Mutation Population

[Southwind17]

I've tried a cold towel around my head in a darkened room, but to no avail. Could somebody, therefore, please help me answer the following question:

If biological evolution relies on random mutations as one of its essential ingredients, then, presumably, the chances of any particular mutation occurring simultaneously in any species at or around the same evolutionary time are minimal. How, then, do mutations 'get a hold' and persist over time, especially in, say, humans?

I can see how a not-detrimental mutation will persist through the beholder's offspring and then through theirs, ad infinitum (essentially), but do the beholders of the said mutation not represent a fixed proportion of the population of that particular species such that the beholders numbers grow only in that same proportion to the species? In other words, what mechanism is at play that leads to all members of the same species acquiring exactly the same traits? It's surely not a simple case of survival of the fittest, is it, especially with humans?

 

[fls]

I've tried a cold towel around my head in a darkened room, but to no avail. Could somebody, therefore, please help me answer the following question:

If biological evolution relies on random mutations as one of its essential ingredients, then, presumably, the chances of any particular mutation occurring simultaneously in any species at or around the same evolutionary time are minimal. How, then, do mutations 'get a hold' and persist over time, especially in, say, humans?

I can see how a not-detrimental mutation will persist through the beholder's offspring and then through theirs, ad infinitum (essentially), but do the beholders of the said mutation not represent a fixed proportion of the population of that particular species such that the beholders numbers grow only in that same proportion to the species? In other words, what mechanism is at play that leads to all members of the same species acquiring exactly the same traits? It's surely not a simple case of survival of the fittest, is it, especially with humans?

By definition, a successful gene is that which can increase its frequency within the population. Equillibria will vary and depend upon the relative advantage of having the gene and the relative disadvantage of not having the gene. Also, it may be that all are members of the same species because they are the ones that acquired that trait (rather than the other way around). For example, humans may all be relatively hairless because back in the day, those who weren't, went on to evolve into different apes.

Linda

 

[Southwind17]

By definition, a successful gene is that which can increase its frequency within the population. Equillibria will vary and depend upon the relative advantage of having the gene and the relative disadvantage of not having the gene. Also, it may be that all are members of the same species because they are the ones that acquired that trait (rather than the other way around). For example, humans may all be relatively hairless because back in the day, those who weren't, went on to evolve into different apes.

Linda

Hey Linda - good to hear from you.

When you say 'frequency' presumably you mean proportion. If so, I'm still struggling to see how a single new-born baby (presumably, per my OP, mutations occur singularly) could, because of a mutation, have, say, larger hands than might be deemed 'normal' and pass that particular genetic fingerprint down its family tree such that, over time, the entire species acquires larger-than-average hands. On the contrary, won't other (many more, in fact) mutations be proliferating at the same time such that, over time, the human species diversifies to a point where we become more than one species? If so, other than the obvious, how come all humans are currently 'the same', or have we already 'split' previously?

 

[Taffer]

Hey Linda - good to hear from you.

When you say 'frequency' presumably you mean proportion. If so, I'm still struggling to see how a single new-born baby (presumably, per my OP, mutations occur singularly) could, because of a mutation, have, say, larger hands than might be deemed 'normal' and pass that particular genetic fingerprint down its family tree such that, over time, the entire species acquires larger-than-average hands. On the contrary, won't other (many more, in fact) mutations be proliferating at the same time such that, over time, the human species diversifies to a point where we become more than one species? If so, other than the obvious, how come all humans are currently 'the same', or have we already 'split' previously?

Are you asking why certain traits do not reach fixation in the human population?

I'm unsure of what your question is.

 

[Southwind17]

Are you asking why certain traits do not reach fixation in the human population?

I'm unsure of what your question is.

Actually, I'm asking the opposite, if by 'fixation' you mean wholesale presence, i.e. how does a single mutation that appears today become fixated in the population as a whole over time? And I'm not restricting the question to the human population, but it seems more apt to ask it in that context given the more limited scope for natural selection compared to, say, wild animals that fall victim to prey.

