Talk:Genetic drift/Archive 4

1. Need to point out Anglo-American feud (Sewall Wright v Ronald Fisher and E.B. Ford)over the relative merits of selection and drift. See scarlet tiger moths for link to Fisher Ford 1950 paper. This probably needs its own page. I think that drift is relatively unimportant at levels that matter, though it is important at the molecular level. Simulations show this. Wright had some awfully wacky ideas about the goodness of molecules, when selfish genes are the real cause.

2. Need some maths.

probablity of fixation over an infinite time equals allele frequency. Time to fixation... I'm not sure the introduction is expressed as well as it could be either.

Idea of drift can be used by picking cubes out of a bag. Pick two cubes at a time, for loci. and adjust allele frequency.

(references Wright 1931/8) or is that F-statistics? Duncharris 11:36, May 3, 2004 (UTC)

3. Nonsense

"But the average is never tallied, because each generation parents the next one only once. Therefore the frequency of an allele among the offspring often differs from its frequency in the parent generation."

This is nonsense. Everyone knows birds are not raised by their grandparents. And what does this have to do with allele frequency anyway?

omg this is cool...writing on this :] —Preceding unsigned comment added by 76.94.30.1 (talk) 23:33, 9 April 2008 (UTC)

There needs to be a simplified explanation for what genetic drift is, in addition to the specifics given in this topic. It appears that genetic drift occurs through neutral mutations that aren't selected against (or for)? I wouldn't know, because the article starts with what genetic drift does, "change the characteristics of species over time," but never explains what is actual is. Then the article explains how the process happens... but again you don't explain what the process is. What is it? I feel that the answer is probably in the article but contained within the more complicated sections. This sections shouldn't be removed by a more simple explanation should be included in the introductory section.

What do you think of the expanded version I just put in? --FOo 00:57, 6 September 2005 (UTC)

I think this does well to clarify the topic for those not already familiar with the process. thanks.

I tried to clarify the intro a bit. —Preceding unsigned comment added by 24.19.21.53 (talk) 06:29, 20 September 2008 (UTC)

There needs to be a simple example in this article. I don't think anything too elaborate is necessary—no charts or graphs—but perhaps someone could write a narrative example based on a particular named animal and some non-vital traits it has which have varied with genetic drift. —Psychonaut 16:40, 9 September 2005 (UTC)

I agree. Two or three examples would really help. Maybe one in humans and a couple from other species. Is hair color in humans an example of genetic drift? -Jeff Worthington 00:12, 24 October 2006 (UTC)

I read this article and did not understand it. Which was frustrating as I would rather have liked to. It needs a simplified explaination and some examples (please). —Preceding unsigned comment added by 81.157.149.12 (talk) 15:26, 22 December 2007 (UTC)

The marbles example has got to go. I don't want to simply remove it and be thought a vandal, but it does more harm than good. It's vaguely worded, and difficult to visualize, so it lends very little to understanding genetic drift. It has to go, but it should be replaced with better examples. ( The last section, evolution of mal-adaptive traits, is a start. )

We need some concrete, historical examples. The Amish show the founder effect and how it contributes to drift-driven [micro]evolution. Elephant seals show an extreme population bottleneck ... as must Mitochondrial Eve and Y-Chromosomal Adam. And so on; hopefully somebody can research less-extreme examples.

But we also need fictional examples, to make the causal chain more clear. This is what the marbles example tries to do. An earthquake and accompanying fires destroy most redwood trees, leaving by chance only those in the north and a few scattered in Big Sur. The remaining population has lost much diversity, and is Balkanized into many small, isolated populations. A mutated gene takes hold "quickly," after a single generation. A larger-population founder effect after a glacier recedes, allowing plant life to fill the void, spread by a small number of individuals from larger populations. Decimation after an oil spill.

I might rewrite this into the main article, if no one objects. I might not find the time, though. —Preceding unsigned comment added by 24.19.21.53 (talk) 05:51, 20 September 2008 (UTC)

Ok, insomnia strikes, so I went ahead and described four examples in hypothetical terms, pointing to historical examples in human and other history. I also removed the confusing marble analogy. And made some improvements to the page's introduction. —Preceding unsigned comment added by 24.19.21.53 (talk) 07:17, 20 September 2008 (UTC)

Suggesting mutation rate be merged with this. I am not a genetics expert though and if such a merge is based on flawed logic, say so. It appears that this article has no links to "mutation rate" and that article has no links to here, so probably they were written in isolation. To me they seem like the same thing except that genetic drift is like a "rate of mutation rate". Anyway, the concepts are so closely related it should be all in one article I think. What do you think? Donama 06:10, 7 June 2006 (UTC)

Oppose. They are only remotely related topics and books have been written on both subjects. Both are big enough to not only warrant their own page, but eventually to be split into subpages. --Aranae 07:08, 7 June 2006 (UTC)

