# Natural selection can put Functional Information into the genome

It is quite common for ID commenters to argue that it is not possible for evolutionary forces such as natural selection to put Functional Information or Specified Information) into the genome. Whether they know it or not, these commenters are relying on William Dembski’s Law of Conservation of Complex Specified information. It is supposed to show that Complex Specified Information cannot be put into the genome. Many people have argued that this theorem is incorrect. In my 2007 article I summarized many of these objections and added some of my own.

One of the sections of that article gave a simple computational example of mine showing natural selection putting nearly 2 bits of specified information into the genome, by replacing an equal mixture of A, T, G, and C at one site with 99.9% C.

This post is intended to show a more dramatic example along the same lines.

Suppose that we have a large population of wombats and we are following 100 loci in their genome. We will make the wombats haploid rather than diploid, to make the argument simpler (diploid wombats would give a nearly equivalent result). At each locus there are two possible alleles, which we will call 0 and 1. We start with equal gene frequencies 1/2 and 1/2 of these two alleles at each locus. We also assume no association (no linkage disequilibrium) between alleles at different loci. Initially the haploytypes (haploid genotypes) are all combinations from 00000…000 to 11111…111, all equiprobable.

Let’s assume that the 1 allele is more fit than the 0 allele at each locus. The fitness of 1 is 1.01, and the fitness of 0 is 1. We assume that the fitnesses are multiplicative, so that a haploid genotype with M alleles 1 and 100-M alleles 0 has fitness 1.01 raised to the Mth power. Initially the number of 1s and 0s will be nearly 50:50 in all genotypes. The fraction of genotypes that have 90:10 or more will be very small, in fact less than 0.0000000000000000154. So very few individuals will have high fitnesses.

What will happen to these multiple loci? This case results in the gene frequency of the 1 allele rising at each locus. The straightforward equations of theoretical population genetics show that after 214 generations of natural selection, the genotypes will now have gene frequency 0.8937253. The fraction of genotypes having 90:10 or more will then be 0.500711. So the distribution of genotypes has moved far enough toward ones of high fitness that over half of them have 90 or more 1s. If you feel that this is not far enough, consider what happens after 500 generations. The gene frequencies at each locus are then 0.99314, and the fraction of the population with more than 90 1s is then more than 0.999999999.

The essence of the notion of Functional Information, or Specified Information, is that it measures how far out on some scale the genotypes have gone. The relevant measure is fitness. Whether or not my discussion (or Dembski’s) is sound information theory, the key question is whether there is some conservation law which shows that natural selection cannot significantly improve fitness by improving adaptation. My paper argued that there is no such law. This numerical example shows a simple model of natural selection doing exactly what Dembski’s LCCSI law said it cannot do. I should note that Dembski set the threshold for Complex Specified Information far enough out on the fitness scale that we would have needed to use 500 loci in this example. We could do so — I used 100 loci here because the calculations gave less trouble with underflows.

I hope that ID commenters will take examples like this into account and change their tune.

Let me anticipate some objections and quickly answer them:

1. This is an oversimplified model, you were not realistic. Dembski’s theorems were intended to show that even in simple models, Specified (or Functional) Information could not be put into genomes. It is therefore appropriate to check that in such simplified models, where we can do the calculation. For if natural selection is in trouble in these simple models, it is in trouble more generally.

2. You have not allowed for genetic drift, which would be present in any finite population. For simplicity I left it out and did a completely deterministic model. Adding in genetic drift would complicate the presentation enormously, but would still result in the achievement of a population with all 11111…1111 genotypes after only a modest number more of generations.

3. If fitness differences are due to inviability of some genotypes, fitnesses could not exceed 1. Yes, but making the 0 allele have fitness 1/1.01 = 0.9900990099… and the 1 allele have fitness 1 could then be used, and the results would be exactly the same, as long as the ratio of fitnesses of 0 and 1 is still 1:1.01.

