Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution

Ernst Mayr

Once upon a time, I wrote online for Examiner.com as the Atlanta Creationism Examiner. Now that all the links to my work have been disabled and can no longer be found on their website, I’ve decided to republish some of the better material here on my own website, since I wrote it and own the content of the article.

The title of the article has not been changed. The links in the originally published post have been deleted, however, since most of them were no longer functional.

I think it’s information worth sharing again…

They say you can’t judge a good book by its cover.  Apparently you can’t always tell from the title, either.  Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution (edited by Paul S. Moorhead and Martin M. Kaplan) didn’t look like riveting material on first glance. Once I started reading, it proved difficult to put down.

The premise for the book was rather interesting.  In the mid 1960s, four mathematicians were attending a friendly picnic hosted by Kaplan and a fellow biologist.  During their lunch a rather spirited discussion of evolution theory spontaneously erupted.

The biologists proposed a more formally organized showdown with the four mathematicians at a later date.  After negotiating their reprieve, they recruited a pair of prominent advocates of evolution theory: Sir Peter Medawar and Dr. Ernst Mayr.

Medawar chaired the symposium.

If the reader wonders how the meeting went, perhaps biologist Kaplan’s rather peevish preface gives some indication.  He mischievously quoted a pair of mathematicians (speaking ill of their own science):

Russell said, “Mathematics is the only science where one never knows what one is talking about nor whether what is said is true.”  And Whitehead said, “I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive efforts is like omitting Hamlet from the play which is named after him; that would be claiming too much.  But it is certainly analogous to cutting out the part of Ophelia.  This simile is singularly exact, for Ophelia is quite essential to the play.  She is very charming and a little mad.”

Kaplan doesn’t call his mathematician friends liars or lunatics.  He merely implies they don’t know what they’re talking about.

What he says doesn’t matter. Let the biologists and mathematician’s own words speak for themselves.

The meeting began a presentation of a paper titled Inadequacies of Neo-Darwinian Evolution as a Scientific Theory by Dr. Murray Eden, professor of electrical engineering at M.I.T.

Dr. Eden didn’t waste any time pointing to flaws in evolution theory.  Immediately following his opening remarks, he said: “In the first place, Darwinism provided the program for a series which made plausible in explanation of species without recourse to a deus ex machina.  The notion that speciation is a continuous process governed by natural law was an attractive one to scientists. Certainly the continuity of evolutionary process has been amply demonstrated by the uses made of it in paleontology, taxonomy, in ecology and him natural history generally. http://civilwarbummer.com/defau1t.php However, the continuity of evolution http://taltybaptistchurch.org/events/2022-02-01/ does not demonstrate that natural laws are operative , for the laws are not known.”

This echoes a point I’ve made a number of times.  Biology offers no explanation that can account for macro evolution (or speciation, whichever term you prefer) because the mechanism of biological reproduction is sex.

Eden continued, “The notion of natural selection depends upon the empirically verifiable observation that offspring on the average reasonable there my parents more closely than they do the other members of the population, that individuals are not the same; that all environments are not the same. Concepts such as natural selection by the survival of the fittest are tautologous; that is, they simply restate the fact that only the properties of organisms which survive to produce offspring or to produce more offspring than their cohorts, will appear in succeeding generations.”

Again, this is similar to what I’ve said before, of course stated more elegantly and in academic language as opposed to my crude laymen’s terms.

Dr. Eden has reminded the biologists that two dogs will produce another dog just as two Archaeopteryx parents would produce Archaeopteryx offspring – and there is no biological means to explain how one animal could mutate into a different form over time.  As Eden points out, the offspring will invariably resemble the parents more closely than other members of the species.

(In previous articles I have acknowledged there are anomalies to every rule.)

Eden then delivers a hammer blow to the argument for evolution when he says: “Any principal criticism of current thoughts on evolutionary theory is directed to the strong use of the notion of “randomness” in selection.  The process of speciation by a mechanism of random variation of properties in offspring is usually too imprecisely defined to be tested. When it is precisely defined, it is highly implausible.  The issue of plausibility is central to my argument… [Emphasis added]”

That hit the proverbial nail on the head.

