Nachman’s Paradox Defeats Darwinism and Dawkins’ Weasel

_{Salvador Cordova

November 14, 2009

Creationism, Darwinism, Evolution, Intelligent Design, Video}

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The following is a crude 1-minute silent animation that I and members of the IDCS Network put together. God willing, there will be major improvements to the animation (including audio), but this is a start. Be sure to watch it in full screen mode to see the details.

http://www.youtube.com/watch?v=SrIDjvpx7w4

The animation asserts that if harmful mutation rates are high enough, then there exists no form or mechanism of selection which can arrest genetic deterioration. Even if the harmful mutations do not reach population fixation, they can still damage the collective genome.

The animation starts off with healthy gingerbread men as parents. Each spawns ginger kids, and the red dots on the kids represent them having a mutation. The missing ginger limbs are suggestive of severe mutations, the more mild mutations are represented by ginger kids merely having a red dot and not severe phenotypic effects of their mutation. The exploding ginger kids represent Selection doing its thing and removing the less functionally fit from the population. The persistence of red dots on the ginger kids represents persistence of bad mutations despite any possible mechanism of selection.

Nobel Prize winner HJ Muller (of Muller’s ratchet fame) suggested that the human race can’t even cope with a harmful rate of 0.1 per new born. The actual rate has been speculated to be on the order of 100-300.

The animation uses a conservative harmful rate of 1 and argues (with some attempts at humor) that deterioration would thus be inevitable even with a harmful rate of 1 per new born.

I save discussion in the comment section the relevant but technical topics of truncation selection, sexual reproduction, recombination, synergistic epistasis, compensatory mutations, relief from Muller’s ratchet etc. These highly technical topics should be addressed and were not included in the animation. We can discuss them in the comment section.

However, the essential problem of mutation rates and deterioration is depicted by the animation. How this cartoon is illustrative of reality (when we consider the technicalities such as recombination, sexual reproduction, synergistic epistasis), can be discussed in the comment section.

In light of such problems Kondrashov posed the rhetorical question, Why have we not died 100 times over?. Kondrashov attempted to answer the question, but I don’t think the problem has been solved. The animation expresses my skepticism of the long term benefit of “synergistic epistasis”.

And if the conclusion symbolized by the animation is true, then on what grounds can we believe Darwinism is true?

The animation was inspired by a paper by Nachman and Crowell. Two years ago I wrote: Nachman’s U-Paradox. This animation helps illustrate the problem of Nachman’s paradox.

I recommend we should build a non-partitioned WEASEL to feature how Nachman’s paradox will trump Dawkins conclusions that somehow Darwin found the answer to appeance of design. One can get an idea of what it would look like given the animation.

[ Admins, I can’t seem to embed the video, can you embed it for me? I think embedded video requires higher privilege than my account has.]

Notes:

1. We could have done the drawings differently to emphasize the mutations are unique and novel and different for each ginger kid, but I save that work for later (including audio).

2. There is a refinement to the animation that is in order based on Nachman’s calculation of average removal rates of harmful mutations assumng trucation selection, “U”=3, and a conservative reproduction rate for humans, but I didn’t get around to it. That is yet another modification for future animations. We’ll need also some technical research on the matter.