4. You just followed gene frequencies — what about frequencies of haplotypes? This case was set up with multiplicative fitnesses so that there would never be linkage disequilibrium, so only gene frequencies need to be followed.

I trust also that people will not raise all sorts of other matters (the origin of life, the bacterial flagellum, the origin of the universe, quantum mechanics, etc.) To do so would be to admit that they have no answer to this example, which shows that natural selection can put functional information into the genome.

This entry was posted in Uncategorized by Joe Felsenstein. Bookmark the permalink.

Been messing about with phylogenies, coalescents, theoretical population genetics, and stomping bad mathematical arguments by creationists for some years.

## 228 thoughts on “Natural selection can put Functional Information into the genome”

1. I would like to see a thread on the proposition that function is isolated and the landscape is rugged. This seems to the the only remaining scientific claim of ID advocates, and I’d like a repository of links to relevant research.

My personal opinion is that if sequences can be shown to be connectable, then ID has nothing to do.

2. SCheesman: I never said it wasn’t interesting. I find the current results rather comforting given my position.

One rarely runs into someone claiming to be a PhD physicist who does not appear to be interested in or knowledgeable about the natural world; especially one who takes his lack of interest to the point of gloating when other researchers “don’t get the instant gratification” he thinks they should be getting in their research.

Obviously research is not for you.

The gap between what we know “natrue” can accomplish and what we know is required only continues to increase, and OOL research continues to find new avenues that are unpromising. Uninteresting? Hardly!

And you “know” this how? Just what are you reading anyway, AiG, the DI, and the ICR? What do those “great bastions of research” have to offer?

What you “know is required” appears to be only in your imagination. I would suggest that you can’t even articulate what “barriers” must be overcome and what is “required” to overcome them. If you have such a clear concept, why aren’t you pulling in research money to demonstrate what you “know is required?”

Can you even lay out a research proposal from “what you know is required?” Just what turned you off to research anyway?

You claim to be a PhD physicist, yet you apparently genuflect to the likes of Dembski, Sewell, Abel, Behe, et. al.? Shouldn’t they be publishing in Physical Review Letters?

3. Mike Elzinga: One rarely runs into someone claiming to be a PhD physicist who does not appear to be interested in or knowledgeable about the natural world; especially one who takes his lack of interest to the point of gloating when other researchers “don’t get the instant gratification” he thinks they should be getting in their research.Obviously research is not for you.And you “know” this how? Just what are you reading anyway, AiG, the DI, and the ICR? What do those “great bastions of research” have to offer?What you “know is required” appears to be only in your imagination. I would suggest that you can’t even articulate what “barriers” must be overcome and what is “required” to overcome them. If you have such a clear concept, why aren’t you pulling in research money to demonstrate what you “know is required?”Can you even lay out a research proposal from “what you know is required?” Just what turned you off to research anyway?You claim to be a PhD physicist, yet you apparently genuflect to the likes of Dembski, Sewell, Abel, Behe, et. al.? Shouldn’t they be publishing in Physical Review Letters?

It is remarkable how you are able to judge my character and intelligence based merely on the fact that my interpretation of current research differs from yours. I will leave you with your anger. At present it is all you have.

4. petrushka: I would like to see a thread on the proposition that function is isolated and the landscape is rugged. This seems to the the only remaining scientific claim of ID advocates, and I’d like a repository of links to relevant research.My personal opinion is that if sequences can be shown to be connectable, then ID has nothing to do.

I completely agree with you. Show me the connections, and I am convinced.

5. SCheesman: I completely agree with you. Show me the connections, and I am convinced.

So you do not infer ID because you think that, in principle, the connections are not possible?

Because if you merely conclude “ID” because not all connections have been demonstrated, then you will always conclude “ID”!

Remember that evolutionary theory is not the theory that “there was no designer”, merely a theory about natural processes that could account for what we observe.

ID, on the other hand, is the inference that there must (with very high probability) have been a designer. The two are not symmetrical. Adopting the first merely leaves you with the claim that ID is “not proven”. Adopting the second is to make the positive claim that ID is highly probable.