 

[Taffer]

Actually, I'm asking the opposite, if by 'fixation' you mean wholesale presence, i.e. how does a single mutation that appears today become fixated in the population as a whole over time? And I'm not restricting the question to the human population, but it seems more apt to ask it in that context given the more limited scope for natural selection compared to, say, wild animals that fall victim to prey.

Any allele which has a higher fitness then other alleles at the some locus will eventually move to fixation in a population, discounting genetic drift. If an allele has the same fitness as all other alleles at that locus, then the allele will either become fixed or will be lost from the population, with the probability of fixation being equal to the initial frequency of that allele in the population.

 

[Paul C. Anagnostopoulos]

It must be the case that the organism with the mutation, and its progeny, ultimately replace the entire population of organisms. Every organism that does not acquire the mutation eventually dies off.

But there are many complications. First, the mutation may occur more than once. Second, not every member of the species will have the mutation. For example, an isolated pocket of organisms won't pick it up, or may have their own mutations. The isolated pocket could then be declared a new specifies, in which case suddenly all the members of the original species do have the trait.

The "fundamental" traits of a species are probably determined in a small initial population of organisms.

~~ Paul

 

[fls]

When you say 'frequency' presumably you mean proportion. If so, I'm still struggling to see how a single new-born baby (presumably, per my OP, mutations occur singularly) could, because of a mutation, have, say, larger hands than might be deemed 'normal' and pass that particular genetic fingerprint down its family tree such that, over time, the entire species acquires larger-than-average hands.

Through Natural Selection. The gene increases in frequency because it makes the organism fitter (survival/fecundity). Alternatively, it could be associated with isolation of that population and become fixed as a trait if the population remains isolated (e.g. geographic, social, speciation)

On the contrary, won't other (many more, in fact) mutations be proliferating at the same time such that, over time, the human species diversifies to a point where we become more than one species? If so, other than the obvious, how come all humans are currently 'the same', or have we already 'split' previously?

We have obviously already split previously. Whether we do so again I think depends upon isolation of populations (unlikely as the trend is in the opposite direction).

Linda

 

[rocketdodger]

If biological evolution relies on random mutations as one of its essential ingredients, then, presumably, the chances of any particular mutation occurring simultaneously in any species at or around the same evolutionary time are minimal. How, then, do mutations 'get a hold' and persist over time, especially in, say, humans?

To answer your simple question, it is exactly nothing more than "survival of the fittest."

Note, however, that the simple "survival of the fittest" concept can be very complicated. For example, a good theory of why there are no cave men alive today is because homo sapiens helped nature kill them off.

 

[balrog666]

Actually, I'm asking the opposite, if by 'fixation' you mean wholesale presence, i.e. how does a single mutation that appears today become fixated in the population as a whole over time? And I'm not restricting the question to the human population, but it seems more apt to ask it in that context given the more limited scope for natural selection compared to, say, wild animals that fall victim to prey.

It doesn't, although it may achieve dispersion over a high percentage of the population (over a large number of generations) or it may disappear in a single generation (or fifty generations). Without catastrophic intervention, the divergence within a gene pool tends to continually broaden and produce new subspecies or species, which may then tend to separate further, depending on a host of other factors such as geographic spread, relative isolation, and sexual selection.

Within humans, we all carry (on average) 3-4 mutations differing from our own parents and the huge mixing bowl of modern travel is spreading them around as fast as possible. Some will spread faster than others (e.g., good looks, health advantages, maybe smarts) and many will just be lost.

 

[jimbob]

Southwind,

One way of looking at is is to ask how many generations you would need to go back before one had more ancestors than currently live on this planet (between 6-8 billion).

The answer is 33 (2^33=8,589,934,592).

There was a lot of inbreeding. So that number is not reached till far later.

Another way of looking at it is that about 8% (IIRC) of the male population of Asia have a single male ancestor, and the best guess is that this came about 700 years ago. The time of the Mongol Horde.

That is an example of how a mutation (in this case fairly "neutral" markers on the Y-chromosome) can spread through a population.

ETA: I think the ancestor is supposed to be Tamerlane and not Ghengis Kahn

 

[Soapy Sam]

southwind- I think you are having difficulty imagining how a single mutation , occurring in a single body, can spread through a population of 10 (or whatever) billion mammals with a generation time around 20 years.

