generations.
In your model there is no life cycle, Why is that so hard for you to grasp?
In your model, anyone in the population can begin reproducing from the second they are into the population, until the second they are dead. They can reproduce as many times as they want, and they can exist in as many generations as you please. There is zero limits to their allowance for breeding.
I saw his comment and took it to be a reductio ad absurdam of your method of calculating generation interval.
With regard to which situation? I see no problem so long as “generation” as it applies in whichever sim is defined and how it is calculated is made clear. It’s clear for OM’s sim.
I told you what I think is a reasonable way to calculate generation time in human beings. Do you think there is something wrong or misleading about such a calculation?
I’m not a mathematician or a computer programmer so I defer to the experts here on those points pertaining to those subjects. In entering the discussion I was actually trying to make sure I was clear what was going on in OM’s sim to myself.
I haven’t been altogether convinced about the effect of drift and how it works but the recent threads on the subject have helped. I’m clearer on the concept now but far from being able to formulate it. I’m going to try reading Kimura’s seminal paper on drift.
ETA “but the recent threads on the subject have helped”
ETA delete superfluous “on”
Mine doesn’t count two hundred grandchildren as 200 generations, you are confused.
If the population is 200, then its 200 grandchildren in one generation. If the population is 10, then its ten children in one generation, with one of the ten receiving a potential new allele. A perfectly reasonable average to work with.
Why is this simple explanation not now blindingly obvious?
@ phoodoo
Do you disagree with what Zachriel writes in the comment I have reproduced?
ETA cross post
The three dumbest parts of Joe’s complaint, if I have to choose just three:
1. He says that my definition of a generation includes the premise that a generation is one week, or in a larger population 9 hours.
This is laughable as there has never been a clock put on any generating, and there is zero logic for assigning an clock time whatsoever.
2.He fails to realize that EVEN IF THERE WAS A CLOCK ASSIGNED TO THE GENERATION TIMES , which there clearly is not, he somehow thinks these M&M’s must have 9 month gestations, as if they couldn’t possibly represent bats or tadpoles, or flies, or bacteria. He actually thinks the M&M’s are human beings. I am curious to know what country he thinks the M&M’s are from? Can they be Denisovans? How about chimpanzees? Did he use an atomic clock, or a solar one? Does his time take into account the gravity of the earth, and Einstein relativity?
3. He tries to claim he must be correct, because everyone here on Lizzies skeptical science blog agrees with him, and he is a teacher, so there! Plus Olegt is a talented physicist, so he gets even more points!
Very poor debate form Joe.
So just to be crystal clear, is phoodoo explicitly agreeing with Zachriel when he states:
I admire the patience of you guys but sometimes it’s a losing battle. There are Creationists out there who absolutely refuse to deal with any reality that threatens their religious beliefs. You can’t reason them out of their denial because they weren’t reasoned into it in the first place.
We saw it in the two week battle to explain that ‘random’ and ‘fair’ aren’t synonyms but that ‘fair’ is a particular subset of ‘random’. We see it now in this equally silly battle over the definition of ‘generation’.
To paraphrase the great Yogi Berra: “if people don’t want to understand how are you going to stop them?” 🙂
Of course I don’t agree, because he is completely wrong. He apparently understands the premise of choosing any M&M, no matter how many ancestors exist inside the bag, as poorly as you understand this problem. Under Olegts, and Joes model, there are not only two generations in the bag, there are as many as there are M&M’s in the bag. So you could have 10, 20, 100, 1000 descendants, all in the bag at the same time. And any of one of them can be selected for replication at any time. They could have existed inside the bag from the beginning of time, and they still can be chosen to replicate again.or they could have just replicated, and then do it again immediately.
A patently ridiculous preposition on so many fronts.
In your model, even using the word generation is unsustainable, because in normal language the term generation means one link in a line of ancestry. but in your models definition, you actually means, it is the M&M’s which stick around inside the bag, until you have chosen an exact number which matches the population size. In other words a completely arbitrary definition of a generation, so when you even use the word generation, do you mean the classical term, or the made up definition, you created?
You are switching back and forth between two meanings. Only one of which is real.
That’s rich!
I’m trying to get you to clarify whether you are discussing a particular model or a particular real organism. I have made clear what generation interval is and how it is calculated for human beings. Here’s a paper that goes into detail on generation interval.
Regarding Zachriel’s exposition. I’m sure it is factually correct.
Do you disagree that it is factually correct?
Do you agree that is factually correct and just disagree with the method used.?
NB in the first paragraph I am referring to human generation interval in the real world. In the second, OM’s sim. Hope that’s clear..
OK
So from this I can assume you are not disputing the facts just the methodology. You understand that “generation” is defined and calculated for the program. You just prefer OM used a different word to describe “bag size divided by draws”.
No, it isn’t. it’s a summary statistic. A measure of central tendency.
Not arbitrary at all. Highly constrained, in fact.
LOL. This is from a guy who can’t decide whether a generation = 1 death or N deaths.
Its neither in this model. Its replacing the entire original population with a completely new one, one time.
And how many deaths is that?