Comments

In comment #75, Sal Cordova wrote:
"There are obvious analogs to the issue of Y-chromsomal heredity..."
An interesting observation. When one examines the genomes of haploid organisms, what is immediately striking is that they tend to be very small. That is, they contain very little information, compared with the genomes of diploid eukaryotes. This includes the y chromosome of mammals, which contains almost no genetic material beyond the coding sequences for a handfull of proteins (including TDF, which causes undifferentiated embryos to develop into males). Why this huge difference? One testable (i.e. falsifiable) hypothesis is that, since all alleles in haploid genomes are "visible" to selection, it may be the case that deleterious mutations (and, perhaps, even neutral mutations) immediately subject to "purifying selection" and removed, leaving only those versions of the alleles that confer functionality. This would also explain why prokaryotes tend to exchange genetic material when their genomes are damaged (for example, when they are exposed to mutagens, such as UV light). To state this in terms of selection: those bacteria who have the ability to exchange genetic material would be much more likely to survive deleterious mutations, since they could use the exchanged genetic material to replace the mutated parts of their genomes. This idea — that sex (defined as exchange of genetic material) first evolved as a means of repairing damage to the genome (i.e. deleterious mutations) was most vigorously proposed by Lynn Margulis and Dorian Sagan in their (1990) book, Origins of Sex (see http://www.amazon.com/Origins-Sex-Billion-Recombination-Bio-Origins/dp/0300046197/ref=sr_1_1?ie=UTF8&s=books&qid=1258553032&sr=8-1 ).
"Before moving to the diploid case, is it correct to say 1 harmful per offspring in that case will lead to deterioration, independent of viability or fecundity, or for that matter selection strength?"
Yes, with two qualifications: 1) that selection does not remove the deleterious mutations, and 2) that some compensating mechanism (such as diploidy and/or sex) does not mitigate the deleterious effects of the mutations. Please note as well that none of this applies to neutral mutations, which cannot be removed by selection (except by accident, such as genetic drift) unless they accumulate to the point that their replication entails a significant energetic cost.Allen_MacNeill_{November 18, 2009
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Salvador T. Cordova: But the animation I provided was haploid, so why is Zach modeling diploid?
Everyone knows that gingerbread people include gingerbread men, gingerbread women and gingerbread children. You didn't provide a model. and there was a lot of discussion about human reproduction. Even bacteria often exchange genes. Your argument was clearly provincial (human-centric). Genetic load in non-recombining organisms is much less because of the very large populations and smaller genomes. Most offspring are perfect clones. However, if your point is that bacteria are due for extinction, I think you might be mistaken.Zachriel_{November 18, 2009
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Yet your original claim that one harmful mutation per offspring is sufficient to guarantee this
But the animation I provided was haploid, so why is Zach modeling diploid? The haploid model will conceptualize the diploid model where the parameters are sufficient for deterioration.scordova_{November 17, 2009
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Of course, if the rate of harmful mutation is high enough, then deterioration and extinction is inevitable. Yet your original claim that one harmful mutation per offspring is sufficient to guarantee this is incorrect for the reasons I explained, and as Zachriel also pointed out.
Before we move forward on this, the animation was the haploid or asexual case. There are obvious analogs to the issue of Y-chromsomal heredity...... Before moving to the diploid case, is it correct to say 1 harmful per offspring in that case will lead to deterioration, independent of viability or fecundity, or for that matter selection strength? Thanks for you input. Salscordova_{November 17, 2009
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Link posted in another thread: http://mendelsaccount.sourceforge.net/ Zachriel has looked at this program and commented on it.Mung_{November 17, 2009
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The fact that a deleterious or neutral allele is linked to another allele in a "large linkage block" (i.e. in the same chromosome without an intervening crossover chiasma) doesn't really apply here. Once again, it matters if the allele is recessive or dominant (and if dominant, what its degree of penetrance is). Furthermore, if a deleterious or neutral allele is linked to an allele that confers increased fitness (i.e. those individuals who have it survive and pass it on more often than other individuals who do not have it), then the increase in frequency of the beneficial allele will "drag" the deleterious and neutral allele frequencies along with it, so long as the benefit of the one allele outweighs the deleterious effect of the other. This phenomenon is similar to genetic drift, and has hence been referred to as "genetic draft" by John Gillespie, the population geneticist who discovered it (based on a suggestion from Will Provine). That is, the slightly deleterious or neutral alleles will "draft" along with the beneficial allele(s) so long as they are all linked in the same non-recombining chromosome. And again, if the deleterious allele is recessive, but beneficial when heterozygous, then your model is completely out to lunch (yum, yum, gingerbread men for dessert ;-).Allen_MacNeill_{November 16, 2009
