evolution: loads and loads of genes

[Dak]

i've only ever really studied evolution from a molecular pov before, and i just realised that theres something that i really dont savvy about the bigger picture of evolution.

 

if we take one gene, and it mutates, and this mutation is a slight inprovement, then natural selection will propogate it throughought a population due to the increase in the fitness to survive/reproduce it confurs upon the organism. i get that it's a bit more complicated than that, but i get the principle; what i dont get is how loads of different genes can be subject to natural evolution at once.

 

eg, imagine you have a whopping great big genome. the organism is going to have one fitness to reproduce, which will be an aggregate of the 'fitness to reproduce bonusus' of all the genes. if we examine one gene, then, my problem is, it seems as if this gene will have it's 'fitness bonus' effectively masked by the millions of other genes (unless it's a huge benifit -- eg, sterility would, obviously, be such a huge disadvantage that it couldn't be masked by the other genes); so, then, how does one gene ever have enough of a relevent effect on the organism to become subject to natural selection?

 

in other words, how does natural selection 'see' an individual gene amongst all the others?

 

(i also see how NS works on an individual level; i'm just having trouble seeing how NS acting upon an individual translates to NS acting upon individual genes simultaniously, even over generations; how does NS acting on individuals translate to a change in allele frequency dependant upon the 'benifit' of said allele?)

[Mokele]

in other words, how does natural selection 'see' an individual gene amongst all the others?

 

It does and doesn't. If the gene has a huge effect, like albinism, then it gets seen. But if it has only a minor effect on selection, say a 1% average increase in offspring, the effect is often not noticeable and the gene frequency is simply subject to genetic drift.

 

For more on this, look up "neutral gene theory" and "nearly-neutral gene theory" along with "haldane's paradox/dilemma".

 

Mokele

[Bluenoise]

in other words, how does natural selection 'see' an individual gene amongst all the others?

 

 

It's see's those most relavent in the Environment the organism experiences to increasing it's chance of survival. Which greatly decrease the total pool of competing influences. Also most genes between individuals are pretty much identical. So selection isn't possible on a gene that is uniform.

 

Generally you can consider which genes may be a limiting factor for the ability to reproduce and ensure the survivial of those offspring.

Now when the best available of that gene becomes overwhelmingly common in a population it is no long very limiting between individuals. This leaves more chance that selection will occur on other less significant traints, or maybe a better version of these genes will emerge and become the most limiting factor for competative survival between individuals.

 

Now this is really a theory made up on the spot. But you can see a example of how this total pool can be drastically reduced. Which virtually enables selection on just a few or even one trait well over all others.

 

(Of course if a negative mutation occurs for the individual this may drastically effect them. But typically they probably wont spread it, and we don't consider evolution on an individual basis.)

[lucaspa]

i've only ever really studied evolution from a molecular pov before, and i just realised that theres something that i really dont savvy about the bigger picture of evolution.

 

if we take one gene, and it mutates, and this mutation is a slight inprovement, then natural selection will propogate it throughought a population due to the increase in the fitness to survive/reproduce it confurs upon the organism. i get that it's a bit more complicated than that, but i get the principle; what i dont get is how loads of different genes can be subject to natural evolution at once.

 

It's simple. It's the individual that is the object of selection, not the individual gene. So it is the package of genes that is the individual organism that is being selected.

 

And that is the genius of natural selection: it can see the totality.

 

so, then, how does one gene ever have enough of a relevent effect on the organism to become subject to natural selection?

 

As long as it has ANY effect, natural selection will "see" it. The equations of population genetics are very precise, and as long as the selection coefficient has ANY positive value, then the equations guarantee that, eventually, that allele will be "fixed" -- be in every member of the population.

 

Here are the equations and, hopefully, they will help:

 

Remember that, in the absence of any outside influence, such as natural selection, the frequency of an allele does not change from generation to generation. That is, if you have a population of 100 and 10 individuals have allele A and 90 have allele a, the next generation will be exactly the same: 10 A and 90 a. This is called the Hardy-Weinberg Law. Frequencies are symbolized mathematically by p and q. W is the relative fitness value. So we have W(A), W(B), and W(AB). The last is the fitness of the heterozygote in a sexually reproducting population.

 

So, for the first generation the frequency p of A in the population is: p^2 +2pq + q^2. Straight Mendelian genetics.

 

The frequency of p in the next generation after selection is: p' = p^2W(A) + pq W(AB)/p^2W(A) + 2pq W(AB) + q^2 (WB).

 

Now, if W(A) and W(AB) are higher than W(B), it can be seen that p' will increase.

 

You can see all this and a lot more in Chapters 4 and 13 in Futuyma's Evolutionary Biology, 1999.

 

Remember Hardy-Weinberg. The frequency of an allele remains unchanged from generation to generation in the absence of outside influence. Therefore, the fitness of a new mutation is defined as the ratio of the number of progeny actually produced divided by the number of progeny expected by Mendelian genetics. This is going to be greater than one in the case of alleles with a survival advantage. From that we get a selection coefficient such that fitness = 1 - s.

 

Now, doing the math we find that the advantageous allele A increases in frequency, per generation, by the amount delta p = (1/2)spq/(1-q).

 

If you look at the equation, you see that delta p is positive as long as s is greater than 0, even if it is very small. Eventually p will equal 1, which means that every member of the population will have the allele. Thus, a characteristic with even a miniscule advantage will be fixed by natural selection. "Fixed" means every individual will have the allele.

[lucaspa]

If the gene has a huge effect, like albinism, then it gets seen. But if it has only a minor effect on selection, say a 1% average increase in offspring, the effect is often not noticeable and the gene frequency is simply subject to genetic drift.

