The Amazing Toxic Asexual Bunny Mutation Simulator
by MikeGeneThe following essay was written by Wonders for Oyarsa and the views/arguments contained within do not necessarily reflect the views of Mike Gene. Mike Gene hosts such essays simply to provoke thought and promote discussion and communication.
As a Computer Scientist, I never was terribly impressed by the notion of "junk DNA". The idea that 90% of our DNA has no function is counter-intuitive at best. The human genome already seems to be surprisingly small to specify all the information required to describe how to build a human being from a single cell (implying to me some pretty good compression), and further reducing this to the information content of Microsoft Office is not what I would expect. But then again, life isn't always intuitive. Stranger truths have been found in nature, so I suppose we need to keep an open mind.
Then I remembered that we have around 96% genetic similarity to the chimpanzee - meaning large chunks of our genome can be matched up with chunks of the chimp genome almost exactly. These things seem completely at odds to me. If a portion of the genome is junk, than there should be no selective pressure to keep this portion the same. In fact, there may be a functional advantage in removing it altogether (the organism can get by with less nucleotides in its cells). Over 5 million years, it certainly feels like these junk sections would become completely scrambled, rather than maintaining almost total similarity.
So, what better way to demonstrate this than with the clear irrefutable scientific proof of a toxic asexual bunny mutation simulator?
Rules:
Toxic asexual bunnies are, well, toxic. As such, they are dangerous to everyone, including each other. A mere touch by one toxic bunny to another may be enough to kill it, though some have been known to evolve greater toxin tolerances (which in turn make them more deadly to other toxic bunnies).
- Each bunny has a DNA string of 30 English characters.
- The toxin defense gene is located in the first three characters, which must spell an English word.
- Furthermore, the organism has evolved such that only an English word starting with "BU" is sufficient to defend it under these conditions (we are simulating only a small evolutionary change).
- Each sample starts with the same bunny with the first three letters as "BUN". The rest of its genome is junk, designated by dashes for the sake of easy reading.
- As the bunnies reproduce, random mutations take place. Most of these mutations will do nothing since it occurs in the junk, but some will occur in the first three letters.
- If the mutation occurs in the first two letters, it is a harmful mutation.
- If it occurs in the third letter, there is a 1/4 chance of a new word generated, indicating a functional advantage.
- Once new bunny species dominate both groups, the new genomes are compared.
Results:
As I expected, getting a positive change in a single character to a new spices garbles the junk DNA to near oblivion. I'm getting a statistical average of about 35% similarity - a far cry from 96%, and not to far from the 9% or so that would indicate total scrambling.
Qualifiers
Obviously the mutations are sped up in my simulation, and I am not including many of the different types of mutations that actually occur (reversals, additions, deletions, splitting, moving, etc). The sample sizes of human and chimp populations are much larger than the ten or so that I show. But I think this easily offset by the sheer size of the genome, as well as the improbability of getting a truly helpful mutation that would provide a serious functional advantage.
I think the simulation sufficient to illustrate the principle - that getting a good mutation in a small area requires a large number of neutral mutations across the board (in the case of junk DNA).
Conclusion:
Folks, the bunnies don't lie. We might not know what this stuff does, but it sure ain't junk.
Wonders for Oyarsa is a programmer somewhere in the United States. When he's not working full-time, pursuing his M.S. in Computer Science part-time, and raising two kids, he likes to investigate the notion that intelligent design was involved in the writing of the Bible on his blog.
September 10th, 2007 at 10:06 am
Kimura showed mathematically that for a neutral mutation the fixation rate is identical to the mutation rate (independently of population size). Since the per nucleotide mutation rate is roughly 10^-8 per generation for eukaryotes (far lower than in your simulation), it takes about a million generations to replace 1% of the neutral nucleotides.
I guess most people would consider that a counter-intuitively slow "scrambling" rate.
Comment by Raevmo — September 10, 2007 @ 10:06 am
September 10th, 2007 at 10:29 am
Hi Raevmo -
I could certainly reduce the mutation rate of my simulation so that it takes that long. However, (besides being rather boring to watch) this would also slow down the helpful mutations, so that the final comparisons would have roughly the same similarity.
Comment by Wonders For Oyarsa — September 10, 2007 @ 10:29 am
September 10th, 2007 at 10:40 am
What's the functional advantage?
Comment by Zachriel — September 10, 2007 @ 10:40 am
September 10th, 2007 at 10:48 am
Extra toxin secretion/tolerance. Don't those purple bunnies just look more deadly? Bunnies with English words starting with "BU" always kill bunnies without them. Bunnies with English words starting with "BU" that aren't "BUN" always kill those with "BUN". I could have stuck some probability in there to make it a little more realistic, but it would just have the effect of more scrambling and making the simulation take longer.
By the way, I think it is actually more like a 1/3 chance. There are nine English three-letter words that start with "BU".
Comment by Wonders For Oyarsa — September 10, 2007 @ 10:48 am
September 10th, 2007 at 12:08 pm
Then there is no advantage. Deleterious mutations are quickly deselected. The only other changes, such as from BUN to BUG, are selectively neutral, just like the other changes in the junk areas of the sequence.
Cute program, but it doesn't seem to show what you think it does.
Comment by Zachriel — September 10, 2007 @ 12:08 pm
September 10th, 2007 at 1:04 pm
I'm saying that BUN to BUG has a selective advantage in the program. I should know - I put it in there. That's why the colored bunnies kill off the grey bunnies, while the grey bunnies kill off the white ones.
Comment by Wonders For Oyarsa — September 10, 2007 @ 1:04 pm
September 10th, 2007 at 1:14 pm
How so? If an english word starting with 'BU' and having a letter other than 'N' allows that mutant to propagate and overtake the 'BUN's it certainly appears to carry a selective advantage.