6. SCheesman: I completely agree with you. Show me the connections, and I am convinced.

So all this “specified information” stuff is entirely superfluous then?

7. olegt: So all this “specified information” stuff is entirely superfluous then?

It would appear that ID has no actual argument that depends on the quantity of information. The ID argument depends entirely on the isolated islands argument.

Which is why I find it odd that they don’t address research that shows function to be a gradient across mutations.

8. olegt: So all this “specified information” stuff is entirely superfluous then?

No, I believe it is a way of measuring the distance between the any two nodes in the connections. I think the language and mathematics could be developed independent of ID. It is the contention of ID that for many of the “necessary” connections the require either a simultaneous or sequential implementation of so many specifications as to render the connection impossible under natural conditions. The same language could, in principle, be used to show the opposite, rendering ID superfluous. The language is an attempt to quantify that distance.

9. petrushka: It would appear that ID has no actual argument that depends on the quantity of information. The ID argument depends entirely on the isolated islands argument.Which is why I find it odd that they don’t address research that shows function to be a gradient across mutations.

I can’t speak for everyone, but I personally can’t see how the mere quantity of information can tell us anything about the origin of that quantity. This debate really is about origins, isn’t it? That there are are mutations and gradients, and small changes both positive, neutral, and negative I don’t dispute. The gaps (and I have no apology for calling them that), I assert, occur at the larger scale, in the origin of complex systems.

10. I’m glad you don’t disavow the term gaps, because that’s what ID boils down to.

But I’m disturbed that at one point you talk about cliffs and vertical slopes and isolated islands, and then accept gradients.

Perhaps you would care to mention an example of a vertical slope.

11. SCheesman: This debate really is about origins, isn’t it? That there are are mutations and gradients, and small changes both positive, neutral, and negative I don’t dispute. The gaps (and I have no apology for calling them that), I assert, occur at the larger scale, in the origin of complex systems.

No, it isn’t about the origins. Not in this thread, anyway. Here we are addressing the question of whether mutations and natural selection can work together to make an organism better adapted to its environment.

12. “Better adaptation” is not really the point, is it? Neutral change is most common form of evolution, isn’t it?

That, plus the fact that a pool of nearly neutral alleles in population makes the population more likely to survive environmental change. Which seems to me to be how adaptation happens.

So the question I have for ID advocates is, if function is really isolated, how do you account for the existence of neutral mutations?

13. olegt: No, it isn’t about the origins. Not in this thread, anyway. Here we are addressing the question of whether mutations and natural selection can work together to make an organism better adapted to its environment.

Sure, in this thread, but you keep asking me questions, so I keep responding.

I would answer the question in the positive, with the caveat that in practice the changes will be minor, and even then it is short-term effects of epigenetics that does the heavy lifting when it comes to environmentally induced changes that we observe. It seens to me that natural selection spends most of its energy removing the effects of deleterious mutations.

14. It seems to me that natural selection spends most of its energy removing the effects of deleterious mutations.

Meaning what? An individual having a truly deleterious mutation will not reproduce. This is not what is generally meant by selection., unless you are referring to purifying selection.

Selection is generally considered to be the label given to differential reproductive success. That implies that some variant actually confers an advantage.

15. SCheesman,

SCheesman: “No, I believe it is a way of measuring the distance between the any two nodes in the connections.”

Do you believe as most IDist’s do, that any string of bits in the window we are interested in, get reset with every generation?

What I mean by this is kairosfocus’s argument that an n bit DNA window has an improbability of 1 in (2^n).

Evolution treats improbability as 1 in (n) bits.

Which position do you take?

16. SCheesman: I would answer the question in the positive, with the caveat that in practice the changes will be minor

But of course they are minor! That’s the whole point about gradients. The systems makes its way up the fitness landscape in minor steps. Major changes occur when lots of minor steps are accumulated. This is Darwinian evolution in a nutshell.