 

Sorry, but that is not true. See the previous post and the equations therein. Genetic drift only operates if the population size is VERY small. Otherwise the number of generations it takes to fixation is simply way too long -- longer than the lifetime of the species by a couple of orders of magnitude.

 

"neutral gene theory" is something different.

[Mokele]

Genetic drift only operates if the population size is VERY small. Otherwise the number of generations it takes to fixation is simply way too long -- longer than the lifetime of the species by a couple of orders of magnitude.

 

Genetic drift is *always* in effect in a non-infinite population; it's just usually overwhelmed to the point of utter insignificance. But chance is *ALWAYS* there, and gene frequencies will always fluctuate slightly due to possum w37083 getting hit by a meteor.

 

And remember, if a mutation occurs, there's a period at the beginning when only *one* animal has it. If that happens to be the animal that got hit by the meteor, well, it drifted to fixation all right, just to zero.

 

Finally, "small population" may be the normal state, depending on species. What about something like a large mammal carnivore? A stable population may only be a few thousand individuals covering thousands or tens of thousands of square miles of range. At those numbers, drift can *definitely* have an effect.

 

Mokele

[lucaspa]

Genetic drift is *always* in effect in a non-infinite population; it's just usually overwhelmed to the point of utter insignificance.

 

Which is what I said.

 

But chance is *ALWAYS* there, and gene frequencies will always fluctuate slightly due to possum w37083 getting hit by a meteor.

And remember, if a mutation occurs, there's a period at the beginning when only *one* animal has it. If that happens to be the animal that got hit by the meteor, well, it drifted to fixation all right, just to zero.

 

That's not fixation, it's elimination. Fixation is defined as EVERY individual in the population has the allele or trait. You are saying that NO individual has it. So, in this case the population genetics doesn't change, does it. The frequency of that particular allele was 0 before the possum was born, and it will be 0 in the next generation.

 

But for the evolution of new traits to occur and populations to permanently change, fixation is required. So the essential part of genetic drift for evolution is NOT the elimination of individuals. After all, the equivalent of that allele or trait will occur again. And again. And again. What matters is whether the allele/trait can become fixed. See below for the odds of that and remember the odds of fixation for an allele/trait under natural selection.

 

Finally, "small population" may be the normal state, depending on species. What about something like a large mammal carnivore? A stable population may only be a few thousand individuals covering thousands or tens of thousands of square miles of range. At those numbers, drift can *definitely* have an effect.

 

Sorry, but "a few thousand" is way to large for genetic drift to have an effect.

 

Mathematics. Futuyma page 393

 

Kimura and then Li and Gauer derived the probability of an allele being fixed in the population. The probability of fixation of an allele A2 where the fitness of the genotypes are: A1A1 = 1, A1A2 = 1 +s, and A2A2 = 1 +2s is:

 

P = 1 - e^2Nsq/1 - e^-4Nq where e = the base of natural logarithms = 2.718, N = effective population size (breeding pairs), s = selection coefficient, and q = the initial frequency of the allele in the population. For a mutation, q = 1/2N

 

Where s = 0 (genetic drift) then the equation reduces to P = 1/2N. The influence on fixation is obvious. Double the population and you halve the probability. Any N > 50 really reduces P. At N = 50 (100 total individuals), p = 0.01 Now, for "a few thousand", say 3,000, P = 1/6,000!

 

No, for genetic drift to have a chance of having an effect, you need N < 50. And most populations are not even close to that. We are seeing that now with some endangered species. Genetic drift is most likely to happen either at founder events or during extinction.

 

If I remember correctly (and let me check this tonight), the number of generations required for fixation by genetic drift is 2^N/2. Look at this as N increases. For a population of even 2,000, that is 1.07 x 10^301 generations. For large carnivores, let's be generous and say that generation time is 3 years. That's 3.21 x 10^301 years! Since the universe is only 13 x 10^9 years old, it ain't never gonna happen.

[Dak]

cheers for all the responses

 

It's simple. It's the individual that is the object of selection, not the individual gene. So it is the package of genes that is the individual organism that is being selected.

 

actually, this is what was confusing me. evolution acts upon individuals, but it doesnt affect individuals -- individuals cannot evolve, and, barring a species that clones, evolution cannot act to propogate an individual.

 

eg, just look at a handfull of alleles, with the following arbritrary 'fitness' bonuses:

 

a 13

b 12

c 2

d 15

e 0

f 6

g 21

 

giving the organism with this very tiny genome an overall fitness of 68.

 

now, lets look at an alternate a allele, which is slightly less good, and has a fitness bonus of only 12.

 

comparing the two alleles:

 

a1: 13

a2: 12

 

it seems reasonable that a1 will dominate the population. however, if we look at two individuals with these alleles:

 

a1bcdefg = 68

a2bcdefg = 67

 

Now, the difference seems less relevent. look at two individuals with bigger genomes:

 

a1bc......z = 953

a2bc......z = 952

 

and the difference looks negligable.

 

works for offspring too:

 

aXb2c1d2....z2 = 947

 

if aX is a1, then the fitness will be 960; if it's a2 it'll be 959. seems practically irrelevent wether the individual inherits a1 from it's dad, or a2...

 

in the above cases, the contribution of the a allele seems negligable, and thus hard for evolution to spot. hence, i was wondering how evolution 'spots' relatively small fitness bonuses amongst all the other alleles in a genome.