Comment by Doug — September 10, 2007 @ 1:14 pm
September 10th, 2007 at 2:20 pm
Thank you for the prompt and courteous clarification. I reread your explanation. So if I understand it now, there are three tiers of fitness; BUx (not a word), BUN and BUG (any of eight words). Is that correct? As we start with BUN, and any deleterious mutation is quickly deselected, we actually only have a single tier with any reasonable viability. (Or does each word have a different immunity?)
After running the simulation several times (as you point out above) there appears to be significant similarities between the final sequences. According to your results screen, and a cursory examination, a significant fraction of the junk sequences appear to be identical (about a third). Though you can't form a phylogenetic tree with just two branches, such identity is certainly not due to chance alone, and significant evidence of their common ancestry remains.
I'm not sure given the parameters that a third is not unexpected due to the low population and sequences sizes.
Comment by Zachriel — September 10, 2007 @ 2:20 pm
September 10th, 2007 at 6:35 pm
One more try:
BUB, BUD, BUG, BUM, BUS, BUT, BUY are best.BUx is next best.
Everything else has no immunity.
Other questions. I assume the Bunnies clone. When they clone do they always mutate? Does that mean there is never any continuity between generations? That's a mutation rate of 3% per individual with 3% required for any chance of a beneficial mutation.
I note that if only one population "speciates" then that should be sufficient. That would cut down the number of generations.
Comment by Zachriel — September 10, 2007 @ 6:35 pm
September 10th, 2007 at 7:18 pm
The words are:
BUB
BUD
BUG
BUM
BUR
BUS
BUT
BUY
Any sequence starting with these gets a score of "2".
BUN gets a score of "1".
All others get a score of "0".
Right now a cell division yields one mutated cell and the original kept the same.
Comment by Wonders For Oyarsa — September 10, 2007 @ 7:18 pm
September 10th, 2007 at 7:20 pm
Thanks.
Comment by Zachriel — September 10, 2007 @ 7:20 pm
September 10th, 2007 at 8:19 pm
One interesting thing to do, which I thought about doing, would be to make the bunnies sexual. I could make male bunnies and female bunnies kill those of the same sex, and mate with those of the opposite sex. They could each have pairs of genomes, which they would give half of to each child (pick a random set of three for each new set of three). I didn't do this simply because it would take more time to code the mechanics of attraction and sex, but it would have been cool.
I presume that doing that would actually greatly increase the rate of scrambling, since scrambles would propagate throughout the population quite quickly.
You are right - the one thing that would make beneficial mutations go quicker would be a larger population size. However, I would note that the human and chimp populations we are speaking of, while large, are not THAT large. Millions, not billions. Each random neutral mutation would have a decent shot of propagating through the entire population - though a beneficial one would do so a little quicker. Also, keep in mind that the chances of getting a beneficial mutation in my example are quite good.
The bottom line is that, if this stuff really were junk, you wouldn't get near 96%. My suspicion is that it isn't junk.
I'm thinking we rename it to "treasure DNA"…
Comment by Wonders For Oyarsa — September 10, 2007 @ 8:19 pm
September 10th, 2007 at 9:20 pm
I don't think you have demonstrated that. Your own model maintains a statistically significant amount of sequence identity. You can increase this by only requiring a single 'speciation'. And you haven't demonstrated how this would scale with substantially different parameters. (Your simulation is also countered by the actual molecular evidence.)
Comment by Zachriel — September 10, 2007 @ 9:20 pm
September 10th, 2007 at 9:22 pm
Wonders, junk DNA is also without function as you understand it correct? Some have used the term to mean anything other than protein coding genes; a holdover from the days that preceeded the RNA revolution. Others believe that RNA transcription does not necessarily signify function.
Comment by Bradford — September 10, 2007 @ 9:22 pm
September 10th, 2007 at 9:33 pm
Wonders:
If I were arguing the case for the other side I would maintain that it is precisely the above type of genomic changes that are likely to produce junk. I have not made up my mind about junk but do think it unlikely that regions of "junk," that are uniform throughout a species, are actually without function. But I think more recent genomic readouts are indicating there is more intra-species genomic variety than at first thought.
Comment by Bradford — September 10, 2007 @ 9:33 pm
September 10th, 2007 at 9:50 pm
I think this is worth mentioning. I suspect you built your model in order to demonstrate your prejudice. Instead, you should attempt to demonstrate the opposite of your actual position. What parameters can you adjust that might raise the relevant ratio? That's what scientists do anyway. If they don't, they find out soon enough when they publish.
I understand Toxic Bunnies was meant more in fun. But then we shouldn't take the results as computationally definitive.
Comment by Zachriel — September 10, 2007 @ 9:50 pm
September 10th, 2007 at 9:53 pm
Now that we're getting into this, what evidence do we have that any of the 96% similarity we have with chimps is junk?
Comment by Wonders For Oyarsa — September 10, 2007 @ 9:53 pm
September 10th, 2007 at 10:00 pm
No, of course not. But I think it is enough to demonstrate the principle, which if nothing else, should be considered formidable and suggestive.
The one parameter that makes a difference is sample size. Obviously, the more samples you have, the more likely you are to get a good mutation in one try. But I hoped to offset that by the fact that I gave the good mutation a very high likelihood of appearing (I could have started with "zoo" for instance), and made its trait so dominant that it achieves mastery without a hitch (100% victory over rivals).
For me to get anywhere near 96%, I'd have to stack the deck so high it wouldn't even be funny. Statistically, we really are talking about getting it perfectly right without a single other mutation.
Comment by Wonders For Oyarsa — September 10, 2007 @ 10:00 pm
September 10th, 2007 at 10:01 pm
Wonders:
Careful Zachriel. I've heard it said many times that lack of evidence for is not evidence against.