17. It seems to be the ID position that minor steps cannot accumulate because the landscape is not composed of gradients. I’m still waiting for evidence of the vertical cliffs, and how ID responds to actual evidence of gradients.

18. SCheeseman (with apologies to Joe for the ongoing derail):

The gap between what we know “nature” can accomplish and what we know is required only continues to increase, and OOL research continues to find new avenues that are unpromising. Uninteresting? Hardly!

If we succeed in creating life from non-life, it will be interpreted as evidence that you need intelligence! So either way you win, with a theory which no evidence could disconfirm.

The limitations to what ‘intelligence’ can achieve are entirely apparent – even though we know the spec, we cannot ‘reverse engineer’ life, and until we do, we can do no more than bicker. When we have a model system, we can evaluate it. But I think that the chaos inherent in interacting living systems renders ‘intelligent’ prediction of utility an almost impossible task. You need a process that can sift alternatives without any regard to prejudged expectations – such as … oooh, let’s say, Natural Selection! But first, you need to get replication.

The problem is a deeper one than most design enthusiasts appreciate. Whatever we can do with ‘macro-world’ objects, manoeuvring them into place and bolting together before finally switching on the juice, it is a completely different world ‘down there’ on the chemical scale. As Mike says, interactions operate entirely differently from those that engineering-types might be used to. In particular, a system that harnesses energy from electrons tumbling down thermodynamic gradients, pumping protons across membranes, using that thermodynamic potential to lock energy in chemical bonds … you cannot simply ‘bolt together’ such a system, and prevent things reacting until you are ready for it. The ID enthusiast has in mind a system so complex that Nature cannot construct it – yet anything trying to construct it has a hard time. The whole operation is akin to attempting to assemble a jumbo jet in mid-air with aviation fuel coursing through the pipes, from components that are massively magnetised and attract or repel accordingly, and whose optimum operating conditions are wet for some and dry for others, or which corrode in microseconds on exposure to oxygen.

So I think you need to infer something a bit more than mere ‘intelligence’ to get this crate off the ground. Something has to suspend physics. The belief that even the simplest cell is ‘too complex’, and must have therefore needed intelligence, adds a quality that is insufficient to the task you have set it. If you believe in the Judaeo-Christian God, of course, he can do anything, but you aren’t appealing to his intelligence then, just his all-round omnipotence.

This puts me in mind of saddling up a sleek racehorse – “Intelligence – see! It’s all around us, and routinely Designs” – and then galloping off into the sunset. As we pant after you towards the OoL, we get there to find no horse in sight. The horse was abandoned, and you proceeded on foot. “Did I say Intelligence?” Sorry, I meant Omnipotence!”.

But I think a better answer for both parties is that the system started simple and built up. No, I don’t know the specification, nor can I rule out intelligence absolutely, but since complexity is routinely observed to be an emergent property, I don’t have any real trouble with it arising from interaction of simpler components, from the beginning. Even the very properties of the periodic table are emergent ones.

19. Alan Miller: “The ID enthusiast has in mind a system so complex that Nature cannot construct it – yet anything trying to construct it has a hard time. ”

This is such an important point for the ID side that their dismissing it allows us to dismiss any other ID argument.

Show us a designer, that without dismissing the laws of physics, can “implement” the design of life in an already running environment.

Show us how a designer, without the gift of prophecy, can predict the needs of life a billion years into the future.

This is not just a designer, but in reality, a god that ID is describing.

20. SCheeseman:

It seems to me that natural selection spends most of its energy removing the effects of deleterious mutations.

Heading back in the general direction of the OP …!

I trust you used ‘energy’ in a metaphorical sense… It does appear that people seem to see NS as some kind of mysterious ‘force’ (not helped by metaphorical usages such as selection ‘pressure’). The implementation of NS is obviously anything that causes some types to produce more offspring than others (which necessitates survival). Lions, cold, drought, disease resistance, sex appeal … that some ‘deleterious’ alleles are disfavoured by these challenges, it should be clear, means that others are simultaneously favoured.