 

I think this makes more sence in my head with the assumption that small improvements/degredations are 'nearly neutral', and the assumption that, untill an allele reaches a certain level within the population, it more-or-less evolves neutrally... tho i'm still having trouble seeing how all these alleles are naturally selected simultaniously.

 

(btw, i'm trying to get a mental model of how it works, not proof that it does... so, if the proof p^2 +2pq + q^2 increases in complexity in an n-power way with each generation and each new allele concidered (which i suspect it does), it's not going to be very good as a mental model )

 

That's not fixation, it's elimination. Fixation is defined as EVERY individual in the population has the allele or trait. You are saying that NO individual has it.

 

that'd be (re)fixation of the alternate allele(s). same difference imo

 

No, for genetic drift to have a chance of having an effect, you need N < 50. And most populations are not even close to that. We are seeing that now with some endangered species. Genetic drift is most likely to happen either at founder events or during extinction.

 

euch. now i'm confused

 

isn't drift based on random chance? so, intuitively, from the pov of randomly passing the allele on significantly above/below base chance level*, wouldn't it be more likely to have a significant effect as the number with the allele decreases, and less likey as the number increases, irreguardless of total population size, in the same way that n repetitions of something is more likely to be anomolous when n is small?

 

from a population pov, small would increase drift overall, but even in a large population drift could happen to an individual allele, with the probability of it significantly occouring being higher for low number alleles, but not inpossible for higher-number alleles?

 

as the number of individuals with a certain allele is limited by total population size, then i'd assume a small population (say, a couple of thousand) would limit the allele distribution such as to allow for drift. eg, if population size is a couple of thousand, you could expect a few alleles to be in HWE such that only a few hundered have the allele, which certainly allows for drift, whereas in a population of a few million, a few 10,000s will have that allele, making drift unlikely.

 

i'd expect any two alleles with equal fitness to drift about the place, irreguardless of population size...

 

*including NS stuffage.

[lucaspa]

actually, this is what was confusing me. evolution acts upon individuals, but it doesnt affect individuals -- individuals cannot evolve, and, barring a species that clones, evolution cannot act to propogate an individual.

 

You are confusing natural selection and evolution. Evolution is, briefly, "descent with modification". Natural selection is a major part of the "modification". Does that help your confusion?

 

We are born with our alleles and our genome does not change during our lifetime. Now, in a population of individuals, each individual varies. So if you plot some character on the x-axis vs the number of individuals who have that character on the y-axis, you get a bell-shaped curve. Let's try just fur length in deer. Say you have the top of the curve (mean) at 1.0 cm and the standard deviation of the curve is 0.25. This means that 2/3 of all the individuals in the population will have fur length between 0.75 and 1.25 cm. 95% of the individuals will have fur length between 0.5 and 1.5 cm.

 

But the fur length of each individual is set by the alleles.

 

Now suppose you have a climate growing colder and, over the next ten years, you have average colder winters that result in all deer below 0.75 cm fur length dying of cold. Now you've shifted the bell shaped curve to the right. The average fur length for the population is now 1.2 cm. In addition, some deer are born with fur length longer than 1.5 cm. These deer do even better over the next 100 years. So they leave even more offsprings and that shifts the curve even more to the right. Coming back 110 years later, you have a population where the average fur length is now 1.75 cm and the standard deviation is still 0.25. So 95% of the deer have fur length between 1.25 cm and 2.25 cm. The population is different from the original

 

eg, just look at a handfull of alleles, with the following arbritrary 'fitness' bonuses:

 

First, we don't have to be arbitrary and invent "fitness bonus". Fitness is the ratio of the progeny actually produced to the progeny expected from Mendelian inheritance. You can see that it is going to be a fraction. From that you get a selection coefficient s = 1 - fitness. So s is between -1 and 1 and 0 = neutral. A page you want is http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/H/Hardy_Weinberg.html

 

it seems reasonable that a1 will dominate the population. however, if we look at two individuals with these alleles:

 

a1bcdefg = 68

a2bcdefg = 67

a1bc......z = 953

a2bc......z = 952

 

You are now talking about polygenic traits. The fallacy you are working under is that relative fitness of alleles is additive when you do a polygenic trait. But remember, it is the trait being selected. So the trait has a selection coefficient. Or even the set of alleles has a fitness coefficient. So the ration doesn't decrease the way you say.

 

In a polygenic trait if a1bcde has s = 0.2 then a1 has s = 0.2. The selection coefficient isn't "diluted" like you are doing.

 

Now that makes your problem go away, doesn't it?

 

(btw, i'm trying to get a mental model of how it works, not proof that it does... so, if the proof p^2 +2pq + q^2 increases in complexity in an n-power way with each generation and each new allele concidered (which i suspect it does), it's not going to be very good as a mental model

 

It doesn't. Instead, what you do is add more terms to the equation, but the power remains the same.

 

that'd be (re)fixation of the alternate allele(s). same difference imo

 

No, because the term "fixation" refers to a specific allele, not a relative term. So we speak of fixation of a1. If a1 is lost, that doesn't say anything about a2, a3, etc. Also, if you use the plural "alleles", you don't have fixation of any of them. Because fixation is when ONE allele only is present in the population.

 

euch. now i'm confused

 

isn't drift based on random chance? so, intuitively, from the pov of randomly passing the allele on significantly above/below base chance level*, wouldn't it be more likely to have a significant effect as the number with the allele decreases, and less likey as the number increases, irreguardless of total population size, in the same way that n repetitions of something is more likely to be anomolous when n is small?

