Poisson Nachman Crowell

Even aside from Basener and Sanford, others including Nobel Prize winner Hermann Muller pointed out the human race cannot tolerate very many mutations per individual per generation. The number Muller arrived at was about 1 bad mutation per generation per individual as the limit the human genome can tolerate.

Additionally, so what if an individual has a good mutation if he has 10 bad to go with it. This is like have a slight increase in intelligence while having 10 heritable diseases to go with it. You go one step forward and ten steps back.

Can natural selection arrest the problem? Only if there are enough reproductive resources relative to the number of offspring per couple.

For human populations there was something published by Nachman and Crowell and Eyre-Walker and Keightley using a Poisson distribution as reasonable model for the probability of a eugenically clean individual appearing in the face of various mutation rates.

If it is improbable that an eugenically clean kid can be reproduced by a couple, this makes it hard to weed out the bad. So this is an alternative way to arrive at Muller’s conclusions, which are also Sanford and Basener’s conclusions, and really everyone else’s conclusions as summarized by Dan Gruar: “If ENCODE is right, evolution is wrong.”

This is a simpler argument than the one Basener and Sanford put forward, but to Sanford’s credit, he’s also put the simpler version in his book Genetic Entropy, although the following derivation isn’t in his book, it’s something I ginned up myself. 🙂

So how can we estimate the probability a kid can be born with no defective mutations?

The following derivation was confirmed in Kimrua’s paper (see eqn. 1.4)


which Nachman and Crowell, and Eyre-Walker and Keightley reference as well.

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:

\huge f(k,\lambda ) = e^{-\lambda }\frac{\lambda^k }{k!}

to conform the wiki formula with evolutionary literature let

\lambda = U


f = P

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:

k = 0

which yields

\large \large P(k,U) = P(0,U) = \frac{U^0 e^{-U }}{0!} = e^{-U}

Given the Poisson distribution is a discrete probability distribution, the following idealization must hold:

\large \sum_{n}P_n =\sum_{i=0}^{\infty}P(i,U) = 1


\large \large P(0,U) + \sum_{i=1}^{\infty}P(i,U) = 1

thus subtracting P(0,U) from both sides

\large  \large P(0,U) + \sum_{i=1}^{\infty}P(i,U) -P(0,U) = 1 - P(0,U)

thus simplifying

\large \sum_{i=1}^{\infty}P(i,U) = 1 - P(0,U)

On inspection, the left hand side of the above equation must be the percent of offspring that have at least 1 new mutation. Noting gain that P(0,U) = e^{-U}, the above equation reduces to the following:

\sum_{i=1}^{\infty}P(i,U) = 1 - P(0,U) = 1- e^{-U}

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 bad mutation rate is 6 per individual per generation (more conservative than Gruar’s estimate if ENCODE is right), using that formula, the chances that a eugenically “ideal” offspring will emerge is:

\large \large P(0,6) = e^{-6} = 0.25\%

This would imply each parent needs to procreate the following number of kids on average just to get 1 eugenically fit kid:

\frac{1}{e^{-U}} =  \frac{1}{e^{-6}} = 403.42

Or equivalently each couple needs to procreate the following number of kids on average just to get 1 eugenically fit kid:

\large \large 2 * \frac{1}{e^{-U}} = 2 * \frac{1}{e^{-6}} \approx 807

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.

Muller’s number of only 1 new bad mutations per generation per individual. So if anything I understated my case.

There are some “fixes” to the problem suggested by Crow and Kondrashov. I suggested my fix. But the bottom line is to look at what is actually happening to the human genome over time. Are we getting dumber and sicker? I think so. It’s sad.

We can test Basener and Sanford’s prediction by observing whether human heritable diseases continue to increase with each generation. Whether their derivation is right or not, some of their conclusions are observationally and experimentally testable.

On some level, I suppose even Basener and Sanford wished it were not so because it is a tragic conclusion.