NS is just a sorting process acting upon a population. Where the bulk of mutations thrown up by mutation are deleterious, then NS does indeed spend most of its ‘energy’ getting rid of them. Where most are neutral, NS expends no ‘energy’ at all – there is no selective differentiial. Where most are beneficial, it promotes a fraction, and the population adapts.

In reality, of course, the mutations thrown at the selective ‘sieve’ are of all kinds – a distribution of selective advantage, from deleterious through neutral to beneficial . NS preserves fewer of the deleterious fraction and more of the beneficial, even though the former may dwarf the latter in frequency.

But it is important that these terms are relative. A new mutation A is deleterious with respect to what it has to compete with (B). It produces fewer offspring, on the average (and that includes the extreme case, lethals, that produce none). But equally, if we had a population of all A, and the B mutant arose, B’s elevated reproductive rate is likely to favour it. Either way, there is a bias for B and against A.

The fundamental process in populations is one of sampling. Each generation is a sample of the one before, because organisms produce variable numbers of offspring (no matter what their genetic makeup). This sampling process will cause any allele to be promoted, regardless of selection. If there is no selection (all alleles are neutral), then gains and losses are balanced out – but the population still evolves towards one random allele from the starting mix. If there is a differential – a gradient – then the tendency is for the population to follow it in the direction of the greater output. But you create a gradient by tilting in any direction. Whichever way you go, outside of neutrality, you will have a discriminatory selective process that is simultaneously diluting (relatively) detrimental alleles and concentrating (relatively) beneficial ones, at each locus.

21. I’m afraid the “design is impossible” claim was sneered at amongst the denizens of UD, and listed at the top of the list of bad arguments against ID.

I haven’t seen it countered.

Of course it’s not a problem for ID advocates, because outside the courtroom, they know the designer is a omnipotent christian God.

22. olegt: But of course they are minor! That’s the whole point about gradients. The systems makes its way up the fitness landscape in minor steps. Major changes occur when lots of minor steps are accumulated. This is Darwinian evolution in a nutshell.

OK, then I need to add minor and limited. Eventually the gradient returns to the mean, like a random walk in a large bowl. This is not what evolution requires, in a nutshell.

23. Again, yes and yes and yes. I grant that beneficial mutations (by definition) will be retained. As you alluded to earlier, though, once you optimize all the particular variables related to survival there’s nowhere to go anymore except to circle about the mean in a random walk of neutral mutations; you can tilt the gradient bowl a bit by changes in the environment, but evolution in the truly transformative sense may be at a “dead end” for that particular organism. It is no more than wishful thinking to say that the surface is more like a saddle, requiring only the proper directional shove to get things evolving again up (or down) a fresh gradient.

24. petrushka: I’m glad you don’t disavow the term gaps, because that’s what ID boils down to.But I’m disturbed that at one point you talk about cliffs and vertical slopes and isolated islands, and then accept gradients.Perhaps you would care to mention an example of a vertical slope.

How about the production of the genetic code and its associated transcription machinery?

25. Are you proposing here that the genetic code happend all at once and nothing first, complete with current transcription machinery? I wonder if there is anyone who wouldn’t find this implausible.

26. Elizabeth: So you do not infer ID because you think that, in principle, the connections are not possible? Because if you merely conclude “ID” because not all connections have been demonstrated, then you will always conclude “ID”!Remember that evolutionary theory is not the theory that “there was no designer”, merely a theory about natural processes that could account for what we observe. ID, on the other hand, is the inference that there must (with very high probability) have been a designer. The two are not symmetrical. Adopting the first merely leaves you with the claim that ID is “not proven”. Adopting the second is to make the positive claim that ID is highly probable.