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Sorry, the link doesn't work. Try this.jitsak_{November 16, 2009
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Salvador:
However, there is a point where if there is insufficient reproductive excess and several harmfuls being added to each offspring, even under truncation selection, the MSE will not exist, or at least the MSE point will be carrying so many mutations, one has to wonder if the organism is viable.
Of course, if the rate of harmful mutation is high enough, then deterioration and extinction is inevitable. Yet your original claim that one harmful mutation per offspring is sufficient to guarantee this is incorrect for the reasons I explained, and as Zachriel also pointed out. You can find some c++ code here to verify this. The parameters of the model are: N=population size K=litter size NC=#chromosomes NG=#biallelic loci per chromosome (0=good allele, 1 =bad allele) r=per chromosome probability of crossing over event (at most 1 event/chromosome) s=selection coefficient mu=expected # mutations per offspring (good->bad, bad->good equally likely) Individuals are non-selfing diploid hermaphrodites and mating is at random. Offspring viability=(1-s)^M, where M is the number of bad alleles. In other words, multiplicative fitness scheme and additive gene action. If you play around with it, you'll see that even with mu>1, an equilibrium can be reached.jitsak_{November 16, 2009
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Along those lines: This video gives a overview of the effects of mutations (Kimura's distribution): Evolution vs Genetic Entropy http://www.youtube.com/watch?v=mmbRbyv2PA0bornagain77_{November 16, 2009
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Outdoor_Engineer: Isn’t this a rather poor representation of reality?
Gregor's Teeth is not devised to be a model of all aspects of biology. It is designed to test the specific claim that if every newborn has a harmful mutation, then genomic deterioration is inevitable, and that no other factors matter. In fact, it depends on a number of variables, some of which are identified in the algorithm.
Outdoor_Engineer:In reality wouldn’t the reduction in fitness caused by any given mutation be a quasi-normally distributed variable?
The original Gregor's Bookkeeper uses a gamma probability density function. It skews so that most mutations only have a very small effect, with only a few being strongly significant. It shows that fitness can increase even when the vast majority of mutations are slightly deleterious (within the limitations of the model).
Outdoor_Engineer:With the majority of mutations doing relatively little damage, but extreme cases certianly existing where a single mutation could cause either an arbitrarily large or and arbitrarily small reduction in fitness?
The accumulation of slightly deleterious mutations is an interesting question, but such a discussion cannot progress without resolving some misconceptions.
Outdoor_Engineer:why is it valid to do away with all that complexity and just assume that all mutations cause a given, constant amount of reduction in fitness?
Not all mutations cause the same change in fitness. Most are neutral—or nearly so, and deleterious mutations far outnumber favorable mutations.Zachriel_{November 16, 2009
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For *each gene* with one damaged allele, the organism’s fitness is reduced by one-tenth (depending on the setting of Recessive). Consequently, ten damaged genes means the organism is no longer viable.
Isn't this a rather poor representation of reality? enough so to invalidate the model? In reality wouldn't the reduction in fitness caused by any given mutation be a quasi-normally distributed variable? With the majority of mutations doing relatively little damage, but extreme cases certianly existing where a single mutation could cause either an arbitrarily large or and arbitrarily small reduction in fitness? why is it valid to do away with all that complexity and just assume that all mutations cause a given, constant amount of reduction in fitness?Outdoor_Engineer_{November 16, 2009
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scordova, Sorry for coming into this late, but I had a weekend offline for once. I'm very interested in these kinds of models. I understand that you haven't implemented yours in a programming language, but do you have a written mathematical description of what is going on behind the scenes in your animation?Mustela Nivalis_{November 16, 2009
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Note: I appreciate the removal of the ban on my comments. I'll endeavor to address the current topic and add value to the discussion. Clarification: Per scordova's scenario, mutation means damaged or harmful. If both alleles for *any gene* are damaged, the organism has a fitness of zero and is not viable. For *each gene* with one damaged allele, the organism's fitness is reduced by one-tenth (depending on the setting of Recessive). Consequently, ten damaged genes means the organism is no longer viable. The algorithm uses Roulette Wheel Mating.Zachriel_{November 16, 2009