Oppose. You misunderstand. Genetic drift is a change in allele frequency. Genetic drift happens AFTER a mutation. They are completely separate and different processes - in fact, they are two of the four microevolutionary forces, where the other ones are selection and migration (aka gene flow). This alone should justify them having separate articles. - Samsara (talk • contribs) 11:26, 7 June 2006 (UTC)

Oppose. They are not the same. The effects are quite different, as well. The reason you don't see mutation mentioned in drift is that the process is generally quite fast, and there are few individuals in the population, so the chance of mutation occurring is very small. There are possible candidates for merge, but this isn't one of them.Ted 13:55, 7 June 2006 (UTC)

Oppose - as Samsara said, they are quite different things. Guettarda 13:57, 7 June 2006 (UTC)

Oppose - Not the same thing. -PhDP 21:05, 7 June 2006 (UTC)

Ok, we'll leave it then. — Donama 22:08, 8 June 2006 (UTC)

I'm a college graduate, and the intro is two technical. I would think that genetic drift could be explained without words like "Allele" and "stochastic". The rest of the article can be technical, but the introduction needs to be mostly free of science words.

Meaning no offense, being a college graduate is irrelevant here. Allele and gene are pretty central. Not using either of these terms would be very much like trying to write an article on computers without mentioning software. Stochastic may be an unfamiliar word, but it's not technical, at least not in the sense of genetics. This could be replaced with random or some other word ... but without understanding at least the basics of alleles and chromosomes, it's not possible to have more than a very shallow understanding of genetic drift. That said, perhaps this needs to be explained here? —Preceding unsigned comment added by 24.19.21.53 (talk) 05:57, 20 September 2008 (UTC)

The article is well-written. However, there is a need to quote sources and give references.

Regards Sandy Chhajjusandeep 07:00, 23 November 2006 (UTC)

I made some changes to the intro - my sole goal was to increase readibility; I think I did so without sacrificing accuracy. I wonder whether it woul be orth saying more about the relationship/difference between drift and natural selection as a way of saying something about drift's place in the modern synthesis, but I leae it to someone else to figure out how and where to do so in an elegant way. Slrubenstein | Talk 14:21, 16 December 2006 (UTC)

I think it is an improvement :) - cohesion 02:58, 17 December 2006 (UTC)

Thanks!! Slrubenstein | Talk 14:43, 17 December 2006 (UTC)

I made further changes. The intro was one giant paragraph; I broke this into three according to the different subjects being communicated. —Preceding unsigned comment added by 24.19.21.53 (talk) 06:31, 20 September 2008 (UTC)

I'm working through the concept & can see the general idea, but I'm perplexed by so long as it does not comprise all or none of the distribution. in the introduction, could someone explain please?

Paxoid 23:27, 26 February 2007 (UTC)

Removed. It made no sense.Professor marginalia 17:22, 18 October 2007 (UTC)

In population genetics, genetic drift is the statistical effect that results from the influence that genetic drift confers to become more common or more rare over successive generations.

Hint: It's supposed to be a definition of "genetic drift." —The preceding unsigned comment was added by 75.36.158.86 (talk) 10:19, 21 March 2007 (UTC).

The first figure in the definition is nice, but irrelevant... furthermore, it indicates that animals came before plants (in Eukaria) which is fairly unlikely...

This is a very important topic in evolutionary biology. My two suggestions for raising to B class is to reduce the size of the lead section (too long relative to the article size) and add references, the latter being the most important. Richard001 21:56, 5 June 2007 (UTC)

I thought that the first sentence of the article should better be a definition of the term. The first sentence says:

In population genetics, genetic drift (or more precisely allelic drift) is the statistical effect that results from the influence that chance has on the survival of alleles (variants of a gene).

I can see that genetic drift is a statistical effect. But what kind of statistical effect is it? That question is more relevant to a definition than the question "From what does it result?" or "How does it come about?" Also, once an effect is statistical, the statement that chance plays a role in it adds little information, as it logically follows from the definition of statistical. A better definition would be welcome. --Dan Polansky (talk) 15:00, 8 December 2007 (UTC)

You are right-it's something of a mess. Professor marginalia (talk) 15:24, 8 December 2007 (UTC)

Made a first go. And the term "chance" does warrant mention in some way--the "chance" in genetic drift needs emphasis because it is distinguished from the other significant evolutionary mechanism, natural selection, where selection is based on adaptive advantage, ie not random chance at all. In natural selection, the "samples" which over time successfully reproduce in a population are not randomly selected. In genetic drift, they are. Professor marginalia (talk) 17:30, 8 December 2007 (UTC)

The text says "natural selection functions non-randomly". This sounds wrong to me. An individual organism with low fitness can still survive with some probability. Selection is stochastic, not deterministic. Can we say that drift is the random element in selection? Or we might say that drift includes the effect of selection being non-deterministic? Afog (talk) 16:50, 23 January 2009 (UTC)