Hello Elizabeth. I choose ID because the evidence I see at present is that only intelligence can span those connections, not because I think in principle it could not. Nor would I cling to it merely because not ALL the connections have been established. I am open to being convinced otherwise, and a few convincing demonstrations of natural process spanning the contentious locations would certainly have me shifting. I have no philosophical objection to Darwinian evolution per se, and recognize that there indeed could even have been a designer who chose Darwinian evolution as a means to an end. ID for me is not a proof for God’s existence. I’m not sure where this puts me on your scale.

27. Flint: SCheesman, Are you proposing here that the genetic code happend all at once and nothing first, complete with current transcription machinery? I wonder if there is anyone who wouldn’t find this implausible.

I would not presume to limit any naturalistic explanation to a particular path. I’m glad that you ver that there actually do exist situations that most will find implausible; the impression I generally get is that the powers of RM+NS are limitless, and it is heresy to try to bracket them.

28. SCheesman,

I too am a skeptic! 🙂

SCheesman: “No, I believe it is a way of measuring the distance between the any two nodes in the connections.”

Do you believe as most IDist’s do, that any string of bits in the window we are interested in, get reset with every generation?

What I mean by this is kairosfocus’s argument that an n bit DNA window has an improbability of 1 in (2^n).

Evolution treats improbability as 1 in (n) bits.

Which position do you take?

29. Toronto: SCheesman,I too am a skeptic! Do you believe as most IDist’s do, that any string of bits in the window we are interested in, get reset with every generation?What I mean by this is kairosfocus’s argument that an n bit DNA window has an improbability of 1 in (2^n).Evolution treats improbability as 1 in (n) bits.Which position do you take?

Sorry, I can’t say I’m familiar with kairfocus’s argument, or that I have any particular view on it. Or maybe I do and I’m not sure where you’re coming from! I’d have to go and find it, read it and think about it. As others have suggested, this might be a bit off topic…

30. SCheesman: Hello Elizabeth.I choose ID because the evidence I see at present is that only intelligence can span those connections, not because I think in principle it could not. Nor would I cling to it merely because not ALL the connections have been established. I am open to being convinced otherwise, and a few convincing demonstrations of natural process spanning the contentious locations would certainly have me shifting. I have no philosophical objection to Darwinian evolution per se, and recognize that there indeed could even have been a designer who chose Darwinian evolution as a means to an end. ID for me is not a proof for God’s existence. I’m not sure where this puts me on your scale.

I don’t really have a scale, but that sound a reasonable position to take 🙂

What, in your view, are the “contentious locations”?

(Mine would be OOL and the ribozome, I think).

31. SCheesman,

SCheesman: “As others have suggested, this might be a bit off topic…”

This has a direct bearing on the generation of “functional information” in the genome which is our topic.

For example, a 16 bit biological window has the pattern, “0000000000000001”.

What are the odds against that last bit changing into a 1 without an Intelligent Designer’s guidance?

Is it 1 in 16 or 1 in 65,535?

This has a direct bearing on the size of population versus generation for any bit pattern to show up statistically which is your argument that you have given the term “vertical slope”.

It is the same argument put forward by Dembski and kairosfocus which they have called the “UPB”.

32. SCheesman: OK, then I need to add minor and limited. Eventually the gradient returns to the mean, like a random walk in a large bowl. This is not what evolution requires, in a nutshell.

Could you unpack this one for me? I am not sure in what sense “a gradient returns to the mean.” A gradient gives you an upward direction. You can reach a peak following the gradient, but you can’t make a loop.

33. Sorry, that should be:

What are the odds against that last bit changing into a 0 without an Intelligent Designer’s guidance?

34. I consider myself a skeptic. At the moment I am most skeptical that ID advocates have established that functional sequences are isolated, or that there is any reason to doubt a history of incremental change.

I am skeptical that any designer that is not omnipotent could design living things from scratch without using evolution. I would love to see a theory of design that does not invoke magic.

I would love to see a theory of OOL coming from a design advocate. I want to know how the designed conceived of the possibility of life, how the designer acquired the knowledge of functional sequences, how the designer anticipated the emergent properties of matter.