 

There is no "above/below base chance level" in genetic drift. In genetic drift, the allele frequency changes by pure chance. If you start out with 2 alleles at a locus, by pure chance one allele will be fixed and the other eliminated -- eventually. Of course, if the population is "large", that "eventually" is so slow that the gene frequency of a1 and a2 doesn't change from generation to generation.

 

However, if the population is very small (<50 breeding pairs), then losing just one individual can skew the process.

 

Let's take simple examples. We have 10,000 individuals (5,000 breeding pairs) and the frequency of both a1 and a2 is 0.5 (5,000 individuals each of a1 and a2). So in the next generation one of the a1 dies accidentally so we have 4,999 of a1 and 5,000 of a2. The frequency of a1 is now 4999/9999 = 0.5

 

BUY, we have 10 breeding pairs (20 individuals) with 10 of a1 and 10 of a2. One of the a1 dies in the next generation. Now we have 9 a1 out of population of 19 = 0.474. The frequency has shifted quite a bit by chance.

 

So the chance that one or the other allele will be fixed by chance alone increases if the population decreases. Extinction lowers a population to a very few individuals right before the end, doesn't it? Founder events are defined as involving 2-10 individuals.

 

i'd expect any two alleles with equal fitness to drift about the place, irreguardless of population size...

 

No, two alleles with equal fitness will reach equilibrium at 0.5 in a large population. In a small population, they will be subject to genetic drift like any other allele. Genetic drift is independent of fitness.

[lucaspa]

lucaspa: "If I remember correctly (and let me check this tonight), the number of generations required for fixation by genetic drift is 2^N/2."

 

OK, I checked and my memory was faulty in regard to the equation. The number of generations required for fixation purely by genetic drift is 4N. N is the effective size of the population -- it is the number of individuals participating in breeding.

 

So, back to "a few thousand" large carnivores. Let's do the minimum of 3,000. That's still 12,000 generations (a lot less than I originally calculated) for fixation by genetic drift alone. However, we have to take the number of years between an individual is born and when it can sire an offspring. For humans generation time is about 20 years. That would be 240,000 years for fixation by genetic drift. Since H. sapiens as a species is, at most, 200,000 years old, that is longer than the lifespan of our species.

 

Lions, cheetahs, tigers, etc. have shorter generation times. For instance, lions reach sexual maturity in about 3 years. So fixation by genetic drift could occur in that species in 36,000 years if the population were 3,000.

 

And yes, to answer questions I'm sure will be asked, if the species is split into demes with smaller N, then genetic drift can take place within the demes within a reasonable period of time.

[Dak]

You are confusing natural selection and evolution. Evolution is, briefly, "descent with modification". Natural selection is a major part of the "modification". Does that help your confusion?

 

We are born with our alleles and our genome does not change during our lifetime. Now, in a population of individuals, each individual varies. So if you plot some character on the x-axis vs the number of individuals who have that character on the y-axis, you get a bell-shaped curve. Let's try just fur length in deer. Say you have the top of the curve (mean) at 1.0 cm and the standard deviation of the curve is 0.25. This means that 2/3 of all the individuals in the population will have fur length between 0.75 and 1.25 cm. 95% of the individuals will have fur length between 0.5 and 1.5 cm.

 

But the fur length of each individual is set by the alleles.

 

Now suppose you have a climate growing colder and, over the next ten years, you have average colder winters that result in all deer below 0.75 cm fur length dying of cold. Now you've shifted the bell shaped curve to the right. The average fur length for the population is now 1.2 cm. In addition, some deer are born with fur length longer than 1.5 cm. These deer do even better over the next 100 years. So they leave even more offsprings and that shifts the curve even more to the right. Coming back 110 years later, you have a population where the average fur length is now 1.75 cm and the standard deviation is still 0.25. So 95% of the deer have fur length between 1.25 cm and 2.25 cm. The population is different from the original

 

yes, i get that bit. i'm just having dificulty seeing how this simultaniously works on all the different genes.

 

You are now talking about polygenic traits. The fallacy you are working under is that relative fitness of alleles is additive when you do a polygenic trait. But remember, it is the trait being selected. So the trait has a selection coefficient. Or even the set of alleles has a fitness coefficient. So the ration doesn't decrease the way you say.

 

In a polygenic trait if a1bcde has s = 0.2 then a1 has s = 0.2. The selection coefficient isn't "diluted" like you are doing.

 

Now that makes your problem go away, doesn't it?

 

no, as i'm not talking about polygenic traits -- i'm talking about polytraitic organisms.

 

My point was that the fitness bonus from a single allele seems to be buried by all the other alleles, which seems as if it would make it invisable to NS...

 

There is no "above/below base chance level" in genetic drift. In genetic drift, the allele frequency changes by pure chance.

 

My appologies, i worded that poorly.

 

what i meant was, for a given allele A, taking natural selection and current allele frequency into account, you can work out that the next generation should probably have x copies of A (what i was reffering to as 'base chance').

 

however, by statistical fluke, you could actually have significantly greater or lesser than x copies of A, which is what i'm taking to mean drift.

 

eg, if an allele is stable at a frequency of 0.5, the next gen might have a frequency of 0.4, when it should be 0.5, with the discrepancy being down to random chance/drift.

 

i'm arguing that this can happen in populations < 50, to remind you of the original context.

 

If you start out with 2 alleles at a locus, by pure chance one allele will be fixed and the other eliminated -- eventually. Of course, if the population is "large", that "eventually" is so slow that the gene frequency of a1 and a2 doesn't change from generation to generation.

 

this sounds bizarre... fixation is not neccesary for a frequency change to occour.

 

don't the frequencies of alleles change by random chance, if all else is equal?