A random process occurs entirely by chance, such as flipping a coin or rolling a dice. If the probabilities of the set of possible outcomes are not equal, the process is non-random. Tim Vickers (talk) 17:10, 23 January 2009 (UTC)

Genetic drift is changes in allele frequencies that come entirely from chance. As an analogy, imagine you have a bag containing 60 marbles, half of them red marbles and half blue marbles. The bag represents a population of bacteria and the different colors the two types of bacteria in that population, which carry two different alleles of a gene. Each generation you randomly reach into the bag and pick out half (30) of the marbles, and are then given new marbles with the same colors as the ones you selected: if you pick out 18 red and 12 blue, you're given 18 new red marbles and 12 new blue marbles, producing a new population containing 60 marbles. These selections and replacements represent the bacteria that manage to divide and reproduce. The marbles remaining in the bag are thrown away - bacteria that don't reproduce die and leave no offspring. If you keep repeating this process, since the numbers of red and blue marbles you pick out will fluctuate by chance, the most common color in the population of marbles will change over time, sometimes more red: sometimes more blue. It is even possible that you may, purely by chance, lose all of one color and be left with a bag containing only blue or red marbles. This is genetic drift - random fluctuations in which organisms survive and reproduce, leading to random fluctuations in the allele frequencies of the population.

TimV, I think an analogy is invaluable, but this analogy is inexact - you're not throwing out marbles first and then sampling, you're sampling from the whole bag N times. I.e., I start out with N marbles in a sack, some red, some blue. I want to create N new marbles. I do this by reaching into the sack and picking a marble. If it is red, I make a red marble. If it is blue, I make a blue marble. Replace the marble in the sack, repeat N times. This describes the dynamics of the process better than your analogy (which implies a much faster collapse in variation - yours implies that every generation, low-frequency variation will disappear). Except this analogy sucks. Graft | talk 18:30, 14 March 2008 (UTC)

I've rewritten it a bit, what do you think? Tim Vickers (talk) 18:43, 14 March 2008 (UTC)

Nein, doesn't work. Is your population size 60? Or 30 (=12+18)? Since the strength of drift is governed by population size, the number of marbles in the bag is crucial. You MUST have sampling with replacement, since that's the way your real population works - more or less. Where the analogy breaks down I think is that you're using marbles to represent both the parental generation and the gametes - but I can't think of a non-gross analogy for generating gametes. Graft | talk 22:09, 17 March 2008 (UTC)

Actually, I'm thinking about an asexual species that divides by binary fission, which is easier to deal with. I've tried making this clearer. Tim Vickers (talk) 16:37, 18 March 2008 (UTC)

I may be missing it, but doesn't this new attempt still lack replacement? That's important, because of course one organism can reproduce numerous times, another zero. I am also confused because it sounds to me like the bacteria splitting into two in the scenario is no longer a parent-offspring duo but a set of twin offspring with the parent somehow transmogrified into one of the twins.Professor marginalia (talk) 17:45, 18 March 2008 (UTC)

Rewritten again. Tim Vickers (talk) 21:08, 18 March 2008 (UTC)

Sorry, I think it confuses "replacements". The "replacement" I was speaking of was "sampling with replacement". In this revision, the process describes "sampling without replacement", which is incorrect for this analogy. It also continues to conflate parent and offspring generations. The organism which splits once has one offspring, not two. If it splits a second time, then there would be two. But in this example, the marble which reproduces is, weirdly, immortal, living on and on in each newly reproduced generation, which is why it's confusing. The organisms in Generation A can reproduce any number of times, within the limits their reproductive lifespan. The way to represent this in the analogy is to take each reproductive event in the analogy as a single independent sample pulled from the same starting population--after its "match" is created, each marble pulled is then returned to the population in the bag before drawing the subsequent sample to reproduce. You can't draw 30 as a set. You can only draw one at a time, each one from the same complete starting population. When that population stops reproducing, then all are thrown away or at least ignored, not just those that didn't reproduce. Professor marginalia (talk) 21:54, 18 March 2008 (UTC)

What about something like this? :

The following simulation represents how genetic drift takes place in a population: First imagine a small jar holding 20 marbles, half of them red marbles and half blue marbles. This jar represents a small population of organisms, and the two colors represent the two different alleles of a single gene found in the population. And also imagine an initially empty second jar which will contain the future offspring reproduced by the first generation. Say the next generation produced in this population will also number 20 organisms. Draw one marble randomly from the first jar. If the marble drawn is red, place a new red marble in the second jar. If the marble drawn is blue, place a new blue marble in the second jar. Return the drawn marble to the first jar. There is now one randomly reproduced organism in the new generation. Repeat the process 19 more times to reproduce a total of 20 new marbles to represent the next generation of the population which is now contained in the second jar.