As far as I can tell, ID advocates simply recite the magic incantation, intelligence, like a spell from Harry Potter. Human inventions evolve incrementally, and require enormous expenditures of trial and error.

35. SCheesman: the impression I generally get is that the powers of RM+NS are limitless, and it is heresy to try to bracket them

I don’t know where you got that impression. Obviously the power of RM+NS is limited, hence the very frequent observation of extinctions.

36. Toronto: SCheesman,This has a direct bearing on the generation of “functional information” in the genome which is our topic.For example, a 16 bit biological window has the pattern, “0000000000000001”.What are the odds against that last bit changing into a 1 without an Intelligent Designer’s guidance?Is it 1 in 16 or 1 in 65,535?This has a direct bearing on the size of population versus generation for any bit pattern to show up statistically which is your argument that you have given the term “vertical slope”.It is the same argument put forward by Dembski and kairosfocus which they have called the “UPB”.

OK, I feel like a trap is about to be sprung, but I guess, if you are specifying that we are looking at one generation, and only 1 bit flips in this window per generation, then you have 1 chance in 16 of flipping the last back to zero in a single generation. I am I missing something?

37. Norm Olsen: I don’t know where you got that impression. Obviously the power of RM+NS is limited, hence the very frequent observation of extinctions.

Fair enough.

38. SCheesman,

SCheesman: “OK, I feel like a trap is about to be sprung, but I guess, if you are specifying that we are looking at one generation, and only 1 bit flips in this window per generation, then you have 1 chance in 16 of flipping the last back to zero in a single generation. I am I missing something?”

It’s not a trap at all but it is an observation that both Dembski and kairosfocus ignore.

When calculating the UPB, they take the probability to be 1 in (2^n) instead of what you and I see as 1 in n.

This means a 32 bit window has a UPB of 1 in 4 billion when they calculate it instead of 1 in 32 when we do.

When a window gets to 500 bits, their calculation is astronomical while evolution has 1 in 500.

This means that there is no reason “natural selection” cannot generate the “information” required for evolution.

Since I cannot post on UD anymore, you might want to see kairosfocus’s take on this.

This is one of those barriers to evolution that I don’t believe exists and yet the UPB keeps coming up constantly.

Depending on the response you get, I hope you will agree that the improbability they suggest is not accurate.

39. olegt: Could you unpack this one for me? I am not sure in what sense “a gradient returns to the mean.” A gradient gives you an upward direction. You can reach a peak following the gradient, but you can’t make a loop.

I think it is the idea that multiple gradients exist due to different factors, and any movement in favour of one factor due to some shift in the environment is tempered by a decrease in fitness in others, tending to keep the over-all “solution” centered among the competing factors.

40. Toronto: This means a 32 bit window has a UPB of 1 in 4 billion when they calculate it instead of 1 in 32 when we do.

They pose the problem differently; in their case you need to specify all the bits to achieve a particular function, like a combination lock, or a series of right/left turn directions to get you to a specific destination. They then ask what are odds of obtaining the required combination given the state of each bit is selected a random, so in their case it is 1 chance in 2^n.

41. SCheesman: I think it is the idea that multiple gradients exist due to different factors, and any movement in favour of one factor due to some shift in the environment is tempered by a decrease in fitness in others, tending to keep the over-all “solution” centered among the competing factors.

Huh? Fitness is a scalar function. It has a single, well-defined direction for its gradient. You can have different factors impacting reproduction but at the end of the day there is one fitness function. You seem to be talking about a flat fitness landscape or something.

42. SCheesman: They pose the problem differently; in their case you need to specify all the bits to achieve a particular function, like a combination lock, or a series of right/left turn directions to get you to a specific destination. They then ask what are odds of obtaining the required combination given the state of each bit is selected a random, so in their case it is 1 chance in 2^n.

One of the problems here is the “specify a particular function” issue. We’re back to bridge hands, where the chances of getting a particular hand (dealt in any order, say) are very small. The odds of getting SOME hand are unity. The odds of getting a winning hand are about 50%, if skill levels are equal.

