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Fisher’s Proof of Darwinism Flipped: William Basener replies to Bob O’Hara

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The paper, by William Basener and John Sanford, shows that the continuous flow of new mutations that would continuously replenish a population’s genetic variability and enable Darwinian evolution does not really happen.  (Paper.)

Much discussion has followed here and here.

Basener has replied to Bob O’H, and for reader convenience, we are reproducing the comments here:

First, Bob O’H:

tjguy – The maths isn’t troubling (except that I’ sure they could have gone further). The simulation section shows that fitness can decrease, but we already knew this. Basener & Sanford don’t say what mutation rate they use though.

It’s obvious, I think, that the paper will be used to claim that mutations mean that evolution can’t work, so it’s a shame they don’t provide such an important parameter.

William Basener replies:

Bob O’H, RE 17: Your question regarding the mutation rate we used in the paper is pertinent. As you stated it has long been known that a high mutation rate can lead to decline in fitness while a low mutation rate allows for adaptation, observed in biological populations and mutation-selection models in the literature discussed in Section 2.2 (differential equations with an infinite-population). Thank you for the good question.

The mutation rate used in the paper is 1 mutation per generation. As with all the parameters in the paper we chose this parameter so that if there is any bias, the parameter selection favors selection and increasing fitness.

This is in the mathematics in the paper, but you are certainly correct that we did not state this as the mutation rate and that would have been helpful to readers. In the math, Equation 5.1 for \$f_{i,j}\$ is the probability distribution provided by Kimura to estimate the effect of a single mutation on fitness. We modify this distribution to add beneficial mutations (at a rate and magnitude that are greater than observed estimates), and this is used as the net effect of all mutations for \$f_{i,j}\$ in Equation 3.2.

Anyone who wishes to explore parameters can use the JavaScript simulation I posted at my RIT web page (referenced in the paper):
https://people.rit.edu/wfbsma/evolutionary%20dynamics/EvolutionaryModel.html
This was used to create the figures in the paper, and thus provides full transparency and opportunity to validate/reproduce/modify our results.

I agree with you that it would have been nice to go further with the math, and done an exploration of the parameters space. But the paper is at 34 pages, and we wanted to provide proper support for the model (hence the beefy literature review in Section 2) and give proper context with regards to Fisher. I think you and I agree that determining behavior for parameters spanning the space of realistic values is an important next step. I think it would beneficial to have multiple different groups explore results for varying parameters.

We’ll keep readers posted re further discussions.

The discussion on this point continues in the comments below, with Bob O’H at 1.

This is Bob O’Hara:

My career has been dedicated to discovering whether I am a biologist or a statistician – I intend to retire once I come to a definite answer. Most of my work has been on ecology and evolution, using statistical methods to put data and models together to try to learnmore about the real world.

My main interest at the moment is the development of methods to model the distributions and dynamics of species an communities, where we have a variety of data sources that need to be respected, and models of the unobserved true distributions and dynamics from which we want to infer what drives the distributions of species, and oredict how this will change in the near future.

and

Fisher’s proof of Darwinian evolution has been flipped?