Comment by Bradford — September 10, 2007 @ 10:01 pm
September 10th, 2007 at 10:03 pm
You can produce all the junk you like. It's near-perfect preservation over 5 million years that I am rather dubious about.
Comment by Wonders For Oyarsa — September 10, 2007 @ 10:03 pm
September 10th, 2007 at 10:11 pm
Yes but mutations occur at an individual level. So why would there be any expectation of uniformity throughout populations when mutations are neutral with respect to fitness?
Comment by Bradford — September 10, 2007 @ 10:11 pm
September 10th, 2007 at 10:28 pm
There wouldn't be. Even if the functional DNA reached a local functional maximum, and stayed the same for hundreds of thousands of years, the junk would continue to scramble all across the population.
Comment by Wonders For Oyarsa — September 10, 2007 @ 10:28 pm
September 10th, 2007 at 10:29 pm
"Junk" is a known misnomer. It was coined more than 30 years ago by Susumu Ohno to apply to noncoding DNA. He found that a lot of DNA was scraps of genes. He suggested these scraps might be repurposed on occasion, like junk in the attic. Researchers have been studying noncoding DNA for decades. That's why we know about regulatory sequences.
I don't find it formidable. I think that sequence identity of 1/3 is reasonable as a first approximation considering the simplicity of the model.
Mutations rates can be measured over many different time-scales, and monotonic molecular clocks are substantially in agreement with evidence from other fields of study.
A reasonable cite to authority is appropriate. Informatics and neutral theory are highly developed fields. If Toxic Bunnies produces data substantially contrary to far more sophisticated models, then it is likely that you may want to revisit your assumptions. Your model should not only explain why your model is right, but why previous models are wrong.
(Unfortunately, we can't examine Toxic Bunnies in detail. It would take some time to recreate the model in order to check the results or to generalize the process.)
Fixation is a natural consequence of the relevant arithmetic. Though any particular mutation will probably be lost, some mutations will become fixed strictly by chance. Somewhat non-intuitively, the rate of neutral evolution is largely independent of population size and even generation time.
This is a very important concept, and is a mathematical result that can be confirmed by observation.
Even Toxic Bunnies shows neutral fixation within each separate population. You will find that each segregated population has a high percentage of identity within the junk sequence.
This is fundamental.
Comment by Zachriel — September 10, 2007 @ 10:29 pm
September 10th, 2007 at 10:38 pm
I completely agree that a chance fixation of a neutral mutation could occur but here is what should not be expected. Individual x experiences a germline duplication of a genomic region that includes gene x and surrounding genomic regions we'll call junk for now. This duplication is neutral with respect to fitness. Why would a future population, many generations after x, show that this duplication is both uniformly ordered and characteristic of that species?
Comment by Bradford — September 10, 2007 @ 10:38 pm
September 10th, 2007 at 10:55 pm
If the reproduction was sexual, this would not be the case. Often in my simulation, the population will fall back to one again, since the box is so small. So all of the bunnies are only a few generations apart.
With sexual reproduction, I would expect huge variation even in the same species, as the various neutral mutations get distributed across the population.
But keep in mind that there was an important reason to separate the two populations from the start. We are working on the assumption that the last common ancestor between chimps and humans was 5 million years ago.
Comment by Wonders For Oyarsa — September 10, 2007 @ 10:55 pm
September 10th, 2007 at 11:19 pm
I don't mind an appeal to authority. Tell me what exactly has been observed, and how it contradicts my model. I am not a biologist, though I am studying bioinformatics, so you'll need to explain the findings in terms I can understand.
Show me how the assumptions of the other models were different from my own, in terms that apply to my highly simplified one. Or, if there is complexity that is absolutely necessary, show me why the complexity invalidates the principle.
Comment by Wonders For Oyarsa — September 10, 2007 @ 11:19 pm
September 11th, 2007 at 7:36 am
A sequence will be subject to neutral evolution at a known rate. The rate is slow, so we expect that humans and chimpanzees will show many areas of identity. Other the other hand, if it does not drift (are conserved), then we can assume other factors are involved, such as selection.
Some recent anomalies have been discovered, conserved regions have been discovered that have no known function and appear not to affect the phenotype. (Nor are they known recent viral invasions.) This could be due to our inexact understanding of the relevant phenotype. It could be due to some unknown process. It might even be due to Jovian psi-rays.
Comment by Zachriel — September 11, 2007 @ 7:36 am
September 11th, 2007 at 7:43 am
That is still incorrect. The arithmetic governing drift and fixation were originally applied to sexually reproducing populations.
Hardy-Weinberg (1908) predicts that if these conditions are true,
then the population will remain at equilibrium. However, if these conditions are not met, such as with a small (finite) population, then drift and fixation are inevitable even in the absence of selection.
Comment by Zachriel — September 11, 2007 @ 7:43 am
September 11th, 2007 at 7:52 am
Because you haven't published the entire algorithm, there are a lot of unknowns about Toxic Bunnies. For instance, we expect biological populations to be capable of reproducing exponentially without bound. In nature, there are limiting factors, but for BUDs and BUGs, there is no obvious limiting factor. What causes the population to crash forcing the genome through such tight bottlenecks?
Comment by Zachriel — September 11, 2007 @ 7:52 am
September 11th, 2007 at 8:35 am
Which I would agree with and expect…if the DNA isn't junk.
It's not an algorithm - it's a simulation. You can watch and see what causes it to crash - the cramped conditions the bunnies are stuck in - constantly bumping into each other.
Comment by Wonders For Oyarsa — September 11, 2007 @ 8:35 am
September 11th, 2007 at 8:58 am
Huh? Drift and fixation are inevitable in small (finite) populations of replicating sequences, even if completely non-functional. It's arithmetic.
