Yeah but those changes would have to all take place simultaneously to be beneficial. In any event, i’m not sure these have any connection to pseudogenes.
Like IzzyR, I find your conclusion hard to believe, and think tha there is a flaw in your logic. I think that this is where it is. You seem to be saying if there are two fluctuations, one of which causes the dominant gene to increase 1%, and the other causes the other gene to increase 1%, this will benefit the dominant gene more because it will increase in absolute numbers more than the other gene. But there are two problems with this. First of all, the absolute number of genes is not important; what’s important is the gene frequencies. Under the scenario you described, the relative frequencies of the genes would not change. Here’s a more dramatic example: suppose there are 501 people with B, and 499 with b. Now suppose the population doubles. Now there are 1002 and 998, respectively. B increased by 501, while b increased by only 499. But b is still 49.9% of the population, just like it was before. Secondly, you focused your attention on what happens when the population increases, and ignored the fact that the opposite effect will happen if the population shrinks.
**
I’m not sure your logic holds, even as stated. If there were no genetic drift, then there would be zero chance of a pseudogene becoming universal- one person in the parental population would have a mutation, and would pass it on to exactly one offspring, ad infinitum. Of course, using your rigid application of the “larger populations snowball” rule, a pseudogene would also have zero chance of becoming fixed in the population, since the overwhelming effect of the presence of all those people without the mutation would cause the parent to inevitably pass on the gene to zero offspring. Is this what you meant to say?
I’m no statistician, but my understanding is that the effects of genetic drift amplify fluctuations. While large populations are generally favored, there is also a probability that a small population can rally (after all, each successive fluctuation in its favor increases the effect of the next fluctuation.) The key point is that in the end, the fluctuations can become large enough to wipe out the last remnants of one of the two genes.
**
Yes, I see your argument, but clearly something’s wrong with it. (I don’t mean to be the evil evolutionist who dismisses counterarguments out of hand; it’s just that in a math argument between IzzyR and, say, Laplace, I’ll vote for the brilliant pre-Darwin mathematician.)
The first thing I see wrong with your argument is the bit where you say “clearly one cannot say that genetic drift would cause any one of these three groups to increase in proportion.” Why not? If you do the math, genetic drift does indeed cause one of the mutations to wipe out the others. That was the whole point of my discussion of genetic drift!
I suspect that if you had the HW equations in front of you, you’d find that the division between AB vs. C made no difference in the end, although it’s difficult to argue these things without having the equations in front of us.
**
Again, I’m no statistician, but the odds can be calculated, and they’re not as inconceivable as you make them out to be. Moreover, it’s well known that evolution takes place faster in smaller populations, precisely because genetic drift takes place more quickly.
**
What “calculations involving mutation rates of pseudogenes” are you referring to?
-Ben
**
It’s been a couple of years since I studied this, so I may have left out an important part of the argument. I’ll see if I can find a good textbook on evolutionary biology and check my facts. Until then:
http://www.talkorigins.org/faqs/genetic-drift.html
**
It’s a little unclear to me what doubling of the population has to do with my argument; I specifically described cases in which a 1% fluctuation in gene frequency favored one gene over the other. It’s also unclear to me why you think I ignored gene frequencies.
-Ben
Searching for “genetic drift” in Google turned up a number of webpages on the topic, including a simulator or two. Give it a try and see if any of the pages answer your question, and I’ll try to find a textbook.
-Ben
Which changes? Bigger eyes in concert with a bigger visual center for the brain? Bear in mind that the changes are linked: a mutation which causes (for example) the retina to have more rods and cones will also result in the brain devoting more neurons to processing the information from them.
-Ben
Izzy says:
Let me try again.
If a gene carries a trait having little or no benefit, but little or no negative effect either it is simply a trait that can be inherited or not without affecting survival. If there are a small number of individuals with that trait in a very robust population there is little chance that the entire portion having that trait will fail to have offspring. So, the trait persists. Let’s call the trait xism.
In the natural course of things individuals mate in patterns which give their own genetic heritage a better chance of survival. Even in life mated pairs such as birds it is common to have mating occurrences outside of the pair. This is certainly the case with humans. Therefore it is likely that those carrying the xism gene will have as much success increasing their genetic inheritance rate as will any other group chosen at random. If the total number of individuals in the species increases over a long time, all traits not specifically deleterious to survival and procreation will increase in frequency in the population, except in cases where the existence of one trait requires the absence of another. Xism will become more common over time, unless there is a specific stress on the population. This is simply a consequence of the random nature of mating and inheritance.
