The mathematical probability of Evolution?

I have seen similar calculations. Not sure how accurate they are and hope to see more work in this area. Thanks for the paper :slight_smile:

Genetic progression is unimaginably faster than purely random. As described in my Open Forum contribution “Genetic-Algorithm Optimization vs Purely Random Search” (11/2015), a simplistic computer simulation of biological genetic processes implies that “natural selection” is 42,800,000,000,000,000,000,000,000 times as efficient as purely random trial-and-error search in finding solutions to a particular very difficult optimization problem.

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Empirically, the probability of evolution seems to be 1.

Computationally, the answer is ‘42’. :slight_smile:


Yes, standing variation varies over a few orders of magnitude. As the review (which is a good one, I think) points out, it varies less than the census population size. Since its the census size (more or less) that determines the amount of new variation available for selection to act on, the contribution of new variation is actually larger than one might naively suppose.

Ignoring that effect, however, I still think that a million-fold greater contribution of standing variation is a substantial overestimate. In an ideal Wright-Fisher population of size N and ignoring any effect of earlier selection, standing variation contributes 4Nμ to the diversity of the population, measured as heterozygosity; new variation contributes 2μ every generation. For a species with N=50,000, say, that means the contribution of standing variation is 100,000 times greater than new variation. The ratio for the number of mutations is much smaller. The number of different standing variants present is roughly 4μNln(N), while the number of new variants introduced every generation is μN; for the same population of 50,000, that gives a ratio of only about 40, which is a lot less than a million.

I would expect the contribution from standing variation in a real population to be lower than than in my cartoon population, since many functional variants (the only kind that could matter to selection) will have been either beneficial or deleterious during the preceding history of the population. Some of the beneficial ones will have already been fixed by positive selection, while the frequencies of the deleterious ones will have been suppressed by purifying selection.


I think that N is rather small for many species.

Can we agree that whether it’s 100000x or 1000000x greater, there’s zero justification for omitting it and pretending that populations are static and “waiting” for new mutations before selection or drift can act?


Returning to the probability issue, the attempt to redefine random here (“Evolution is not random”) I find not helpful. “Random” always includes a basic assumption of “within the laws of physics.” That’s the same thing we mean about dice, coins, and cards, as well as the path a water molecule will follow down a hill. So why keep insisting that it’s not random? Stating that some mutations are more likely, or that Natural Selection is dependent on whatever seems to me to evade the point. “Within the laws of physics, Evolution is random.” Isn’t that what is meant by “Evolution is random.”?

My other comment is about those who have tried to calculate odds, such as Fred Hoyle, Hubert Yockey, and David Berlinski. No matter how generous the assumptions they give to the underlying processes, the numbers are outrageous. Hoyle stated, “A commonsense interpretation of the facts suggests that a superintellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question.” Berlinski argues that being unable to come up with a working mathematical model is one of ToE’s biggest failures, and a reason why it lacks credibility (as a single explanation of all we see).

Why do they say things like this? Because regardless of how many zeroes you decide you can put in the numerator, there are too many zeroes in the denominator. Feel free to suggest ways that the number of zeroes in the denominator can be reduced reasonably. I find evolutionists frequently argue that there are trillions and trillions of attempts, but they never characterize the denominator. And after suggesting trillions of attempts, when someone brings up the denominator, they then say that probability arguments are meaningless, and for some of the reasons given here.

Certainly many creationists use shallow probability arguments. But so do many Evolutionists. The web is absolutely awash in invalid probability support for and against Evolution. Let’s stay away from both.

I find that those who believe “Evolution did it all on it’s own” push most aggressively against probability arguments. They do this IMO for the same reason that Hoyle stated, that any truly thoughtful and informed probability attempt comes up indistinguishable from zero.


Because of the sometimes ambiguous properties of English syntax, that sentence just won’t do.

Many YEC’s, maybe even most YEC’s, would quickly interpret that sentence to mean, “… within the laws of physics, evolution isn’t even theoretically determined by natural laws…”

The word “random” is a complete “bomb” waiting to go off in the middle of a perfectly reasonable discussion.