Since in this process, each of the red and blue marbles chosen to reproduce from the first jar were picked randomly, the number of red and blue marbles now contained in the second jar are unlikely to be equal, as was the case with the red and blue marbles in the original population in the first jar. Represent the eventual death of the original parent population by emptying and discarding all the marbles in the first jar, and re-use it to hold a third new generation of marbles reproduced from the second generation in the same manner. This process can be repeated for a fourth new generation of marbles, and so on. With each new generation of marbles, the number of red and blue marbles in the jar holding the offspring population can fluctuate from the number of reds and blues in the jar holding the parent population: sometimes there will be more red, sometimes more blue. Because the number of marbles in this population is small, there will be a tendency over time for one color to eventually become predominant throughout the population. This is the process seen in genetic drift, in which random fluctuations determine which organisms are reproduced, resulting in changes over time in the allele frequencies in the population.

Professor marginalia (talk) 17:34, 18 March 2008 (UTC)

Genetic drift is changes in allele frequencies that come entirely from chance. As an analogy, imagine having a large number of marbles, half of them red and half blue, with the two colors representing organisms with two different alleles of a gene. Put 10 red and 10 blue marbles in a jar, representing a small population of these organisms. Each generation the organisms will reproduce at random and the old generation will die. To see the effects of this, imagine randomly picking a marble from the jar and putting a new marble of the same color as the one you picked into a second jar. After your selected marble has "reproduced", put it back, mix the marbles, and pick another. After you've done this 20 times, the second jar will contain 20 "offspring" marbles of various colors. This represents the next generation of organisms.
Now throw away the marbles remaining in the first jar - since the older generation of organisms eventually die - and repeat this process over several generations. Since the numbers of red and blue marbles you pick out will fluctuate by chance, the most common color in the population of marbles will change over time, sometimes more red: sometimes more blue. It is even possible that you may, purely by chance, lose all of one color and be left with a jar containing only blue or red offspring. This is genetic drift - random variations in which organisms manage to reproduce, leading to changes over time in the allele frequencies of a population.

Tim Vickers (talk) 23:00, 18 March 2008 (UTC)

I think it's really good. And by isolating a sub-population (the 20 in the jar) from the larger population in the analogy, and describing how the allele frequency in the sub-population's next generation randomly diverges from the 50-50 in the larger population, you've also simulated in a sense the origins of these small isolated populations that undergo drift.Professor marginalia (talk) 23:22, 18 March 2008 (UTC)

The mathematical model of sampling error can be used also for modeling genetic drift. But sampling error carries substantial meaning that is not at hand in evolution. The statistician wants to measure the overall frequency and uses a sample to get an approximation. This approximation has an error, a difference between the frequency in the sample and the frequency in the population. In the breeding of a natural population there is no intention to measure the overall frequency, so there is no error. --Etxrge (talk) 08:38, 18 May 2008 (UTC)

Okay, can you suggest a more correct term? Graft | talk 09:17, 18 May 2008 (UTC)

One of the synonyms for genetic drift is genetic sampling error. Professor marginalia (talk) 14:11, 18 May 2008 (UTC)

This approximation has an error, a difference between the frequency in the sample and the frequency in the population - and that is why the analogy is made. The population "samples" its genetic pool. The fact that there is a difference between the allele frequency of the population and the allele frequency of the sample creates a "sampling error". There is an "attempt" to sample the overall gene frequency because each individual attempts to pass on its genes. Of course it's an analogy, but it matches pretty well.

More importantly though, this is how it is generally represented by our sources. Guettarda (talk) 15:25, 18 May 2008 (UTC)

The marbles analogy of genetic drift in this article is not illuminating. I don't know that much about genetics, so I think I am in a fair position to claim so. Here is a better definition of genetic drift from Bryan Sykes. It's taken from his book "The Seven Daughters of Eve". ISBN 0-393-02018-5. 2001. W.W.Norton & Company. New York, NY. Pg. 43

"Anthony Edwards explained his thinking [about genetic drift] in an ingenious article in New Scientist in 1965. He imagines a tribe that carries with it a pole along which are arrayed 100 discs which are either black or white. Every year, one disc, chosen at random, is changed to the other colour. When the tribe splits into two groups, each group takes with it a copy of the pole with the discs in their current order. The following year they each make one of the random changes to the discs. The next year they each make another, the next year another and so on, continuing the custom of one random change every year. Since the changes they make are completely random, the order of the discs on the two poles becomes more and more dissimilar as each year passes. If follows that if you were to look at the poles carried by the two tribes you could estimate how long ago, in a relative sense, they separated from each other by the differences in the order of the black and white discs. Providing an absolute date was very difficult from the gene frequency alone, but the comparative separation between the two tribes, known as "genetic distance", was a useful measure of their common ancestry. The bigger the genetic distance between them, the longer they had spent apart. This was a clever image of the process of "genetic drift", brought about by the random survival and extinction of genes as they pass from one generation to the next."