When there are such stresses on population, so long as xism does not create a specific reduction in inheritance rates, xism will decrease proportionally with all other traits. When stress is relieved, the increase in inheritance rate will occur again. While it will probably not become universal without some other factor being introduced, it will become more common over time.
If you choose mates at random, when you are an xist, and only 10 percent of your species is xist, then it is much more likely that you will add your xist gene to a non xist line than that you will reinforce an already xist line. If I then kill half the infants of a subsequent generation, I will kill xist bearers only at the rate at which they occur in the population. Over time, xism increases, unless some specific stress alters that.
Does that make sense, without the math?
Tris
" It is when I struggle to be brief that I become obscure." ~ Horace ~
For selectively neutral genes, the frequency of the alleles will change as a result of random happenstance, rather than selective pressures (this is the essence of genetic drift).
Among a group of populations, as the gene frequency in different populations changes, the variance of the gene amongst all populations increases - that is, the curve of gene frequency distributions tends to flatten out. This is not diffcult to visualize, since, given random conditions, in some populations the gene frequency will increase, and in others it will decrease. The net effect is an increase in the range of frequencies. Further, as gene frequencies in a population increase, the odds of them increasing again in the next generation are proportional to their distribution - that is, the more prevalent the gene, the more likely you are to breed with someone who has it, thus perpetuating it.
Eventually, because of this “flattening of the curve” (the distrubution curve among all opulations, that is), some populations will reach a state of either 100% or 0% frequency for the gene in question. Once that happens, the gene is “fixed” for that population (to conitnue the Bb example, a population could become fixed at either BB or bb). The remaining populations continue breeding, the gene frequency continues to change by random fluctuation (and again, because it is random, the higher the gene frequency, the more likely it is to increase; similarly, the lower the frequency, the more likely it is to decrease), and eventually more populations become fixed. After several generations, all populations eventually become fixed.
Now, one can go one of two ways from here:
The first, is to look at one population. Eventually, because of genetic drift, any given selectively-neutral gene within that population will either come to be present in 100% of the population, or 0%. It should be obvious that the larger the population, the longer this will take. If there are multiple such genes, some of them will be present, some will be absent. Obviously, the ones which are absent we would have no knowledge of, unless we had prior knowledge of their existence. We would thus only see those “pseudogenes” which are 100% prevalent (unless, of course, the population is not yet fixed).
The second is to continue inbreeding amongst all populations. You basically start over, except you have fewer, but larger, populations. The end result will be the same - eventually all populations become fixed, one way or the other. Then you start over. And so on. Eventually, any fully inbreeding population will become fixed.
One could look at humans either way, really. Either as distinct populations, all of which will eventually become fixed, with continuous breeding between populations to extend the time before all populations reach the same “fixed” state. Or, you could look at us as one big population, and see that eventually, as all populations do, we will reach said “fixed” state.
In either case, the end result is the same: selectively neutral genes will, eventually, either be completely eliminated from the genepool, or be present in all individuals.
Egads…this:
(the distrubution curve among all opulations, that is)
Should read:
(the distribution curve among all populations, that is)
See, now if weren’t for corrective lenses, bad eyesite might have been eliminated from the genepool, and I wouldn’t have this problem…
It was said that “neutral” genes, i.e. genes that express neither selectively advantageous nor disadvantageous phenotypes, would tend to become more frequent in an otherwise freely breeding population.
This is probably true up to a point. The gene pools of most organisms, especially sexually reproducing ones, are full of genetic “junk” that seems to persist only because it is difficult to jettison the excess baggage: it is easier to keep the useless stuff onboard.
I would guess that at some point, however, there would be some disadvantage to having a cluttered gene pool.
Ben
No, I think population increases for different groups might be subject to statistical variations, and as such, any mutation might, by pure random chance, increase disproportionately. But the odds against that would be high.
Well you may not be the evil evolutionist, but if indeed you are “no statistician” you would do well to consider the possibility that you may have misunderstood Laplace. As I noted, the genetic drift process that you describe would be statistically valid if we were dealing with actual survival advantages (as opposed to random fluctuations) and Laplace may have been describing such a process, or some other circumstance that also differs in some subtle way.
The reason is because each of these populations is identical at this point. The genetic drift argument would have to predict with regard to each one of them that they will be wiped out by the other two, simply by grouping the other two into one larger group. This is paradoxical.
Meaning that if such mutations are happening at a X rate, and we see Y such mutations, we cannot simply multiply X*Time elapsed to see if it equals Y. We must assume that the Y mutations that we actually see are the surviving remnants of many multiples of such mutations (e.g. if a given neutral mutation has a .01% chance of dominating a population, we must multiply Y by 10,000).