 

However, if the population is very small (<50 breeding pairs), then losing just one individual can skew the process.

 

Let's take simple examples. We have 10,000 individuals (5,000 breeding pairs) and the frequency of both a1 and a2 is 0.5 (5,000 individuals each of a1 and a2). So in the next generation one of the a1 dies accidentally so we have 4,999 of a1 and 5,000 of a2. The frequency of a1 is now 4999/9999 = 0.5

 

BUY, we have 10 breeding pairs (20 individuals) with 10 of a1 and 10 of a2. One of the a1 dies in the next generation. Now we have 9 a1 out of population of 19 = 0.474. The frequency has shifted quite a bit by chance.

 

So the chance that one or the other allele will be fixed by chance alone increases if the population decreases. Extinction lowers a population to a very few individuals right before the end, doesn't it? Founder events are defined as involving 2-10 individuals.

 

i wasn't aware we were talking about fixation. your words were 'effect', which i changed to 'significant effect'.

 

your examples pretty much reiterate what i said -- as the number of individuals with an allele increases, the probability of something happening by random chance that will effect the allele frequency decreases.

 

even in a large population i'd have expected an allele with a low enough frequency to be susceptable to significant drift

 

take the original population size of 2,000, and an allele with a frequency of, say, 0.25, making it present in only (roughly) 500 individuals. say the next generation is also 2,000 strong, and only 450 individuals having this trait will be a significant change.

 

the probability of only 450 having the allele by statistical fluke, when we'd expect 500, is high enough that, over a couple of generations, and given how many alleles with f=0.25 there probably are, i'd expect at least one of these alleles to jump/drop significantly in frequency due only to chance (again, what i'm understanding drift to be).

 

compare that with a population size of, say, 10,000,000, meaning an allele with f=0.25 is present in 500,000 organisms, the probability of a comparable shift by chance (from the expected 500,000 to 450,000) comparitavely tiny.

 

eg, i would have thought drift effects populations >50, that drift is likely to have an effect in inverse proportion to the number with a given allele, and that, yes, in small populations, even alleles with frequencies approaching 1 will be susceptable to drift, due to the obviouse relationship between population size and number of individuals with a given allele.

 

No, two alleles with equal fitness will reach equilibrium at 0.5 in a large population. In a small population, they will be subject to genetic drift like any other allele. Genetic drift is independent of fitness.

 

do they? that sounds counter-intuitive. if two alleles are equally good, then there should be nothing acting to promote one over the other... i'd have suspected that the most recent one (i.e, the mutant form) would be at a lower frequency, and the frequencies would randomly change?

[foodchain]

yes, i get that bit. i'm just having dificulty seeing how this simultaniously works on all the different genes.

 

 

 

no, as i'm not talking about polygenic traits -- i'm talking about polytraitic organisms.

 

My point was that the fitness bonus from a single allele seems to be buried by all the other alleles, which seems as if it would make it invisable to NS...

 

 

 

My appologies, i worded that poorly.

 

what i meant was, for a given allele A, taking natural selection and current allele frequency into account, you can work out that the next generation should probably have x copies of A (what i was reffering to as 'base chance').

 

however, by statistical fluke, you could actually have significantly greater or lesser than x copies of A, which is what i'm taking to mean drift.

 

eg, if an allele is stable at a frequency of 0.5, the next gen might have a frequency of 0.4, when it should be 0.5, with the discrepancy being down to random chance/drift.

 

i'm arguing that this can happen in populations < 50, to remind you of the original context.

 

 

 

this sounds bizarre... fixation is not neccesary for a frequency change to occour.

 

don't the frequencies of alleles change by random chance, if all else is equal?

 

 

 

i wasn't aware we were talking about fixation. your words were 'effect', which i changed to 'significant effect'.

 

your examples pretty much reiterate what i said -- as the number of individuals with an allele increases, the probability of something happening by random chance that will effect the allele frequency decreases.

 

even in a large population i'd have expected an allele with a low enough frequency to be susceptable to significant drift

 

take the original population size of 2,000, and an allele with a frequency of, say, 0.25, making it present in only (roughly) 500 individuals. say the next generation is also 2,000 strong, and only 450 individuals having this trait will be a significant change.

 

the probability of only 450 having the allele by statistical fluke, when we'd expect 500, is high enough that, over a couple of generations, and given how many alleles with f=0.25 there probably are, i'd expect at least one of these alleles to jump/drop significantly in frequency due only to chance (again, what i'm understanding drift to be).

 

compare that with a population size of, say, 10,000,000, meaning an allele with f=0.25 is present in 500,000 organisms, the probability of a comparable shift by chance (from the expected 500,000 to 450,000) comparitavely tiny.

 

eg, i would have thought drift effects populations >50, that drift is likely to have an effect in inverse proportion to the number with a given allele, and that, yes, in small populations, even alleles with frequencies approaching 1 will be susceptable to drift, due to the obviouse relationship between population size and number of individuals with a given allele.

 

 

 

do they? that sounds counter-intuitive. if two alleles are equally good, then there should be nothing acting to promote one over the other... i'd have suspected that the most recent one (i.e, the mutant form) would be at a lower frequency, and the frequencies would randomly change?

 

Not to interrupt but looking at various tests on the subject the mechanisms behind mutation, drift and so on are dynamic and of course happen to be tied to the environment in terms of fitness. Tigers teeth represent something needed in order to survive for example, such as it does not have the type of teeth you would find in something that feeds on plants.

 

Taking evolution into account of course the tiger evolved from some other life form and at some point did not exist. Its evolution and of course survival is based on its ability to survive in its host environment, or niche.