Nest of Letters is a simulation of replicating sequences in the absence of selection. It demonstrates how fixation occurs. All the parameters can be adjusted, and it is open source. But really, it's just very simple arithmetic and doesn't require a simulation. Hardy didn't have a computer in 1908. He considered it a trivial result.
Are you saying that when two BUGs bump into each other they kill one another? I thought they were immune? Without more information about how the simulation works, there is no way to verify if it supports your claims.
Comment by Zachriel — September 11, 2007 @ 8:58 am
September 11th, 2007 at 9:02 am
Bradford:
I completely agree that a chance fixation of a neutral mutation could occur but here is what should not be expected. Individual x experiences a germline duplication of a genomic region that includes gene x and surrounding genomic regions we'll call junk for now. This duplication is neutral with respect to fitness. Why would a future population, many generations after x, show that this duplication is both uniformly ordered and characteristic of that species?
The answer to your question is in your first sentence.
(We all know that in this context, "fixed" means found in all individuals of the species/population, right? Fixed does not mean "repaired.")
If individual x experiences a germline duplication that is selectively neutral, it may become fixed in later generations (i.e. uniform and characteristic of the species) due to drift. Alternatively, the duplication may be lost and the non-duplicated allele fixed. There will be a period of time during which a sample of the population will identify both the duplicated and non-duplicated alleles, but in a finite population, one of the alleles will eventually become fixed.
Comment by Nick — September 11, 2007 @ 9:02 am
September 11th, 2007 at 9:15 am
No - not immune - if two bunnies of equal strength bump, one will die. I thought this was stated clearly.
Comment by Wonders For Oyarsa — September 11, 2007 @ 9:15 am
September 11th, 2007 at 9:32 am
Sorry. I'm a slow learner and always need to double-check my understanding.
Interesting. That explains the extreme genetic bottlenecks. You think this is a reasonable rule to represent generalized biological populations? Of course, there has to be some sort of limits. If we modify the rule, would our results vary, or can you show how this applies to the more general case? Or is this just a bit of bunny fluff? (Not that there's anything wrong with bunny fluff.)
Comment by Zachriel — September 11, 2007 @ 9:32 am
September 11th, 2007 at 9:42 am
It is a reasonable rule to limit population size - you can only cram so many bunnies in that tight little space. Now, the population is rather small, and you would certainly evolve in fewer steps with a larger population. But then, a new species is quite easy to achieve probabilistically (one out of every ninety mutations).
Comment by Wonders For Oyarsa — September 11, 2007 @ 9:42 am
September 11th, 2007 at 10:10 am
Is it? You don't usually see such dramatic and complete collapses in population without some proximate cause. (We often see a chaotic oscillation, though.) I'm not sure if that affects your overall results in such as a way as to cause it to be substantially different from a more generalized case. But I don't think you do either.
Comment by Zachriel — September 11, 2007 @ 10:10 am
September 11th, 2007 at 10:18 am
I'm saying that this is a reasonable mechanism to limit population size. The population size itself may be too small, but the mechanism for limitation seems quite reasonable to me.
But you're certainly right, in that if the population were larger, I would expect their DNA to be less uniform, since it would be far rarer for it to collapse down to just one or two bunnies.
Comment by Wonders For Oyarsa — September 11, 2007 @ 10:18 am
September 11th, 2007 at 11:30 am
Nick:
Or alternatively there may be other types of duplications and many variations in a large population. I did not rule out the possibility of fixation but used the term expected to emphasize selective neutrality.
Comment by Bradford — September 11, 2007 @ 11:30 am
September 11th, 2007 at 11:35 am
Bradford:
Or alternatively there may be other types of duplications and many variations in a large population. I did not rule out the possibility of fixation but used the term expected to emphasize selective neutrality.
Sorry, I have no idea what you are trying to communicate. Could you perhaps reword it and explain how it is relevant to your question at 10:38 pm.
Comment by Nick — September 11, 2007 @ 11:35 am
September 11th, 2007 at 11:53 am
The question points to the same issue raised by Wonders. If you assume a neutral mutation became fixed in deep time there should be no further expectation that the sequential order of nucleotides within that region remains invarient throughout the population of that species.
Comment by Bradford — September 11, 2007 @ 11:53 am
September 11th, 2007 at 1:11 pm
Bradford:
The question points to the same issue raised by Wonders. If you assume a neutral mutation became fixed in deep time there should be no further expectation that the sequential order of nucleotides within that region remains invarient throughout the population of that species.
Who expects that it would? The questions are, how rapidly will new variants arise, how rapidly will they be fixed or lost, and how long will it take for neutral mutations to eliminate recognizable homology? The observed variation in the region will depend on the mutation rate, the size of the population, and its history. Mutations that occur when a population is small are more likely to become fixed and thus appear invariant in later generations. Mutations that occur when a population is very large are likely to remain at equilibrium with other alleles and appear as variation in later generations.
Since allopatric models of speciation imply that new species arise from relatively small, isolated populations, it isn't surprising that there will be mutations (e.g. duplications, inversions, etc) which become fixed in the new species and distinguish it from its sibling species. Since mutation continues in the population, there will also be features that vary among members of a single species. A species with a larger population will tend to retain more intraspecies variation. There may even be ancestral variation that has been retained in both species, although this becomes less likely if one or the other species goes through a dramatic population bottleneck.
These issues have been investigated by geneticists and population biologists for the 100 years, as even a cursory glance at a genetics textbook would make clear. Wonders for Oyarsa would probably do better starting with some reading on Hardy Weinberg equilibrium and then moving on to other issues in population genetics, rather than attempting to reinvent a century genetics in a blog posting.