In fact, it probably can't. This has led some people to suggest that the human race is somehow no longer subject to selection. That's false, but it's evident that no mutation , however advantageous, can spread fast through a gene pool that large if it starts in a single body. But it need not start that way.

Remember, mutations are not entirely random. They are decreed by the nature of what mutates. Some are far more likely than others and occur frequently. A point mutation that leads to a minor change in a specific protein may exist commonly in the gene pool and may occur spontaneously in a significant percentage of germ line replicators. Let's say 3% of sperm carry it and 3 % of eggs. It may be only one copy is needed to have a very minor developmental effect, or it may need two copies.
Both effects will then exist all the time in a population, perhaps at quite high frequency. They may have existed for millennia, at a stable level. If some environmental or behavioural change then gives this mutation a selective advantage, it may spread explosively, replacing an alternative gene in a few generations.

For example, if a particular mutation gives immunity to a fatal disease such as Bird Flu?
It may be stable now in 1% of the populace, but in the absence of bird flu, it produces a protein which has a trivial difference from the "normal" protein, with no physiological effect at all. But after an epidemic, that gene might be found in 25% of survivors.
That sounds a bit SF-ish, till you ask this question - is there any significant difference in allelle distributions between the male population of any AIDS affected African area amongst (say) males aged 2-19 and those aged 30-60?

If global warming reintroduced malaria to America and Europe, the significant percentage of folk with genes for Thallassaemia and sickle cell anaemia (both of which offer malaria resistance) would have an advantage. Since those folk tend to be African or Mediterranean types, the appearance of the North American population might change significantly in just a few hundred years.

 

[DavidS]

If biological evolution relies on random mutations as one of its essential ingredients...

This bothers me every time I hear one of its variations.

Somebody please correct me if I'm wrong below:

The essential ingredient of "biological evolution" is selection.

"Biological evolution" does not rely on random mutations. That is, evolution operates not on the mutations' randomness, but on their subsequent survival and reproduction advantage.

The beauty of evolutionary selection is that it works in spite of, rather than because of, random mutations. If mutations could be generated deterministically, evolution would still work just fine to select the most advantageous for survival. Random mutations simply include (probably) a higher proportion that are not advantageous and get "filtered out" by selection pressures.

 

[jimbob]

DavidS,

I'd say that without any supernatural intervention, you need both.

The random variations that might by chance be "better". And the natural selection to cull those that aren't.

ETA: Once sufficient variation exists within a population limited evolution can occur within sexual recombination, but mutation was needed to build up this variation.

 

[drkitten]

Actually, I'm asking the opposite, if by 'fixation' you mean wholesale presence, i.e. how does a single mutation that appears today become fixated in the population as a whole over time?

Simple. Everyone that doesn't have that mutation eventually dies off.

Let's take a simple (overly simple) boom-bust reproductive cycle as an example. We have a population of 1000 common or garden widgets, happily living their widget life as long as they're not killed and eaten by widget hawks or killed by the periodic widget plagues that sweep through the land. Over its lifetime, each widget generally produces four offspring, of which two survive to adulthood. So next generation, there will be 2000 widgets, then 4000, then 8000, until overcrowding triggers a plague and the population gets cut down to 1000 again.

I am a unique mutant, better at avoiding widget hawks, and as a result, three of my four children (heritably) survive until adulthood. So next generation there will be 2001 widgets, of which 1998 are normal and three are mutants. The next generation will have 3996 normal widgets and 9 mutants, the generation after that will have 7992 normal widgets and 27 mutants.

Notice that already the frequencies have increased from 1:999to 27:7992, from 0.1% of the population to nearly 0.3%. So when the plagues come (and kill everyone unformly), on average 3 -- not 1 -- mutants will survive in every group of 1000 surviors. Let's assume only two survive, for conservatism.

So now run the numbers again. Starting with a pool of 998 normals and two mutants, you get 1996 normals and 6 mutants, 3992 normals and 18 mutants, and 7984 normals and 54 mutants. At this point, nearly one percent of the population carries my mutant hawk-avoidance gene.