 

On a molecular scale the mechanisms behind evolution are not fully understood. The idea to me though is the amount of genetic load an organism has comes into play with mutation, and that generic mutation is not rapid. The amount of variance from say humans to our closest ancestor is around 2% if memory serves. Studying the timeline though of how long this evolution took you can see how long it takes for a successful or surviving 2% of mutation takes. Plus we are not error free overall. This to me feeds the idea of micro adding up to macroevolution.

 

Another avenue to look at such is that what mechanisms are behind evolution on a molecular scale and are they the same across the board. IN an article I posted in another debate on this forum virus attempt to mutate to survive in the host environment in response to the immune system. The immune system has a rate that cannot match the virus though, or the virus can mutate fast enough for surpass the immune system response, the other end of this though like anything is that the virus population can be killed of by its own mutation just as it can survive by such, it could be studied as both pertaining factors to the evolution of both you will then. This is why many biological mechanisms exist if I remember correctly to actually combat mutation and mutation on its own might simply naturally occur even in the form of an error. Though If memory also serves mutation in itself is not simply just one type, there are many types of mutation along with different reasons or mechanisms behind them.

 

Here is a brief link on the subject from Wikipedia.

 

http://en.wikipedia.org/wiki/Genetic_code

 

I also have another link that would be of interest to you I think as the debates probably cross paths.

 

http://www.scienceforums.net/forum/showthread.php?t=23324&page=2

[lucaspa]

no, as i'm not talking about polygenic traits -- i'm talking about polytraitic organisms.

 

My point was that the fitness bonus from a single allele seems to be buried by all the other alleles, which seems as if it would make it invisable to NS...

 

First, there is no such thing as a "fitness bonus". It's simply "fitness".

 

Second, fitness is not diluted as you are saying. Yes, in a complex organism with lots of traits, there is going to be selection on each of the traits -- separately. Why? Because each of the traits is either beneficial or not to the organism and there are so many individuals. So let's go to the trait level and have traits A1B1C1D1. What you seem to be trying to say is that having trait D2 would lower fitness and therefore trait A1 would be lowered in the individual with A1B1C1D2. A1 would not be lowered, but the fitness of the individual would be, so we would get individual A1B1C1D1 that would survive and reproduce, thus still propagating allele a1 which is responsible for trait A1.

 

what i meant was, for a given allele A, taking natural selection and current allele frequency into account, you can work out that the next generation should probably have x copies of A (what i was reffering to as 'base chance').

 

That's not "base chance". That's determinism based on natural selection. And yes, you can do that calculation. You can calculate the frequency (proportion of individuals) that have allele A in the next generation. The equation is: delta p = (1/2)spq/(1-q) where delta p = change in frequency of allele a1. q = frequency of allele a2. s = selection coefficient which is 1- fitness. So, you can calculate the x copies of a.

 

however, by statistical fluke, you could actually have significantly greater or lesser than x copies of A, which is what i'm taking to mean drift.

 

yes, that is genetic drift. BUT, such a significant change can only happen in very small populations as long as p > 0.1. That is, if p is in 10% of the population and you have a population of 1,000, changing 1 individual by accidental death isn't going to make a significant change; it will be a change of 1 individual out of 100.

 

i'm arguing that this can happen in populations < 50, to remind you of the original context. ... take the original population size of 2,000, and an allele with a frequency of, say, 0.25, making it present in only (roughly) 500 individuals. say the next generation is also 2,000 strong, and only 450 individuals having this trait will be a significant change.

 

the probability of only 450 having the allele by statistical fluke, when we'd expect 500, is high enough that, over a couple of generations, and given how many alleles with f=0.25 there probably are, i'd expect at least one of these alleles to jump/drop significantly in frequency due only to chance (again, what i'm understanding drift to be).

 

Supposedly you are arguing <50, but use an example of 2,000?

 

You never calculated the probability of your shift. And, in fact, it is quite high. You are talking a considerable selective mortality/breeding here. Hardy-Weinberg says that, by chance, the next generation should also have 500 with the allele. That is the outcome of Mendelian genetics: unless acted upon by an outside force, frequency remains constant. To go from 500 to 450 in one generation -- a 10% change in frequency from 0.25 to 0.225 in that population, you are going to have to have gene flow, selective mating, or natural selection. Chance isn't going to be that large.

 

this sounds bizarre... fixation is not neccesary for a frequency change to occour.

 

But fixation is necessary for evolutionary change to occur. In order to make a new population A1 really different from the original population A, then some alleles must be fixed and other alleles lost, so that the genetic makeup of A1 is irreversibly different from A. Otherwise you have vacillation of frequencies like you see in the peppered moth and no permanent change.

 

don't the frequencies of alleles change by random chance, if all else is equal?

 

If all else is equal, frequencies of alleles don't change at all. That's Hardy-Weinberg Law.

 

i wasn't aware we were talking about fixation. your words were 'effect', which i changed to 'significant effect'.

 

The end result of "effect", for evolutionary change, is fixation.

 

even in a large population i'd have expected an allele with a low enough frequency to be susceptable to significant drift

 

In a large population, an allele with a low frequency can be eliminated by drift. Remember, the frequency of a new mutation is 1/2N. In any population of 1,000 or more, that is very low. Thus, an allele can be eliminated by accident if the sole possessor of that allele dies. Mokele made that point earlier.

 

eg, i would have thought drift effects populations >50, that drift is likely to have an effect in inverse proportion to the number with a given allele, and that, yes, in small populations, even alleles with frequencies approaching 1 will be susceptable to drift, due to the obviouse relationship between population size and number of individuals with a given allele.

