Fixation rate, what about breaking rate?
|March 31, 2014||Posted by scordova under Genetics, News|
Hats off to VJTorley for vindicating claims I’ve made about neutral theory (non-Darwinian evolution) for almost the last eight years at UD. He found this by PZ Myers:
M]aybe we should be honest from the very beginning about the complexity of modern evolutionary theory and how it has grown to be very different from what Darwin knew.
First thing you have to know: the revolution is over. Neutral and nearly neutral theory won.
Oh you mean PZ you all weren’t honest from the very beginning. Just kidding!
I would argue a slightly different Achilles heel, not the rate of “fixation” (awful term as it suggests improvement when in fact it could just as well mean permanent damage!), namely the rate of breaking.
I pointed out most evolution is free of selection. I still stand by that where the term “selection” refers to Darwinian selection. Neutral theory partially helps ID, but it fails in one critical aspect, the problem that random walks destroy design.
In If not Rupe and Sanford 8/6/13, would you believe Wiki, I showed a widely accepted formula that fixation rate equals mutation rate. I believe it is sound from a mathematical standpoint, but flawed from a functional standpoint.
The population size is N and the Greek symbol μ (mu) is the mutation rate.
Ok, so let’s do an experiment. Let’s subject bacteria or plants or any organism to radiation and thus increase the mutation rate mutation rate by a factor of 1 million or 1 billion. Do you think the above formula will still hold? We tried it in the lab, it killed the plants, and at some point rather than speeding evolution we are doing sterilization.
And VJ quoted Moran:
Random genetic drift is a mechanism of evolution that results in fixation or elimination of alleles independently of natural selection. If there was no such thing as neutral mutations then random genetic drift would still be an important mechanism…
Random genetic drift is a mechanism of evolution that was discovered and described over 30 years before Neutral Theory came on the scene.
What Neutral Theory tells us is that a huge number of mutations are neutral and there are far more neutral mutations fixed by random genetic drift that there are beneficial mutations fixed by natural selection. The conclusion is inescapable. Random genetic drift is, by far, the dominant mechanism of evolution.…
The revolution is over and strict Darwinism lost.
Not quite, Larry. Most alleles disappear by drift, but it’s like people waiting in line and the line gets longer and longer, even though many alleles are getting purged, if the rate of introduction exceeds the rate of purging, then the genome starts to get packed with junk. So yeah, neutral theory predicts “fixing” but it fails to account for breaking! The experiments with accelerated mutation rates highlights the folly of blindly following a mathematical idealization like the formula above.
Though the below formulas based on the Poisson distribution needs some amendments because of synergistic epistasis and the binomial distribution, here is a problem that I’ve pointed out repeatedly at UD. So the above formula of fixation is true, but so are the formulas below for breaking. The problem is we focus on the “fixes” but forget about the breaks that come along!
Excerpt from Death of the Fittest
The following video is a crude 1-minute silent animation that I and others 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.
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 parents. Each parent spawns 2 gingerbread kids, and the red dots on the kids represent them having a mutation. To simplify the animation, the reproduction was depicted as asexual, but the concept can easily be extended to sexually reproducing species.
The missing gingerbread limbs are suggestive of severe mutations, the more mild mutations are represented by gingerbread kids merely having a red dot and not having severe phenotypic effects of their mutation. The exploding gingerbread kids represent natural selection removing the less functionally fit from the population. 4 generations are represented, and the fourth generation has three mutations per individual.
Note the persistence of bad mutations despite any conceivable mechanism of selection.
When I posted this video earlier at UD, I got complaints about the simplicity of the model. I will suggest two refinements which will show that even with moderate rates of mutation per individual per generation, genetic deterioration will happen. Further, this claim is reinforced by the work of Nobel Prize winner Hermann Muller who said a deleterious mutation rate of even 0.5 per individual per generation would be sufficient to eventually terminate humanity. So the simple model I present is actually more generous than Muller’s. Current estimates of the number of bad mutations are well over 1.0 per human per individual. There could be hundreds, perhaps thousands of bad mutations per individual per generation according to John Sanford. Larry Moran estimates 56-160 mutations per individual per generation. Using Larry’s low figure of 56 and generously granting that only about 11% of those are bad, we end up with 6 bad mutation per individual per generation, 6 times more than the cartoon model presented, and 12 times more than Muller’s figure that ensures the eventual end of the human race.