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This is based on a modification of Gregor's Bookkeeper An original isogenic population with a fitness of one. Mutation is considered damage to an allele. If both alleles are damaged, then the fitness for the entire organism is zero. Otherwise, we can adjust the effect. With a slight deleterious effect of 0.1 per gene, the population is more stable than if the damage is completely hidden. Here is a typical scenario, each with a stable population after a hundred generations. Population = 100 Offspring per individual = 2 Recessive = -0.1 Average Fitness = 0.62 Population = 100 Offspring per individual = 1.5 Recessive = -0.1 Average Fitness = 0.41 Population = 200 Offspring per individual = 1.5 Recessive = -0.1 Average Fitness = 0.53 No beneficial mutations, no variance, no phylogenetic noise. Doesn't change the overall result anyway. Population = 100 Offspring per individual = 2 Recessive = -0.0 Average Fitness = 0.58 With silent recessives (i.e. Recessive = -0.0), the Offsprings have to be at least ~1.9 per individual for a stable population.Zachriel_{November 16, 2009
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Back in 2006, there was an interesting ARN discussion with Sal on this very subject: http://www.arn.org/ubbthreads/showflat.php?Cat=0&Board=13&Number=30321663&PHPSESSID=&fpart=1#Post30321663 Note: I post on ARN as 'KC"Dave Wisker_{November 16, 2009
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Allen, Like you I'm pressed for time. Perhaps we can continue our discussion at TT where you will be freer to comment. You are correct that large linkage blocks are not subject exactly to the same kind of ratcheting as Muller's ratchet as the Y-chromosomes, but there is comparable problem since bad mutations can be randomly carried over along with the good on a large linkage block. The notion came from John Sanford's book. Perhaps that consideration should be given to using different terminology so as to avoid confusion. Thank you again for your valuable criticisms. I hope we can continue at TT later today. regards, Salscordova_{November 16, 2009
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jistak: I can explain why in mutation-selection equilibrium (MSE) the average number stays the same from one generation to the next, even if children receive on average more than one deleterious mutation. The reason is recombination. As mutations accumulate before MSE is reached, there will be variation in the population in the number of mutations per chromosome. Therefore, when two partners mate, it’s likely that they have different numbers of mutations on each chromosome. Because of recombination, there will be variation among the offspring in the number of mutations they carry. Even if all offspring receive an extra deleterious mutation, if the variation in numbers of mutations is large enough, and if selection is strong enough, then the number of mutations need not increase from one generation to the next
I alluded to that issue in comment Comment #49
Average number of parent mutations: 3.0 .... Average number of mutations of living children is 1.0.
And you said:
if the variation in numbers of mutations is large enough, and if selection is strong enough, then the number of mutations need not increase from one generation to the next
Which I alluded to when I said:
This is the case described by Nachman using truncation selection.
But this assumes sufficient reproductive excess and truncation selection. Nachman himself said truncation selection was unrealistic. However, there is a point where if there is insufficient reproductive excess and several harmfuls being added to each offspring, even under truncation selection, the MSE will not exist, or at least the MSE point will be carrying so many mutations, one has to wonder if the organism is viable. There will be an improvement to future animations. I mentioned that there have to be correctons to in the animation in the OP:
2. There is a refinement to the animation that is in order based on Nachman’s calculation of average removal rates of harmful mutations assuming truncation selection, ...That is yet another modification for future animations. We’ll need also some technical research on the matter.
The the dots of the parents are shown to be always inherited by the kids. That will happen only in situations where Muller's ratchet directly applies (like Y-chromosomes) and female mitochondira (some controversy over possible recombination, but still a reasonable assumption). That adjustment needs to be made so that sometimes the dot from the parent is not always inherited. I mentioned this situation in comment #48. We can then add mothers and fathers and show the children with some dots from mom and some dots from dad, and some situations where none of the dots are inherited. Thanks for your criticisms. I find them valuable.scordova_{November 16, 2009
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Allen: P.S. Please see what you can do about removing me from permanent moderation, so that my comments will be timely, rather than afterthoughts. Thanks!
I working on starting another discussion forum. Not only in that place will you not be moderated, but you can even be a moderator if you should ever choose. I don't have the authority to have you removed from any moderation here at UD. I'm sorry. As you can see, even I post infrequently at UD. I cannot even post at most threads at UD without being on the moderation queue (a peculiarity of the software which is a legacy of DaveScot which no one here has been able to uncork). Please accept my regrets. The most I can offer is we can reconvene elsewhere where we are not under so much restriction. I apologize for the delays in your display of comments. Thank you for your informative criticisms. I will attempt to address them, and also acknowledge where I feel you have made a valid critique, and where I must amend or withdraw my claims. Thank you again for your willingness to provide pointed and insightful objections. Salscordova_{November 16, 2009