So let's say that 992 of the post-plague survivors are normal and 8 are mutants. Next generations, we will have 1984 normals and 24 mutants, 3968 normals and 72 mutants, and finally 7936 normals and a whopping 216 mutants, more than 2.5% of the population (one in forty).

It took only nine generations for my mutant gene to spread from one person in one-thousand to one person in forty. Given a hundred generations, how many non-mutant widgets do you think would be left?

 

[Southwind17]

Simple. Everyone that doesn't have that mutation eventually dies off.

Let's take a simple (overly simple) boom-bust reproductive cycle as an example. We have a population of 1000 common or garden widgets, happily living their widget life as long as they're not killed and eaten by widget hawks or killed by the periodic widget plagues that sweep through the land. Over its lifetime, each widget generally produces four offspring, of which two survive to adulthood. So next generation, there will be 2000 widgets, then 4000, then 8000, until overcrowding triggers a plague and the population gets cut down to 1000 again.

I am a unique mutant, better at avoiding widget hawks, and as a result, three of my four children (heritably) survive until adulthood. So next generation there will be 2001 widgets, of which 1998 are normal and three are mutants. The next generation will have 3996 normal widgets and 9 mutants, the generation after that will have 7992 normal widgets and 27 mutants.

Notice that already the frequencies have increased from 1:999to 27:7992, from 0.1% of the population to nearly 0.3%. So when the plagues come (and kill everyone unformly), on average 3 -- not 1 -- mutants will survive in every group of 1000 surviors. Let's assume only two survive, for conservatism.

So now run the numbers again. Starting with a pool of 998 normals and two mutants, you get 1996 normals and 6 mutants, 3992 normals and 18 mutants, and 7984 normals and 54 mutants. At this point, nearly one percent of the population carries my mutant hawk-avoidance gene.

So let's say that 992 of the post-plague survivors are normal and 8 are mutants. Next generations, we will have 1984 normals and 24 mutants, 3968 normals and 72 mutants, and finally 7936 normals and a whopping 216 mutants, more than 2.5% of the population (one in forty).

It took only nine generations for my mutant gene to spread from one person in one-thousand to one person in forty. Given a hundred generations, how many non-mutant widgets do you think would be left?

I don't think it's this simple, because you make a huge assumption, namely that the mutation to which you allude leads to a greater chance of survival. What if we're talking about an 'indifferent' mutation? This is why I chose humans as the specimen species, because there can, presumably, be many mutations, even 'detrimental' varieties, that, because of human protectionism (medicine, lack of natural threats, social security, etc), do not lead to premature death prior to procreation.

Let's say we use the arguably ludicrous hypothetical example of somebody acquiring a sixth finger on each (or one!) hand. Assuming that person procreates we should, presumably, expect to see the number of six-fingered people increasing over time. But the number of five-fingered people is also increasing, generally directly proportionally. Should we expect everybody in the future to have six fingers, given a geological timescale? If not, how did the vast majority of current members of each species essentially come to be biologically identical (I don't know many six-fingered people!)?

 

[Southwind17]

This bothers me every time I hear one of its variations.

Somebody please correct me if I'm wrong below:

The essential ingredient of "biological evolution" is selection.

"Biological evolution" does not rely on random mutations. That is, evolution operates not on the mutations' randomness, but on their subsequent survival and reproduction advantage.

The beauty of evolutionary selection is that it works in spite of, rather than because of, random mutations. If mutations could be generated deterministically, evolution would still work just fine to select the most advantageous for survival. Random mutations simply include (probably) a higher proportion that are not advantageous and get "filtered out" by selection pressures.

DavidS,

I'd say that without any supernatural intervention, you need both.

The random variations that might by chance be "better". And the natural selection to cull those that aren't.

ETA: Once sufficient variation exists within a population limited evolution can occur within sexual recombination, but mutation was needed to build up this variation.

I agree with jimbob. DavidS, if you read my post carefully you will see that I wrote "... one of its essential ingredients ..." (emphasis added).

 

[Taffer]

I don't think it's this simple, because you make a huge assumption, namely that the mutation to which you allude leads to a greater chance of survival. What if we're talking about an 'indifferent' mutation? This is why I chose humans as the specimen species, because there can, presumably, be many mutations, even 'detrimental' varieties, that, because of human protectionism (medicine, lack of natural threats, social security, etc), do not lead to premature death prior to procreation.