I too do not understand The Ryan’s post.
Trisk
What you seem to be saying then is that an xist mating with a non-xist will add this gene to the line, IOW that the descendents will take after the xist. (I always thought this was called a dominant gene). To return to Ben’s example, this would imply that someone who had a mutation that turned off some of his olfactory receptor genes and had say 4 children should expect more than 2 of them to have this same mutation. Is this your intention (and does this tend to be true of pseudogene mutations?).
Darwin’s Finch
I don’t understand why this should be so. Unless you are saying, again, that all children who have one parent with the gene will themselves have it, this would not appear to be true.
IzzyR, would you mind if I posted your intriguing paradox to talk.origins? Even if I knew the equations, I doubt I have the mathematical sophistication to solve the paradox.
-Ben
Feel free.
talk.origins on genetic drift.
This particular article makes no mention of the idea that genetic drift favors the larger group.
Note that in the final paragraph they say that
So it would appear to be purely random.
Why would all the changes have to happen simultaneously? Why can’t they happen gradually? Would a slightly better eye be beneficial or detrimental?
I never said it had anything to do with pseudogenes. ultrafilter said our sense of smell is adequate, that a better sense of smell would be costly and I was saying the same thing about sight.
Doubling is equal to a 100% increase, and I thought that the numbers would be clearer with a larger increase. But if you want to retain the 1% number, then how about this:
There is a population with 51000 instances of B, and 49000 instances of b. Suppose B increases by one percent. Now there are 51000+(51000*.01)=51000+510=51510 instances of B. Okay, what happens if b increases by one percent? Now there’s 49000+490=49490 instances of b. Like you said, B increased by 510, and b increased by 490. So in absolute numbers, B profited more from the increase. But in percentages, 49490/(51510+49490)=.49, which is the same percentage of b at the beginning. So the percentages did not change.
Because you compared 1% of 50.5% to 1% of 49.9%. These two numbers represent the absolute number of new instances, not the relative frequency increase (even though they have percentage signs, they aren’t relative frequencies).
Triskadecamus
Perhaps this is part of the confusion. By frequency, do you mean absolute frequency (the number of instances), or relative frequency (number of instances of one type divided by the total number of instances)? I mean the latter, and so I would say that the frequencies would stay the same.
But thee is no guarentee that you will pass on the gene. Remember, every time a creature mates, only half of its gene are passed on. Why would the xist genes be favored over the non xist genes? Here’s a calculation for B and b, where 10% of the genes are b. (So 81% are BB, 18% are Bb, and 1% are bb).
Possibility one: BBxBB
Probability of possibility one: 65.61%
Results: 100% BB
Possibility two: BBxBb
Probability of possibility two: 29.16%
Results: 50% BB, 50% Bb
Possibility three: BbxBb
Probability of possibility two: 3.24%
Results: 25% BB, 50% Bb, 25% bb
Possibility four: Bbxbb
Probability of possibility four: .36%
Results: 50% Bb, 50% bb
Possibility five: BBxbb
Probability of possibility five: 1.62%
Results: 100% Bb
Possibility six: bbxbb
Probability of possibility six: .01%
Results: 100% bb
Adding these up, I get: 81% BB, 18% Bb, 1% bb. Exactly what they were before.
Izzy,
Ok, lets get specific.
I am an early human male.
There is a genetic nonsense string in my genetic makeup. It does not code for proteins, and does not alter the folding for any of the functions which my growth or metabolism requires. It is a totally useless, but harmless unique characteristic. I call it the superme gene. I am the only man in the world to have the gene.
Times are good. I don’t die. I am a handsome devil, and a pretty good hunter. I mate sixteen times in my brief brutal life, and in half those cases, I pass on the chromosome that has the superme gene. None of my mates has the superme gene, of course. Half my offspring die before procreating. Four people now carry the superme gene. There are lots more people in my tribe, though, what with times being good.
My kids are a fecund bunch, and the females are promiscuous. (Good genetic strategy, although I suspect they just like sex a lot, and want more than their primary mates will give them.) My kids mostly mate with non-relatives. (another good strategy, but I think they just like a little strange, you know?) My eight surviving kids mate successfully eight times each, but times are tough, and only about one in four survives. Half of the superme chromosomes are passed on in the thirty two available cases, in each case to a mate without the superme gene. Eight survivors have the superme gene.