So it’s one thing to say that every bit must be specified to get some observed result, and something different to calculate the odds of getting some USEFUL result. Hume pointed out 250 years ago that seen in retrospect, ANY sequence of events looks preposterously unlikely. Looking into the future, all too many are entirely plausible, and what actually happens isn’t usually even in that set!

I don’t understand this emphasis on being thunderstruck by the improbability of some specific result. ALL results are just that improbable, but SOME result seems to happen every time.

43. olegt: Huh? Fitness is a scalar function. It has a single, well-defined direction for its gradient. You can have different factors impacting reproduction but at the end of the day there is one fitness function. You seem to be talking about a flat fitness landscape or something.

No, a landscape which is the sum of a number of factors having their own maxima. In 2D like a bi-modal histogram where the peaks are close enough together to sum to a single peak. Modifying the environment might change the amplitudes of the individual peaks, and shift the location of the sum back and forth along the axis. Extend that to 3D; as the individual factors’ “attractions” weaken or strenghten with changes in the environment, the surface gradients change, and the “solution” moves toward the strenghened factor maximums. But unless you get new underlying peaks, there is only so far you can go from “center”. That’s the idea anyway. I’m not saying that is necessarily genetic reality in all cases, I’m just trying to explain how you might get “stuck”.

44. If function is like a lock combination, why are there alleles? And why do actual experiments reveal gradients?

45. Flint: I don’t understand this emphasis on being thunderstruck by the improbability of some specific result. ALL results are just that improbable, but SOME result seems to happen every time.

It just depends on the rules. Obviously if there are a lot of ways to achieve a result, it is less improbable. If it is just SOME result that is required, it’s a whole lot easier to get. But you are really comparing apples and oranges here.

46. SCheesman,

SCheesman: “They pose the problem differently; in their case you need to specify all the bits to achieve a particular function, like a combination lock, or a series of right/left turn directions to get you to a specific destination. ”

I think we can agree that all of the steps don’t have to be there for it NOT to work.

All the bit combinations however, are “explored” in “n life-form/generations”.

That’s the take away point, that the “key” we are looking for can be obtained in “n steps”, not “(2^n) steps”.

When that last bit, in the last generation flips, we have our functionality, and we have it in “n” bits, not (2^n) bits.

47. SCheesman: No, a landscape which is the sum of a number of factors having their own maxima. In 2D like a bi-modal histogram where the peaks are close enough together to sum to a single peak. Modifying the environment might change the amplitudes of the individual peaks, and shift the location of the sum back and forth along the axis. Extend that to 3D; as the individual factors’ “attractions” weaken or strenghten with changes in the environment, the surface gradients change, and the “solution” moves toward the strenghened factor maximums. But unless you get new underlying peaks, there is only so far you can go from “center”. That’s the idea anyway. I’m not saying that is necessarily genetic reality in all cases, I’m just trying to explain how you might get “stuck”.

So, you are starting with a population that is initially near a peak of its fitness. The fitness landscape changes and the peak shifts away from its previous position. The population will follow the gradient toward the new (local) maximum. Once it reaches the maximum, it will stay there. Right?

(I am neglecting jumps to other valleys that can occur in more sophisticated models including effects of random walk.)

48. petrushka: If function is like a lock combination, why are there alleles? And why do actual experiments reveal gradients?

Not all functions are like locks. That would be applicable to the construction of a new complex function like a molecular machine. Throw a bunch of proteins into your experimental beaker and make me ATP synthase (and yes, I’m aware of better ideas for making ATP synthase, I’m just giving an example of a “lock” type problem, not a description of the origin of ATP synthase). Yes, alleles have nice gradients and experiments designed to reveal them do so. I’ve already said that the whole genome is not CSI. Are you being argumentative for the sake of argument? OK… catch you tomorrow. (Yeh I know I said I’d be off a few days… man this is addictive)

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