The first refinement of the cartoon model comes from Nachman and Crowell’s paper Esitmate of the Mutation Rate per Nucleotide in Humans and The Mutational Load by Kimura. Nachman provides a way to relate mutation rates with the probability of having a eugenically “ideal” child.
I hypothesized Nachman and Crowell were using a Poisson distribution as reasonable model for the probability of a eugenically clean individual appearing in the face of various mutation rates. And sure enough, with a little sleuthing help from my UD colleague “JoeCoder”, it was confirmed in Kimrua’s paper (see eqn. 1.4) which Nachman and Crowell, and Eyre-Walker and Keightley referenced.
This was important because up until that realization, I felt uncomfortable not knowing how those probabilities were derived. But now that it is clear that professional population geneticists are using the Poisson distribution to estimate probabilities, there is transparency in their model, and that makes the cartoon model defensible. The Appendix Notes in the comment section will provide a justification for the Poisson distribution.
So now the details:
let U = mutation rate (per individual per generation)
P(0,U) = probability of individual having no mutation under a mutation rate U (eugenically the best)
P(1,U) = probability of individual having 1 mutation under a mutation rate U
P(2,U) = probability of individual having 2 mutations under a mutation rate U
The wiki definition of Poisson distribution is:
to conform the wiki formula with evolutionary literature let
Because P(0,U) = probability of individual having no mutation under a mutation rate U (eugenically the best), we can find the probability the eugenically best individual emerges by letting:
Given the Poisson distribution is a discrete probability distribution, the following idealization must hold:
On inspection, the left hand side of the above equation must be the percent of offspring that have at least 1 new mutation, and this reduces to the following:
which is in full agreement with Nachman and Crowell’s equation in the very last paragraph and in full agreement with an article in Nature: High genomic deleterious mutation rates in homonids by Eyre-Walker and Keightley, paragraph 2. The simplicity and elegance of the final result is astonishing, and simplicity and elegance lend force to arguments.
So what does this mean? If the mutation rate is 6 per individual per generation, using that formula, the chances that a eugenically “ideal” offspring will emerge is:
This would imply each parent needs to procreate the following number of kids on average just to get 1 eugenically fit kid:
Or equivalently each couple needs to procreate the following number of kids on average just to get 1 eugenically fit kid:
In other words parents would have to be acting roughly like 100 Octomoms or 800 Richard Dawkins just to make one eugenically “ideal” baby that doesn’t have any new mutation (but still has all the bad mutations inherited from mom and dad). These calculations suggest, if Darwinism is true, the world needs far more women with the virtues of Octomom.
For humanity to survive, even after each couple has 807 kids on average, we still have to make the further utterly unrealistic assumption that the eugenically “ideal” offspring are the only survivors of a selective process. Hence, it is absurd to think humanity can purge the bad out of its populations — the bad just keeps getting worse.
In truth, since most mutations are of nearly neutral effect, most of the damaged offspring will reproduce, and the probability of a eugenically ideal line of offspring approaches zero over time. Therefore the cartoon model which assumes at least 1 new mutation per individual per generation is reasonable, and as I pointed out, the cartoon model is actually generous given Muller’s number of only 0.5 new mutations per generation per individual. The cartoon however graphically conveys the gravity of the problem.
Finally, how does this relate to the flaws in Dawkins weasel, Avida or any other conceivable genetic algorithm falsely used to defend Darwinism? These models notoriously don’t allow the offspring to move progressively farther from a desirable ideal with each generation (as illustrated in the cartoon model). Dawkins assumes cumulative selection, but this suffers from the flaw of assuming that all descendants are at least as good as the ancestor (the implementation of Dawkins Weasel disguises this fact). Computer simulations that assume offspring are at least as good as parents are obviously flawed, and more subtly, simulations that allow offspring to be on average better than their parents are also flawed. I leave it to the developers of these simulations to fix their bugs and conceptions. This is the 2nd refinement to the cartoon model. Let developers of evolutionary simulation incorporate the above considerations into their programs.
We have models from nature that show “death of the fittest” better describes what’s going on in nature, and the notion of “survival of the fittest implies inevitable improvement with each generation” is Darwin’s, Dennett’s, and Dawkins’ delusion (DDDD).