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A little addendum to my post #52. The problem with Salvador's examples in 48 and 49 is that they do not allow for variation between parents in the number of harmful alleles they carry. No variation = no response to selection. If he had allowed for (inevitable) variation, then the average number of harmful alleles per offspring may decrease (depending on the details) by more than one during selection, thus compensating for any new harmful mutation acquired by the offspring.jitsak_{November 16, 2009
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Just a little musing - If Scordovas or any 'model' of mutation accumulation is run in reverse does it not lead through a serial 'removal' of mutations to a specific 'perfect' gene with no 'mistakes' ?butifnot_{November 15, 2009
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ok, so Sal has offered some adjustments to his model. I think this is an important step forward. So what we have now is a rate at which mutations are introduced (1 per individual in the population), and a rate at which mutations are inherited (.5 per individual in the population). Now how many generations does it take us before even these figures are known to be absurd? (I am using for an anology the chessboard, with one grain on the first square, two grains on the second, etc.) Also, we still need to know the level at which the accumulated mutations become lethal (else we have no reason to terminate our gingerbread man). But since everyone in the population is accumulating at the same rate and has the same probability, why wouldn't the entire population go extinct at once? So I think the animation should show accumulation, then "poof," no more gingerbread men. And if we can extrapolate backwards in time, I think it becomes obvious that we could never be here. Therefore, I conclude, we are all merely a part of a computer simulation.Mung_{November 15, 2009
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A commentator at another ID website (Mung at http://telicthoughts.com/mutations-fitness-and-more/comment-page-2/#comment-248496 ) pointed out that Müller's Ratchet should also apply to mitochondrial DNA. To which I replied that, indeed, Müller's Ratchet would apply to mitochondrial DNA, and also to the DNA of chloroplasts. In my (lame) defense, I usually think of mitochondria and chloroplasts as modified prokaryotes, as they almost certainly evolved from prokaryotic ancestors via serial endosymbiosis (as proposed by Copeland and expanded by Margulis). Which raises an interesting point: since the mitochondria in every multicellular eukaryote are virtually always inherited via mitochondria contained in the maternal egg cell, it would seem likely that there would be a "founder-flush" event that purges deleterious mutations every generation, as the sample of mitochondria in each egg cell would be an almost infinitesimal fraction of the total mitochondrial population of the eukaryotic mother (who made the egg cells). If this were indeed the case, it would explain why there is an unusually low frequency of deleterious mutations in mitochondria (with the exception of some rare forms of muscular dystrophy).Allen_MacNeill_{November 15, 2009
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You should also check out "founder-flush" speciation, as this is a variant of negative/purging selection.Allen_MacNeill_{November 15, 2009
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Sal: For your model to be a reasonable representation of biological reality it must also take into account a variant of natural selection that can remove deleterious alleles from gene pools when effective breeding population sizes become very small. This form of natural selection is often referred to as either “negative selection” or “purging selection”. Here is a definition (from Wikipedia) with references, followed by three empirical studies showing that negative/purging selection does in fact take place: NEGATIVE SELECTION: Negative selection, in natural selection, is the selective removal of alleles that are deleterious. This can result in stabilizing selection through the purging of deleterious variations that arise. It is also known as purifying selection. Purging of deleterious alleles can be achieved on the population genetics level, with as little as a single point mutation being the unit of selection. In such a case, individuals bearing the allele selected against might simply have less offspring on average generation after generation. In the case of strong negative selection on a locus, the purging of deleterious variants will result in the occasional removal of linked variation, producing a decrease in the level of variation surrounding the locus under selection. The accidental purging of non-deleterious alleles due to such spatial proximity to deleterious alleles is called background selection.[1] This effect increases with higher mutation rate but decreases with higher recombination rate.[2] References: 1. Charlesworth, B., Morgan, M. T. and Charlesworth, D. 1993. The effect of deleterious mutations on neutral molecular variation. Genetics 134, 1289-1303. 2. Hudson RR, Kaplan NL (December 1995). "Deleterious background selection with recombination". Genetics 141 (4): 1605–17. PMID 8601498. http://en.wikipedia.org/wiki/Negative_selection_%28natural_selection%2 9 ************ How are deleterious mutations purged? Drift versus nonrandom mating. Glémin S. Evolution. 