I didn't put this in the main article because I don't know if it infringes copyright or not, but I wanted to give an analogy from which I was able to make sense of genetic drift. HeWasCalledYClept (talk) 05:09, 23 May 2008 (UTC)

I find all of these analogies equally outlandish. This one manages to confuse drift with plain old divergence - if the array of discs represents the tribe's "genome", then the analysis makes sense, but does not represent drift. If the array of discs represent individuals with specific alleles, the analysis represents drift, but doesn't make sense, since you can't determine how two populations diverged just by looking at a single locus. Graft | talk 07:21, 23 May 2008 (UTC)

I think the description of drift given in Sykes' book is better to picture how genetic distance between two populations is measured, and that's getting a bit ahead. The analogy ignores completely the effect probability plays on the frequency distribution--how random sampling from small populations impact genetic frequencies in a population over time. It introduces random mutation-which only occurs in individuals-, but also fails to connect it in any way to the population, probability or gene frequencies. It also completely ignores heredity which is the key "event" sampling taking place in the dynamic or process of genetic drift, not spontaneous mutation. Graft's correct, the analogy is more apt for divergence, and I'm not sure I understand how the pole-discs analogy wouldn't apply to comparing selected alleles just as much as changes to allele frequency due to drift, ie from "chance" in sampling. I don't get it. I think Sykes was using the analogy to illustrate genetic distance. But the book's focus is on research in mtDNA differences, and this strange analogy maybe does make rough sense when talking about a "population" of mtDNA. Professor marginalia (talk) 16:55, 23 May 2008 (UTC)

Do people think these are useful? Thay are unreferenced at the moment, so if we are going to add them we'll need to find some sources. Tim Vickers (talk) 15:29, 20 September 2008 (UTC)

• If two competing alleles in a population have exactly a 50 % / 50 % share in one generation, this will change by a small amount because of minor, chance events as each individual comes into existence. In a mid-sized group, this level of randomness will account for a fraction of a percent difference per generation; 50 % to 49.8 %, etc. In large populations, in absence of selective pressure, the share will hover near 50 %; in smaller groups, one or the other allele is likely to become progressively more common until it has taken hold.

Often, the process is driven by more than statistical buzzing.

• Plants broadcast seeds into the wind, or recruit animals and insects to carry them. Occasionally new land is colonized, perhaps by a bird carrying a seed to a new island.

• Population movements can lead to a founder effect where a small number of individuals from a larger group splinters off to form a new population. Genetic diversity is lost as a result, and the smaller new population allows genetic drift to ripple through it. One of the most well-known examples is the peopling of the Americas, when perhaps thousands crossed the Bering land bridge into Alaska, and only 72 individuals left descendants whose lineage lived on through modern times. Other cases are too numerous to count; the Austronesian expansion brought small numbers of pigs to large numbers of islands, where isolated founder populations of both species drifted slowly apart from each other.

• A catastrophy kills large numbers of a species. This often happens as much to unlucky individuals as to unfit ones; a fire burns trees wherever the winds take it, and a mudslide is a very local event. This changes the frequency of competing alleles in the "gene pool." In extreme cases, this is known as a population bottleneck. A well known example in human pre-history is the Toba supervolcano. There have certainly been others, as suggested by Mitochondrial Eve and Y-Chromosomal Adam, or by the lack of genetic diversity in cheetahs. Elephant seal s were driven almost to extinction in the 1880s and 1890s, to a minimum of about 25 individuals. While the numbers have rebounded, genetic diversity takes much longer to accumulate.

Yes, these are useful. And, by contrast, the example with marbles being moved between jars is confusing, obfuscates the concept.

Somebody with time can look up references connecting the historical examples: mtDNA Eve, Austronesian expansion, Toba, etc. However, these were meant to be explanatory ... see under "example" above, for a discussion of why hypothetical examples are proposed to have as much value as real ones ... to show causal chains, rather than observed correlation. The example these replace ( and were replaced by ) accomplishes neither of these aims. —Preceding unsigned comment added by 24.19.21.53 (talk) 19:16, 20 September 2008 (UTC)

I think real-world examples are useful, but none of these give any explanation of the mechanism of drift, which is what the marbles analogy attempts to do. These are probably useful to show outcomes, but telling a reader instances of when drift has occurred will not give them any clearer idea as to why it occurs. p.s. your last edit added a duplicate list of these examples, they are presently listed in a separate section at the end. Tim Vickers (talk) 20:38, 20 September 2008 (UTC)

Tim, the term 'statistical buzzing' seems ambiguous to me in the sense that it makes assumptions about how the reader visualises such things. How about replacing it with something like 'random fluctuations in allele frequency' or something similar ? Sean.hoyland - talk 10:50, 20 October 2008 (UTC)