A mutation which does not have any selection pressures working upon it will be affected by genetic drift. It will, eventually, either be lost from the population, or drift to fixation. The probability of such a mutation becoming fixed in a population is directly proportional to the frequency of that mutation.

 

[Roboramma]

I don't think it's this simple, because you make a huge assumption, namely that the mutation to which you allude leads to a greater chance of survival. What if we're talking about an 'indifferent' mutation? This is why I chose humans as the specimen species, because there can, presumably, be many mutations, even 'detrimental' varieties, that, because of human protectionism (medicine, lack of natural threats, social security, etc), do not lead to premature death prior to procreation.

So you only want to talk about mutations that are not subject to selection pressures?

Let's say we use the arguably ludicrous hypothetical example of somebody acquiring a sixth finger on each (or one!) hand. Assuming that person procreates we should, presumably, expect to see the number of six-fingered people increasing over time.

Why?
If the total population size is also increasing, and six-fingered people aren't selected against, then sure. But if the population stays stable the progress of the mutation (increasing or decreasing in abundance in the population) should also stay relatively stable. Actually it will change basically randomly.

But the number of five-fingered people is also increasing, generally directly proportionally. Should we expect everybody in the future to have six fingers, given a geological timescale?

Depending on the size of the population and the frequency of the mutation (how often it occurs that five fingered parents give birth to six-fingered offspring), we might expect one mutation or the other to come to fixation at some point.
But then I'd imagine that the mutation will occur again some time after that.

If not, how did the vast majority of current members of each species essentially come to be biologically identical

But of course they aren't biologically identical. You and I are not identical twins. Nor were your parents - and lucky for you because if they were you'd have a decent chance of genetic disease.
There is a certain amount of genetic variation in the population. How is this maintained? It's a good question, but one way is exactly what you referred to - neutral mutations.

(I don't know many six-fingered people!)?

You don't know many six fingered people, but perhaps this is because six-fingered people are selected against? Perhaps the mutation isn't a neutral one?

The fact is that there is a decent amount of genetic variation in the population, and yet most humans still have two arms, two legs, two eyes, functioning red blood cells, livers, etc.
The mutations that would alter those things are selected against. The mutations that make those small differences, like how wide apart your eyes are, or a tiny chance in the shape of your bladder, are not. Or, though they may be selected against, are selected against weakly enough, and occur often enough, that they are still present in a high percentage of the population.

 

[Roboramma]

A mutation which does not have any selection pressures working upon it will be affected by genetic drift. It will, eventually, either be lost from the population, or drift to fixation. The probability of such a mutation becoming fixed in a population is directly proportional to the frequency of that mutation.

Hey Taffer, I remembered reading this, and so looked it up before writing my last post. Found the relevant section in that old and probably out of date textbook - Sociobiology - where he says the same thing. He goes in to why but I don't quite understand it. I remember spending about twenty minutes trying to understand exactly and making sense of it when I first read it, but now it escapes me:

Here's the relevant quote:

The probabiliy that a particular mutant will ultimately be fixed is u*, the rate at which this kind of mutant appears in the population as a whole. This remarkably simple result is obtained as follows. Once the individual mutant gene comes into being, it constitues exactly 1/2N of all genes at it's locus in the population. Since it is neutral, it has the same chance as every other gene present at the moment of its origin of having its descendants fixed at some future date in all 2N positions in the population. In other words, the chance that the descendants of a particular neutral mutant will be fixed to the exclusion of all other genes is 1/2N. It follows that the probability that some neutral gene that arose (2Nu) times the probability that one in particular will be fixed (1/2N); this product is u. Also, the average interval between the origination of successful mutants is 1/u.

Could you explain this to me?
Specifically I don't understand this part: "Once the individual mutant gene comes into being, it constitues exactly 1/2N of all genes at it's locus in the population."
Why?
Maybe I'm unclear as to what N is...

PS Southwind, maybe if they can explain this to me it will make sense to you too...

* I don't know how to write greek characters.