2003 Dec;57(12):2678-87. Accumulation of deleterious mutations has important consequences for the evolution of mating systems and the persistence of small populations. It is well established that consanguineous mating can purge a part of the mutation load and that lethal mutations can also be purged in small populations. However, the efficiency of purging in natural populations, due to either consanguineous mating or to reduced population size, has been questioned. Consequences of consanguineous mating systems and small population size are often equated under "inbreeding" because both increase homozygosity, and selection is though to be more efficient against homozygous deleterious alleles. I show that two processes of purging that I call "purging by drift" and "purging by nonrandom mating" have to be distinguished. Conditions under which the two ways of purging are effective are derived. Nonrandom mating can purge deleterious mutations regardless of their dominance level, whereas only highly recessive mutations can be purged by drift. Both types of purging are limited by population size, and sharp thresholds separate domains where purging is either effective or not. The limitations derived here on the efficiency of purging are compatible with some experimental studies. Implications of these results for conservation and evolution of mating systems are discussed. http://www.ncbi.nlm.nih.gov/pubmed/14761049 ************ Testing alternative methods for purging genetic load using the housefly (Musca domestica L.). Meffert LM, Regan JL, Hicks SK, Mukana N, Day SB. Genetica. 2006 Sep-Nov;128(1-3):419-27. When a population faces long-term inbreeding, artificial selection, in principle, can enhance natural selection processes for purging the exposed genetic load. However, strong purge pressures might actually decrease fitness through the inadvertent fixation of deleterious alleles and allelic combinations. We tested lines of the housefly (Musca domestica L.) for the effectiveness of artificial selection to promote the adaptation to small population size. Specifically, replicate populations were held at average census sizes of 54 for nine generations or 30 for 14 generations while being subjected to artificial selection pressure for increased fitness in overall mating propensity (i.e., the proportion of virgin male-female pairs initiating copulation within 30 min), while also undergoing selection to create differences among lines in multivariate components of courtship performance. In the 14-generation experiment, a subset of the lines were derived from a founder-flush population (i.e., derived from three male-female pairs). In both experiments, we also maintained parallel non-selection lines to assess the potential for natural purging through serial inbreeding alone. Sub-populations derived from a stock newly derived from the wild responded to artificial selection for increased mating propensity, but only in the short-term, with eventual rebounds back to the original levels. Serial inbreeding in these lines simply reduced mating propensity. In sub-populations derived from the same base population, but 36 generations later, both artificial selection and serial inbreeding increased mating propensity, but mainly to restore the level found upon establishment in the laboratory. Founder-flush lines responded as well as the non-bottlenecked controls, so we base our major conclusions on the comparisons between fresh-caught and long-term laboratory stocks. We suggest that the effectiveness of the alternative purge protocols depended upon the amount of genetic load already exposed, such that prolonged periods of relaxed or altered selection pressures of the laboratory rendered a population more responsive to purging protocols. http://www.ncbi.nlm.nih.gov/pubmed/17028969 ************ Purging of inbreeding depression within the Irish Holstein-Friesian population Sinéad Mc Parland, Francis Kearney and Donagh P Berry Genetics Selection Evolution 2009, 41:16doi:10.1186/1297-9686-41-16 The objective of this study was to investigate whether inbreeding depression in milk production or fertility performance has been partially purged due to selection within the Irish Holstein-Friesian population. Classical, ancestral (i.e., the inbreeding of an individual's ancestors according to two different formulae) and new inbreeding coefficients (i.e., part of the classical inbreeding coefficient that is not accounted for by ancestral inbreeding) were computed for all animals. The effect of each coefficient on 305-day milk, fat and protein yield as well as calving interval, age at first calving and survival to second lactation was investigated. Ancestral inbreeding accounting for all common ancestors in the pedigree had a positive effect on 305-day milk and protein yield, increasing yields by 4.85 kg and 0.12 kg, respectively. However, ancestral inbreeding accounting only for those common ancestors, which contribute to the classical inbreeding coefficient had a negative effect on all milk production traits decreasing 305-day milk, fat and protein yields by -8.85 kg, -0.53 kg and -0.33 kg, respectively. Classical, ancestral and new inbreeding generally had a detrimental effect on fertility and survival traits. From this study, it appears that Irish Holstein-Friesians have purged some of their genetic load for milk production through many years of selection based on production alone, while fertility, which has been less intensely selected for in the population, demonstrates no evidence of purging. http://www.gsejournal.org/content/41/1/16Allen_MacNeill_{November 15, 2009