Comment by Nick — September 11, 2007 @ 1:11 pm
September 11th, 2007 at 2:11 pm
Hi Nick,
No need to be snappy about things. If I were planning on reinventing a century of genetics, I probably wouldn't be doing it in a field outside my degree, nor would I be doing it with toxic mutant asexual bunnies in a flash application. I am a layman, not an expert. You need to lighten up a bit.
I have some knowledge, and would like to gain more, though I'm probably not going to be pouring through dense studies with specialized vocabulary. If there are things I need to be educated about, I'm all ears - enlighten me.
I've proposed my simulation as a starting point for discussion. Please show me what factors I am leaving out, and how the simulation would need to change.
Comment by Wonders For Oyarsa — September 11, 2007 @ 2:11 pm
September 11th, 2007 at 2:19 pm
The population genetics questions are secondary to the junk DNA issue and questions as to whether all "junk" is non-functional. Does Hardy Weinberg allow one to distinguish unknown function from junk with certainty?
Comment by Bradford — September 11, 2007 @ 2:19 pm
September 11th, 2007 at 2:27 pm
That's his schtick thus far.
Comment by Doug — September 11, 2007 @ 2:27 pm
September 11th, 2007 at 3:59 pm
Bradford:
The population genetics questions are secondary to the junk DNA issue and questions as to whether all "junk" is non-functional. Does Hardy Weinberg allow one to distinguish unknown function from junk with certainty?
No. Hardy Weinberg is not a method for distinguishing the functionality of DNA. It is a description of the relationship between allele frequencies in a large randomly mating population. I mentioned it specifically, because it is usually the starting point in classes on population genetics.
Our little discussion started with your question about a hypothetical situation involving a selectively neutral mutation and genetic drift. You're the one who specified that the mutation was selectively neutral, and my response was based on that. Now, instead of engaging anything I've written, you're jumping off to a discussion of how to identify non-functional DNA. How is that relevant to your question? I honestly can't figure out what point you are driving at here. I'm not trying to be snarky.
wfo:
I have some knowledge, and would like to gain more, though I'm probably not going to be pouring through dense studies with specialized vocabulary. If there are things I need to be educated about, I'm all ears - enlighten me.
It doesn't need to be dense studies, or even the primary literature. An introductory textbook would, I think, be helpful.
Sorry, if I seem humorless, but did you not write the following?
and
If you think my response was snappy, does the above not strike you as just a little bit arrogant or mocking? When I read that, my first impression is not that the writer wants to start an honest discussion.
I've proposed my simulation as a starting point for discussion. Please show me what factors I am leaving out, and how the simulation would need to change.
Haven't MikeGene and Zachriel already done that when they discussed mutation rates and population sizes? Furthermore, your Bunnies are asexual. Humans and chimpanzees are not. Seems to me that would fundamentally alter the way that allele frequencies vary in the population.
Your final comment "getting a good mutation in a small area requires a large number of neutral mutations across the board" is more-or-less a restatement of the concept that most mutations are selectively neutral; beneficial mutations are only a small subset of the total mutations. But the devil is in the details. Natural selection can fix a beneficial mutation much more rapidly than drift fixes a neutral mutation. What's the basis for your intuition that the genomes of humans and chimps should be scrambled relative to each other? How many beneficial mutations do you think distinguish humans from chimpanzees? If there are only a handful, why would you expect an enormous number of neutral mutations? What population sizes do you think humans and chimpanzees have had over the past 5 million years? Won't that influence the accumulation of mutations?
Comment by Nick — September 11, 2007 @ 3:59 pm
September 11th, 2007 at 4:20 pm
I have not accused you of being snarky. Correct me if I'm wrong Wonders of Oyarsa, but it seems to me that your doubts about claims like 96% of a genome being junk are linked to your doubts that that great a percentage is without function. I share that doubt. Like most threads discusions meander in different directions but it is not difficult to see how the matter of selectively neutral mutations bears of the junk issue. Just in case you are wondering Nick, I do not doubt that genomes contain junk or even substantial amounts of it. There are obvious reasons to think so. The issue for me is getting the figures right. I do think you may be overreacting to statements made in this thread.
Comment by Bradford — September 11, 2007 @ 4:20 pm
September 11th, 2007 at 4:22 pm
The statement was preceded by "Folks, the bunnies don't lie", for God's sake! It's playful tongue-in-cheek bombastic hubris. Lighten up.
All very good questions. My half-educated guesses would be:
1.) My Computer Science education, particularly what I know of Monte Carlo methods.
2.) Quite a few. It wouldn't surprise me if the number of mutations is on the order of 1% of the length of the genome - multiple mutations per significant feature. Granted, you are doing more than replacing individual nucleotides - but you are moving parts into place, throwing correct switches, putting in slight modifications, etc, which may even require some temporary scaffolding.
It would be something akin to the number of line changes to convert a large software project from one release to another, relative to the total size of the project, though it would probably be a good deal more than this, since each subsequent step has to be better than the last (no short term losses for long term gains).
3.) Because the chances of getting a good mutation are incredibly slim, much less a good mutation that is the foundation for an even better one later on related to other parts.
4.) In the millions
5.) Yes, the population size certainly will.
Comment by Wonders For Oyarsa — September 11, 2007 @ 4:22 pm
September 11th, 2007 at 5:03 pm
2.) Quite a few. It wouldn't surprise me if the number of mutations is on the order of 1% of the length of the genome - multiple mutations per significant feature. Granted, you are doing more than replacing individual nucleotides - but you are moving parts into place, throwing correct switches, putting in slight modifications, etc, which may even require some temporary scaffolding.