It is much more clear, and less likely to derail a discussion, to say that “…God controls the process and results of Evolution.”

Side Note: It should be noted that some supporters of BioLogos construe God’s love as requiring that he not control evolution. But I am not moved by that kind of rationalization/logic.

Related Conclusion: It is 100% likely that a valid Ring Species in existence today, demonstrating that the entire population of the ring, treated as an aggregate, is a genetically related Whole! The relationship between the two end populations and the intermediate populations in-between, is 100% beyond doubt. That’s what Science does.

But if a natural disaster would eliminate the intermediate populations, we would also have an 100% probability of two closely related species. The whole probability issue is a red herring, a straw man. We have real cases, 100% probability, where evolutionary shifts in genetic configuration of two populations can be demonstrated, with virtually no doubt.

That’s too bad. Evolution isn’t random, because selection isn’t random. That isn’t “redefining” anything.

Nope. There are only two aspects of evolution that reasonably earn the ‘random’ descriptor. One is mutation. The phrase ‘random mutation’ has a specific meaning in biology, and it’s been explained in this thread and many other times, I bet, at BL. The second is genetic drift, in which allele frequencies change over time independent of selection. Genetic drift occurs due to “random” sampling, since the lives of organisms (including their reproductive systems) lead to certain alleles becoming more common in a subsequent generation without any explanation other than “well, that was random.” Standard illustrative examples include disasters that reduce population sizes “randomly.” In neither of these aspects of evolution is there a claim of true randomness, nor is there a technically unrelated but commongly conflated claim of equal probability of all possible outcomes.

Knowing these things, one should immediately be able to tell whether a person talking about “randomness” or probability of evolution overall is a person who understands the basics of the theory. The calculations you refer to in your post are irrelavant, but more importantly they reveal a misunderstanding of how evolution works. The short version is this: show me someone calculating the odds of “evolution happening” and I’ll show you someone who is actually calculating the odds of “something happening all at once.”


Hi George.

It certainly does depend on who we are talking to as to how we posit ideas! Do you run across YECs a lot? I find that a discussion of Evolution with them is not particularly meaningful anyway.

But we sure do have to be careful with definitions. I recently gave a presentation at a TE/EC group, and we spent half the time making sure our terms made sense to each other.

As to “God controls the process and results of Evolution", that seems like a theological statement to me. It’s certainly true, but kinda vague. I have seen with TE/EC friends that your quote is a foundational point for them. Someone asked earlier if that is not implying teleology – it seems to me it is. In any case, it seems to imply that there is something more than just the natural processes, yet people don’t want to go there. I acknowledge that there could be a process we don’t yet know about.

As to whether God is required to not control evolution, that again is a theological, not a scientific question. I’m not moved by it either, and really don’t care whether he developed life by evolution only or if he intervened and helped evolution along. Obviously I lean to the latter.

I honestly don’t get your “Related Conclusion” and how it shows probability to be a straw man. The distribution of alleles is at the macro level, and it changes almost continuously by mutations, regardless of other events. I don’t think that’s what criticisms of Evolution based on probability are addressing, at least not the ones who understand how it works. Are we talking about the same thing here?


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I was disappointed GJDS dropped out of this thread, but not surprised. His comments were thoughtful and his questions seemed honest, yet the tone here sometimes comes across superior and disrespectful.

Berlinski is a nice guy, a philosopher turn, who apparently does not know about this mathematical model.

That is a nice thought, except we do have a working mathematical model. So it is hard to take this criticism seriously.

Hoyle is an astrophysicist, talking about abiogenesis, not evolution. He has a point, in that we do not know how the first life evolved. So any calculation involving known processes will come up with absurd probabilities. I don’t know of a serious scientist that would disagree with this. But that isn’t evidence that the there isn’t a process we do not yet know of that does exist.

Yockey is the same. He is talking primarily about abiogenesis, not evolution. And regarding evolution, there is a theory that works.