There are no facts to dispute or not dispute Alan. Bag size divided by draws does not equal a generation, just because you all claim it does. A generation has a real meaning. It is a link in the ancestry of a lineage.
Bag size divided by the draws has no meaning which is applicable to populations, It is a made up component of the model, which means it no longer analogous to the real world.
It’s the other way around, phoodoo.
Slow down, dude. 🙂
Generations is not defined by the number of deaths.
You slow down dude, Alan is the one who just suggested that phrase.
I am not saying it is. 🙂
Now that you have given a new definition of what one generation is, make the next step and tell us how many deaths that would entail. I can tell that it is clearly not 1 and furthermore is not less than N.
I think that’s clear now. You understand how the sim works. You don’t think the methodology is analogous to how the concept of random drift allows mutations to spread through (markedly in small) populations of organisms in the real world.
How many minutes is it?
There is no new definition, it has been the same all along. I honestly don;t know why you can’t get that when I have said it one hundred times.
Yes, my bad, sorry!
“Generation (Trial/Bag Size)” from the sim.
My error, Oleg. Slip of the keypad that got copied. Apologies.
ETA to correct citation
Oh, no. You have defined one generation in three different ways.
Definition 1:
Then you switched to N deaths = one generation.
Now it’s an entirely new definition.
phoodoo,
There is. The generational cycle is effectively the individual coming to exist through to it siring a new … ummm … generation. It carries on ‘living’, of course. Just as we do.
So what? Every offspring they produce is 1 generation on from them.
Do you propose we have a different definition of ‘generation’ for every model, or every population? Keeping a common one seems eminently sensible to me.
How ’bout photocopies? Would you understand the concept of a 1st-generation copy, a 2nd-generation copy etc? Or can photocopies not have generations because they don’t have a life cycle (because, presumably, they are not alive)? Say you take a sheaf of blank papers and write “0” on each. Then you start photocopying, shuffling and discarding (an exact replicate of the M&M model). Each time you copy, add 1 to the copied number and write it on the sheet where the old number was. After several rounds of this, you will have a census of mixed photocopying generations with a variance and a mean. And you will have the exact number of generations separating each member of your descendant population from its first ancestor.
And this is why their model is not logical Alan. In their model there doesn’t exist one generation, every M&M is part of a different generation, So one M&M has ten descendants (links in the chain) in the population, another has four, another none, and another 7. But they are all existing in one snippet of time. Its like counting a population which includes George Washington along with 7 generations of his descendants, and also Jesse Owens, Ghenghis Kan and one of his grandkids and two of his great grandkids, plus Jesus Christ and Brad Pitt, and Angelina Jolie. That’s one test sample.
My model are all from the same generation.
OK
So in OM’s sim it is possible (indeed certain) that individual M&Ms will stay in the bag for shorter or longer periods than the norm of turnover. You would like individuals all to have the same generation time. Why is that more analogous to the real world? It doesn’t happen with humans but we can just take sample and average the results to give a mean generation interval of around 25 – 30 years depending on what groups we sample.
No Allan, in your model, if we began the experiment with a full bag of M&M’s existing at time zero, and then began doing your shuffling as described, with out calling it a new generation each time, what we end up with is M&M’s who now all are from completely different time zones. Some get changed to six generations later, some to four, some to none, and if its a large bag, some can go to 100 generations later-but when we look at the gene distribution, we are counting it as ONE snip of time, even though they have all changed.
The time doesn’t change equally for all the M&M’s because we can’t reset our clock for each new draw. Now they are Jesus Christ and Brad Pitt and George Washington all living together.
It roughly happens with humans, but it actually does happen with some species. How about salmon? Groups are all from the same generation.
And in fact, we do assume that a similar thing happens with humans. If we trace your ancestry back 100 generations, it would come out to roughly the same time as if you trace my ancestry back 100 generations. Not so in their model. Their times are totally scrambled, depending on when and how often any M&M is drawn.
The two counts can easily be off by 10 generations or so. I have a cousin the same age as me.
And the further back you go, the more generations will disperse.
I think “phoodoo” is just pulling your legs, but let’s be generous and assume not.
It seems that (s)he feels that the Moran model is not such a great model because it doesn’t have an intuitively obvious generation time. Fine – let’s use the Wright-Fisher model instead. All N adult haploid members of the population reproduce asexually at the same time, immediately after which they all die at the same time, leaving N surviving offspring that become the adults of the next generation, and the cycle starts again. It’s pretty clear what a generation is for this model, I hope. And for this model it takes on average approximately 2N generations for a single mutation to become fixed by drift. You with me, “phoodoo”?
Oh, let’s not go there, IdoP. Phoodoo can’t make heads or tails of the Moran model. Throwing in a new model will only confuse the poor thing even more.
Yes, its much closer to reality. And why do you think the Wright Fisher model does it that way anyway? ,Because I am crazy and I don’t know what I am talking about, but now see once we can give it a name, like say Wright Fisher, well, now its a valid point about generation times, so now we can believe its true! It has a name afterall!
Of course I don’t know more about the specifics of what is and not allowed in their model, nor do I care too much,so I can’t comment about how close this is to real drift, but clearly Joe’s claim of well, everyone agrees with me, so I am right, is BS.