Absolute Fitness in Theoretical Evolutionary Genetics

Joe Felsenstein, like other population geneticists, holds a special place in the Creation/Evolution controversy because his works are regarded highly by many creationists who are familiar with genetics. This is a thread for all of us (myself included) to try to learn and understand one of the key concepts in his book Theoretical Evolutionary Genetics, namely absolute fitness. He has generously made his book available on his website (a book of this calibre could sell for hundreds of dollars).
Continue reading Absolute Fitness in Theoretical Evolutionary Genetics

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i\hbar\frac{\partial}{\partial t}\left|\Psi(t)\right>=h\left|\Psi(t)\right>

Hey Brother! The Lord bless you.

An historical footnote — the great irony of history is that as much as Einstein hated QM, he won the Nobel Prize for his contribution to quantum Mechanics!!! Here is one of his famous equations about E that he shares with Max Planck, the famous Plank-Einstein relation of Quantum Mechanics:

E = h \nu


of course Einstein’s other famous equation about E 🙂 is:

E = mc^2

As much as Einstein was famous for his theories of QM (which he ironically hated but also pioneered), he was more famous for Special and General Relativity. What I found very bizarre was that in Relativity we often drop the measurement of time in terms of seconds but use METERS! That is units of distance.

Below is my General Relativity book, by Bernard Shutz. During the Thanksgiving/Christmas season last year, Phoodoo began a thread on relativity, and when I started going through the ideas again, I could no longer resist and just had to revisit my old books…

And then you were the only one in the last several years who was interested in QM’s connection to ID and that also helped spark a revival in me of old ideas I was almost losing to forgetfulness. It was in the process of shaking the dust off Griffiths book that I finally saw his discussion of the realist, the mentalist (aka Copenhagen), and agnostic interpretations of QM. When I studied QM, all the theological and philosophical implication was sanitized out of by the professor since he was focused on the math. Many of my classmates were more interested in QM’s implications for lasers and semiconductors and chemistry. Half the US economy is based on QM, so the theological implications were thrown by the wayside while I studied.

But then, because of your interest, I revisted some of my old essays and then Griffiths book and then it came alive in a way I had not appreciated previously, especially the last chapter which I never learned in his book because the professor didn’t cover it 7 years ago! But that was the best chapter, on Bell’s theorem that establishes the “mentalist” (aka Copenhagen) interpretation.

So to what you said:

maybe on subatomic level, time, distance past and future don’t matter or they simply don’t exist…

this is what Einstein said:

Einstein’s belief in an undivided solid reality was clear to him, so much so that he completely rejected the separation we experience as the moment of now. He believed there is no true division between past and future, there is rather a single existence. His most descriptive testimony to this faith came when his lifelong friend Besso died. Einstein wrote a letter to Besso’s family, saying that although Besso had preceded him in death it was of no consequence, “…for us physicists believe the separation between past, present, and future is only an illusion, although a convincing one.”


Although perhaps Einstein was saying this because of relativity, it is moreso true because of QM. And in my experience, if Physicists had to choose which theory takes precedence over all others, it would be QM.

And now it makes sense why a prominent professor at my school said:

“The ultimate cause of atheism, Newton asserted, is ‘this notion of bodies having, as it were, a complete, absolute and independent reality in themselves.’”

The 1925 discovery of quantum mechanics solved the problem of the Universe’s nature. Bright physicists were again led to believe the unbelievable — this time, that the Universe is mental.
According to Sir James Jeans: “the stream of knowledge is heading towards a non-mechanical reality; the Universe begins to look more like a great thought than like a great machine. Mind no longer appears to be an accidental intruder into the realm of matter…we ought rather hail it as the creator and governor of the realm of matter.”
The Universe is immaterial — mental and spiritual.
Richard Conn Henry
Nature 2005, vol 436, The Mental Universe

Now it’s coming back to me, and now it’s making more sense than ever. There is a God. Praise be!