Simplify and clarify by all means. Tim Vickers (talk) 16:26, 20 October 2008 (UTC)

Are there any online simulators that allow you to watch random fixation of alleles (allowing you to adjust starting frequency, population size and such)? That would be good for the external links section (or better still, to have here, but that technology doesn't seem to exist yet). Richard001 (talk) 03:30, 1 November 2008 (UTC)

Here are a couple [1], [2]. The manual version is quite nice [3] Sean.hoyland - talk 10:32, 3 November 2008 (UTC)

Arr. I just noticed that a pretty significant chunk of text was changed/added in September by an anonymous user. I would like to remove and/or revert most of this text. It suggests that drift represents the collective action of all chance events (like, say, a rockslide burying 3/4 of your population) on the species. This is NOT accurate, and the greater emphasis placed on this sort of stuff, especially in the intro, really obscures the real meaning of drift, which is just the shift in allele frequencies introduced by sampling error. While the new examples are colorful and interesting, they really give the wrong idea about what drift is.

I'd like to more-or-less return the article to its previous state. Does anyone have any objection to this? Graft | talk 17:40, 18 December 2008 (UTC)

To save time and avoid any confusion, can you give us the diff? Professor marginalia (talk) 19:46, 18 December 2008 (UTC)

Ignoring edits like including interwiki links and so on, this is more or less the edits I'm talking about: diff. Graft | talk 20:35, 18 December 2008 (UTC)

Thanks. The IP raised several objections to the content but they were buried above in old discussions. Little existing content looks to have been removed, and the change to the marble example may have improved it. The biggest changes were the additions in the examples section, which may help, I don't know. But I don't think they're well executed. I think the examples wander around the periphery of the subject, which is the "genetic drift" - not the "different whims or natural calamities that lead a few genes to separate from the pack".Professor marginalia (talk) 21:26, 18 December 2008 (UTC)

"Natural calamities" is what I have the biggest problem with; I'd prefer to do a considered and partial revert, since I agree there's good material there. But people already have the tendency to think of rocks crushing things when they hear "chance" mentioned in the context of evolution (I did, before I knew what drift was - I think I even made edits to that effect many years back), and that is simply not what drift is at all; I'd like to maintain clarity on that subject by excising that sort of commentary. Graft | talk 21:45, 18 December 2008 (UTC)

I'd delete the examples given in the section-I don't much like the first one given either. It might make sense to opt instead to use a few of the more notable real world examples, one population bottleneck example maybe, another founder effect, etc, but if we do that, I'd rework the maladaptive traits section so it doesn't have redundancies with the examples. See the "examples needed" section of the talk page to read the issues/examples proposed by IP before the changes.Professor marginalia (talk) 22:20, 18 December 2008 (UTC)

The referenced article in EB says genetic drift can occur only in small, isolated populations. This is wrong. The opening example on genetic drift on page 297 in Evolutionary Biology, 1998, by Douglas Futuyma is a new allele "in a large population". On page 303 it says that for two alleles at a particular locus and with equal frequency, the variance in probability distribution for the gene frequency of one of the alleles in the next generation is p(1-p)/2N, where p is the frequency for both genes and N is the number of diploid individuals. Since N is always finite, the variance is always finite. Our article should state that genetic drift is smaller for larger populations, not as it does right now, that little or no change would take place. --Ettrig (talk) 20:53, 16 February 2009 (UTC)

No, you're confusing "small probability of drift" with "small drift". They're not the same thing. Yes, it's less clear cut than it used to be whether drift can occur in large populations. But when you're talking about random sampling, if there is any heterozygosity, then the probability of a change in allele frequency will never be absolutely zero. But there are unlikely extremes allowed by any theory. What we need to do is a better job of shading the issue. It is absolutely true that genetic drift has traditionally been thought to be a non-issue in large populations, and that selection pressures tell the story over time. This is overly simplified though. Professor marginalia (talk) 21:42, 16 February 2009 (UTC)

I reworded and simplified the "Basic concept" marble example. I think I included everything, except I didn't see the point of trying to say that the population was initially large, but some factor restricted reproduction to be within a collection of 20 organisms. Did I miss anything?

If reaction to the change is favorable, I'll have a go at the "Simple example" fish section. However, I have some questions. Is there some subtlety I'm missing because I don't see much difference between the marble and fish examples (except for the realistic scenario). For the fish, we have the point about a different genotype but the same phenotype (no natural selection), and the Y chromosome and the males, and we have the calculations. Seeing as this is a fairly introductory article, the implications of these items should probably be briefly spelled out.