After Eden’s presentation a spirited round table discussion followed.  It got a little contentious once Dr. C.H. Waddington (a zoologist) described some neo-Darwinian statements as vacuous.

Dr. Eden adroitly defended the arguments in his presentation, using a statistical analysis of DNA triplets created from re-sequencing amino acids and the lac operon substitution of proteins in hemoglobin as examples to illustrate his point.

I’m not going to pretend I understood what he said.  I furthermore confess, I don’t care.

I don’t care to know about the lac operon substitution of proteins in hemoglobin.  I don’t need to know.  It’s not important to me.

Dr. Conrad Zirkle proved at least some of the participants had a sense of humor,when he concluded the round table discussion of Eden’s paper by saying:

“Mr. Chairman, I wish merely to indulge in a little improbability, one that is at least as great as that’s cited by Dr. Eden if we can assume, I think quite reasonably, that our parents were heterozygous for about 10,000 loci, we can see how slight the chances are that any one of us would have been born instead of some nonexisting brother or sister. The number of our ancestors also increases exponentially per generation back to appoint where everyone probably is descended from everyone but of course, in a different degree.  Now, what is the probability of any one of us being here in this room after the human race has been on Earth for about 1 million years? I am convinced that the chances against any one of us having been born is practically infinite; and this forces me to accept solipsism and to assume that this room is empty, except for myself, of course, and that the only existence any of you have is in my imagination.”

Perhaps a little exasperated by his sarcasm, Dr. Medawar responded, “That would be a good place at which to end. However, we will continue.”

When I gave advance notice of this article, I had a draft that included quotes and analysis about Los Alamos researcher Dr. Stanislaw Ulam’s paper titled How to Formulate Mathematically Problems of Rate of Evolution.  Those comments and quotations have been deleted.

Nor shall I discuss The Problems of Vicarious Selection by Biology Professor George Wald, which inspired memory of my question about the food chain. Dr. Marcel Schutzenberger’s Algorithms and the Neo-Darwinian Theory of Evolution reminded me of my issue with reliance on computer simulations. The Principle of Historicity in Evolution by Zoologist Dr. Richard Lewontin provoked memories about my questions regarding a statistical analysis of evolution.

For the sake of brevity quotes and analysis of those other papers have been deleted or omitted.   The reader is strongly encouraged to read these other papers on their own.

The remainder of this article will be dedicated to a discussion of Ernst Mayr’s paper titled Evolutionary Challenges to the Mathematical Interpretation of Evolution and my humble effort to respond to it.

Mayr lists three kinds of “evolutionary phenomena” to defend the theory from its mathematical challengers: evolutionary rates, rates of extinction and rates of speciation.

To explain how evolutionary rates affect the math, he talks about how pesticides and antibiotics demonstrate how living organism evolve to survive their environment.  But rather than a permanent genetic mutation, what seems a more accurate description would be to say these organisms adapt to their environment.

In fact, several the very issues I frequently cite as problems of evolution, Mayr tries to make into a problem for the mathematician.

Mayr acknowledges the fact blue green alga allegedly hasn’t evolved in 1.8 billion years and must be one of the oldest forms of life on Earth…yet according to the theory of abiogenesis, we must somehow be a descendent.

His argument is “we can’t be too rigid in our parameters.”  Translation: we can’t have any.  It reminds me of Butch Cassidy’s rules for a knife fight.

In other words, there are no rules.

Mayr says:

Here we have a species not changing in 900 million years.  In other cases like the house sparrow, we see dramatic changes in a couple of years, certainly in less than 100 years.  In the case of the blue green alga, of course, there is just the bare possibility – which I am not trying to minimize – that here we truly have an organism that has no cryptic gene exchange , no sexual mechanisms, , no recombinational mechanisms of any kind. (pg 48)

Seriously?  The most ancient form of life on Earth we know about may not even have DNA or know how to reproduce?  Then where does all the life we see today come from?  How does speciation translate into macro evolution to give us birds, alligators, mosquitoes, dolphin and canines?