So, roughly 30 million mutations, then. Seems kinda high to me, and I'm betting that my intuition as at least has much support as yours:mrgreen:
Wild back of the envelope calculation: Humans and chimps have ~26,000 protein coding genes. Of those, 29% are identical in humans and chimps. The remaining have an average of 2 nucleotide differences. That means that (very) roughly, there are 36,000 single nucleotide differences in the coding sequences of humans and chimps. So, you are saying that the differences between humans and chimps involve ~800 functional non-coding substitutions for every coding substitution.
3.) Because the chances of getting a good mutation are incredibly slim, much less a good mutation that is the foundation for an even better one later on related to other parts.
yeah, but how slim?
This is the crux of the matter. We can expect the nonfunctional portions of the genome (if any) to be scrambled, if you are correct about the large number of functional differences between humans and chimps and if the chances of getting a good mutation are sufficiently slim (and if the more rapid rate of fixation for those good mutations doesn't muck up our expectations). If your assumptions are wrong, then the degree of divergence we see in the human and chimp genomes could be entirely consistent with them being largely nonfunctional. I dunno about you, but I don't think the bunny simulator tells us much about those "ifs".
Comment by Nick — September 11, 2007 @ 5:03 pm
September 11th, 2007 at 9:42 pm
The goal is the evolution of a population of an enhanced species of bunny. However, there are eight equivalent strains. Is the goal when a single enhanced strain dominates, or when any collection of enhanced strains dominates?
This is a winner.
But is this a winner?
Comment by Zachriel — September 11, 2007 @ 9:42 pm
September 11th, 2007 at 10:14 pm
Thanks for the simulator Wonders for Oyarsa. Although I enjoy such things I believe there are too many unknowns to realistically simulate what occurred by means of a program. It seems to me that programs would have to be replaced every so often to accomodate newly acquired knowledge. They are however good tools by which to make a point in a way that will stick in the mind of a viewer.
I note the use of the word mutations in exchanges between you and Nick. The word is not specific enough to realistically describe a process. You would want to break down the nature of the different types of mutations and ask for example, what is the rate of gene duplications and does the rate vary for different types of genes? You could probably create a good video game by simulating a complex series of changes.
Comment by Bradford — September 11, 2007 @ 10:14 pm
September 11th, 2007 at 10:43 pm
I would still be curious about your answer, but it doesn't seem to matter with larger populations and longer sequences. Once a fortuitous mutation occurs, it quickly reaches 50%+, so the population tends to be dominated by a single strain. I'll try to provide some stats in a day or so.
Let me point out that evolutionary algorithms are members of a mathematical class. Hence, it is possible to draw some valid generalizations that pertain to the entire class. However, quantitative results depend very much on the parameters. Such simulations might still be useful for qualitative understanding, but we have to proceed very carefully.
Consider this typical result from Toxic Bunnies.
Even though we know that the junk was changed by a stochastic process, we can observe decidedly non-trivial correlations. Just look at it. What is the "meaning" of
vf- lpv fz-. Why is thesorwso often found in the same position. It looks as if it should be functional or been constructed in that specific pattern somehow. But we know it's not. And if we examine more of the population, we will be able to construct a phylogenetic tree from the randomized portions of the genome.Zachriel's Nest of Letters
Comment by Zachriel — September 11, 2007 @ 10:43 pm
September 11th, 2007 at 11:07 pm
Zachriel,
Both are winners. And the similarities in your typical result happen from bunnies being very very closely related.
Comment by Wonders For Oyarsa — September 11, 2007 @ 11:07 pm
September 12th, 2007 at 8:05 am
Yes, but your intuition said "Even if the functional DNA reached a local functional maximum, and stayed the same for hundreds of thousands of years, the junk would continue to scramble all across the population."
Then you shifted, "If the reproduction was sexual, this would not be the case… With sexual reproduction, I would expect huge variation even in the same species, as the various neutral mutations get distributed across the population.". But this is still wrong. In other words, even though you ran the simulation presumably hundreds of times! your intuition apparently caused you to ignore the data before your very eyes.
Meanwhile, I don't have specific data yet, but I have experimented with a version of Toxic Bunnies.
Is this your understanding:
* We have a population of sequences of length L.
* A particular letter change will cause a significant increase in fitness.
* The chance of this particular letter being mutated is 1/L per generation, and of these, 1/3 of a significant increase in fitness.
* Therefore, we expect many other letter changes before the evolutionary algorithm finds the significant letter.
* The result will be a fitter organism, but with many other letter substitutions.
Is this your understanding of what Toxic Bunny demonstrates?
Comment by Zachriel — September 12, 2007 @ 8:05 am
September 12th, 2007 at 8:49 am
I don't see the contradiction there. I still say the population will continue to mutate in the junk, even if it selects out changes to the important stuff. I also continue to think that sexual reproduction will distribute junk more quickly - since the perpetrator of junk doesn't need to conquer the population - though here I may be mistaken (it may be about the same).
As for your own test, I am curious about step 3:
Do you mean ANY letter has a 1/3 chance of increasing fitness? I took it that a good chunk of it needs to be the same. Only a small portion of the DNA can be changed (in my case a single letter). 1/3, in my view, is ridiculously high, but I needed it to make mutations happen in a reasonable amount of time for the app.
Comment by Wonders For Oyarsa — September 12, 2007 @ 8:49 am
September 12th, 2007 at 10:37 am
You predicted junk in a population would have a generally random distribution across the population indicating you didn't understand how neutral drift and fixation work. You repeated your claim for sexually reproducing populations emphasizing to the reader that your statements were being correctly interpreted. I have little doubt as to your original intended meaning.
Of course the junk region will continue to mutate, but you can run your simulation for a million years and there will still be striking patterns and correlations within a population of Toxic Bunnies. With a larger population, you will be able to reconstruct at least partial phylogenetic trees. (There are a number of relevant parameters; e.g., if the mutation rate is too high, then we may not be able to determine a single trunk of the tree, though we should still be able to determine many family relationships.)