 

The effect of genetic drift on populations > 50 is negligible. The effect is so small compared to the effects of non-random mating, gene flow, and natural selection that it effectively does not exist. And yes, in populations < 50, all alleles are susceptible to drift. All you have to do is take my example of a population of 10 and plug in whatever frequency you want. However, the magnitude of the shift becomes less if you are close to fixation.

we have 10 breeding pairs (20 individuals) with 10 of a1 and 10 of a2. One of the a1 dies in the next generation. Now we have 9 a1 out of population of 19 = 0.474. The frequency has shifted quite a bit by chance.

I used p = 0.5. But lets use p = 0.9 (almost fixed) and have 18 of a1 and 2 of a2. Now one of a1 accidentally dies so we have 17 of a1 and 2 of a2. The frequency has shifted from 0.9 to 0.89. Not nearly as big a change as when we were at p = 0.5.

 

do they? that sounds counter-intuitive. if two alleles are equally good, then there should be nothing acting to promote one over the other... i'd have suspected that the most recent one (i.e, the mutant form) would be at a lower frequency, and the frequencies would randomly change?

 

Not from the equations I see. Normally, the less fit homozygote a2a2 is eliminated. Instead, in this case it has just as much fitness as a1a1 and is, therefore, kept. Therefore the number of a2a2 and a1a2 heterozygotes increase until p = 0.5. If a2 is the dominant allele, then it happens faster than if it is the recessive allele.

[Dak]

First, there is no such thing as a "fitness bonus". It's simply "fitness".

 

Second, fitness is not diluted as you are saying. Yes, in a complex organism with lots of traits, there is going to be selection on each of the traits -- separately. Why? Because each of the traits is either beneficial or not to the organism and there are so many individuals. So let's go to the trait level and have traits A1B1C1D1. What you seem to be trying to say is that having trait D2 would lower fitness and therefore trait A1 would be lowered in the individual with A1B1C1D2. A1 would not be lowered, but the fitness of the individual would be, so we would get individual A1B1C1D1 that would survive and reproduce, thus still propagating allele a1 which is responsible for trait A1.

 

by fitness bonus, i meant the increase in fitness confired unto the organism that posesses the allele, rather than the alleles fitness.

 

I get the above, but when you concider the entire organism, this still seems as if minor fitness bonuses will be watered down... the cap on bad mutations due to error catastrophy and also 'nearly neutral' mutations that mokele directed me towards help a bit, but i'm still having trouble getting my head around how so many alleles are selected for/against at once. the relative fitness of each allele -- ie, the contribution that it actually has upon the organism -- seems somewhat trivial when concidered with all the other alleles.

 

barring big, significant changes in an allele, i'm having trouble seeing how the majority of alleles can be concidered above 'nearly neutral', i suppose.

 

yes, that is genetic drift. BUT, such a significant change can only happen in very small populations as long as p > 0.1. That is, if p is in 10% of the population and you have a population of 1,000, changing 1 individual by accidental death isn't going to make a significant change; it will be a change of 1 individual out of 100.

 

yes, but changing 10 would, which is hardly on par with winning the lottery.

 

Supposedly you are arguing <50, but use an example of 2,000?

 

i meant >50, sorry.

 

You never calculated the probability of your shift. And, in fact, it is quite high. You are talking a considerable selective mortality/breeding here. Hardy-Weinberg says that, by chance, the next generation should also have 500 with the allele. That is the outcome of Mendelian genetics: unless acted upon by an outside force, frequency remains constant. To go from 500 to 450 in one generation -- a 10% change in frequency from 0.25 to 0.225 in that population, you are going to have to have gene flow, selective mating, or natural selection. Chance isn't going to be that large.

 

it's not just breeding/mortality. if i have genotype aA and have four kids with someone genotype AA, you'd expect 2 of the kids to have the allele a.

 

however, only one of them could, with a probability of 0.125. this also contributes to 'random divergences from expectation'.

 

the probability of 500 copys of an allele giving rise to 450 copies of an allele would require 50 to randomly not be passed on, through chance or through death, which i doubt is that unlikely given that several thousand alleles are probably present at this frequency, and that it could happen over more than one generation.

 

But fixation is necessary for evolutionary change to occur. In order to make a new population A1 really different from the original population A, then some alleles must be fixed and other alleles lost, so that the genetic makeup of A1 is irreversibly different from A. Otherwise you have vacillation of frequencies like you see in the peppered moth and no permanent change.

 

adaptation is still evolution. 'the change in allele frequencys over time'... if an allele frequency changes, then the species has evolved.

 

take the plague, for example. it increased the frequency of the delta-9 mutation. this change in allele frequency in responce to environmental changes in order to increase the average fitness is evolution, despite delta-9 not becoming fixed.

 

or the fact that humans used to be black, and now they're black or white. i'd still call this evolution, despite that 'white' has not become fixed.

 

If all else is equal, frequencies of alleles don't change at all. That's Hardy-Weinberg Law.

 

if two alleles are at frequency 0.4 and 0.6, and both have equal fitness, will there be pressue on the frequencies to both become 0.5?

 

if yes, i'll go of and refresh myself on HW

 

 

In a large population, an allele with a low frequency can be eliminated by drift. Remember, the frequency of a new mutation is 1/2N. In any population of 1,000 or more, that is very low. Thus, an allele can be eliminated by accident if the sole possessor of that allele dies. Mokele made that point earlier.

 

yes, and you said that it was untrue.

 

I think our majour disagrement is in what counts as an evolutionary change. I certainly dont think that fixation is required.