The women in our tribe get kidnapped by a larger tribe, including two of my superme carrying grandkids. The six superme left kids here include two women who now pretty much have to mate more with the remaining male members. Most of them don’t have the superme gene. In the other tribe, one of the women dies in childbirth, and the other raises two children, one a male with the superme gene.
Whenever the gene is in the extreme minority, even with the reduced inheritance of single chromosome expression that provides a statistically better chance of dissemination into the genome. Each conservation of the gene has the potential to be passed on. When times are bad, everyone dies at the same rate, except by chance. When chance reduces the rate of occurrence in the carrying population, it increases the number of chances of each individual survivor mating with a non superme carrier. While it is possible that the entire superme carrying population will die, it is unlikely, unless the numbers are very small. In times of very low stress, population increases make non-carrier mates much more probable. Over time there will be those who have two expressions of the gene, one from each ancestor. The absence of survival value of superme makes the gene itself independent of environmental fluctuations. It remains in the gene pool, increasing in frequency at a slow but steady rate.
At any time in the future, the loss of a large portion of the population due to a genetic factor might be linked to the presence or absence of some characteristic that is coincidentally associated with the superme gene. If those who have this characteristic also carry the superme gene it could well become statistically present in overwhelming numbers, or be entirely eliminated. If the coincidental gene requires expression on both chromosomes to be effective, and the survivors happen to have superme on both of those chromosomes, then superme becomes universally present in the population, even though it has no function.
Those cases where the gene disappears of course are as likely as the cases where it becomes more prominent. We just don’t have any reason to remember those.
Tris
“The most important thing our ancestors have left for us is . . . descendants.”
I don’t agree with this. In your example above you indeed passed on the gene to 4 people in the next generation. But this was accomplished by you and your various mates having 8 surviving descendents in the next generation, meaning 4 times as many descendents as ancestors. Assuming that all the non-superme carriers also produced 4 times as many descendents as ancestors, the proportion of superme carriers in the next generation would remain identical.
This is irrelevant. This may cause the genes to be distributed over a wide area, but will not increase the absolute number of carriers. (Presumably, if a carrier hooked up with another carrier all descendents will be carriers - if a carrier hooks up with a non-carrier only half will).
Also erroneous apparently, is my own assertion above that
I have calculated this and it does not add up. Imagine 5,100 member of Group A and 4,900 members of Group B. In Year 1 Group A has a 1% survival advantage. They increase to 5,151 and now make up 51.25% of the population. In Year 2 Group B has the advantage. They increase by 1% to 4,949. Total population = 10,100. Percent in Group A = 5,151/10,100 = 51% - same as before. (This may be the point made by The Ryan). So the question of what Laplace meant is even more intriguing.
Again, the article that I linked from talk.origins seems to indicate that genetic drift is a purely random process - that as populations drift this way and that, it can at some point fluctuate so far in one direction that one type is eliminated entirely. (This would be accentuated if the population was reduced at some point to a relatively small group). Still, the odds against any given mutation making it all the way from 1 mutation to 100% purely at random would seem pretty steep.
Bingo! You got it right on the money: genetic drift is a result of random events. Check out this genetic drift simulation:
http://darwin.eeb.uconn.edu/simulations/drift.html
You’ll have to run it several times, but it’s pretty quick. Notice how, as you decrease the population size (N), you’ll tend to get gene fixation (either p=0 or p=1) in a much shorter generation time.
Actually, as I re-read that, I see that it doesn’t necessarily follow. Ignore that. However, the crux of the argument is this: when only random chance is involved in the perpetuation of a gene, it will either become completely prevalent over time, or it will completely disappear over time. In larger populations, this process will, obviously, take much longer. This is all based upon variance statistics for multiple populations.
These “random” events can be a result of simple random mating, an asteroid strike in B (or b) central, plague, or whatever. Regardless of the source of the randomness, the end result, given enough time, will be the same: 100% or 0% occurance of a selectively-neutral gene throughout a population.
Another way of stating all of this is that, in any inbreeding population, the number of heterozygous individuals in each subsequent generation will decrease over time. This is, of course, why familial inbreeding is generally bad. However, the same fate awaits any inbreeding population. In a single family, it may only take a few generations before a gene becomes fixed (meaning only homozygotes exist within the population). In a slightly larger population, it will take a bit longer. And so on. Eventually, however, all individuals become homozygous, regardless of the size of the population. Again, this can take a very long time for a very large population.
Note that a given pseudogene may well have first appeared early in the evolution of humans. Since gene fixation occurs more rapidly in small populations, it likely reached that point long ago. Once the gene becomes fixed, barring a random mutation (or re-introdution from an outside population), the gene will remain fixed forevermore.