The calculations add rigor but may not be entirely convincing because they stop after one generation, and are somewhat peripheral to the concept. It might be better to simply announce the fact that of the 1024 possibilities, 252 will have five A alleles and five C alleles (with link to a suitable article). Why are letters A and C chosen? Why not A and B? --Johnuniq (talk) 10:35, 17 February 2009 (UTC)

The following is not intended as argument, just telling you what I thought about it. My motivation for the fish example is that it is less removed from the real phenomena where genetic drift occur. My hope is that the marbles can be removed eventually. Y chromosome is to remove the complexity of double genes. Also makes large intermediate population and random fertilization more credible. Not important to me. I wanted to provide something conrete that can be easily checked. The table has numbers that can be recognize in the triangle in pascals triangle. I don't see why it is a problem that only one genertion is mentioned. A (Adenine) and C (Cytosin) are used to symbolize nucleotides. B is not. --Ettrig (talk) 11:33, 17 February 2009 (UTC)

I think we need some rethinking of all the examples given, including these two and the allele frequency chart. I think we're expecting too much of the reader...unless they already know the subject, they're not going to track this. Starting with the allele frequency chart, there isn't sufficient labeling to read it easily. Both an n=10 and n=100 are very small populations to look at. Since there are 20 alleles, the top chart, with n of 10, leads me to assume these are on paired chromosomes, I'm guessing with 2 variants for each shared locus (p=.5)? Then I don't get how, for n=10, we can see a loss of 9 alleles yet only 5 with fixation-there would have to be new alleles taking the spot of the missing 4 (mutation), no?
For the other two examples, the marble example modeled the "sampling" aspect of genetic drift. Populations undergoing drift are subsets of an ancestral population that become for at least some period of time reproductively isolated (geographically, ecologically, behaviorally, etc) from that ancestral population, or are random survivors of a population bottleneck, something to that effect. There is also some advantage to keeping clear of organisms that sexually reproduce because there are much fewer permutations to juggle. The marble example describes a tendency towards homogeneity, but maybe not well enough.
The fish example is nice because it is an organism, not a marble. But I do not want to infer that genetic drift requires that the allele's have no phenotypic expression to select on-and the fish example may do this. I question a couple of other points. Once we're talking about fish, it becomes more difficult to emphasize this is an entirely random process. We need in the example for exactly 10 males, 10 females to survive to each new spring-yet we're pretending it would be completely random which of the many, many fish these ten will be. Are readers new to the topic able to keep this in mind? That's probably the intention behind the digression into look-alike amino acids formed from alternative nucleotides and the phenotype, genotype discussion, but that might be too strong. Again, genetic drift doesn't demand there be no advantage/disadvantage associated with alleles; instead it theorizes the situation in which the probability of random sample error is so high that the frequency distribution is expected to change through pure chance rather than selection. I like the idea of introducing the calculation of these probabilities, with examples, but that should come later in the article. And in its current form, it takes too many shortcuts with the concepts. Either readers already know this stuff, or they're going to be completely lost, guaranteed.
I'd scrap any reference to nucleotides or amino acids. Alleles are as specific as we need to be. I think it's better to start at least with distributions in a hypothetical asexual population--simpler. I also recommend we pick a number format and stay with it...either fractions or decimal, without flipping back and forth much. If we want to use pascal's triangle to illustrate, we should use a smaller n and make an illustration labeling where the coefficients are found and what they represent. Here we've used a table listing them instead of showing how to "find" them on the Pascal triangle. The triangle is impractical, imo, for any bigger n. Would showing a factorial equation be better? Include both maybe? Start with a smaller n and the diagrammed triangle, and then show it in factorial form? That might be good, now that I think about it. The math is going to throw so many readers off, and we do need a bit more step-by-step to help them along.
Professor marginalia (talk) 17:37, 17 February 2009 (UTC)

I see a lot of good angles here, but not really where to start. As stated elsewhere I disagree with the notion that drift is significant only in "small" populations. Will come back to that later. But it would be nice to start cooperating on something we agree on. So yes, N = 6, triangle first, leading on to factorial form, which can be used as basis for discussing normal populations. (?) Diploid or haploid asexuals? A problem with haploids is that there is not a numerous intermediate generation, so the large multiplications of rare genes will be impossible. Maybe we can just close our eyes to that aspect? --Ettrig (talk) 18:50, 17 February 2009 (UTC)