These patterns are evidence of common descent. In biology, we also have the direct observation of mutation which allows us to determine what is expected from neutral evolution, and thereby empirically determine if other factors (such as selection) are involved. There's a huge amount of mathematical analysis in modern biology.
Huh? It's your Bunnies. Only one letter position leads to a significant improvement in function (the third letter position), with an 8/26 chance of a change for the better.
Is this your understanding?
Comment by Zachriel — September 12, 2007 @ 10:37 am
September 12th, 2007 at 10:38 am
Anyway, Zachriel, I understand the rebuttal - that mutations with a selective advantage grow very quickly, so much so that this would overcome the fact that lots of other neutral mutations are happening all over the place.
If the probability of a good mutation per mutation is 1/n, and the population is n, then you will get a good mutation with only minimal cost to the junk. If every step has that likelihood, you will indeed get the sort of thing we are talking about.
As far as the speed of neutral changes in sexual reproduction verses asexual, my hunch goes to sexual being faster, but I'd need to test it, because I'm not sure.
So Nick is correct (though I hate to say it, since he's been such a bastard ;-)) - the devil is in the details. But I think we could create a useful simulation based on these principles, and figure out the probability of a good mutation based on our beliefs about junk, and our knowledge of population size. I think 1/n rather high, based on my experience with large software products.
Comment by Wonders For Oyarsa — September 12, 2007 @ 10:38 am
September 12th, 2007 at 10:52 am
Good grief, Zachriel - if our above conversation is any indication, you should have continuous grave doubts about my original intended meaning about everything. It has been constant accusation and clarification. Remember when BUX didn't have any selective advantage?
I wasn't saying that the population would be different relative to each other - but that it would continue to grow different from the original ancestor, and thus to any branches.
I understand this - however, this will not hold for the separated populations. The point of my simulation was related to the assumption that our last common ancestor with the chimps was 5 million years ago. That's why I separated the populations.
Comment by Wonders For Oyarsa — September 12, 2007 @ 10:52 am
September 12th, 2007 at 10:59 am
That's an empirical question actually and depends on the selection coefficient as well as various other parameters. Many of the neutral mutations may or may not have time to become fixed in the population. Your Toxic Bunnies is quite ingenious. (It just doesn't show what you think it does.)
Among lions, the males often kill the cubs of other males when they take over a pride. So let's try a thought-experiment.
We call it Killer Rabbits. We have 1000 Rabbits, all with the same 30-length genome "
BUN...", much like your simulation. After one generation, we have up to 2000 Rabbits. Some of them will probably have been eliminated by your existing rules. Pairs of BUNs annihilate either other. A few may become BUGs or BUMs.But we have introduced a new mutation in our arsenal of adaptations. We call it the BUN to GUN mutation. If a GUN mutation occurs, this phenotype seeks out and kills every non-GUN rabbit. We expect in a population of 1000 that at least some will be GUNs. But these GUNs will have no neutral mutations after a single generation. The population will thereby consist only pure GUNs and a few runts hiding in the corners.
This is an extreme example, but shows the relationship between the various parameters such as selection, population size, etc. By the way, after many generations, you will still see drift resulting in fixation. Eventually, there will be striking patterns and correlations in the junk genome.
Comment by Zachriel — September 12, 2007 @ 10:59 am
September 12th, 2007 at 10:59 am
Yes - that's the way it works. Do you want my code?
Comment by Wonders For Oyarsa — September 12, 2007 @ 10:59 am
September 12th, 2007 at 11:07 am
Right - which is why my instincts said that sexual reproduction would scramble more junk - because for the GUNS to propagate, it would also mix with the other mutations in the neutral sections.
I ought to make a new one: sexual bunnies. Each has two strains, and when they mate, they give their children a new single strand from each parent - composed of three from one, three from the other, randomly. Oh for more time to goof off!
Comment by Wonders For Oyarsa — September 12, 2007 @ 11:07 am
September 12th, 2007 at 11:22 am
It isn't necessary to belabor the point. You repeated the claim for sexual populations. Even if the population of Toxic Bunnies never falls below a hundred, some mutations will become fixed in the junk. I provided the information you need to find the answer; Hardy-Weinberg.
I appreciate the offer. I don't think it will be necessary as I already have a not-so-fluffy working version. My question concerned your understanding of what Toxic Bunny demonstrates.
I believe your original claim was incorrect. It is quite possible for a few selectable changes to quickly take over a population before many neutral mutations are fixed in a population. That it depends on population and genome size, selection coefficient, and a large variety of other factors. Toxic Bunny shows 30% identity between isolated populations, and a few changes to the parameters can change this substantially.
And I think you have modified your views during the thread, something that very rarely happens.
This is very vague. Neutral drift and fixation occurs in sexually reproducing populations too. In biology, this occurs at a known rate which allows for monotonic molecular clocks.
Anyway, as I said, Toxic Bunny is very ingenious. I am sure that MikeGene is very appreciative.
Comment by Zachriel — September 12, 2007 @ 11:22 am
September 12th, 2007 at 11:57 am
Indeed - I have been shown a way that the two statements could coexist - namely if the probability of a good mutation is on the order of 1/n where n is the population size. Don't ever let anyone tell you I don't have an open mind.
I'm far from convinced that the human, chimp situation is anything near this, but there you go - the devil is in the details.
I'm not convinced of the claim for sexual populations, though - It seems to me that, if I made sexual bunnies, I could get at least two different versions of each chromosome and it be somewhat stable. Is the counter-argument that any slight tipping of the scale would have a domino effect?