 

The effect of genetic drift on populations > 50 is negligible. The effect is so small compared to the effects of non-random mating, gene flow, and natural selection that it effectively does not exist. And yes, in populations < 50, all alleles are susceptible to drift. All you have to do is take my example of a population of 10 and plug in whatever frequency you want. However, the magnitude of the shift becomes less if you are close to fixation.

we have 10 breeding pairs (20 individuals) with 10 of a1 and 10 of a2. One of the a1 dies in the next generation. Now we have 9 a1 out of population of 19 = 0.474. The frequency has shifted quite a bit by chance.

I used p = 0.5. But lets use p = 0.9 (almost fixed) and have 18 of a1 and 2 of a2. Now one of a1 accidentally dies so we have 17 of a1 and 2 of a2. The frequency has shifted from 0.9 to 0.89. Not nearly as big a change as when we were at p = 0.5.

 

 

 

Not from the equations I see. Normally, the less fit homozygote a2a2 is eliminated. Instead, in this case it has just as much fitness as a1a1 and is, therefore, kept. Therefore the number of a2a2 and a1a2 heterozygotes increase until p = 0.5. If a2 is the dominant allele, then it happens faster than if it is the recessive allele.

 

what about an allele with frequency = 0.5 in a population of size = 100? or frequency = 0.1 population size = 5,000? in each case, population size > 50, but the number of organisms with the allele = 50

[lucaspa]

Not to interrupt but looking at various tests on the subject the mechanisms behind mutation, drift and so on are dynamic and of course happen to be tied to the environment in terms of fitness.

 

Both mutations and drift are NOT tied to the environment. Drift is chance. Mutations are unrelated to the needs of the individual as imposed by the environment. That is, there is no tendency to have mutations that are more fit than others. Not that we have observed, anyway. Such a skew toward beneficial mutations would require a completely different mechanism than Darwinian evolution -- such as interference by another mechanism or entity.

 

The reason you get tiger's teeth instead of horse's teeth in tigers is selection. Those individuals lucky enough to be born with teeth that worked better on a meat diet got selected. Similarly, in horses individuals that were lucky enough to be born with teeth that were fit to eat plants got selected. But in both populations there are individuals born who are unlucky and have variations for teeth more adapted to plants in tigers and more adapted to meat in horses. Those unlucky individuals don't do well in the "struggle for existence".

 

On a molecular scale the mechanisms behind evolution are not fully understood.

 

What "molecular mechanisms" are you referring to? Do you mean the genetics that result in traits visible to the naked eye, such as the shape and size of teeth? Or do you mean the mechanisms to cause mutations?

 

The idea to me though is ... that generic mutation is not rapid. The amount of variance from say humans to our closest ancestor is around 2% if memory serves. Studying the timeline though of how long this evolution took you can see how long it takes for a successful or surviving 2% of mutation takes. Plus we are not error free overall. This to me feeds the idea of micro adding up to macroevolution.

 

Evolution can be much more rapid than we have seen. In the fruit fly experiment I referred to, the new species that appeared after 2,500 generations of natural selection had a genetic difference of 3%.

 

Other experiments have shown that selection can change characteristics up to 10,000 times faster than found in the fossil record!

 

IMO, what happens is that there is quite a bit of stabilizing selection in nature. When a species is well-adapted to its niche, then natural selection works to keep the genome unchanged, because any change will result in less fitness. This is called "stabilizing" or "purifying" selection.

 

IN an article I posted in another debate on this forum virus attempt to mutate to survive in the host environment in response to the immune system. The immune system has a rate that cannot match the virus though, or the virus can mutate fast enough for surpass the immune system response, the other end of this though like anything is that the virus population can be killed of by its own mutation just as it can survive by such, it could be studied as both pertaining factors to the evolution of both you will then.

 

First, you need to be careful about teleological language. The virus did NOT "attempt to mutate". Instead, mutations happen. Because the virus population is so large -- into the trillions -- the rate of mutation is faster than what the immune system can change. If the immune system changes to one virus protein, the odds are that, out of the trillions of viruses, there will be ONE virus lucky enough to have a mutated protein that the immune system doesn't react to. And, since viruses reproduce so quickly, the lucky virus will reproduce and keep the infection going even if the immune system kills off all the other viruses.

 

Second, traits are advantageous only with respect to a particular environment. There is no such thing as a pure benefit. Every "benefit" has its cost. In HIV treatment one way to keep the virus under control is treat with anti-virals. This kills off the non-resistant viruses. A small population of resistant viruses will then slowly build up the population again. But the cost of the resistance is decreased metabolism and ability to reproduce. Once the resistant strain is dominant, then the antiviral is withdrawn. Now the resistant strain can't compete with the normal strain of HIV and it dies off as the normal HIV strain becomes dominant. Then start the anitvirals again and start the cycle over.

 

if I remember correctly to actually combat mutation and mutation on its own might simply naturally occur even in the form of an error. Though If memory also serves mutation in itself is not simply just one type, there are many types of mutation along with different reasons or mechanisms behind them.

 

ALL mutations are errors in copying DNA. Every mutation is an error -- the new DNA is not what the old DNA was. The question is how that mutation affects the individual in its present environment. Is it beneficial, harmful, or neutral?

 

Yes, there are several different types of mutations: insertions, single deletions, substitutions, duplication of various stretches of the DNA -- part of the gene, the whole gene, several genes, or even an entire chromosome. Then there are translocation, where part of a one chromosome is broken off and attaches to another chromosome. Often this happens by reversing the original base sequence. Kind of like turning a caboose end for end and hooking it up backwards to a train.