Well that is admirable.

You are right, it is a theological statement. I no not know to make it a scientific statement.

Either way, that is a position consistent with EC/TE. I do not deny that God could have helped evolution along, I just have no way of demonstrating it scientifically. I also do not know why it matters so much.

It appears we have a lot of common ground.


Vague? @Marty, not the way I intend it. Perhaps your religious scruples prevent you from making such an explicit/specific statement.

But mine are fine with it. God evolved exactly what he wanted to evolve, when he wanted to evolve it. To me, there is no “that’s about right” kind of evolutionary steps.

As a teenager, I had a strong Calvinist bent. As an adult, I have a lot more interest in human volition. But no compunction about making God-ordained and God-controlled evolution as the basis of Earth’s biosphere.

Scientists may not want to go where I’m traveling … but my position on evolution is not qualitatively different from the YEC viewpoint about all of Earth’s life forms being miraculously >poofed!< into existence!

As far as “the probability criticism” goes, @Marty, I don’t think they know what they are talking about at all. But it seems pretty clearly irrelevant to the reality of evolution.

They talk about zero probability, and I talk about 100% probability. You can choose which style of nonsense you prefer I suppose.

It’s not clear to me what’s even being discussed here. The probability of what, exactly? We have no mathematical model that would let us calculate the probability of, say, a land mammal evolving into a marine mammal, or the probability that a hominin will evolve to be more intelligent (or less intelligent, or become extinct). No one does.


And the reply will be “Therefore, goddidit.”

George – interesting perspectives!

Along similar lines of “choosing which style of nonsense”, I find atheists who rail at the notion of God as nonsense, and are perfectly willing to accept the existence of the universe and the multiverse. But really, they believe in infinity, eternity, and uncreated stuff. How is that any less nonsense?


Thanks for your thoughtful comments.

I’ll push back gently that Berlinski is no slouch, and I’m not so comfortable dismissing him so easily. But that may be a much longer conversation than we want to get into here.

Hoyle’s quote “ physics, as well as with chemistry and biology” I take to imply the Anthropic Principle (physics), origins of life (chemistry), and evolution (biology). I may be wrong, but that’s how I read it.

Yes, Yockey was focused on origins, but some aspects of evolution are similar. I’ll post more detail about that in a minute to Steve.

I think you’re right about common ground. Do you find that most people would have a lot of common ground, if they take the time to find it? Too many seem to focus on where they think they disagree.


Steve – love your handle! It sounds like the name of a dwarf in Lord of the Rings. Is that your algorithm of the same name on github?

To be more specific about probability, the most meaningful for this discussion would, I think, be the probability of first arriving at some particular enzyme. Once an enzyme is in place, it’s clear that microevolution can refine it. But how do we get the first one? We would exclude those that have ancestor homologues, because proteins get repurposed often enough.

This seems to me closely related to origins of life, since the first proteins had to arise somehow. But after origins, new stuff still arises, so the issue is the same. The question for both origins and development of life is “How?”, and probability can be discussed. Though it would be impossible to characterize precisely, some useful and reasonable assumptions could be made. But everyone who has tried has walked away saying, “there’s something wrong with this picture.”


Oh, that Atheist stuff is nonsense, but for me I have narrowed it down to a pretty clean little hypothesis:

I don’t believe the Universe would have ever created an epiphenomenon like consciousness. Consciousness/Awareness in a Godless universe is like having a Mona Lisa painting, painted by a blind man, in a room full of blind men. It doesn’t compute in my view.

So, when I’m debating atheists, once we all agree that there is something called Consciousness, then my internal deduction is that there is a Cosmic source for this Consciousness. They say I can’t prove it, and I say they are trying to convince a man who loves Chocolate that he doesn’t really love Chocolate. It can’t be done. I tell them not to even think it can be successfully done more than a few times in a lifetime.

I love my God. I love my Chocolate.

I think my views on God and Consciousness would fit in well with discussions on this thread, when it gets under way!

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