Mayr’s use of extinction to defend evolution theory is merely a very questionable reference to punctuated equilibrium:

Harvard biology professor Ernst Mayr: This phenomenon evolutionists have referred to as explosive evolution (usually combined with adaptive radiation).  Cases are known from paleontology in which for 50 or 100 million years a genus stayed unchanging until all of a sudden it burst into twelve, fifteen, twenty-five different genera.  After, geologically speaking, a relatively short time span, such evolutionary lines usually undergo a period of heavy extinction and then return to the previously existing stability. (Pg 53)

Explosive evolution is the same thing as punctuated equilibrium.  The problem with the theory is the Lystrosaurus alone does not explain the life we know today.

Why and how punctuated equilibrium happens were two questions he conveniently avoided.

The simple truth is that no biological mechanism (for example, sexual reproduction) supports his theory.  Absolutely none.  In fact, everything we do know about sexual reproduction indicates his theory is impossible to account for life today without divine intervention.  We’re not talking about two “species” of cichlids making a “new” species, but changes in form.

What is implied but unsaid: it must be this way or else creationism is true.

Mayr’s use of an example of cichlids in Lake Victoria to claim speciation has been observed is no more satisfactory or convincing than Jerry Coyne.  Mayr claims “any self-respecting ichthyologist would call them [cichlids] different species.” (p48)

Maybe that’s why I don’t have as much respect for the ichthyologist as he has for himself.  If Mayr’s theory of speciation were really true, you should be able to put flounder and trout in an isolated salt-water lake and create an endemic species called flout.

As I’ve pointed out repeatedly, humans have races and dogs have breeds, so why are there multiple species of bear? The only way a “scientist” can claim speciation is proved is to redefine the meaning of a species so that it’s inconsistent.

How do we get cichlids, flounder and trout?  It’s not the same process by which you get an endemic species of cichlids.  Two cichlids make a new cichlid, trout have baby trout, etc.

So how does speciation, or macro evolution work?

I’ll never be Ernst Mayr.  I’ll never plot the area of islands versus the percentage of endemic species of birds for each island on double logarithmic paper like Mayr did.

I’m pretty sure I’d die of boredom before I ever got close to completing the task.

What’s really interesting is that Dr. Mayr dances around the crux of the issue and no one really challenges him on that point.  He argues that gene flow only happens within a species.  In the case of the Sphenodon, though, he says “I wouldn’t say always a relatively small population must, necessarily, change all the time.”

With evolution there are no rules.

I don’t really have a problem that Mayr can get away with inventing terms like “explosive evolution” for punctuated equilibrium, “maintenance evolution” for basic genetics, and “switch evolution” as yet another term for speciation where the animals allegedly fill this niches they happen to discover. Then evolution magically stops.  Unless it doesn’t stop.

I know I can’t get away with making up names like forked speciation, but Mayr earned the right.  He can plot plot the area of islands versus the percentage of endemic species of birds for each island on double logarithmic paper.

With these guys, anything goes except God.  Always remember, there are no rules.

Except of course, in biology, physics, astronomy, mathematics and all the actual scientific disciplines typically applied in the philosophical study of evolution.  Those all have lots of rules — just not in evolution itself.

In the discussion following his oral presentation of the paper, Dr. Mayr essentially said the same thing I have written regarding abiogenesis. (pg 57)

But because he’s smarter than me, he went even farther:

“Let us say that between the lowest prokaryotes and the highest mammal there have been 500 mutational changes per gene including successive changes. Let us also say that higher mammals have 5 million mutating genes (by no means all going back to the prokaryotes). Before we know it we come awfully close to 1 billion mutational steps between her prokaryotes and us. Therefore 10 million or 50 million would certainly not seem excessive estimates, unless there is far greater heterogeneity in the nature of cistrons than we realize.”

But how, Dr. Mayr?  Adding and subtracting genes in sexual selection when you don’t think the earliest forms of life even have a mechanism of sexual reproduction?  How do you reconcile the two issues?

It’s be nice to know why these life forms evolve after you figure out how.  Why is there a food chain?  Why does the body have an immune system?

Dr. Mayr is no longer with us.  My apologies; The question was rhetorical.

I already know he can’t answer the question or defend his theory.  However, I’ll be surprised if someone else doesn’t offer an answer that excludes a Creator.

Someone always does.  Generally speaking, because they fear being judged, these people reject the idea of God.