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I'm no geneticist, so please correct me If I misunderstand. But here's an observation from an outsider perspective that might help: It would seem that the lack of any neutral or beneficial mutations invalidates the conceptual model. Wouldn't an individual's reproduction rate be dependent on the net effect of all mutations, instead of just on the number of harmful mutations? how can we justify ignoring the effect of beneficial mutations or mutations that are neutral or harmful at the time of introduction and then become beneficial at some later time due to changing circumstances? It would seem that the author is claiming that if all offspring are guarunteed to have a net harmful effect from mutation then genetic collapse of the population will surely follow. I don't think anyone would disagree with this assertion, however the question is whether or not, in reality, all offspring are actually guaranteed to have a net harmful effect from mutation? I doubt this is the case but I am willing to be persuaded by a relevant study or logical explanation.Outdoor_Engineer_{November 15, 2009
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Continuing OT: any YEC should watch Ross vs Hovind (it won't hurt OECs of course).tremor_{November 15, 2009
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Salvador,
If this is the case, do you think any value of fecundity or viability will change the fact that the children of parents will have on average more mutations than their parents? Please inform the reader the reasons you think there exists values of fecundity and viability which will ensure the average number of mutations in the children will be less than their parents on average.
I can explain why in mutation-selection equilibrium (MSE) the average number stays the same from one generation to the next, even if children receive on average more than one deleterious mutation. The reason is recombination. As mutations accumulate before MSE is reached, there will be variation in the population in the number of mutations per chromosome. Therefore, when two partners mate, it's likely that they have different numbers of mutations on each chromosome. Because of recombination, there will be variation among the offspring in the number of mutations they carry. Even if all offspring receive an extra deleterious mutation, if the variation in numbers of mutations is large enough, and if selection is strong enough, then the number of mutations need not increase from one generation to the next. If you don't believe me, I have just coded a little c++ program that proves my point. Do you want to see it? Finally, I find it pretty sad that you make such grandiose claims in the OP based on a cartoon without an underlying model. If you would try to pull a stunt like this in the competitive world of science, you would be toast. cheersjitsak_{November 15, 2009
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Sal: In a thread at Telic Thoughts on this same subject (see XX ), you implicitly acknowledged my criticisms by stating
Müller's ratchet will apply to large linkage blocks in the genome and the Y-chromosome of humans, the Y-chromosome and linkage blocks exist in sexually reproducing species like humans.
I agree that Müller's ratchet should apply to alleles located in the y chromosome of mammals (as well as to alleles in the chromosomes of haploid eukaryotes and the DNA of prokaryotes and viruses), but I do not see how it could apply to alleles located in "large linkage blocks" or anything else located in the autosomes or X chromosome of mammals or other eukaryotes. In my understanding, "large linkage blocks" are just another name for chromosomes. Indeed, that's how they were first defined in the early 20th century, before the congruence between linkage groups and chromosomes was empirically verified in the early 20th century by Bridges, Stephens, and Sturtevant. If you disagree, please explain how Müller's ratchet might apply to alleles located in the autosomes or X chromosome of mammals (or provide a link to such an explanation). Thanks!Allen_MacNeill_{November 15, 2009
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Sal in comments 48 and 49: Once again, you have neglected to factor in dominance and recessiveness, and so your analysis is irrelevant. P.S. Please see what you can do about removing me from permanent moderation, so that my comments will be timely, rather than afterthoughts. Thanks!Allen_MacNeill_{November 15, 2009
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Another scenario: Mom has mutation J1 J2 J3 Dad has mutation J3 J4 J5 Average number of parent mutations: 3.0 it is remotely possible if Mom and Dad have 40 kids, we'll have: Kid_1 : K1 J1 J2 ... .... Kid_39 : K39 Kid_40 : K40 Kid_39 and Kid_40 live, the rest are killed (truncation selection) Average number of mutations of living children is 1.0. This is he case described by Nachman using truncation selection. But the reduction is only temporary, and it can't reduce the average number of mutations per individual below one. And realistically speaking, truncation selection doesn't happen in the wild, not to mention, if there is insufficient reproducitve excess, the average number of mutations in the children will be greater than 1.0. Thus over time, on average, the number of mutations in kids will keep increasing.scordova_{November 15, 2009
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