Adding to the above conversation - I believe there is no better view of the universe from which to make hypothesis and assemble rocks than that of a universe designed by an biblical Creator.Bill B
January 5, 2018
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January 5, 2018
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BA77 -- welcome back ... you've been missed.ayearningforpublius
January 2, 2018
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It's a lot easier to publish a bad paper than a good paper showing that a bad paper is bad, particularly if the bad paper is long and elaborate.Erasmus Wiffball
January 2, 2018
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Bob, You are correct that the mutation rate is one mutation per individual. I am honestly somewhat surprised you find the numerical simulation in Section 5.4 so interesting. I expected that in this paper there would be a large number of things that people would say, "yeah well we already knew that...", but things in this "yeah we already knew that" bag would be known only to active researchers in certain communities, and would not be part of the general Neo-Darwinian discussion. A finite population with realistic parameters that has fitness decreasing to negative values should not be surprising, given the work of Lynch etc. which we review in Section 2 of the paper. The simulation in Section 5.4 is not presented in the paper as a model of any specific organism, or of what is generally to be expected behavior. We do not claim that most species are driven to negative reproduction in 1000 years. I will quote the last line of Section 5.4: "We observe that it problematic to define parameter settings that are biologically realistic yet result in continuous fitness increase, supporting the modeled buildup of very slightly deleterious mutations described in Kondrashov’s paradox." or from the abstract: "The expanded theorem has biological implications significantly different from what Fisher had envisioned." I contend that the simulation in Section 5.4, in combination with the rest of the paper, supports those conclusions. We could go back and forth over mutation rates and parameters for biological populations, but I find such exchanges unfruitful. As I said earlier, I would like see a proper evaluation of our model across a comprehensive span of realistic parameters, including some various estimates of specific organisms. (Since you mentioned it, I'll include a simulation using estimates for E. Coli if I do a parameter evaluation, which is likely.) I could point out that the human mutation rate is 100 per individual (we could argue over whether they should all count against fitness given possible junk DNA, and we could argue if Kimura's Gamma distribution for mutational effect considered mutations in junk DNA and if it matters) but in any case, 1 mutation per individual is well below human mutation rates. You have pointed out that our system is set up for asexual reproduction, which I agree although 1) Fisher did not restrict his FTNS only to asexual reproduction and 2) Lynch's work (Section 2 of our paper) indicates that sexual reproduction slows genetic collapse rather than preventing it. I am sure we find more to go back and forth over, maybe debate what it means to be ‘realistic’, but it would be far more productive (and less wasteful of both our efforts) to just put estimated parameter values into a mathematical model and check the results. If you are concerned that the single simulation will be taken out of context to say that species generally reach negative reproduction rates within 1000 years (or something like that), I'll agree up front that nobody should draw that conclusion. The point of that simulation is to show that using Fisher's equations with realistic mutations can result in continual fitness decline; combined with the rest of the paper we can say continual up is really hard to find. This might be surprising to some because Fisher's work originally was thought to be a rigorous proof of continual up as universal as entropy. Fisher’s view on how his theorem works in combination with mutations (which we label “Fisher’s Corollary”) is logically false because his assumptions about mutations wrong, and it is also contrary to what we see in mutation-selection models. The thing that I would expect to be more troubling (for someone who believes that mutations plus selection has created the diversity of life from a very simple start) would be the substantial amount of research into the mutation-selection process (See Section 2 of our paper, but also papers you have cited) that does not show an intrinsic upward push; to the contrary the main question seems to be how do we avoid fitness decline and maintain equilibrium. There are other more interesting things in our paper. You cited a paper with an error threshold on the mutation rate and effect separating fitness decline from staying at equilibrium – our main theorem gives a formula separating fitness decrease from increase based on the mutation distribution (which includes rate and magnitude) and the population distribution. Our model is more comprehensive than assuming every mutation has the same fixed affect (as with Lynch’s model), which could provide more comprehensive information on fitness decline in small populations – i.e. endangered species. Anyhow, I am going to try to drop out of this debate. I have work I have to get to, and blog debates consume my focus too much. I prefer the pace of publishing papers. Best wishes to all, especially Bob.Bill B
January 2, 2018
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BA77 is back. That's the best news I've heard so far today!Truth Will Set You Free
January 2, 2018
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William Basener (Bill B): Do you agree that ID proponents commonly mistake mathematical models of evolution as attempts to prove that evolution works? Would you please tell everyone here what Fisher's objective was in formulating his model? What was he attempting to model? To what degree did he succeed or fail in what he was attempting to do? (Surely he did not fail categorically.)Erasmus Wiffball
January 2, 2018
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Happy new year bornagain77.Origenes
January 2, 2018
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BA77, a very happy new year, we have been concerned, noted your vids with interest. God's richest. KF PS: Could you email me?kairosfocus
January 2, 2018
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Glad to see Bob O’Hara applying his expertise in statistics, trying to help finally develop a proper mathematical model for Darwinian evolution.
“It is our contention that if ‘random’ is given a serious and crucial interpretation from a probabilistic point of view, the randomness postulate is highly implausible and that an adequate scientific theory of evolution must await the discovery and elucidation of new natural laws—physical, physico-chemical, and biological.” Murray Eden, “Inadequacies of Neo-Darwinian Evolution as a Scientific Theory,” Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution, editors Paul S. Moorhead and Martin M. Kaplan, June 1967, p. 109. https://people.eecs.berkeley.edu/~christos/evol/compevol_files/Wistar-Eden-1.pdf
Hopefully, he is helping to develop a proper mathematical model for Darwinian evolution that finally realistically reflects reality. Such as the fact that biological form is not even reducible to mutations in DNA in the first place:
Darwinism vs Biological Form - video https://www.youtube.com/watch?v=JyNzNPgjM4w
Or perhaps he will incorporate the fact that quantum biology also now shows us that Darwinists, with their reductive materialistic framework, are not even on the correct theoretical framework to begin with in order to properly understand and/or 'mathematically model' biology?
Darwinian Materialism vs Quantum Biology - video https://www.youtube.com/watch?v=LHdD2Am1g5Y
Of course one is always hopeful that those who unquestionably accept Darwinism will finally make mathematical models that properly reflect reality and thus finally reject Darwinism, but, having been down this road for a number of years, I am not holding my breath for that hope.
Darwinian Evolution: A Pseudoscience based on Unrestrained Imagination and Bad Liberal Theology - video https://youtu.be/KeDi6gUMQJQ
Verse and video:
2 Corinthians 10:5 Casting down imaginations, and every high thing that exalteth itself against the knowledge of God, and bringing into captivity every thought to the obedience of Christ;
bornagain77
January 2, 2018
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Bob O'H is my brother!Mung
January 2, 2018
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Bob O'H at 2, update posted.News
January 2, 2018
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Bob O’Hara spotted?
That's an old me (photo taken on "Birdshit Island"). The new me is here. I have yet to examine the islands around Trondheim for avian excrement. Anyway, to the main point of the post. First, it's not clear if the mutation rate is per individual per generation or per population. I suspect the former: if it's the latter, then the expected reduction in mean fitness is (using their assumed population size of 10^9) is 10^-12 if we ignore selection. This is clearly too low: after 3000 generations it would still be almost the initial population size. If the mutation rate is per individual, then the result make more sense: the reduction in mean fitness due to mutation would be 10^-3. We know that in the short term, fitness cannot compensate for mutation if -U d > s, where U is the mutation rate per genome, d is the average effect of mutation on fitness (so the left hand side is the mean change in fitness due to mutation, and s is the genetic variance in fitness (I assume the Basener & Sandford model will reduce down to this too: it looks like it should). In the simulation in §5.4 of the B & S paper, their initial genetic variance in 0.000025, and d is -10^-3 (as near as makes no difference). So clearly the inequality is true, i.e. selection can't compensate unless the genetic variance is increased 40 times. So how realistic is this mutation rate of one mutant per individual per generation? The simulation is for an asexual species, so we can look at bacteria. For E. coli the mutation rate per genome has been estimated as about 10^-3. So it seems to be too high.Bob O'H
January 2, 2018
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