Comment by Wonders For Oyarsa — September 12, 2007 @ 11:57 am
September 13th, 2007 at 9:47 am
KILLER RABBITS, preliminary analysis.
(Xposted to Wonders For Oyarsa.)
My evolutionary algorithm will not match yours exactly, but that is immaterial. We are interested in the general case. However, it should be reasonably close. The rules are the same as Toxic Bunny, BUN BUG, while I can significantly modify the parameters.
Take Purity as the percentage of the original founding genome junk that has been left untouched; Genome as the length of the genome; and Field as the crowding limit.
Smaller Genomes and Fields are characterized by chaotic behavior; population crashes, non-linear decline in Purity, and a highly variable onset and survivability of BUG Predominance.
With large Genomes, the Purity remains high for many generations. For example, with Genome = 1000 and Field = 250, Purity is 94% after 100 Generations. Predominance (50%) occurs in less than 10 Generations once the BUG mutation occurs, which is usually after ~50 generations with a resulting Purity = 97%. Purity makes a predictable, almost linear decline with these larger Genomes, and we have a reasonably consistent monotonic Junk Genome Clock.
KILLER RABBITS is only meant to show that changing the parameters can significantly change the results and that simplistic generalizations are inappropropriate. Evolution can proceed rapidly while leaving much of the junk Genome untouched. And we can use the junk Genome to construct phylogenetic trees and for timing various historical events.
Nor does this have all that much to do with biological evolution which entails more complex mechanisms. Recombination and duplication along with point-mutation are far more powerful, and modern evolutionary biology posits many mechanisms of variation (such as migration and population splintering; plus regulatory mechanisms, and even perhaps some custom mechanisms in the mammalian and hominid lines). Any quantitative assertions should be avoided, and even qualitative assertions must be carefully considered.
KILLER RABBITS , Not-so-fluffy Bunnies
Comment by Zachriel — September 13, 2007 @ 9:47 am
September 13th, 2007 at 10:05 am
Hey Zach, you ought to link to this page on your site, so that folks see the context.
Comment by Wonders For Oyarsa — September 13, 2007 @ 10:05 am
September 13th, 2007 at 10:26 am
If I were to continue the project, I might officially add it to my collection of algorithms. It's kind of an orphan right now. (Traffic is only one way.) But I will add the link to this discussion and to your blog.
Comment by Zachriel — September 13, 2007 @ 10:26 am
September 14th, 2007 at 10:52 pm
I've optimized and simplified the algorithm somewhat. Also, I added a bit more data.
Genome = 2000, Field = 100, Generations = 255. Only 0.15% of the Genome is subject to selection, while 99.85% is junk.
BUG predominance normally occurs around Generation = ~100, but it doesn't matter for the following observations which concern the results after 255 Generations. At that point, the purity is 93%. That means that out of 2000 letters, an average of 1863 junk letters will be the same as from the Founding Genome. And this varies very little among the population"”a standard deviation of only about 1½! (In other words, very consistent, as shown on the pink line graph.)
These are just the first 50 letters of sequences from two 2000-letter sequences. The sequences are from *different* populations.
BUR,,,,,,W,,,,,,,,,,,,,,,,D,,,,,,,,,,,,,,,,,,,,,,,BUG,,,,,,,,,K,,,,,,,,,,,,,,,J,,,,N,,,,,,,,,,,,,,,,
This allows us to devise a statistically accurate monotonic Junk Genome Clock, and to devise a phylogenetic tree that applies within each individual population while leaving substantial evidence of the common descent of divergent populations.
I believe this is not the result you originally expected. You indicated that the junk would be scrambled by the time the BUG mutation occurred. You based this on the expectation that evolution would have to more-or-less try each letter position. But most of those mutations will not be fixed, fixation occurring at a slow, constant rate in such populations. In fact, evolution can try all those letter positions with the vast majority being lost to neutral drift.
Again, this is explained within the context of Hardy-Weinberg.
Comment by Zachriel — September 14, 2007 @ 10:52 pm
September 15th, 2007 at 2:45 am
You got me, Zach. I hadn't thought of the case where mutations were likely enough that a good one was probable each generation (though to get the next step you need to wait for the new one to dominate). In that case, the specific organism that got the good mutation got that instead of garbling, and then replaces all the others.
So population size would be as strong of a driving force behind evolution as time.
I'm still far from convinced, however, that good mutations in a human/chimp ancestor would be anywhere on the order of 1/n.
Comment by Wonders for Oyarsa — September 15, 2007 @ 2:45 am
September 15th, 2007 at 9:04 am
That's not the case under consideration. With a Genome of 2000 and a population of only ~100, we definitely do not expect beneficial mutations each Generation, but a very irregular appearance after many Generations.
In our example, the Genome size is 20+ times the size of the Field. (The Field is actually a crowding limit and the population rarely exceeds this value.) Within the limitations of our program, the Genome was very large compared to the Field, and it provides results contrary to your expectation.
You were the one making claims. This is why I originally suggested you try to disprove your own intuition, rather than merely attempt to support it.
Comment by Zachriel — September 15, 2007 @ 9:04 am
September 15th, 2007 at 10:30 am
Genome = 10000, Field = 100 (average population 50-60), Ratio 100+
We expect a BUG mutation once in every 100 Generations or so. Perhaps in a hundred generations, or maybe in a few hundred. After a thousand generations, Purity = 95% reliably. Here's the first couple of hundred letters with Generation = 1000.
BUT,,,,,,,,,,,,,,,,,,,,,,,,,G,,,,,,,,,,,,,,,,,,,,,,,,F,,,,,,,,,,,,,,,,O,,,,,,,,,,,,,,,R,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,A,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,O,,L,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
The large majority of the sequence is identical to the Founding Genome and to other populations that diverged