Yes, same with me. We can incorporate more examples - we would do well to start with the haploid reproduction just to illustrate the concept. It's been pointed out by others that many have mistaken notions about what it is, and that this article should make attempt to explain it more plainly and simply. Examples from diploid organisms would be okay for showing the multiplicity of possible outcomes it affords-we could introduce standard notation there too, growing past the "red marble" type analogy to simple genetic ideas. But what we have now are two examples that are the same in this respect, really, because the alleles in question in the fish example reside on the Y chromosome. We introduce 10 female fish but they're ignored - their genes don't factor and our n represents just the 10 males. I'm still mystified trying to interpret the allele frequency chart. I guess it tries to show how much more rapidly the frequencies change in the smaller population, but I think it would be better to pick a number of variants at the common locus- and if it's more dramatic to start with 50% distribution, that only leaves 2 variants. With this kind of chart, we can splurge and raise the n's to see better how sensitive the process is to population size, showing the trend toward equilibrium in the larger pop and homozygosity in the smaller.
We can start another section to talk more about the different assumptions about probability and random sampling between very large and small populations. What's not sorted out well here is the "noise" or normal variation in a large population and genetic drift in some isolated tiny population, or the different views of genetic drift in terms of its potential significance in an evolutionary context, such as with speciation. Generally speaking, frequencies that changed little aren't considered "drift" if they don't trend, but simply wiggle up and down a little bit around the equilibrium point-which is what Hardy Weinberg predicts. The distinctions related to population size are important for many reasons in terms of the modern synthesis and evolutionary theory. Historically, those probabilities pertaining to populations assumed with infinite size played a large part to growing favor with the mechanism of natural selection in evolutionary theory. Fisher was hugely influential there. But more on that later. Professor marginalia (talk) 20:02, 17 February 2009 (UTC)

One of the many problems: I wanted an example free of selection, to show that drift in itself can have significant effects. You raise the problem that this may give the impression that drift is significant only when there is no selection. Is there a solution to this dilemma? Maybe first a drift only example, and then a similar one, with selection added? --Ettrig (talk) 20:28, 17 February 2009 (UTC)

I don't want to overstate it here either. Traditionally, it was felt that slight selection pressures can result in significant change over time in large populations. But in small populations, selection pressures were thought not be an important factor in its evolution because the effects are overshadowed by the random sample errors, canceling any pull or push from selection. (Then there are scenarios in which a "drifted" population is reintroduced back into the larger breeding population, an evolutionary "hybrid" between mechanisms of drift and selection, so these aren't clean dividing lines.) In population genetics research, I believe, the expected values predicted by probability calculations are compared to observed values to try and measure out the allele's non-random effect in terms of selection. But there again, in too small a population there won't be a large enough n to do this. For example, with n=10, and a 75% probability of purely random change in the freq distribution, there is no room left for measurable incremental change. I don't know how we could tackle a comparison. We'd need to compare like populations, but we have the population size issue-smaller is sensitive to drift but larger is sensitive to selection. Compare both ways? Professor marginalia (talk) 21:38, 17 February 2009 (UTC)

Note, I've come across charts in a reference that are almost exactly like the two charts of allele frequency distributions included here, and now I see what it was looking at. I think I'll redo it a little bit to include clearer labeling just to avoid having to use any guesswork to follow it. Professor marginalia (talk) 16:27, 19 February 2009 (UTC)

Here is a synopsis for an example suggested to replace the existing two early examples: 4 bacteria in a small drop with food. The same genes except for one that make them stain differently and distinguishable in microscope. No difference in survival or reproduction. They divide in unison until food is depleted. Then starve off until only 4 remain. Alleles A and B. 16 different outcomes. AAAA, BAAA, ABAA, BBAA, AABA, BABA, ABBA, BBBA, AAAB, BAAB, ABAB, BBAB, AABB, BABB, ABBB, BBBB All outcomes are equally probable. Distribution is 1, 4, 6, 4, 1. These are the binomial coefficients and according to pascals triangle. 1, 4, 4, 1 are together more likely than 6. Non-6 constitutes drift. Give the formula for any population size. Generalize to different frequencies. Modify by introducing selection bias. Show there is finite probability for allele that is selected against. --Ettrig (talk) 19:28, 19 February 2009 (UTC)

My hope is that the marbles can be removed eventually

I suspected that, and understood while I was rewriting that the section may eventually disappear, however I wanted to clean up both examples so we could better assess the next step. I think the marble story now reads well. Later we can judge the relative merits of the marble and fish examples (fish: realistic, but may introduce too many details for easy comprehension). --Johnuniq (talk) 09:52, 18 February 2009 (UTC)

A (Adenine) and C (Cytosin) are used to symbolize nucleotides

But the text talks about five A alleles. Is that consistent? --Johnuniq (talk) 09:52, 18 February 2009 (UTC)

calculations ... Pascal's triangle

We can wait and see how it turns out, but I don't think there is a reason to have any calculations. Just outline that a random sample would pick five A alleles and five C alleles 252 times in 1000 trials (see [link to article]). The problem is that the calculations are a brick wall to comprehension (even to readers with a reasonable grasp of probability basics; only people who have studied genetic drift would understand the calculations). If the marble example is to be removed, I think the fish example needs to be greatly simplified. If calculations are wanted, add them as an expansion of the basic example. --Johnuniq (talk) 09:52, 18 February 2009 (UTC)

I hesitated about the description of genetic drift theory, but removed it because it is circular. --Ettrig (talk) 20:26, 19 February 2009 (UTC)